SAT Algebra practice questions
Linear equations, systems, inequalities and functions — the largest single slice of the Digital SAT Math section.
1575 free questions, each with a full worked solution and an explanation of what each wrong answer means.
Practise this domain adaptively →Easy (314)
- Linear equations in one variable
If 3x + 7 = 22, what is the value of x? - Linear equations in one variable
If x/4 = 9, what is the value of x? - Evaluating linear functions
The function f is defined by f(x) = 6x − 5. What is the value of f(3)? - Solving a literal equation (rearranging a formula)
The perimeter P of a rectangle with length l and width w is given by P = 2l + 2w. Which of the following expresses w in … - Writing a linear function from a table of values
Which equation defines the function f? - Finding the x-intercept of a line
In the xy-plane, the graph of the equation y = 4x − 12 crosses the x-axis at the point (a, 0). What is the value of a? - Solving a two-step linear equation containing a fraction
If (x − 5)/3 = 6, what is the value of x? - Solve a system by elimination in context
How many pounds of clay are used to make one mug? - Solve a system by substitution in context
How many medical kits does the team prepare? - Set up a system from a word problem
Which system of equations represents this situation? - Solve a system by elimination in context
What is the cost, in dollars, of one bag of flour? - Solve a system from a counting word problem
How many pairs does the team own? - Writing a one-variable inequality from context
Which inequality represents the possible numbers n of layers the scientist can analyze in the available laboratory time? - Solving a linear inequality for a maximum whole number
What is the greatest number of solar panels the town can install without exceeding its budget? - Testing ordered pairs in a system of inequalities
Which ordered pair (x, y) satisfies both conditions? - Interpreting a linear inequality to find a minimum count
What is the least number of timed intervals the team must complete to meet the coach's requirement? - Find the constant giving no solution
In the xy-plane, the system of equations 4x + 3y = 12 and kx + 6y = 30, where k is a constant, has no solution. What is … - Solving a one-variable inequality and interpreting the maximum
What is the greatest number of remaining sections the rider can complete without exceeding the 150-minute limit? - Solving a strict inequality for a least whole number
What is the least number of quilts the guild must sell for its profit to be more than $1,000? - Evaluating a linear model in context
What is the total cost of a trip of 7 miles? - Two-step linear equation
If 5x − 8 = 27, what is the value of x? - One-step inequality
For which values of x is 2x + 3 greater than 11? - Evaluating a linear function from its slope and intercept
The graph of the linear function f in the xy-plane has a y-intercept of 4 and a slope of −2. What is the value of f(3)? - Equation whose solution is zero
For which value of x is the expression 4x + 9 equal to 9? - Reading a linear function's parts
A plumber charges a call-out fee of $40 plus $3 for each minute of work. Which function gives the total charge C(m), in … - Evaluating a decreasing linear function
The function h is defined by h(x) = 9 − 2x. What is the value of h(4)? - Translating words into a two-step equation
Four times a number, decreased by 1, is equal to 9. What is the number? - Variable on the right side
If 6 = x − 9, what is the value of x? - Translating 'less than' into an inequality
A number x decreased by 7 is less than 10. Which inequality represents this statement? - Input that gives a stated output
The function f is defined by f(x) = 4x − 3. For what value of x is f(x) = 9? - Evaluating a rental cost model
The cost, in dollars, of renting a bicycle for h hours is given by C = 5h + 2. What is the cost of renting the bicycle f… - Height of a growing plant
A seedling is 4 centimetres tall and grows 1.5 centimetres each week. How tall, in centimetres, will it be after 6 weeks… - Pages printed in a given time
A printer prints 20 pages every minute, so the number of pages it prints in m minutes is P = 20m. How many pages does it… - Monthly cost of a phone plan
A phone plan costs $25 a month plus $0.10 for each text message sent. What is the cost, in dollars, for a month in which… - Height of a burning candle
A candle is 24 centimetres tall and burns down at a constant 3 centimetres per hour. How tall, in centimetres, is the ca… - Recognising the graph of a constant function
Which of the following describes the graph of y = 4 in the xy-plane? - Unit price after removing a fixed item
Ana paid $37.50 for 5 identical notebooks and a pen that cost $7.50. What was the price, in dollars, of each notebook? - Number of boxes in a stack
A stack consists of a 15-centimetre base with a number of identical boxes, each 24 centimetres tall, on top of it. The s… - One-step equation by adding
What value of x makes the equation x − 5 = 2 true? - Two-step equation
For what value of x is 2x + 1 equal to 9? - One-step equation by dividing
If 4y = 20, what is the value of y? - Evaluating a linear function
If f(x) = 2x + 1, what is the value of f(4)? - Evaluating a simple cost model
The cost, in dollars, of x apples at a market stall is given by C = 0.5x. What is the cost, in dollars, of 6 apples? - Reading the slope from slope-intercept form
What is the slope of the line y = 5x − 7? - Point on a horizontal line
In the xy-plane, the graph of y = 2 is a horizontal line. Which of the following points lies on this line? - Output of a proportional line
The line y = 2x passes through the origin. What is the value of y on this line when x = 3? - Rise of a line for one step in x
In the xy-plane, a line passes through the points (0, 3) and (1, 5). By how much does y increase when x increases by 1? - Writing a line from its slope and y-intercept
Which of the following is an equation of the line with slope 2 and y-intercept 3 in the xy-plane? - Second variable from a known first
If x = 2 and x + y = 7, what is the value of y? - System where the two variables are equal
The solution of the system y = x and x + y = 10 is the point (a, a). What is the value of a? - Checking a value against a one-step inequality
Which of the following values of x satisfies x + 3 > 5? - Greatest integer under a strict inequality
If x − 2 < 4, what is the greatest integer value of x? - Word equation with a multiple
Three times a number is 27. What is the number? - Subtraction equation
If 10 − x = 3, what is the value of x? - Word equation with an addition
A number increased by 6 is 15. What is the number? - Proportional cost
Hiring a car costs $30 per day. What is the cost, in dollars, of hiring the car for 4 days? - Evaluating a linear function in context
The function f is defined by f(x) = 4x, where f(x) is the number of legs on x dogs. How many legs do 6 dogs have? - Point on the y-axis
In the xy-plane, which of the following points lies on the y-axis? - Equation of a horizontal line
Which of the following is an equation of a horizontal line in the xy-plane? - Distance of a point from the x-axis
In the xy-plane, the point (2, 5) is plotted. How many units is the point from the x-axis? - Slope of a horizontal line
In the xy-plane, a line has slope 0. Which of the following must be true about the line? - Second number from a sum
Two numbers add up to 9, and one of them is 4. What is the other number? - Solution of a system given directly
Which ordered pair (x, y) is the solution of the system x = 1 and y = 2? - Price of one item from a pair's total
A pen and a pencil together cost $3. The pen costs $2. What is the cost, in dollars, of the pencil? - Greatest value under a non-strict bound
If x ≤ 10, what is the greatest possible value of x? - Translating 'at least' into an inequality
Which inequality means that x is at least 3? - Working backwards from a giveaway
Ben had some marbles. After giving 4 of them away, he had 9 left. How many marbles did Ben have to start with? - Division equation in words
A number divided by 3 is equal to 5. What is the number? - One-step equation with a negative result
If x − 8 = −3, what is the value of x? - Fixed charge plus a rate
A plumber charges $50 for each visit plus $20 for each hour of work. What is the total charge, in dollars, for a visit t… - Completing a table of a proportional function
The table shows values of y = 2x. x | y 1 | 2 2 | 4 3 | ? What is the value of y when x = 3? - y-coordinate of points on the x-axis
In the xy-plane, every point on the x-axis has the same y-coordinate. What is that y-coordinate? - Line through the origin
In the xy-plane, which of the following equations has a graph that passes through the origin? - Equation of a vertical line through two points
In the xy-plane, the points (1, 2) and (1, 5) both lie on the same vertical line. What is the equation of that line? - Direction of a line with positive slope
In the xy-plane, a line has a positive slope. Which of the following describes the line? - Substituting a known value into a second equation
If y = 2x and x = 3, what is the value of y? - Second part of a split length
A rope 12 metres long is cut into two pieces. One piece is 7 metres long. How long, in metres, is the other piece? - Pair satisfying two simple equations
Which ordered pair (x, y) satisfies both x = 4 and x + y = 9? - Comparing negative numbers
Which of the following numbers is less than −2? - Smallest integer above a decimal bound
What is the smallest integer that is greater than 5.5? - Zero of a quantity from a bill
A phone plan costs $2 per month plus $2 for each gigabyte of data used. In a month when the bill was exactly $2, how man… - Original price before doubling
The price of a ticket doubled to $16. What was the price, in dollars, before it doubled? - Age from a future age
Ana is x years old. In 3 years she will be 15. What is the value of x? - Decreasing linear model
A candle is 12 centimetres tall and burns down by 1 centimetre every hour. How tall is the candle, in centimetres, after… - Correct row of a table for a linear rule
A table lists values of y = 3x + 1. Which of the following rows is correct? - Point directly above another
In the xy-plane, which of the following points is exactly 2 units directly above the point (3, 1)? - Quadrant of a point
In the xy-plane, in which quadrant does the point (−3, 4) lie? - Where the axes meet
In the xy-plane, at which point do the x-axis and the y-axis meet? - Comparing the steepness of two lines
In the xy-plane, which of the following lines is steeper than the line y = 2x? - Equal variables with one known
If x = y and x = 7, what is the value of y? - Larger of two numbers in a doubling relationship
One number is twice another number. The smaller number is 4. What is the larger number? - Count of one kind from a total
A pencil case holds 5 items, each of which is either a pen or a pencil. If there is exactly 1 pencil, how many pens are … - Largest integer under a strict bound
What is the largest integer that is less than 10? - Translating 'no more than' into an inequality
Which inequality means that x is no more than 8? - Line with a given slope through the origin
Which equation represents a line in the xy-plane with slope 3 that passes through the origin? - Meeting a vertical line
In the xy-plane, the line y = 2x + 1 crosses the vertical line x = 3 at the point (3, k). What is the value of k? - Where a graph meets the x-axis
The equation 3x + 2y = 12 is graphed in the xy-plane. What is the x-coordinate of the point where the graph meets the x-… - Equation of a horizontal line
Which of the following equations has a graph in the xy-plane that is a horizontal line? - Cost of one item from two purchases
Two muffins and a coffee cost $7. One muffin and a coffee cost $5. What is the cost of one muffin, in dollars? - Missing coordinate of a system's solution
The point (2, k) is the solution of the system y = x + 2 and y = 2x. What is the value of k? - System of two parallel lines
In the xy-plane, the lines y = x + 1 and y = x − 3 are parallel. Which statement about the system of these two equations… - Adult ticket price from a total
Two adult tickets and one child ticket cost $7 altogether. A child ticket costs $1. What is the cost of one adult ticket… - Inequality for a minimum height
A ride requires riders to be at least 120 centimetres tall. If h is a rider's height in centimetres, which inequality mu… - Most tokens within a budget
Mae has $10. She buys a $3 entry pass and then as many $1 game tokens as she can afford. How many tokens can she buy? - Graph of a simple inequality on a number line
The solutions of x − 4 ≤ 1 are graphed on a number line. Which of the following describes the graph? - Greatest whole-number rise below a limit
The temperature in a greenhouse must stay below 30°C. It is currently 24°C. By at most how many whole degrees can the te… - Litres after two minutes of filling
A tank already holds 3 litres of water and is filled at a steady 2 litres per minute. How many litres will it hold after… - Starting amount from a halving and a gain
Lena gave half of her sweets to her brother and then received 3 more sweets, leaving her with 8. How many sweets did she… - Younger sibling's age
Tom is 4 years older than his sister. If Tom is 15, how old is his sister? - Translating words into an equation
Which equation states that 5 more than twice a number n is 17? - Passengers before a stop
At its first stop, 12 passengers got off a bus and nobody got on, leaving 20 passengers on board. How many passengers we… - Cost function with a joining fee
A gym charges a $10 joining fee plus $5 for each visit. Which function gives the total cost C, in dollars, for v visits? - Paper left after several jobs
A printer is loaded with 200 sheets of paper and uses 15 sheets for each print job. How many sheets are left after 4 job… - Equation from an intercept and a rise
In the xy-plane, the graph of a linear function passes through (0, 2) and rises 3 units for every 1 unit it moves to the… - Unit cost from a two-variable equation
The equation y = 5x gives the total cost y, in dollars, of buying x tickets. What is the cost, in dollars, of one ticket… - Bananas from a total
In a fruit bowl, the number of apples a and the number of bananas b satisfy a + b = 6. If there are 2 apples, how many b… - Rewriting an equation in slope-intercept form
Which of the following equations has the same graph in the xy-plane as 2y = 4x + 6? - Hardbacks on a shelf
A shelf holds 10 books. There are 2 more hardbacks than paperbacks. How many hardbacks are there? - Sum of coordinates where two lines cross
In the xy-plane, the horizontal line y = 2 and the vertical line x = 5 cross at one point. What is the sum of the coordi… - Meaning of a system's solution
A system of two linear equations in x and y has the solution (1, 2). Which of the following must be true? - Inequality for more than an amount
Kim needs more than $50 to buy a game. If m is the amount, in dollars, that Kim needs, which inequality describes m? - Room left in a lift
A lift can carry at most 8 people. Six people are already in it. What is the greatest number of additional people who ca… - Break-even from a profit equation
A stall's profit p, in dollars, from selling c cups of coffee is given by p = 2c − 10. How many cups must be sold for th… - Graph of x equals a constant
Which of the following describes the graph of x = −2 in the xy-plane? - Fuel remaining from a two-variable equation
The fuel f, in litres, left in a car's tank after it has driven d kilometres is given by f = 40 − 0.1d. How many litres … - Equation from a table of pairs
The table shows three pairs of values that satisfy a linear equation. x | y 0 | 1 1 | 3 2 | 5 Which equation relates x… - Goals split across two matches
A team scored 12 goals over two matches, scoring three times as many goals in the second match as in the first. How many… - System whose solution is the origin
Which of the following systems has the solution (0, 0)? - Price of a badge
A sticker costs $3. A sticker and a badge together cost $10. How much does the badge cost, in dollars? - Two equations for the same line
The two equations in a system are y = 2x + 1 and 2y = 4x + 2. How many solutions does the system have? - Whole chapters under a page limit
Zara wants to read fewer than 20 pages tonight. Each chapter of her book is 5 pages. What is the greatest number of whol… - Age that fails a half-price rule
A cinema charges half price for children aged 12 or under. Which of the following ages is NOT eligible for the half-pric… - Lowest whole-number temperature from a comparison
Tomorrow's temperature will be more than 3 degrees warmer than today's temperature of 2°C. What is the lowest whole-numb… - Solving a two-step inequality
The inequality 2x + 1 < 7 is equivalent to which of the following? - Minutes passed on a parking meter
A parking meter showed 120 minutes when it was paid. It now shows 45 minutes remaining. How many minutes have passed? - Interpreting a function value
A cyclist's distance d, in kilometres, after t hours is given by d(t) = 15t. Which statement best interprets d(2) = 30? - Bottles bought within a total
Mia paid $14 in total for a $2 bag of ice and some bottles of water that cost $3 each. How many bottles of water did she… - Equation with a given solution
Which of the following equations has the solution x = 6? - Height of a growing tree
A tree is 150 centimetres tall and grows 25 centimetres each year. How tall, in centimetres, will the tree be after 4 ye… - Meaning of the constant in a cost function
The monthly cost C, in dollars, of a phone plan with m minutes of calls is given by C(m) = 25 + 0.5m. What does the numb… - Child tickets from a total
Adult tickets cost $2 each and child tickets cost $3 each. A family spent exactly $12 and bought no adult tickets. How m… - Girls in a group from an equation
The equation y = 10 − x gives the number of girls y in a group of 10 children that has x boys. If the group has 6 boys, … - Equation from a slope and an intercept
Which equation has a graph in the xy-plane with slope −1 and y-intercept 4? - Equal shares of a total
Two friends have the same number of marbles, and together they have 8 marbles. How many marbles does each friend have? - What a system's solution looks like on a graph
In the xy-plane, the solution of a system of two linear equations with exactly one solution is the point where the two g… - Pears in a box
A box holds 9 pieces of fruit, all apples or pears. There are twice as many apples as pears. How many pears are in the b… - Solving a one-step inequality by division
Which of the following describes all solutions of 3x ≤ 12? - Extra cups within a limit
A recipe must use fewer than 12 cups of flour in total. Five cups are already in the bowl. What is the greatest whole nu… - Inequality from a number-line graph
On a number line, a graph shows an open circle at 3 with shading to the right. Which inequality is graphed? - Least score needed to reach a total
Sam must score at least 90 points in total over two games. He scored 52 points in the first game. What is the least numb… - Shorter piece of a cut ribbon
A ribbon 30 centimetres long is cut into two pieces. One piece is 8 centimetres longer than the other. How long, in cent… - Operation that solves a one-step equation
The equations 4x = 20 and x = 5 have the same solution. Which operation turns the first equation into the second? - Takings from a linear model
A bakery's takings T, in dollars, on a day when it sells c cakes are given by T(c) = 40 + 6c. What are the takings, in d… - Function with a negative slope
Which of the following linear functions has a graph with a negative slope? - Passengers who can still board
A bus can carry at most 40 passengers, and 27 are already on board. How many more passengers can board? - Rolls per bag
A baker packs 24 rolls equally into 6 bags. How many rolls go in each bag? - Millilitres per glass
A jug held 1,200 millilitres of juice. After three equal glasses were poured from it, 450 millilitres remained. How many… - Equation for a number decreased by 6
Which equation states that a number n decreased by 6 is equal to 15? - Original length of a ribbon
A ribbon was cut into 5 equal pieces, each 12 centimetres long, with nothing left over. How long, in centimetres, was th… - Height function for a growing sunflower
A sunflower is 30 centimetres tall and grows 5 centimetres each week. Which function gives its height h, in centimetres,… - Cost of a ten-minute call
The cost C, in dollars, of a phone call lasting m minutes is given by C(m) = 0.1m + 0.5. What is the cost, in dollars, o… - Describing the graph of a decreasing linear function
Which of the following describes the graph of f(x) = −2x + 6 in the xy-plane? - Change in y per unit of x from a table
The table shows values of a linear function. x | y 0 | 4 1 | 6 2 | 8 By how much does y change each time x increases b… - Where a line meets the x-axis
In the xy-plane, the graph of x + y = 5 passes through the point (a, 0). What is the value of a? - Chairs from a two-variable equation
In a café, the number of chairs c and the number of tables t satisfy c = 2t. How many chairs are there when there are 7 … - Line through a point with a given parallel
Which of the following is the equation of the line in the xy-plane that passes through (0, 3) and has the same slope as … - Value that satisfies a two-step inequality
Which of the following values of x satisfies 2x − 1 > 5? - Dividing an inequality by a negative
The inequality −x < 3 is equivalent to which of the following? - Inequality from a closed dot and left shading
A number line shows a closed dot at −1 with shading to the left of it. Which inequality is graphed? - Price of one pen from a box
A box of 8 identical pens costs $6.40. What is the price of one pen, in dollars? - Number added to itself
When a number is added to itself, the result is 26. What is the number? - One-way walking time
Meg's walk to school and back takes 45 minutes in total, and the two directions take the same time. How many minutes doe… - Depth function for a leaking pool
A pool is 150 centimetres deep and loses 2 centimetres of depth each day. Which function gives the depth d, in centimetr… - Pay for five hours
The function P(h) = 12h gives the pay, in dollars, for h hours of work. How many dollars are paid for 5 hours of work? - Slope of a flat line
In the xy-plane, the graph of a linear function passes through (0, 5) and (2, 5). What is the slope of the graph? - Child's entry fee from a total
Two adults and one child pay $10 in total to enter a museum. Each adult pays $3. How many dollars does the child pay? - Kilometres left when the fuel runs out
A scooter's remaining fuel f, in litres, after it has travelled d kilometres is given by f = 6 − 0.5d. After how many ki… - Missing value in a table of solutions
Each pair (x, y) in the table satisfies 3x + 4y = 24. x | y 0 | 6 4 | 3 8 | ? What is the missing value of y? - Line through three listed points
The points (1, 2), (2, 4), and (3, 6) all lie on the same line in the xy-plane. Which equation describes the line? - Inequality for remaining tickets
A cinema hall seats at most 200 people, and 140 tickets have already been sold. Which inequality describes the number t … - Multiplying an inequality by 2
The inequality x/2 > 4 is equivalent to which of the following? - Inequality for notebooks within a budget
Kim has $20 and wants to buy as many $3 notebooks as she can. Which inequality describes the number n of notebooks she c… - Temperature that keeps a pool open
An outdoor pool opens only when the air temperature is at least −5°C. At which of the following temperatures would the p… - Smaller of two numbers in a 4 : 1 split
Two numbers add up to 20, and one of them is 4 times the other. What is the smaller number? - Translating a word problem into a system
Which system of equations describes the statement: the sum of two numbers x and y is 9, and their difference is 1? - Price of a bookmark
A book and a bookmark together cost $11. The book costs $10 more than the bookmark. What does the bookmark cost, in doll… - Sum of coordinates of a simple solution
The system y = 3 and y = x has exactly one solution (a, b). What is the value of a + b? - Older brother's age
Two brothers' ages add up to 7 years and differ by 1 year. How old is the older brother? - Solution of two coordinate equations
Which of the following points is the solution of the system x = 1 and y = −2? - Goats among ducks
A farmer keeps ducks and goats. She has 10 animals with a total of 28 legs. How many goats does she have? - Marbles per bag from a total
Ivy shares 27 marbles equally among 3 bags. How many marbles go in each bag? - Money left after a purchase
Dan had $40. After buying a book he had $25 left. How many dollars did the book cost? - Equation for a number tripled
Which equation states that three times a number n is 42? - Function for money in a jar
A jar holds $12, and $3 is added to it every week. Which function gives the amount A, in dollars, in the jar after w wee… - Distance after three hours
A walker's distance d, in kilometres, after t hours is given by d(t) = 4t. How far has the walker gone after 3 hours? - Reading a rate from a function
The function c(m) = 0.2m gives the cost, in dollars, of sending m text messages. What is the cost of one message? - Missing addend in a two-variable equation
The equation p + q = 10 relates the number of pears p and quinces q in a basket. If there are 4 pears, how many quinces … - Equation of a line with slope 1 through the origin
Which of the following equations describes the line in the xy-plane on which every point has a y-coordinate equal to its… - Value of y for a given x
In the xy-plane, the point (2, k) lies on the line y = 3x + 1. What is the value of k? - Two drinks with the same price
A coffee and a tea cost the same amount, and together they cost $6. What is the price of the coffee, in dollars? - Checking a proposed solution of a system
Which of the following ordered pairs (x, y) satisfies both x + y = 5 and x − y = 1? - Cats and dogs at a shelter
A shelter has 12 animals, all cats and dogs, with twice as many cats as dogs. How many dogs are there? - Inequality for a maximum weight
A lift can carry a load of no more than 600 kilograms. If w is the load in kilograms, which inequality describes the loa… - Most stamps within a budget
Stamps cost $4 each. Mo has $20. What is the greatest number of stamps Mo can buy? - Volume of one glass from a jug
A jug holds 2 litres of juice. After 6 glasses of equal size are filled from the full jug, 0.5 litres of juice remain. W… - Number of pens from a budget
A pen costs $3 and a notebook costs $6. Kai buys one notebook and some pens for a total of $30. How many pens does Kai b… - Undoing a bracket
If 2(n + 3) = 24, what is the value of n? - Sheets left in a printer tray
A printer tray is loaded with 500 sheets of paper, and each report printed uses 30 sheets. Which equation gives the numb… - Rate of an oven heating up
An oven's temperature rises at a steady rate after it is switched on. Two minutes after switching on, the temperature is… - Parking meter minutes
A parking meter shows 10 minutes when it is switched on and adds 8 minutes for each coin inserted. How many minutes does… - Flour for loaves and muffins
A baker uses 3 cups of flour for each loaf and 2 cups of flour for each batch of muffins. One morning the baker used 24 … - Finding x from a two-variable equation
For the equation x − 4y = 8, what is the value of x when y = −1? - Two-variable equation with equal variables
If x and y satisfy 4x + 6y = 36 and x = y, what is the value of y? - Intersection of two lines through equations
The lines y = 3x and y = x + 8 intersect at a single point. What is the x-coordinate of that point? - System with one variable given
In the system 3x + y = 14 and y = 2, what value of x makes both equations true? - Price of a sandwich from two orders
Two sandwiches and one soup cost $11. One sandwich and one soup cost $7. What is the price, in dollars, of one sandwich? - Crates in a lift
A lift can carry at most 600 kilograms. Each crate loaded into it weighs 40 kilograms. Which inequality gives the possib… - Smallest whole number satisfying an inequality
What is the smallest whole number x for which 2x − 7 > 5? - Score needed on a second test
Nadia needs a total of at least 90 points across two tests. She scored 42 on the first test. Which inequality shows the … - Dividing an inequality by a negative
Which of the following describes all values of x that satisfy −3x ≥ 12? - Taxi fare split three ways
Three friends split a taxi fare equally, and each of them pays $7. What was the total fare, in dollars? - Next value of a linear function
A linear function g has a slope of 4. If g(2) = 11, what is the value of g(3)? - Number of boxes from a total of eggs
Eggs are sold in boxes of 6. Nia needs 24 eggs. How many boxes must she buy? - Money left after a purchase
Tom had $35. After buying a book, he had $9 left. How much did the book cost, in dollars? - Cost of a pool visit with a locker
A swimming pool charges $8 for entry and $2 per hour for a locker. What does a visit with a locker for 5 hours cost, in … - Reading a rate from a linear equation
A plant's height h, in centimetres, after w weeks is given by h = 2w + 5. By how many centimetres does the plant grow ea… - Checking a point on a line
For the equation y = 2x + 5, what is the value of y when x = 3? - Equation for a total of two items
Apples cost $1 each and pears cost $2 each. Which equation shows that a apples and p pears together cost $9? - System with x already known
If x = 5 and x + y = 8, what is the value of x − y? - Inequality for a speed limit
The speed limit on a road is 50 kilometres per hour. Which inequality represents the speeds s, in kilometres per hour, t… - Finding y from x in a simple relation
The equation y = 3x + 4 relates two quantities. What is y when x = 2? - Equation for pencils and pens in a pack
A pack contains p pencils and q pens, and there are 12 items in the pack altogether. Which equation represents this? - Coffees from a ratio and a total
In one hour a cafe sold 24 hot drinks, and it sold twice as many coffees as teas. How many coffees did it sell? - Checking a solution of a system
If x = 1 and y = 2, what is the value of 3x + 2y? - Inequality for a minimum age
Riders on a certain roller coaster must be at least 12 years old. Which inequality represents the ages a, in years, of p… - Most muffins within a budget
Muffins cost $4 each. With $40, what is the greatest number of muffins that can be bought? - Price of a pen from a small purchase
Two pens and a $6 notebook cost $36 in total. What is the price, in dollars, of one pen? - Distance remaining on a walk
A walker is 50 kilometres from a town and walks toward it at 4 kilometres per hour. How many kilometres from the town is… - Inequality for a maximum weight
A lift can carry a load of no more than 500 kilograms. Which inequality represents the loads L, in kilograms, that the l… - Chairs per table
A hall has 9 identical tables, and there are 36 chairs in all, shared equally among the tables. How many chairs are at e… - Stamps after buying more
Omar had some stamps. After buying 7 more he had 19. How many stamps did he have to begin with? - Height of a stack of crates
A pallet is 20 centimetres high, and each crate stacked on it adds 5 centimetres. How high, in centimetres, is the stack… - Reading the starting value of a linear model
The cost C, in dollars, of hiring a hall for h hours is C = 60 + 25h. What is the cost of hiring the hall for 0 hours? - Ordered pair on a line
Which ordered pair (x, y) satisfies the equation x + y = 6? - Equation for a two-item purchase
Notebooks cost $2 each and folders cost $3 each. Which equation shows that n notebooks and f folders cost $24 in total? - Two numbers from a sum and a difference in words
Two numbers add up to 10, and one of them is 4 more than the other. What is the larger number? - Value of y when x is given by one equation
If x = 3 and 2x + y = 11, what is the value of y? - Two equal shares from a total
Two friends have $10 between them, and they have the same amount each. How many dollars does each friend have? - Inequality for a minimum height
Riders on a certain ride must be at least 120 centimetres tall. Which inequality represents the heights h, in centimetre… - Most pencils for a sum of money
Pencils cost $3 each. What is the greatest number of pencils that can be bought with $25? - Cost of one bus fare
Five bus fares of the same price cost $30 in total. What is the price, in dollars, of one fare? - Total pages read from a daily rate
Ivo has read 2 pages of a book and reads 3 pages every day from now on. How many pages will he have read after 6 more da… - Equation relating two counts with a total cost
Balloons cost $1 each and ribbons cost $3 each. Which equation shows that b balloons and r ribbons cost $15 in total? - Two numbers from their sum and difference
Two numbers have a sum of 7 and a difference of 1. What is the smaller number? - Inequality for a maximum number of passengers
A minibus may carry no more than 16 passengers. Which inequality represents the number of passengers p it may carry? - Marbles given away
Leo had 45 marbles. After giving some to his sister, he had 20 left. How many marbles did he give away? - Cost of a taxi ride
A taxi charges a flat $5 plus $3 for each kilometre. What is the cost, in dollars, of a 4-kilometre ride? - Equation for a total number of wheels
A yard holds c cars with 4 wheels each and t tricycles with 3 wheels each, and there are 50 wheels in all. Which equatio… - Two lengths from their sum and difference
Two planks have a combined length of 13 feet, and one is 3 feet longer than the other. How long, in feet, is the longer … - Weeks to save a sum
Nadia saves $4 every week. How many weeks will it take her to save $28? - Length of a growing vine
A vine is 12 centimetres long and grows 2 centimetres each day. How long, in centimetres, will it be after 5 days? - Solving when the unknown is halved
If 7 = x/2 − 3, what is the value of x? - Solving an equation with a fraction
Which value of x satisfies x/3 + 4 = 6? - Cost function for a gym membership
A gym charges 20 dollars to join and 15 dollars for each month of membership. Which function gives the total cost C, in … - Rate of change from two pairs of values
In a linear relationship between x and y, y = 4 when x = 0 and y = 10 when x = 2. By how much does y increase for each i… - Equation for a total cost of two items
A shop sells pencils for 2 dollars each and pens for 3 dollars each. Which equation states that x pencils and y pens cos… - Finding a coordinate on a line
The line 5x − y = 7 passes through the point (3, k). What is the value of k? - Value satisfying a strict inequality
Which of the following values of x satisfies 2x + 1 > 9? - Ordered pair satisfying two equations
Which ordered pair (x, y) satisfies both x + y = 5 and y = x + 1? - Price of a pencil from a pair of facts
A pen and a pencil cost 3 dollars together, and the pen costs 2 dollars more than the pencil. What is the cost of the pe… - Intersection of two lines
In the xy-plane, the graphs of y = 2x and y = −x + 6 intersect at which point? - Inequality for at most
Which inequality represents the statement that a number x is at most 12? - Smallest integer in a solution set
What is the smallest integer x that satisfies 3x − 4 > 11? - Inequality for a lift's capacity
A lift can carry at most 600 kilograms. If each person weighs 75 kilograms on average, which inequality describes the nu… - Stickers from a three-to-one relationship
Ali has 3 times as many stickers as Ben. If Ali has 27 stickers, how many stickers does Ben have? - Equation with a given solution
Which of the following equations has x = 4 as its solution? - Table that could be a linear function
Each table below gives the values of y for x = 0, 1, and 2. Which table could represent a linear function? - Height of a burning candle
A candle is 20 centimetres tall and burns down by 2 centimetres every hour. How tall, in centimetres, is the candle afte… - Line with a given y-intercept
Which of the following is an equation of a line in the xy-plane with a y-intercept of 4? - Point on the graph of a sum
The graph of x + y = 6 in the xy-plane passes through which of the following points? - Five-dollar notes from a total
The equation 5x + 10y = 100 relates the number of 5-dollar notes x and 10-dollar notes y that make up 100 dollars. If th… - System for a sum and a difference
Two numbers x and y have a sum of 15 and a difference of 3. Which system of equations describes x and y? - Substituting to find y
If 2x + y = 14 and y = 2x, what is the value of y? - Number satisfying a simple inequality
Which of the following numbers is a solution to x − 3 < 2? - Least value satisfying an inequality
If x + 6 ≥ 10, what is the least possible value of x? - Age from a sibling's age
Sam is x years old, and his sister is 3 years older than Sam. If his sister is 14 years old, what is the value of x? - Expression for a growing plant's height
A plant is 5 centimetres tall and grows 2 centimetres each week. Which expression gives the plant's height, in centimetr… - Y-intercept of a line in standard form
Which of the following is the y-intercept of the graph of 2x + 3y = 12 in the xy-plane? - Value that fails an inequality
Which of the following values of x does NOT satisfy x + 4 ≤ 9? - Twice a number from a simple relation
Three more than a number is 11. What is twice the number? - Cost of hiring a hall for a number of guests
Hiring a hall costs 100 dollars plus 5 dollars for each guest. What is the cost, in dollars, for 40 guests? - Pair solving a difference and a sum
Which of the following ordered pairs (x, y) is a solution to the system x − y = 1 and x + y = 9? - Restaurant bill from equal shares
Four friends split a restaurant bill equally, and each pays 18 dollars. What was the total bill, in dollars? - Height at planting from a linear model
The height h, in centimetres, of a plant t weeks after it was planted is given by h = 2t + 6. What was the height of the… - Horizontal line through a point
Which of the following is an equation of the line in the xy-plane that passes through the point (2, 7) and is parallel t… - Value allowed by an inequality with equality
If x ≥ 3, which of the following could be the value of x? - Price of one notebook
Lena bought 3 notebooks at the same price each and paid 12 dollars in total. What was the price, in dollars, of one note… - Expression for water left in a draining tank
A tank holds 500 litres of water and drains at 20 litres per minute. Which expression gives the number of litres left af… - Point on two lines
Which of the following points lies on both of the lines y = x and y = 6 − x in the xy-plane? - Pages left in a book
Priya has read 84 pages of a 200-page book. How many pages does she have left to read? - Expression for a monthly membership
A club membership costs 10 dollars per month with no joining fee. Which expression gives the total cost, in dollars, aft… - Recognising a linear equation in two variables
Which of the following is a linear equation in two variables? - Inequality with a negative variable
If −x > 3, which of the following must be true? - One more than a solution
If 3x = 27, what is the value of x + 1? - Point on a vertical line
Which of the following points lies on the line x = 4 in the xy-plane? - Intersection of a horizontal and a vertical line
In the xy-plane, the lines y = 4 and x = −2 intersect at the point (a, b). What is the value of a + b? - Solving for y at a given x
The equation 3x + 2y = 18 relates two quantities. If x = 4, what is the value of y? - Reading the y-intercept from standard form
What is the y-coordinate of the point where the graph of 5x − y = 10 crosses the y-axis? - Substitution with y given in terms of x
In the system y = x + 3 and x + y = 11, what is the value of y? - Direct substitution of a known value
In the system 2x + y = 10 and y = 4, what is the value of x? - Checking which pair solves both equations
Which ordered pair (x, y) is the solution to the system x + y = 6 and x − y = 2? - Solving a one-step-and-divide inequality
Which of the following describes all solutions of 3x + 5 < 20? - Clearing a fraction in an inequality
Which of the following describes all solutions of x/4 ≥ 3? - Greatest number within a budget
T-shirts cost $12 each. What is the greatest number of t-shirts that can be bought with at most $50?
Easy–Medium (315)
- Slope of a line
A line passes through the points (0, 3) and (2, 7). What is the slope of the line? - Linear models from context
A gym charges a $25 one-time signup fee plus $15 per month. Which equation gives the total cost C, in dollars, for m mon… - Linear equations with variables on both sides
If 5(x − 2) = 3x + 4, what is the value of x? - Linear equations from context
A taxi charges a $3.50 base fare plus $2.25 per mile. If a ride costs $19.25 total, how many miles was the ride? - Linear equations in two variables
The equation of a line is 3x + 2y = 12. What is the y-coordinate of the point where the line crosses the y-axis? - Linear equations in two variables
A line in the xy-plane passes through the points (1, 5) and (4, 11). What is the y-intercept of the line? - Solving a linear equation in one variable with a fractional coefficient
If (2/3)x − 5 = 7, what is the value of x? - Equations of parallel lines in the xy-plane
In the xy-plane, line m is parallel to the line with equation y = −3x + 5 and passes through the point (2, 1). If the eq… - Set up and solve a two-variable system
How many brain coral colonies did the biologist count? - Solve a cost-and-count system from context
How many child tickets were sold on Saturday? - Solve a system arising from a training plan
How many long runs does the plan call for that week? - Translate a context into a system of equations
Which system of equations represents this situation? - Find the constant making a system inconsistent
In the xy-plane, the system of equations 2x - 5y = 9 and ax + 15y = 4, where a is a constant, has no solution. What is t… - Use elimination to find one unknown quantity
What is the cost, in dollars, of one poster board? - Interpreting slope in context
What does 0.12 represent in this model? - Slope from two points
What is the slope of the line in the xy-plane that passes through the points (1, 4) and (5, 16)? - Dividing an inequality by a negative
If −3x ≤ 12, which of the following describes every possible value of x? - Solving a system by elimination
If x + y = 10 and x − y = 4, what is the value of x? - Interpreting the constant term in context
Which statement best describes the meaning of the number 40 in this context? - Testing whether a point is on a line
Which of the following points lies on the graph of 4x − y = 10 in the xy-plane? - Testing a value in an inequality
Which of the following values of x satisfies 4x − 7 ≥ 9? - Writing a linear model for a decreasing quantity
A tank holds 500 litres of water and drains at a constant rate of 20 litres per minute. Which function gives the volume … - Equation with a subtracted variable term
If 7 − 2x = 15, what is the value of x? - Slope from standard form
What is the slope of the line 2x + 5y = 10 in the xy-plane? - Inequality with a negative coefficient
Which of the following describes all values of x for which 5 − 2x > 11? - Equation from slope and y-intercept
Which equation represents the line in the xy-plane with slope 4 and y-intercept −7? - Function from a table
Which equation defines the linear function f? - Fraction of a variable equals a total
A recipe uses 3/4 of a cup of sugar for each batch of biscuits. Priya used 6 cups of sugar in total. How many batches di… - Point on a line
Which of the following points lies on the line y = 3x − 2 in the xy-plane? - Greatest value in a solution set
If −2x + 7 ≥ 1, what is the greatest possible value of x? - Meaning of a slope in context
The number of litres of paint, P, needed to cover w square metres of wall is given by P = 0.1w + 0.5. What does the numb… - Intercepts from standard form
In the xy-plane, the line 2x + 3y = 6 crosses the x-axis at (a, 0) and the y-axis at (0, b). What are the values of a an… - Function from a slope and one value
A linear function f has a slope of 3, and f(2) = 5. Which equation defines f? - Equation from the two intercepts
Which equation represents the line in the xy-plane with an x-intercept of 3 and a y-intercept of 6? - Testing values against an inequality
For which of the following values of x is 3x − 4 greater than 8? - Substitution with y given as a multiple of x
If y = 3x and x + y = 16, what is the value of x? - Evaluating a fee-plus-rate model
A car park charges $3 to enter plus $2 for each hour parked. How many dollars does it cost to park for 5 hours? - Three times a sum
Three times the sum of a number and 2 is equal to 21. What is the number? - Missing coordinate of a point on a line
The point (3, k) lies on the line 2x + 3y = 3 in the xy-plane. What is the value of k? - Meaning of the constant in a cooling model
The temperature, in degrees Celsius, of a cup of coffee t minutes after it is poured is modelled by T(t) = 90 − 2t. What… - Half of a number, increased by 3
Half of a number, increased by 3, is equal to 11. What is the number? - Where a line crosses the x-axis
What is the x-coordinate of the point where the line y = 5x − 15 crosses the x-axis in the xy-plane? - Inequality with a negative fraction
Which of the following describes all values of x for which −x/3 > 2? - Variable on both sides with a subtraction
If 5 − x = 2x − 4, what is the value of x? - Line with slope zero
Which of the following equations represents a line in the xy-plane with a slope of 0? - Value satisfying two inequalities
Which of the following values of x satisfies both x > 2 and x ≤ 5? - Distributing a negative before solving
If 9 − 2(x + 1) = 1, what is the value of x? - Intercept of a line through a given point
In the xy-plane, the line y = 2x + b passes through the point (3, 1). What is the value of b? - Solving a two-step inequality
Which of the following describes all values of x for which 3x + 2 ≤ 11? - Sum of the coordinates of an intersection
What is the sum of the coordinates of the point where the lines y = x + 1 and y = 3 − x cross in the xy-plane? - Four times a difference
Four times the difference between a number and 3 is equal to 8. What is the number? - Slope from a rearranged form
A line in the xy-plane has the equation y = 4 − 3x. What is the slope of the line? - Value that makes an expression negative
For which of the following values of x is the expression 4 − x/2 negative? - Two multiples of a number set equal
Seven times a number, plus 3, is equal to five times the same number, plus 11. What is the number? - Line through the origin with slope −1
Which equation represents a line in the xy-plane that has a slope of −1 and passes through the origin? - Value satisfying an inequality with a fraction
Which of the following values of x satisfies x/2 − 1 > 3? - Two multiples of sums set equal
Five times the sum of a number and 1 is equal to three times the sum of the same number and 5. What is the number? - Where a line crosses the y-axis
In the xy-plane, the graph of y = −2x + 5 crosses the y-axis at which point? - Inequality with a given solution set
Which of the following inequalities has the solution set x ≥ 4? - Minutes from a linear cost
A ride-share company charges a fixed $3 plus $0.50 per minute. How many minutes long is a ride that costs $18? - Jar of marbles with a fractional part
A jar holds x marbles, and two-thirds of them are red. After 4 red marbles are taken out, 6 red marbles remain in the ja… - A second point on a line given by an equation
The line 3x + 2y = 10 in the xy-plane passes through the point (4, −1). Which of the following points also lies on the l… - Product of the solution values
If 2x + y = 11 and x − y = −2, what is the value of xy? - Reading a linear model at a given input
The amount of grain, in kilograms, left in a silo d days after it is filled is modelled by w(d) = 1200 − 45d. How many k… - Ages from a relationship
A brother is 3 years older than his sister. Four times the brother's age is 60. What is the sum of their ages? - Intercept of a line in standard form
The line 2x + 5y = 16 is graphed in the xy-plane. What is the x-coordinate of the point where the line crosses the x-axi… - Solving an inequality with a negative coefficient
Which of the following describes all solutions of −2x + 7 > 1? - Interpreting a system's solution in context
At a bake sale, a muffin costs m dollars and a cookie costs c dollars. The system m + c = 5 and 3m − c = 7 describes the… - Recognising a linear function's constant rate
Which of the following tables could represent a linear function? - Splitting a total with a fixed extra
Three friends split the cost of a $48 gift equally, and each also pays $4 toward the wrapping. How many dollars does eac… - Rate from two points in context
A hiker was at an altitude of 700 metres at 2 p.m. and 1,300 metres at 5 p.m. If the altitude increased at a constant ra… - Greatest integer under a limit
A box can hold at most 42 kilograms. Each brick weighs 3.5 kilograms. What is the greatest number of bricks the box can … - Evaluating a cost function
A taxi charges a $12 base fare plus $2 per kilometre. What is the fare, in dollars, for a 9-kilometre trip? - y-intercept from standard form
The line 2x + 3y = 6 is graphed in the xy-plane. What is the y-coordinate of the point where the line crosses the y-axis… - Graphing an inequality: dashed versus solid boundary
In the xy-plane, the solution set of y < 2x + 3 is shaded. Which statement about the graph is true? - Greatest value satisfying a two-part budget
A student has $42 and buys 3 notebooks at $8 each. Pens cost $2 each. What is the greatest number of pens the student ca… - When a linear model reaches zero
A candle is 200 millimetres tall and burns down at a constant 8 millimetres per hour. After how many hours will the cand… - y-intercept of a line in standard form (negative)
The line 4x − 2y = 14 is graphed in the xy-plane. What is the y-coordinate of its y-intercept? - Product from a sum and difference
Two numbers have a sum of 8 and a difference of 2. What is their product? - Most items under a spending cap
A parent gives a child $100 for a school trip. The trip's coach ticket costs $25, and museum entries cost $4 each. What … - Output of a linear model
A phone plan costs $30 per month plus $0.25 per gigabyte of data used. What is the cost, in dollars, of a month in which… - Point on a line with a given x
In the xy-plane, the line 3x + y = 12 passes through the point (4, k). What is the value of k? - Fewest whole units to reach a target
A water tank must hold at least 45 litres for a camping trip. Water is sold in 6-litre containers. What is the fewest nu… - Remaining amount from a linear model
A phone battery is at 90% and loses 6 percentage points per hour of video. What percentage will remain after 10 hours of… - Interpreting a system's solution in context
At a fair, 3 ride tokens and 2 game tokens cost $23, and 1 ride token and 1 game token cost $9. What is the cost of a ri… - Most trips under a weight limit
A lift can carry at most 360 kilograms. Boxes of tiles weigh 12 kilograms each. What is the greatest number of boxes the… - Value of a linear function from a rate and a start
A snow depth gauge read 3 centimetres at midnight, and snow fell steadily at 0.5 centimetres per hour. What did the gaug… - Translating a sentence into an equation
Four more than three times a number n is 19. Which equation represents this? - Two prices from a total and a difference
A pen and a pencil together cost $14, and the pen costs $10 more than the pencil. What is the cost of the pencil, in dol… - Fewest whole units to exceed a threshold
A tank holds 75 litres of fuel. A generator uses 9 litres per hour. After how many whole hours of running will the tank … - Value of a decreasing linear model
A prepaid transport card holds $500 and is charged $35 for each weekly pass. How many dollars remain after 10 weekly pas… - Missing coordinate on a line in standard form
The line 5x − 2y = −4 passes through the point (−2, k). What is the value of k? - Product of two quantities from a system
Four notebooks and one pen cost $14, and one notebook costs $1 more than one pen. What is the product of the two prices,… - Greatest number of tickets within a budget
Cinema tickets cost $4 each for a school group. The group has $90 to spend on tickets. What is the greatest number of ti… - Total from a base and a rate
A tutor charges a $40 registration fee plus $12 per lesson. How many dollars does a student pay in total for 6 lessons? - Slope of a line through the origin and a point
In the xy-plane, a line passes through the origin and the point (4, 6). What is the slope of the line? - Solving a sum-and-difference system
Two numbers have a sum of 13 and a difference of 3. What is the larger number? - Fewest weeks to save a target
A student saves $7 a week and wants at least $40 for a concert ticket. What is the fewest number of whole weeks needed? - Evaluating a cost model
A car rental costs $25 per day plus $0.20 per kilometre driven. What is the cost, in dollars, of a one-day rental in whi… - Solving a two-variable equation for one value
Sandwiches cost $4 and drinks cost $2 at a stall. The equation 4x + 2y = 40 relates the number of sandwiches x and drink… - Two pieces from a total and a difference
A 10-metre rope is cut into two pieces, and one piece is 4 metres longer than the other. How long is the shorter piece? - Greatest number of purchases within a balance
A gift card holds $250. Each cinema visit costs $18. What is the greatest number of visits that can be paid for entirely… - Output of a linear model
A plant is 2 centimetres tall when bought and grows 0.5 centimetres per day. How tall, in centimetres, will it be after … - Missing coordinate on a line
The line 4x + 3y = 2 passes through the point (2, k). What is the value of k? - Solution of a simple system
Which ordered pair (x, y) satisfies both 2x + y = 15 and x − y = 3? - Solving a two-variable equation in context
A café sells muffins for $3 and scones for $2. The equation 3m + 2s = 18 relates the numbers of muffins m and scones s b… - Two lengths from a total and a difference
Two planks together measure 10 metres, and one is 2 metres longer than the other. How long, in metres, is the longer pla… - Two people's ages from a sum and a gap
Ana is 2 years older than Ben, and their ages add up to 26. How old is Ana? - Most items under a cost limit
Tickets to a fair cost $11 each. A group has $100. What is the greatest number of tickets the group can buy? - Total from a starting amount and a rate
A savings jar starts with $200, and $15 is added each week. How many dollars are in the jar after 12 weeks? - Reading one variable from a two-variable equation in context
A florist sells roses for $2 each and lilies for $5 each. The equation 2r + 5l = 20 relates the numbers of roses r and l… - Two numbers from a sum and a multiple condition
The sum of two numbers is 13, and three times the smaller number equals the larger number plus 3. What is the smaller nu… - Greatest whole number within a limit
A lift can carry at most 120 kilograms of parcels. Each parcel weighs 16 kilograms. What is the greatest number of parce… - Total from a base and a rate
A gym charges a $30 joining fee plus $4 per visit. What is the total cost, in dollars, for a member who visits 15 times? - One value from a two-variable equation in context
A café sells sandwiches for $6 and juices for $4. The equation 6s + 4j = 26 relates the numbers of sandwiches s and juic… - Two kinds of book from a total and a difference
A shelf holds 10 books, all of them novels or atlases. There are 4 more novels than atlases. How many atlases are on the… - Greatest number within a limit
A shelf can hold at most 50 kilograms. Each dictionary weighs 6 kilograms. What is the greatest number of dictionaries t… - Total from a fixed part and a rate
A ferry ticket costs $12 plus $3 for each bicycle brought aboard. What is the cost, in dollars, of a ticket with 8 bicyc… - One quantity from a two-variable equation in context
A garden centre sells shrubs for $5 and bulbs for $3 a bag. The equation 5s + 3b = 35 relates the numbers of shrubs s an… - Most items within a budget with a fixed charge
A taxi charges a $15 flat fee plus $4 per kilometre. A passenger has $65. What is the greatest whole number of kilometre… - Value of a linear model
A plant nursery has 80 seedlings and grows 2.5 more per day on average from cuttings. How many seedlings will it have af… - Number of items from a remaining amount
A roll of ribbon is 36 metres long. After 7 equal pieces are cut from it, 8 metres remain. How long, in metres, is each … - Fewest whole units to exceed a target
A tank must be filled with at least 125 litres of water. Water is carried in 8-litre buckets. What is the fewest number … - Value of a linear function in context
A seedling is 2 centimetres tall and grows 0.75 centimetres per day. How tall, in centimetres, will it be after 8 days? - Number of boxes from a total with a remainder
A crate of 48 apples is packed into boxes of 5, with 3 apples left over. How many boxes are filled? - Most units within a stock
A café has 60 litres of milk. Each batch of a dessert uses 4.5 litres. What is the greatest number of batches the café c… - Remaining amount from a linear model
A prepaid card holds $900 and is charged $60 each month. How many dollars remain after 12 months? - Equation from two descriptions of the same result
When a number is multiplied by 4 and the result decreased by 7, the outcome is the same as when the number is tripled an… - Equation with distribution and like terms
If 5(x − 2) − 3x = 18, what is the value of x? - Interpreting the slope of a cost function
The cost, in dollars, of renting a rowing boat for h hours is given by C(h) = 6.5h + 12. What is the best interpretation… - A number plus a fraction of itself
The sum of a number and three fifths of the same number is 48. What is the number? - Inverting a linear cost function
The cost, in dollars, of printing n leaflets is C(n) = 0.08n + 35. How many leaflets can be printed for exactly $75? - Evaluating a linear cost model
A van rental costs $55 per day plus $0.20 per mile. What is the cost, in dollars, of renting the van for one day and dri… - Splitting a bill unequally
Three friends share a restaurant bill of $62. One of them pays $8 more than each of the other two, who pay the same amou… - Time for a steadily rising temperature to reach a value
At 6 a.m. the temperature was −4°C, and it rose at a steady 1.5°C per hour. How many hours after 6 a.m. did the temperat… - Identifying a point that is not on a line
In the xy-plane, which of the following points is NOT on the graph of 4x + 3y = 24? - System with decimal coefficients and equal variables
If 0.5x + 0.2y = 7 and x = y, what is the value of x? - Consecutive multiples of 5
The sum of three consecutive multiples of 5 is 105. What is the largest of the three? - Days until a linearly falling quantity reaches a value
The number of tickets remaining t days after sales open is given by R(t) = 2,400 − 150t. After how many days will 900 ti… - Interpreting the constant term of a linear model
A club's membership m months after it opened is modelled by N(m) = 320 + 45m. What is the best interpretation of the num… - Evaluating a linear drain model
A swimming pool holds 40,000 litres and is drained at a constant rate. After 3 hours, 31,000 litres remain. How many lit… - Number sold from a per-item profit
A stationer buys pens for $1.50 each and sells them for $2.25 each. How many pens must be sold to make a total profit of… - Least number of extra items to reach a target
A gardener wants at least 200 plants for a border. She buys 14 trays that each hold 12 plants and makes up the rest with… - Equal increases from a start to an end value
A bus fare was $2.40. It was increased twice, by the same amount each time, and is now $3.10. By how much, in dollars, w… - Input where two linear functions agree
The functions g and h are defined by g(x) = −2x + 9 and h(x) = x. For what value of x is g(x) = h(x)? - Slope of a horizontal line through two points
In the xy-plane, the graph of a linear function passes through the points (−3, 7) and (5, 7). What is the slope of the g… - Identifying the system with a given solution
Which of the following systems of equations has the solution (x, y) = (−1, 3)? - Inequality from a perimeter limit
The side length of a square is x + 3 units. Which inequality represents all values of x for which the perimeter of the s… - Original value before a percent decrease
When a number is decreased by 12%, the result is 66. What is the original number? - Two pieces of a rope with a fixed difference
A rope 9.6 metres long is cut into two pieces, one of which is 1.4 metres longer than the other. What is the length, in … - Time from odometer readings and a speed
A car's odometer reads 24,150 kilometres at the start of a journey and 24,480 kilometres at the end. If the car averaged… - Direct proportion
The quantity y is directly proportional to x, and y = 12 when x = 5. What is the value of y when x = 20? - Point on a line given a point and a slope
In the xy-plane, a line has slope 3 and passes through the point (2, 5). Which of the following points also lies on the … - Greatest length under a combined-dimension limit
A parcel service accepts a parcel only if its length plus its girth is at most 300 centimetres. A parcel has a girth of … - Equal shares from a total with a remainder
A jug holds 1.5 litres of juice. After 6 glasses of equal size are filled from it, 0.3 litres remain in the jug. How man… - Identifying a line by the signs of its slope and intercept
Which of the following functions has a graph in the xy-plane that is a line with a negative slope and a positive y-inter… - Selecting the ordered pair that solves a system
Which ordered pair (x, y) is the solution of the system y = 2x − 3 and x + y = 9? - Minutes to cover a distance at a constant speed
A train leaves a station at 9:15 a.m. and travels at a constant 80 kilometres per hour. How many minutes after 9:15 a.m.… - Properties of a vertical line
In the xy-plane, line ℓ has equation x = 5. Which of the following statements about line ℓ is true? - Original price from a percent rise given as an amount
The price of a ticket rose by $12, which was a 15% increase. What was the price, in dollars, before the rise? - Net fill rate
A tank is empty. Water flows in at 12 litres per minute while a drain lets water out at 4 litres per minute. After how m… - Larger of two numbers from a sum and a ratio
Two numbers have a sum of 60 and are in the ratio 2 : 3. What is the larger number? - Number of people under two limits
A lift can carry at most 10 people and at most 750 kilograms. If the people using it weigh 82 kilograms on average, what… - Line through a point perpendicular to the y-axis
In the xy-plane, which of the following is an equation of the line that passes through the point (−2, 0) and is perpendi… - Least number of days to reach a reading target
Lin must read at least 300 pages of a book this week. If she reads 45 pages each day, what is the least number of days s… - Fifth number from a known mean
The mean of five numbers is 12. Four of the numbers are 9, 10, 15, and 17. What is the fifth number? - Time to reach home from a distance model
A cyclist's distance from home, in kilometres, t hours after setting off is given by d(t) = 40 − 15t. After how many hou… - Temperature after a fixed number of cooling intervals
A liquid cools at a steady rate, losing 3°C every 5 minutes. It starts at 95°C. What is its temperature, in degrees Cels… - Inequality from a perimeter condition
A rectangle has sides of length x and x + 5. Which inequality describes all values of x for which the perimeter of the r… - Months for which a monthly option is cheaper
A gym charges $40 per month, or $400 for a full year. For which numbers of months m of use in a year is paying monthly c… - Number of passengers from a crossing's takings
A ferry charges $18 for each car and $6 for each passenger. On one crossing it carried 20 cars and some passengers, and … - Sum of a linear function's values at opposite inputs
The function f is defined by f(x) = 2.5x − 4. What is the value of f(2) + f(−2)? - Greatest whole side under a perimeter limit
The side length of an equilateral triangle is a whole number of centimetres, and its perimeter is less than 45 centimetr… - Facing pages from their sum
The page numbers on two facing pages of a book add up to 137. What is the smaller of the two page numbers? - Zero of a linear function from its intercept and rate
For the linear function f, f(0) = 12, and f(x) decreases by 4 each time x increases by 1. For what value of x is f(x) = … - Comparing two linear costs at one input
One taxi company charges $4 plus $2 per kilometre; another charges $7 plus $1.50 per kilometre. For a 10-kilometre trip,… - Least value from a condition on an average
The average (arithmetic mean) of x and 3x must be at least 20. What is the least possible value of x? - Inequality that holds for every real number
Which of the following inequalities is true for every real value of x? - Solving by elimination
If x + 2y = 6 and x − y = 3, what is the value of y? - x-coordinate where two lines meet
In the xy-plane, the lines y = 3x and y = x + 4 intersect at the point (a, b). What is the value of a? - Taller of two candles
Two candles have a combined height of 15 centimetres, and one is 3 centimetres taller than the other. How tall, in centi… - Cost of a notebook
Three notebooks and two pens cost $16. A pen costs $2. What is the cost of one notebook, in dollars? - Sum of the coordinates of a solution
The solution of the system y = x + 3 and y = −x + 7 is the point (a, b). What is the value of a + b? - Weight of a cup
Two cups and a saucer weigh 11 ounces. One cup and a saucer weigh 7 ounces. What is the weight of one cup, in ounces? - Input where two expressions agree
For what value of x do the expressions x + 5 and 3x − 1 have the same value? - Large candles from a total
A shop sells small candles for $2 each and large candles for $3 each. Priya spent exactly $12 and bought 3 small candles… - System of a horizontal and a vertical line
Consider the system of equations y = 5 and x = −2. Which of the following statements about the system is true? - Larger of two related numbers
One number is 4 more than a second number, and three times the second number is 2 less than twice the first. What is the… - Left-handed pupils in a class
In a class of 15 pupils, there are four times as many right-handed pupils as left-handed pupils. How many pupils are lef… - Price of a melon from two purchases
Ines bought 3 apples and a melon for $10. At the same prices, 3 apples cost $2 more than a melon. What is the price of a… - Slope that removes every solution
For which value of k does the system y = kx + 2 and y = 3x − 5 have no solution? - Food cost per person from a bill with tips
Three friends split a $21 restaurant bill equally. Each person's share included a $2 tip. How many dollars did each pers… - Starting number from a fraction given away
After giving away a quarter of her stickers, Mia had 15 stickers left. How many stickers did she have to begin with? - Point further along a line through two intercepts
In the xy-plane, a line passes through (0, −3) and (6, 0). What is the y-coordinate of the point on the line where x = 1… - Slope from a point on the line
In the xy-plane, the line y = mx + 2, where m is a constant, passes through the point (3, 11). What is the value of m? - Menu price before a discount
Four friends each ordered the same dish. Each received a $3 discount, and together they paid $20. What was the price of … - Class size from a third plus helpers
A third of the pupils in a class went on a trip, along with 2 teachers, making 7 people in total. How many pupils are in… - Distance at which two fares are equal
One taxi firm charges $2 per kilometre plus a $10 booking fee. A second firm charges $3 per kilometre but gives a $4 dis… - Monthly payment on a phone plan
A phone costs $240. A customer pays a $60 deposit and then 12 equal monthly payments. How many dollars is each monthly p… - Number giving equal results under two rules
When a number is multiplied by 6 and then decreased by 9, the result is the same as when the number is multiplied by 3 a… - Savings from a quarter plus ten
A quarter of Sam's savings, plus $10, comes to $22. How many dollars are Sam's savings? - Pair that fails an equation
Which of the following ordered pairs (x, y) does NOT satisfy the equation 5x + 2y = 40? - Hours until a battery is empty
The charge C, in percent, of a laptop battery after t hours of use is given by C = 100 − 20t. After how many hours of us… - Sum of a line's intercepts
In the xy-plane, the line y = 3x − 6 crosses the x-axis at (p, 0) and the y-axis at (0, q). What is the value of p + q? - Another point on a line through two given points
In the xy-plane, a line passes through (2, 5) and (4, 11). Which of the following points also lies on the line? - Reciprocal of a slope from standard form
In the xy-plane, the line 2x − 4y = 8 has slope m. What is the value of 1/m? - Hours from a plumber's bill
A plumber charges a $40 call-out fee plus $25 for each hour of work. The bill is given by B = 40 + 25h. For a bill of $1… - Pages in the shorter book
Priya's book has three times as many pages as Tom's book. Together the two books have 200 pages. How many pages does Tom… - Intersection of two lines
In the xy-plane, at which point do the graphs of y = x + 1 and y = 2x − 1 intersect? - Smallest integer from a two-step inequality in words
Five times a number, minus 3, is greater than 22. What is the smallest integer the number could be? - Counting positive integer solutions
How many positive integers x satisfy 4x + 3 ≤ 19? - Most tickets with a booking fee
Concert tickets cost $7.50 each, and a single booking fee of $4 is added to any order. Maya has $50. What is the greates… - Whole hours of video before an app closes
A phone's battery holds 7 units of charge, and playing video uses 2 units per hour. The video app closes as soon as the … - Largest integer in an overlap of two inequalities
What is the largest integer that satisfies both 2x < 15 and x > 3? - Compound inequality from a number line
On a number line, a graph has a closed dot at −2, an open dot at 4, and shading between them. Which compound inequality … - Books on the upper shelf
Two shelves hold 12 books between them, and the upper shelf holds 2 more books than the lower shelf. How many books are … - Slices Ben ate
A pizza was cut into 16 slices. Ann ate three times as many slices as Ben, and between them they ate every slice. How ma… - System whose solution has equal coordinates
The solution of the system 2x + y = 9 and x + 2y = 9 is the point (a, a). What is the value of a? - Price of one apple from two purchases
Three apples and two pears cost $2.60. One apple and two pears cost $1.80. What is the price of one apple, in dollars? - Where a decreasing linear function reaches zero
A linear function f has f(1) = 10, and f decreases by 4 for each increase of 1 in x. For what value of x is f(x) = 0? - Hours parked from a stepped charge
A car park charges $2.50 for the first hour and $1.75 for each additional hour. A driver paid $11.25. For how many hours… - Weekly spending from savings
Kofi had saved $84. He spent the same amount each week, and after 7 weeks he had $21 left. How many dollars did he spend… - Straight-line depreciation of a machine
The value of a machine decreases linearly from $9,000 when new to $3,000 after 5 years. What is the value of the machine… - Change in y for a change in x
For the equation 2x + 5y = 40, when x increases by 5, by how much does y change? Give a negative value for a decrease. - Price of a pen from two purchases
One pen and two pencils cost $2.10. Two pens and one pencil cost $2.70. What is the cost, in dollars, of one pen? - Inequality for hours under a budget
A tutor charges $25 per hour. Priya has at most $180 to spend on tutoring this month. Which inequality gives the possibl… - Hardbacks bought with a fixed total
A bookshop sells used paperbacks for $3 each and used hardbacks for $8 each. Rosa bought 5 paperbacks and some hardbacks… - Meaning of the constant in a pressure model
The pressure p, in kilopascals, at a depth of d metres in a lake is modelled by p = 100 + 9.8d. What does the number 100… - Slope plus intercept after rearranging
The equation 6x − 2y = 12 can be rewritten in the form y = mx + b, where m and b are constants. What is the value of m +… - Point of a given form on a line
The point (a, 3a) lies on the line 2x + y = 25 in the xy-plane. What is the value of a? - Price of a juice from two orders
Two smoothies cost $9. Three of the same smoothies and one juice cost $16. What is the price, in dollars, of the juice? - Five-point questions on a test
A test has 20 questions. Each question is worth either 2 points or 5 points, and the test is worth 61 points in total. H… - Compound inequality for a storage temperature
A vaccine must be stored at a temperature t, in degrees Celsius, that is at least 2 and at most 8. Which inequality repr… - Ticket price from a group total
A group of 3 adults bought cinema tickets and used a voucher worth $15 off the total. They paid $120. What was the price… - Equation for a draining pool
A pool holds 12,000 litres of water and drains at a constant 400 litres per minute. Which equation gives the volume V, i… - Value of y from a two-variable equation
If 5x − 2y = 2 and x = 2, what is the value of y? - Two lengths from a total and a relation
A ribbon 13 metres long is cut into two pieces. The longer piece is 1 metre more than twice the shorter piece. How long,… - Solving a system by substitution
If y = x + 1 and 2x + y = 10, what is the value of x? - Inequality for a minimum order
A florist requires each order to contain at least 12 stems. Which inequality represents the number of stems s in a valid… - Balance after weekly deposits
Kim opens a savings account with $200 and deposits $15 every week. How much is in the account, in dollars, after 8 weeks… - Rides from a fair budget
Entry to a fair costs $8 and each ride costs $3. Lena spent exactly $50 at the fair, all on entry and rides. How many ri… - Length of each piece of rope
A rope 90 metres long is cut into 6 pieces of equal length. How long, in metres, is each piece? - Water left in a tank
A tank holds 300 litres and is drained at 12 litres per minute. How many litres remain after 15 minutes? - Equation for a bicycle hire
A bicycle hire shop charges a fixed $10 plus $4 for each hour. Which equation gives the total charge T, in dollars, for … - y-intercept from standard form
In the xy-plane, the graph of 3x − 2y = 12 crosses the y-axis at the point (0, b). What is the value of b? - Equation of a horizontal line
In the xy-plane, a line passes through the points (1, 4) and (7, 4). Which equation represents the line? - System solved by substitution with a difference
If x − y = 1 and x + 2y = 10, what is the value of x? - Solving a one-step inequality
Which of the following describes all values of x that satisfy x − 4 < 3? - Smallest integer satisfying an inequality
What is the smallest integer x for which 2x + 3 is greater than 24? - Greatest integer solution of an inequality with a negative coefficient
What is the greatest integer x for which 7 − 3x is greater than 1? - Number of tickets from a booking fee
Concert tickets cost $12 each, and a booking adds a single $2 fee however many tickets are bought. Jae paid $50 for one … - Cost of a hire from a linear model
The cost C, in dollars, of hiring a boat for h hours is C = 8h + 20. What is the cost of hiring the boat for 5 hours? - Second quantity from a relation between two
Two quantities a and b are related by 5a + 2b = 40. When a = 4, what is the value of b? - Two lengths from a total and a relation in words
A board 15 metres long is cut into two pieces so that the longer piece is 3 metres more than twice the shorter piece. Ho… - Inequality for a delivery window
A parcel will arrive at a time t, in hours after midnight, that is no earlier than 9 and before 13. Which inequality rep… - Number of chairs from a delivery total
A furniture shop delivered a table costing $15 and some chairs costing $3 each for a total of $42. How many chairs were … - Height of a stack from a base and layers
A base block is 30 centimetres high, and each tile added on top raises the stack by 2 centimetres. What is the height, i… - Interpreting the slope of a cost model
The cost C, in dollars, of a phone plan for m months is C = 25m + 40. What does the number 25 represent? - Finding the second variable in a relation
The quantities p and q satisfy 2p − 3q = 4. When q = 2, what is the value of p? - Two piles of coins from a total and a relation
Two piles hold 13 coins in total. The larger pile has one more than twice the coins in the smaller pile. How many coins … - Solving a one-step inequality with multiplication
Which of the following describes all values of x that satisfy 4x ≥ 20? - Number of long planks from a total length
A carpenter cuts a 30-foot board into some 2-foot pieces and three 4-foot pieces, using the whole board. How many 2-foot… - Equation for a shrinking stack of paper
A printer tray holds 250 sheets and uses 5 sheets per document. Which equation gives the number of sheets s left after d… - Second variable from a relation between two
The quantities m and n satisfy 4m + 5n = 22. When n = 2, what is the value of m? - Two teams from a total and a difference
Two teams have 14 players between them, and one team has 4 more players than the other. How many players are on the larg… - Inequality for a weight limit on a shelf
A shelf can hold at most 25 kilograms. Which inequality represents the total mass m, in kilograms, that may be placed on… - Chairs bought with a delivery charge
A cafe buys some chairs at $6 each and pays a single $8 delivery charge, spending $50 in all. How many chairs does the c… - Fuel left after driving
A car's tank holds 80 litres when full, and the car uses 6 litres for every hour of driving. How many litres remain afte… - Equation for a plant's height
A sunflower is 30 centimetres tall today and grows 4 centimetres each day. Which equation gives its height h, in centime… - First variable from a relation between two
The quantities u and v satisfy 2u + 5v = 26. When v = 4, what is the value of u? - Two jars from a total and a ratio
Two jars hold 16 marbles between them, and the first jar holds three times as many as the second. How many marbles are i… - Inequality for a maximum weight of luggage
An airline allows each bag to weigh no more than 23 kilograms. Which inequality represents the allowed masses m, in kilo… - Solving after distributing and combining
If 6(x + 1) − 2x = 30, what is the value of x? - Textbooks sold from a total
A bookshop sold 60 copies of a novel at 8 dollars each and t copies of a textbook at 15 dollars each, taking 780 dollars… - Equation with a decimal coefficient
If 0.5x + 7 = 12, what is the value of x? - Function for cooling tea
A cup of tea at 90 degrees cools by 3 degrees every minute. Which function gives the temperature T, in degrees, after m … - Line parallel to a line in standard form
Which of the following is an equation of a line that is parallel to the line 6x − 3y = 12 in the xy-plane? - Third point on a line
The points (1, 5), (3, 11), and (5, k) lie on the same line in the xy-plane. What is the value of k? - X-intercept from a slope and a point
A line in the xy-plane has slope −4 and passes through the point (2, 3). What is the x-coordinate of the point where the… - Price of a coffee from two orders
At a cafe, 2 coffees and 3 teas cost 13 dollars, and 1 coffee and 1 tea cost 5 dollars. What is the price, in dollars, o… - Sum of the coordinates of an intersection
In the xy-plane, the lines 2x − y = 7 and x + y = 5 intersect at the point (a, b). What is the value of a + b? - Area of a rectangle from perimeter and a difference
A rectangle has a perimeter of 40 units, and its length is 4 units more than its width. What is the area of the rectangl… - Solving an inequality with a negative coefficient
Which of the following is equivalent to −2x + 5 > 11? - Greatest distance within a budget
A taxi ride costs 3 dollars plus 2 dollars for each kilometre. Maya has 25 dollars. What is the greatest whole number of… - Inequality for fencing still needed
A gardener needs at least 40 metres of fencing and already has 15 metres. Which inequality describes the length f, in me… - Equation with a sum divided by two
If (x + 7)/2 = 6, what is the value of x? - Where a line crosses the x-axis
In the xy-plane, the line y = −3x + 12 crosses the x-axis at what value of x? - Combination of the solutions of a system
If 3x − y = 5 and x + y = 7, what is the value of x + 2y? - Days of car hire from a total cost
A car hire costs 45 dollars per day plus a one-time fee of 25 dollars. Ana paid 250 dollars in total. For how many days … - Line sharing a y-intercept
Which of the following lines has the same y-intercept as the line 4x + 2y = 10 in the xy-plane? - Least fourth score for a target average
A student needs an average of at least 80 on four tests. Her first three scores are 74, 85, and 79. What is the least sc… - Equation with the unknown on both sides
If 7 − 2x = 3x + 22, what is the value of x? - Equation of a line through two points
The graph of a linear function passes through the points (0, 5) and (2, 1). Which equation defines the function? - Dozen boxes from a count and an egg total
A farmer sells eggs in boxes of 6 and boxes of 12. One morning she sold 20 boxes containing 180 eggs in all. How many bo… - Number from a tripling and a subtraction
A number is tripled, and then 8 is subtracted from the result, giving 25. What is the number? - Intercept from a point on a line
The line y = 3x + b passes through the point (2, 11). What is the value of b? - Slope from two intercepts
In the xy-plane, a line has an x-intercept of 6 and a y-intercept of 3. What is the slope of the line? - Greatest number of pens within a budget
Sara has 40 dollars. She buys a book for 12 dollars and then as many pens as she can at 3.50 dollars each. What is the g… - Number plus half of itself
A number plus half of itself equals 36. What is the number? - Difference of two outputs of a linear function
The function f is defined by f(x) = 6 − 2x. What is the value of f(−1) − f(1)? - Product of the coordinates of a solution
The system y = x + 1 and 2x + y = 7 has the solution (a, b). What is the value of a·b? - Monthly payment for a phone
A phone costs 240 dollars. A customer pays a deposit of 60 dollars and then 6 equal monthly payments. What is the amount… - Line with the same slope
Which of the following lines has the same slope as the line y = 4x − 1? - Evaluating a linear function from its rule
The function f is defined by f(x) = 4x + 9. What is the value of f(6)? - Interpreting slope in a depreciation model
The value of a bottling machine is modeled by v(t) = 48,000 − 3,200t dollars, where t is years since purchase. What does… - Finding an x-intercept
The graph of 4x + 6y = 24 crosses the x-axis at the point (a, 0). What is the value of a? - Slope of a perpendicular line
In the xy-plane, line q is perpendicular to the graph of 7x − 2y = 8. What is the slope of line q? - Point with related coordinates on a line
The point (a, 2a) lies on the graph of 3x + 4y = 44. What is the value of a? - Ticket prices by elimination
Three adult tickets and two child tickets to a fair cost $33. One adult ticket and two child tickets cost $19. What is t… - Elimination then back-substitution
In the system 5x + 2y = 24 and 3x + 2y = 16, what is the value of y? - Recognizing an equation of the same line
A system consists of the equation 2x − y = 5 and one equation below. Which choice creates a system with infinitely many … - Dividing by a negative flips the sign
Which of the following describes all solutions of −2x + 7 ≤ 1? - Inequality with distribution
Which of the following describes all solutions of 5(x − 2) > 15? - Rides within an amusement budget
Entry to a fair costs $18, and each ride costs $2.50. With $40 to spend in total, what is the greatest number of rides a… - Smallest integer satisfying an inequality
What is the smallest integer x for which 4x − 9 > 10?
Medium (316)
- Systems of linear equations
A system: 2x + y = 11 and x − y = 1. What is the value of x + y? - Solving linear inequalities
Which of the following describes all solutions to 4x − 9 ≤ 2x + 5? - Interpreting linear models
A phone's battery percentage is modeled by P = 100 − 8t, where t is the number of hours since it was unplugged. What doe… - Systems by substitution
If y = 2x − 1 and 3x + y = 14, what is the value of x? - Absolute value equations
If |2x − 3| = 7, what is the sum of all possible values of x? - Parallel and perpendicular lines
Line k has equation y = (2/3)x + 1. Which equation represents a line perpendicular to line k? - Systems of linear equations
At a bakery, 2 muffins and 3 cookies cost $13, while 4 muffins and 1 cookie cost $16. What is the cost, in dollars, of o… - Finding the initial value from a table
What is the value of f(0)? - Solving a linear model for the input
A repair was charged $135 in total. How many hours of labour did it take? - Equation requiring distribution
What value of x satisfies the equation 3(x − 4) = 2x + 5? - Equation of a line from slope and a point
A line in the xy-plane has slope 2 and passes through the point (3, 1). Which equation represents the line? - Finding an x-intercept
The line crosses the x-axis at the point (a, 0). What is the value of a? - Inequality from a budget
What is the greatest number of notebooks Priya can buy? - System from a word problem
A theatre sold 40 tickets for a total of $275. Adult tickets cost $8 each and child tickets cost $5 each. How many adult… - Extending a linear pattern from a table
The total cost of a subscription is a linear function of the number of months. After 1 month the total cost is $14, and … - Converting between forms of a linear equation
Which equation is equivalent to y = (3/4)x − 2? - Rate of change from two readings
At 6 a.m. the temperature was 68°F, and at noon it was 86°F. If the temperature rose at a constant rate, by how many deg… - Translating words into an inequality
A number x is at least 5 more than twice a number y. Which inequality represents this relationship? - Eliminating a variable by adding equations
If 4x − 3y = 6 and 2x + 3y = 12, what is the value of y? - Finding the input for a given output
For the linear function f, f(1) = 7 and f(4) = 16. For what value of x is f(x) = 25? - Equation with decimal coefficients
If 0.4x − 1.2 = 2.8, what is the value of x? - Slope from the two intercepts
A line in the xy-plane has an x-intercept of 4 and a y-intercept of −6. What is the slope of the line? - Greatest whole number satisfying a limit
A lift can carry at most 600 kilograms. A worker who weighs 80 kilograms rides the lift with some boxes, each weighing 2… - Two unknowns from a count and a total
A pet shop sells hamsters for $15 each and mice for $6 each. On one day it sold 20 of these animals for a total of $174.… - Function with a fractional rate
The linear function g is defined by g(x) = (1/4)x + 6. For what value of x is g(x) equal to 8? - Nested parentheses on both sides
What value of x satisfies 2(3x − 1) + 4 = 4x + 6? - Slope-intercept from standard form
The line 4x + 2y = 8 is written in the form y = mx + b. What is the value of b? - Elimination with a fractional answer
If 3x + 2y = 4 and x − 2y = −8, what is the value of y? - Equation with two fractions of the same variable
If x/2 + x/4 = 6, what is the value of x? - Another point on a line through two points
A line in the xy-plane passes through the points (1, 4) and (4, 10). Which of the following points also lies on the line… - Inequality with parentheses
Which of the following describes all solutions to 3(x − 2) < 2x + 1? - Two prices, a count and a total
A stall sells pens for $3 each and notebooks for $2 each. A customer buys 20 items for a total of $52. How many pens did… - Zero of a linear function from two points
The graph of the linear function f in the xy-plane passes through the points (0, −2) and (4, 6). For what value of x is … - A number less 40% of itself
When 40% of a number is subtracted from the number, the result is 27. What is the number? - Line through two points with the same y
Which equation represents the line in the xy-plane that passes through the points (2, 3) and (6, 3)? - Value between two known outputs
The linear function f satisfies f(0) = 12 and f(6) = 0. What is the value of f(2)? - Intercept from a slope and a point
A line in the xy-plane has a slope of −3/2 and passes through the point (4, 1). What is the y-intercept of the line? - Greatest integer length under a perimeter limit
A rectangle has a width of 5 centimetres, and its perimeter must be less than 40 centimetres. What is the greatest possi… - Two numbers from a multiple and a difference
One number is 3 times another number, and the difference between the two numbers is 24. What is the smaller number? - Parallel line with a given intercept
In the xy-plane, line m is parallel to the line 3x − y = 4 and has a y-intercept of −2. Which equation represents line m… - Greatest number of parcels under a weight limit
A delivery drone can carry at most 150 kilograms, including a 30-kilogram container. How many 12-kilogram parcels, at mo… - Elimination, then a difference
If 2x + y = 7 and 3x − y = 8, what is the value of x − y? - Rate from two readings of a draining pool
A swimming pool is being drained at a constant rate. At 1 p.m. it contains 20,000 litres, and at 4 p.m. it contains 14,0… - Twice a number less 7
Twice a number, decreased by 7, is equal to the number increased by 5. What is the number? - Rectangle from its perimeter and a difference
A rectangle has a perimeter of 40 centimetres, and its length is 4 centimetres greater than its width. What is the lengt… - Substitution with a fractional relation
If y = x/3 and 2x + 3y = 27, what is the value of x? - Joining fee from two totals
A gym membership costs a one-time joining fee plus a fixed amount each month. After 2 months a member has paid $90 in to… - A number plus its half
The sum of a number and half of that number is 24. What is the number? - y-intercept from standard form with a negative y coefficient
What is the y-intercept of the line 4x − 2y = 10 in the xy-plane? - Where two linear functions are equal
The functions f and g are defined by f(x) = 2x + 3 and g(x) = 5x − 6. For what value of x is f(x) = g(x)? - Missing value from an average
The average (arithmetic mean) of x, 7 and 11 is 10. What is the value of x? - Coins from a count and a value
A purse holds 30 coins, all nickels (5 cents) and dimes (10 cents), with a total value of $2.20. How many of the coins a… - Slope from a point and the y-intercept
The graph of the linear function f in the xy-plane passes through the point (2, 5) and has a y-intercept of −1. What is … - Two distributions on one side
If 2(x − 1) + 3(x + 2) = 19, what is the value of x? - Integers in an interval
How many integers x satisfy both x ≥ −2 and x < 3? - Larger of two numbers from a sum and a multiple
The sum of two numbers is 20, and one number is three times the other. What is the larger number? - Extending a constant filling rate
A tank is being filled at a constant rate. At noon it holds 5 litres, and at 4 p.m. it holds 17 litres. How many litres … - Two descriptions of the same result
A number is doubled and then 7 is subtracted. The result is the same as when the number is halved and 8 is added. What i… - Price of one ticket from two purchases
Three adult tickets and two child tickets cost $34, while one adult ticket and four child tickets cost $28. What is the … - Meaning of the x-intercept in context
The function p(t) = 220 − 4t models the number of litres of fuel in a generator's tank t hours after it is switched on. … - Equation of a linear function from two values
For a linear function f, f(1) = 5 and f(4) = 11. Which equation defines f? - Equation with distribution on one side
What value of x satisfies 5(x − 2) − 3x = 8? - Slope between two points
In the xy-plane, a line passes through (−1, 5) and (3, −1). What is the slope of the line? - Greatest whole number within a budget
A student has $80 to spend on a $20 entry ticket and rides that cost $6 each. What is the greatest number of rides the s… - Identifying a linear function from a table
The table gives three values of a linear function f. Which equation defines f? - Equation with variables on both sides and a distribution
What value of x satisfies 3(2x − 1) = 4x + 11? - Equation from intercepts
A line in the xy-plane has x-intercept 6 and y-intercept 4. Which equation represents the line? - Fewest hours to clear a minimum
A worker earns $8 per hour and must pay a $40 transport pass each week. What is the fewest number of whole hours the wor… - Input from a linear model's output
A plant was 15 centimetres tall when it was bought and has grown 0.75 centimetres per day since. After how many days wil… - Equation from a verbal description
Six less than two and a half times a number is 14. What is the number? - Missing coordinate on a line
The line 3x − 4y = 10 passes through the point (−2, k). What is the value of k? - Graph of a linear inequality: which side is shaded
In the xy-plane, which point lies in the region defined by y ≥ 2x − 1 but NOT on its boundary line? - Two prices from two purchases
At a stall, 4 apples and 2 pears cost $22, and 1 apple and 1 pear cost $8. What is the cost, in dollars, of one apple? - Graph of a linear function: which passes through two points
A linear function's graph passes through (2, 7) and (5, 16). Which of the following points is also on the graph? - Tickets at two prices from a total
A school sold adult tickets for $3 and child tickets for $2 for a play. The number of child tickets sold was 5 fewer tha… - Which equation has a given slope and passes through a point
Which equation represents a line with slope −3 that passes through the point (1, 4) in the xy-plane? - Greatest number within a remaining budget
A student has $200 for a trip and must keep at least $5 in reserve. Each museum ticket costs $15. What is the greatest n… - Solution of a system by elimination
Which ordered pair (x, y) satisfies the system 2x + 3y = 14 and x − y = 2? - Translating 'at least' and 'no more than'
A lift's sign says it carries at least 2 and no more than 12 people. Which inequality represents the number of people p … - Meaning of the slope's sign
The function d(t) = 480 − 60t gives the distance, in kilometres, between a train and its destination t hours after depar… - Two numbers from a sum and a relation
The sum of two numbers is 35, and the larger is 7 less than twice the smaller. What is the smaller number? - Inequality for a minimum score
A student's marks on three tests were 72, 85, and 78. The student wants an average of at least 80 across four tests. Whi… - Comparing two linear models
Gym A charges a $50 joining fee plus $20 per month. Gym B charges no joining fee and $30 per month. After how many month… - Ages from a difference and a multiple
A father is 30 years older than his son, and the father's age is 3 times the son's age. How old is the son? - Solving a system by substitution
Which ordered pair (x, y) is the solution to the system y = x − 2 and 2x + y = 16? - Interpreting a solution set in context
A theatre must sell at least 150 tickets to cover the cost of a performance, and it has 300 seats. If t is the number of… - Identifying the graph feature from the equation
The function f is defined by f(x) = −(3/4)x + 6. Which statement about the graph of y = f(x) in the xy-plane is true? - Equation from a geometric description
A rectangle's length is 4 times 1 less than its width w, and its length is also 8 more than twice its width. What is w? - y-intercept from two points
In the xy-plane, a line passes through (1, 3) and (4, 9). What is the y-coordinate of the point where the line crosses t… - Choosing the inequality for a minimum with a fixed cost
A charity run costs $250 to organise. Each runner pays a $15 entry fee. Which inequality gives the numbers of runners n … - Reading a linear function's rate from two outputs
For a linear function f, f(2) = 11 and f(6) = 3. Which statement is true? - Intercepts of a line in standard form
The line 3x + 4y = 18 is graphed in the xy-plane. Which statement is true? - Inequality from 'no more than' with two rates
A baker has no more than 5 kilograms of sugar. Each cake uses 0.4 kilograms and each batch of biscuits uses 0.25 kilogra… - Interpreting the intercept in a decreasing model
The function w(t) = 18 − 1.5t models the depth, in centimetres, of water in a paddling pool t hours after a leak begins.… - Ages: sum with a relation
Maya is 4 years younger than her brother. Twice her brother's age plus three times Maya's age is 48. How old is her brot… - Compound inequality from 'between'
A recipe says the oven temperature must be between 160°C and 180°C, inclusive. Which inequality represents the acceptabl… - Meaning of the slope in a savings model
The amount of money in a savings jar is modelled by S(w) = 15 + 8w, where w is the number of weeks since the jar was sta… - A number from two descriptions
Seven less than three times a number equals two more than twice the number. What is the number? - Inequality with 'at most' and a fixed deduction
A café's daily takings T must cover $180 of fixed costs and leave at least $120 profit. Which inequality represents this… - Interpreting a point on a linear graph
The graph of y = f(x) in the xy-plane is a line that passes through (0, 30) and (10, 0), where x is the number of days s… - A number from two equal expressions
Six less than four times a number is equal to twice the sum of the number and six. What is the number? - Inequality for a minimum with a per-item cost and a target
A club sells raffle tickets at $3 each and must raise at least $450 after paying $60 for prizes. Which inequality gives … - Interpreting the y-intercept of a decreasing line
The function d(t) = 500 − 20t gives the distance, in metres, between a walker and a gate t seconds after the walker star… - A number from two equal expressions with distribution
Twice the sum of a number and four is equal to seven less than three times the number. What is the number? - Slope between two points, with a negative
In the xy-plane, a line passes through (1, 4) and (5, −2). What is the slope of the line? - Choosing the system for a word problem
A stall sold large and small candles. Two large and three small candles cost $16, and a large candle costs $3 more than … - Graph of a line from its equation
The line y = −(1/2)x + 3 is graphed in the xy-plane. Which statement about the graph is true? - Choosing the system for a situation
At a stall, 3 pies and 2 tarts cost $14, and one pie with one tart costs $6. If p and t are the prices of a pie and a ta… - Two quantities from a relation and a weighted sum
A shelf holds novels and atlases. There are 5 more atlases than novels, and three times the number of novels plus twice … - Reading slope and intercept from standard form
The line 3x − 6y = 12 is graphed in the xy-plane. What is the slope of the line? - System for a word problem
A stall sold 5 items — some pens at $2 each and some notebooks at $5 each — for a total of $16. If p pens and n notebook… - A number from two equal descriptions
Three less than four times a number is the same as eleven more than twice the number. What is the number? - Which point lies on a given line
Which of the following points lies on the line 4x − 3y = 6 in the xy-plane? - Sum of squares from a sum and a difference
Two numbers have a sum of 16 and a difference of 6. What is the sum of their squares? - System for a purchase problem
Three cakes and two pies cost $19, and one cake and one pie cost $8. If c and p are the prices of a cake and a pie, whic… - A number from two descriptions
Eight less than five times a number equals sixteen more than three times the number. What is the number? - Equation from a two-part description
Twice the quantity 'one more than three times a number', added to the number itself, equals 37. What is the number? - Inequality for a range with a fixed fee
A hall charges a $200 booking fee plus $15 per guest. A club wants to spend at most $800. Which inequality gives the pos… - Missing coordinate on a line
The line 7x − 2y = 8 passes through the point (2, k). What is the value of k? - Price of one item from two purchases
At a market, 5 apples and 3 pears cost $26, and an apple costs $2 more than a pear. What is the price, in dollars, of on… - Equation with a bracket and a subtraction
Three times the quantity 'one more than twice a number', minus twice the number, equals 27. What is the number? - Inequality for staying under a weight limit
A lift can carry at most 450 kilograms. A porter weighing 70 kilograms rides with n crates of 25 kilograms each. Which i… - y-coordinate where a line meets a vertical line
In the xy-plane, the graph of 9x − 4y = 6 intersects the vertical line x = 2 at exactly one point. What is the y-coordin… - Product of two prices from two purchases
At a fair, 3 rides and 2 games cost $21, and a ride costs $2 more than a game. What is the product of the ride price and… - Equation with fractions on both sides
If (x − 3)/4 = (x + 1)/6, what is the value of x? - Ages now from a future sum
Ana is 4 years older than Ben. In 6 years, the sum of their ages will be 40. How old is Ben now? - Linear function from a difference in outputs
The function g is linear. It is known that g(4) − g(1) = 9 and that g(1) = −2. What is the value of g(7)? - Missing x-coordinate of a point on a line through two points
In the xy-plane, the line through the points (−2, 5) and (4, −1) also passes through the point (k, 3). What is the value… - Counting items of two sizes from a total volume
A vending machine holds 90 cans of two sizes, 330 millilitres and 500 millilitres, and the cans contain 36,500 millilitr… - Greatest number within a budget after a fixed purchase
Mia has at most $50 to spend on notebooks at $3.20 each and pens at $1.40 each. If she buys 8 notebooks, what is the gre… - Fractional coefficients on both sides
Three quarters of a number, decreased by 15, equals one third of the number, increased by 5. What is the number? - Time to reach a target under a constant rate
A water tank holds 60 litres and drains at a constant 4.5 litres per minute. After how many minutes will 24 litres remai… - Linear function value from a table with a gap
A linear function h has h(5) = 7 and h(9) = −5. What is h(0)? - Equation of a line perpendicular to a given line through the origin
In the xy-plane, line ℓ is perpendicular to the line 2x + 5y = 10 and passes through the origin. Which of the following … - System where one equation gives a substitution
If 5x + 2y = 23 and y = 3x − 4, what is the value of x? - Least integer satisfying a strict inequality
What is the least integer x for which 3x − 5 is greater than 2x + 1? - Bill with a charge above an allowance
A phone plan costs $18 per month and includes 200 text messages; each message beyond 200 costs $0.10. A customer's bill … - Three pieces of a ribbon
A ribbon 240 centimetres long is cut into three pieces. The second piece is twice as long as the first, and the third pi… - Time for a linearly shrinking quantity to reach a value
A candle 25 centimetres tall burns at a constant rate. Two hours after it is lit, it is 21 centimetres tall. How many ho… - Point on a line in a specified quadrant
In the xy-plane, which of the following points lies on the graph of 3x − 2y = 12 and in quadrant IV? - Vertical gap between two parallel lines
In the xy-plane, the lines y = 2x + 1 and y = 2x − 7 are parallel. For any value of x, how many units is the point on th… - Two-variable pricing problem
At a bake sale, 12 muffins and 8 scones cost $36, and 6 muffins and 12 scones cost $30. What is the price, in dollars, o… - Vertex of a triangle formed by two lines and the y-axis
In the xy-plane, the lines y = 3x − 2 and y = −2x + 8 and the y-axis form a triangle. What is the x-coordinate of the ve… - Greatest distance within a rental budget
A car rental costs $40 per day plus $0.25 per kilometre driven. A driver rents the car for 2 days and has a budget of at… - Equation with a distributed subtraction
If 7x − 4(x + 2) = 19, what is the value of x? - Two items whose prices differ by a fixed amount
A hardware shop sells a brush for $4 more than a roller. Three brushes and four rollers together cost $194. What is the … - Linear model from a rate: when a quantity runs out
A pond holds 18 centimetres of water and loses 0.75 centimetres of depth per day in a dry spell. If no rain falls, after… - Difference of a line's intercepts
In the xy-plane, the graph of 3x + 4y = 24 crosses the x-axis at (a, 0) and the y-axis at (0, b). What is the value of a… - Reading a coordinate off the intersection of two standard-form lines
In the xy-plane, the lines 2x − 5y = 11 and 4x + 5y = 7 intersect at the point (p, q). What is the value of q? - Two quantities from a ratio and a difference
In a car park there are four times as many cars as vans, and there are 9 more cars than vans. How many vehicles are in t… - Least number of weeks to reach a savings target
Nia has $200 saved and adds $35 each week. What is the least number of whole weeks after which she will have at least $7… - Unknown from an average of expressions
The average (arithmetic mean) of x, 2x, and 3x + 6 is 14. What is the value of x? - Percent increase followed by a subtraction
A number is increased by 20%, and 15 is then subtracted from the result, giving 33. What is the original number? - Missing table value for a linear function
The table shows values of a linear function g. x | g(x) −2 | 9 0 | 5 2 | 1 5 | ? What is the value of g(5)? - Slope from a point and an x-intercept
In the xy-plane, a line passes through the point (−1, 2) and has x-intercept 3. What is the slope of the line? - Constants from a known solution of a system
The ordered pair (3, −2) is the solution of the system x + 2y = k and 3x − y = m, where k and m are constants. What is t… - Unknown intercept from a known intersection
In the xy-plane, the lines y = 3x + b and y = −x + 8 intersect at a point whose x-coordinate is 1, where b is a constant… - Greatest number of extra items within a weight limit
A van can carry at most 900 kilograms. It is already loaded with 12 crates that weigh 35 kilograms each. What is the gre… - Greatest integer satisfying a compound inequality
If −3 ≤ 2x + 1 < 9, what is the greatest integer value of x? - Word equation with a half
Five less than twice a number is equal to 7 more than half the number. What is the number? - Equation with decimal coefficients
If 0.3(x − 10) = 0.2x + 1, what is the value of x? - Finding the input that gives a specified output
A line in the xy-plane passes through the point (1, 4) and has slope −3. For what value of x is y equal to −11 on this l… - Change in y for a given change in x along a line
In the xy-plane, a point moves along the line 5x + 2y = 20 so that its x-coordinate increases by 4. By how much does its… - Point on a line with equal coordinates
In the xy-plane, a point on the graph of 3x − 4y = 12 has its x-coordinate equal to its y-coordinate. What is the x-coor… - Greatest integer length under a perimeter limit
A rectangle has a width of 7 centimetres, and its perimeter must be less than 50 centimetres. What is the greatest possi… - Two speeds for a total distance
A cyclist rides at 18 kilometres per hour for t hours and then at 24 kilometres per hour for 2 hours, covering 84 kilome… - Linear function from a difference and an intercept
For the linear function f(x) = mx + b, f(3) − f(1) = 8 and f(0) = −1. What is the value of f(5)? - Slope of a line through points given in terms of a parameter
In the xy-plane, a line passes through the points (a, 0) and (0, 2a), where a is a positive constant. What is the slope … - Rooms and guests
A hotel has 60 rooms, each either a single room for one guest or a double room for two guests. When every room is full, … - Counting notes of two values
A cash box holds 23 notes, all either $5 or $20, worth $250 in total. How many $20 notes are in the box? - Sum of the coordinates of an intersection point
In the xy-plane, the lines y = 2x − 1 and y = −3x + 14 intersect at point Q. What is the sum of the x- and y-coordinates… - Minimum score for a target average
A student's scores on three tests are 78, 92, and 84. What is the least whole-number score the student can get on a four… - Value that is not a solution of an inequality
Which of the following values of x is NOT a solution of 2x + 5 ≤ 3x − 1? - Capacity from two fractional fill levels
A tank is two fifths full. After 36 litres are added, it is seven tenths full. What is the capacity of the tank, in litr… - Temperature where two scales agree
Temperatures in degrees Celsius, C, and degrees Fahrenheit, F, are related by F = 1.8C + 32. At what temperature, in deg… - Function value from its two intercepts
The graph of a linear function f in the xy-plane has x-intercept 6 and y-intercept −3. What is the value of f(10)? - Checking statements about a linear graph
Which of the following statements is true about the graph of y = −(3/4)x + 6 in the xy-plane? - First year a linearly depreciating value falls below a threshold
The value of a machine t years after purchase is V(t) = 18,000 − 1,500t dollars. After how many whole years will the val… - Distance between a line's intercepts
In the xy-plane, the line x/3 + y/4 = 1 crosses the x-axis and the y-axis at two points. What is the distance between th… - Parameter for which a described point lies on a line
For what value of k is the point (k, k + 1) a solution of the equation 2x + 3y = 18? - Counting integers in a compound inequality
How many integer values of x satisfy 5 < 3x − 4 < 17? - Base of an isosceles triangle from its perimeter
An isosceles triangle has a perimeter of 46 centimetres. Each of its two equal sides is 5 centimetres longer than its ba… - Solving, then evaluating an expression
If 3(x + 2) = 5x − 4, what is the value of x + 2? - Zero of a linear function from two values
A linear function f has f(0) = 4 and f(6) = 1. For what value of x is f(x) = 0? - Slope of a line reflected across the y-axis
In the xy-plane, line ℓ has equation y = 5x − 3. Line m is the reflection of line ℓ across the y-axis. What is the slope… - Meeting time of two trains approaching each other
Two trains are 300 kilometres apart on the same line and travel toward each other, one at 80 kilometres per hour and the… - Greatest average daily use within a remaining allowance
A phone plan includes 6 gigabytes of data per 30-day month. After 20 days, a customer has used 4 gigabytes. What is the … - Years for linear growth to reach a height
A tree was 1.2 metres tall when it was planted and grows 0.35 metres each year. After how many years will the tree be 4 … - Composing a linear function with itself
The function f is defined by f(x) = −4x + 20. What is the value of f(f(2))? - Slope of a line through the origin and a point on another line
In the xy-plane, the line 3x + 2y = 12 and the line y = kx intersect at a point whose x-coordinate is 2, where k is a co… - Heads and legs
A field holds ducks and cows, 26 animals in all, with a total of 68 legs. How many cows are in the field? - Range of a dimension from bounds on an area
A rectangle has a width of 8 units. Its area must be at least 120 square units and at most 200 square units. Which inequ… - Compound inequality from a membership range
A club must have at least 12 members and at most 30. It currently has m members, and 5 more people are about to join. Wh… - Hours from a bill charged in half-hour units
A mechanic charges a $45 call-out fee plus $30 for each half hour of work. A customer's bill was $165. How many hours of… - Equation with a fraction subtracted from a constant
If 6 − (x − 4)/2 = 1, what is the value of x? - Fare from a rate per fixed distance
A taxi meter starts at $3.20 and adds $0.40 for every 200 metres travelled. What is the fare, in dollars, for a journey … - Time for a linearly draining quantity to reach a level
A phone's battery drains at a constant rate, from 100% at 8 a.m. to 40% at 2 p.m. How many hours after 8 a.m. will the b… - Ratio of a line's intercepts
In the xy-plane, the line y = −3x + 12 has x-intercept a and y-intercept b. What is the value of b/a? - Supplementary angles with a described relationship
Two angles are supplementary. The measure of one angle is 30° more than twice the measure of the other. What is the meas… - Product of two numbers from a sum and a weighted difference
The sum of two numbers is 25, and twice the first number minus the second number is 8. What is the product of the two nu… - Least number of sales to exceed a target after costs
A club sells raffle tickets for $3 each and pays $80 for prizes. What is the least number of tickets the club must sell … - Least number of additional sessions to meet a target
Elena must practise for at least 400 minutes this week. She has already done 4 sessions of 45 minutes each. What is the … - Height of a picture from a fractional ratio and perimeter
The width of a rectangular picture is two thirds of its height, and the perimeter of the picture is 100 centimetres. Wha… - Height at which a linear temperature model reaches a value
The temperature, in degrees Celsius, at a height of h kilometres above a town is modelled by T(h) = 20 − 6.5h. At what h… - Line sharing a y-intercept with a given line
In the xy-plane, line ℓ has the same y-intercept as the graph of 3x + 2y = 10 and a slope of 2. Which of the following i… - Sales with a fixed ratio between two items
A bakery sells loaves for $4 each and rolls for $1 each. On one day it sold three times as many rolls as loaves, taking … - Ages from a ratio now and a difference later
Kai is twice as old as Lee. In 6 years, Kai will be 8 years older than Lee. How old is Kai now? - Greatest number of higher-priced tickets within a budget
Cinema tickets cost $9 for adults and $6 for children. A group of 12 people has at most $90 to spend on tickets. What is… - Greatest weight per item under a total limit
A box holding 24 identical cans must weigh at most 9 kilograms in total. The empty box weighs 0.6 kilograms. What is the… - Largest angle of a quadrilateral from expressions
The measures of the four angles of a quadrilateral are x°, (x + 10)°, 2x°, and (2x − 10)°. What is the measure, in degre… - Width of a path from the outer perimeter
A rectangular garden measures 12 metres by 8 metres and is surrounded on all sides by a path of uniform width. The outer… - Input change from an output change and a slope
The graph of a linear function has slope 2/3. If the output of the function increases by 6, by how much does the input i… - y-intercept from a table of a linear relationship
The table shows three pairs of values for a linear relationship between x and y. x | y 1 | 7 3 | 13 7 | 25 What is the… - Ratio of the x-intercepts of two parallel lines
In the xy-plane, the lines 3x + 4y = 24 and 3x + 4y = 48 are parallel. What is the ratio of the x-intercept of the secon… - y-axis crossing of a line given with x in terms of y
In the xy-plane, the graph of x = 2y + 6 is a line. At what y-coordinate does the line cross the y-axis? - Sharing money with a described relationship
Amir and Bea share $150. Amir's share is $30 more than twice Bea's share. How much, in dollars, is Bea's share? - System with fractional terms solved by adding
If x/2 + y/3 = 4 and x/2 − y/3 = 2, what is the value of x? - Greatest integer width under a perimeter limit
A rectangle's length is 3 centimetres more than its width, and its perimeter is less than 50 centimetres. What is the gr… - Compound inequality through a conversion formula
The Fahrenheit temperature F of a room must satisfy 68 ≤ F ≤ 86, where F = 1.8C + 32 and C is the temperature in degrees… - Range from a fundraising target and a distance limit
In a sponsored walk, Sam raises $5 for each kilometre walked. Sam wants to raise at least $120 but can walk at most 30 k… - Ages of three siblings from a sum and two differences
The ages of three siblings add up to 34. The middle sibling is 2 years older than the youngest and 3 years younger than … - Value of a linear function from its slope and one value
The graph of the linear function f has slope 1/4, and f(8) = 5. What is the value of f(−4)? - Mass from a spring's linear extension
A spring is 12 centimetres long with nothing hung on it, and it stretches 2.5 centimetres for every 100 grams hung from … - Line with the same x-intercept as a given line
In the xy-plane, which of the following equations has a graph with the same x-intercept as the graph of 2x − 3y = 8? - x-intercept after finding the constant
In the xy-plane, the line 5x − 2y = c passes through the point (2, −3), where c is a constant. What is the x-intercept o… - Distance from an intersection point to the x-axis
In the xy-plane, the lines y = x + 2 and y = 3x − 4 intersect at point P. What is the distance from P to the x-axis? - Current speed from an upstream journey
A boat's speed in still water is 12 kilometres per hour. Travelling upstream against a steady current, the boat takes 5 … - Months after which an upfront plan becomes cheaper
One phone plan costs $240 upfront plus $35 per month. A second plan costs $60 per month with nothing upfront. After how … - Range of a side from a perimeter limit and an area minimum
A square must have a perimeter of at most 60 centimetres and an area of at least 100 square centimetres. Which inequalit… - Overtime rate from a week's pay
A worker is paid $14 per hour for the first 40 hours in a week and a higher rate for each hour beyond 40. In a week of 4… - Longest side of a triangle from a perimeter
A triangle has sides of length x, x + 4, and 2x − 8 units, and its perimeter is 60 units. What is the length of the long… - Time for a candle to reach half its height
A candle is 20 centimetres tall and burns down at 1.5 centimetres per hour. After how many hours will the candle be half… - Constant difference of consecutive outputs
A linear function f satisfies f(3) = 10 and f(7) = 22. What is the value of f(x) − f(x − 1) for any value of x? - Line midway between two parallel lines
In the xy-plane, the lines y = 2x + 1 and y = 2x − 3 are parallel. What is the y-intercept of the line that is parallel … - Parameter that appears twice in a line's equation
In the xy-plane, the line y = ax + a passes through the point (3, 8), where a is a constant. What is the value of a? - Ratio of the coordinates of an intersection point
In the xy-plane, the lines 2x + y = 10 and x − 2y = 0 intersect at the point (a, b). What is the value of a/b? - Range of a side from a fencing limit and an area minimum
A rectangular plot has one side of length 12 metres. The plot must be enclosed with at most 60 metres of fencing and mus… - Range of a total cost from a range of attendance
The number of people p attending an event will satisfy 50 ≤ p ≤ 80. The cost of the event is $200 plus $12 per person. W… - Inequality with no solution
Which of the following inequalities has no solution? - Vertex angle of an isosceles triangle
In an isosceles triangle, the vertex angle is 30° less than each of the two equal base angles. What is the measure, in d… - Input at which a linear function is half its starting value
The function f is defined by f(x) = −(2/5)x + 6. For what value of x is f(x) equal to half of f(0)? - Slope that is the negative reciprocal of another
In the xy-plane, which of the following lines has a slope that is the negative reciprocal of the slope of the line y = 4… - Equation of a line after doubling both intercepts
In the xy-plane, line ℓ has equation 5x + 2y = 20. A second line has both its x-intercept and its y-intercept twice thos… - Correct answers from a scoring rule
In a quiz of 30 questions, each correct answer scores 4 points and each wrong answer loses 1 point. A student answered e… - Constant shared by two intersecting lines
In the xy-plane, the lines y = kx + 2 and y = −kx + 8 intersect at the point (1, 5), where k is a constant. What is the … - Greatest number of items under a weight limit
A parcel must weigh less than 2,000 grams. The empty box weighs 350 grams, and each item placed in it weighs 120 grams. … - Least number of parcels to reach a pay target
A delivery driver is paid $12 per hour plus $3 for each parcel delivered. In a 6-hour shift, what is the least number of… - Rectangle with the same perimeter as a square
A rectangle's width is 5 centimetres less than its length. Its perimeter equals the perimeter of a square with side leng… - Function value from one value and the y-intercept
The graph of the linear function g in the xy-plane has y-intercept 7, and g(−1) = 4. What is the value of g(2)? - Equation of a line reflected across the x-axis
In the xy-plane, the graph of 2x + 3y = 6 is reflected across the x-axis. Which of the following is an equation of the r… - x-intercept of a line after a horizontal translation
In the xy-plane, the graph of 3x + 4y = 12 is translated 2 units to the right. What is the x-intercept of the translated… - Combined unit price from two purchases
Three notebooks and two pens cost $19, and five notebooks and four pens cost $33. What is the cost, in dollars, of one n… - Ratio changed by adding to one part
A jar holds red and blue beads in the ratio 3 : 5. If 12 red beads are added, the two colours are equal in number. How m… - Minutes a heater can run within a temperature band
A room's temperature must be kept between 18°C and 24°C. A heater raises the temperature by 0.5°C per minute. Once the r… - Length of a whole from the difference of two fractional pieces
A rope is cut into two pieces. One piece is three fifths of the whole rope and is 2.4 metres longer than the other piece… - Altitude from a linear boiling-point model
Water boils at 100°C at sea level, and the boiling point falls by 1°C for every 300 metres of altitude. At what altitude… - Line that meets a given line at exactly one point
In the xy-plane, which of the following is an equation of a line that intersects the line y = 2x + 1 at exactly one poin… - x-intercept from a point and the y-intercept
In the xy-plane, line ℓ passes through the point (4, 1) and has y-intercept −7. What is the x-intercept of line ℓ? - Chairs and a table
Four chairs and a table cost $340. The table costs $40 more than two chairs. What is the cost of one chair, in dollars? - Least perimeter under a length condition
A rectangle has a width of 4 centimetres, and its length must be at least 3 times its width. What is the least possible … - Value not attainable under a strict bound
If 1 < x < 4, which of the following is NOT a possible value of 3x + 2? - Sessions at which two clubs cost the same
One club charges $5 per session but gives the first 2 sessions free. Another club charges a $4 joining fee plus $3 per s… - Intercept from two points on a linear function
The graph of the linear function f passes through (2, 7) and (5, 16). What is the value of f(0)? - Slope plus intercept from standard form
When the equation 5x − 2y = 10 is written in the form y = mx + b, what is the value of m + b? - Age from a sum of multiples
Ren is 4 years older than Sol. Twice Ren's age plus three times Sol's age equals 23. How old is Sol? - Inequality for a total that must not exceed a limit
An order of n items costs $4 per item plus $6 for shipping, and the total must not exceed $50. Which inequality represen… - Smallest of three consecutive multiples of 5
The sum of three consecutive multiples of 5 is 90. What is the smallest of the three? - Stamps of two values
Lena buys 24 stamps. Some cost 20 cents each and the rest cost 50 cents each, and she pays $7.80 in total. How many 50-c… - Hours for a hiker to descend
A hiker starts at an altitude of 2,400 metres and descends at a steady rate of 300 metres per hour. After how many hours… - Sum of a line's intercepts
For the line 5x − 2y = 20 in the xy-plane, what is the sum of the x-intercept and the y-intercept? - Cars on a ferry from fares
A ferry charges $12 for each car and $3 for each bicycle. On one crossing it carried 25 vehicles in total and collected … - Minimum cakes to reach a fundraising goal
A club has already raised $120 and needs to raise at least $500 in total. It sells cakes for $4 each. What is the minimu… - Counting integers in a compound inequality
How many integers x satisfy −2 < x + 3 ≤ 5? - Width of a pen fenced on three sides
A farmer builds a rectangular pen against a straight wall, so fencing is needed on only three sides: two sides of length… - Time at which a rising temperature reaches a value
The temperature in a greenhouse rises at a constant rate from 15°C at 6 am to 24°C at 9 am. How many hours after 6 am do… - f(0) from slope and one value
The graph of the linear function f has slope −2, and f(4) = 1. What is the value of f(0)? - Coefficient from a y-intercept
In the xy-plane, the graph of 4x + ky = 20 has a y-intercept of −5, where k is a constant. What is the value of k? - Coffees sold from a mixed total
A cafe sold 40 cups of coffee and tea in total for $150. A coffee costs $4.50 and a tea costs $3. How many coffees were … - Largest whole-number side under a perimeter cap
The perimeter of an equilateral triangle is at most 50 centimetres. If the side length is a whole number of centimetres,… - Number from a doubled expression
Twice the result of subtracting 5 from three times a number is 32. What is the number? - Ticket prices from a family total
A family bought 4 adult tickets and 3 child tickets for $160. A child ticket costs $5 less than an adult ticket. What is… - Starting balance from two later balances
A savings account's balance grows by the same amount each month. After 2 months it holds $90 and after 5 months it holds… - Value of y where a line meets the x-axis
In the xy-plane, the line 2x + 5y = 6 crosses the x-axis at the point (a, 0). What is the value of a? - Bicycles in a shed from a wheel count
A shed holds bicycles and unicycles, 14 vehicles in all with 20 wheels in total. How many bicycles are in the shed? - Most classes within a budget
A dance school charges a $15 registration fee plus $12 per class. With $80, what is the greatest number of classes a stu… - Age from a relation in words
Five more than twice Ana's age is 33. How old is Ana? - Boxes from a delivery with a shortfall
A supplier promised 6 boxes of apples per shop to some shops, but 4 boxes were damaged and thrown away, leaving 50 boxes… - Starting fee from two readings
A courier's total charge is a linear function of the number of parcels. Three parcels cost $22 and seven parcels cost $3… - Smallest positive integer solution of a two-variable equation
In the equation 3x − 2y = 7, both x and y are positive integers. What is the smallest possible value of x? - Adult tickets from a mixed sale
A cinema sold 11 tickets to one family group for $31. Adult tickets cost $5 and child tickets cost $2. How many adult ti… - Most items after a fixed cost
A club pays $25 to hire a hall and $6 per person for food, and it has at most $100 to spend. What is the greatest number… - Number from a bracketed product
Three times the result of subtracting 4 from a number is 48. What is the number? - Fixed fee from two totals
A window cleaner's charge is a linear function of the number of windows. Two windows cost $28 and six windows cost $52. … - Where a line crosses the y-axis
In the xy-plane, the line 7x − 3y = 12 crosses the y-axis at (0, b). What is the value of b? - Blue marbles from a conditional relation
A bag holds 24 marbles, each red or blue. If there were 3 more red marbles, there would be twice as many red marbles as … - Equation from a slope and a point
In the xy-plane, a line with slope 1/2 passes through the point (−2, 3). Which equation represents the line? - X-intercept from a value and a slope
A linear function f has a slope of −2, and f(3) = 10. What is the x-intercept of the graph of f? - Five-dollar items from a count and a total
A stall sold 20 items, some at 3 dollars each and the rest at 5 dollars each, for a total of 76 dollars. How many 5-doll… - Coefficient from a y-intercept
In the xy-plane, the graph of 2x + by = 10, where b is a constant, has a y-intercept of −5. What is the value of b? - Two-digit number from its digits
The digits of a two-digit number add up to 9, and the number is 27 more than the number formed by reversing its digits. … - Slope of a perpendicular line
Line l has the equation y = (2/3)x − 1. What is the slope of a line perpendicular to l? - Solving an inequality with distribution
Which of the following gives all values of x that satisfy 2(x − 1) ≤ 3x + 4? - Another point on a line of slope 3
In the xy-plane, a line with slope 3 passes through the point (1, 1). Which of the following points also lies on the lin… - Number of batches within two limits
A bakery must make at least 200 rolls today and has enough flour for at most 350 rolls. It makes rolls in batches of 25.… - Counting integers that satisfy two inequalities
How many integer values of x satisfy both 4 − x ≥ 1 and x > −2? - Constant growth read from two measurements
A bamboo shoot grows at a constant rate. It measured 11 centimeters at the end of week 3 and 23 centimeters at the end o… - When a draining tank reaches empty
A tank holds 840 liters at noon and drains at a constant rate. At 12:45 p.m. it holds 300 liters. How many minutes after… - Finding the input for a given output
The linear function f has slope −2 and f(0) = 5. For what value of x does f(x) = −9? - Value on a parallel line
Line k passes through (2, 7) and is parallel to the graph of 3x + y = 5. What is the y-coordinate of the point on line k… - Parameter for a point on a line
The point (k, k + 3) lies on the graph of 5x − 2y = 9. What is the value of k? - Heads and legs on a farm
A farmyard holds chickens and goats — 24 animals in all, with 68 legs among them. How many goats are there? - System with a fractional coordinate
In the system 3x − 2y = 7 and x + 2y = 9, what is the value of y? (Enter your answer as a fraction or decimal.) - Coffee blend mixture
A roaster blends beans costing $9 per kilogram with beans costing $14 per kilogram to make 10 kilograms of a blend worth… - Intersection of two lines
In the xy-plane, the graphs of y = 2x − 1 and y = −x + 8 intersect at the point (a, b). What is the value of b? - Counting integers in a compound inequality
How many integers x satisfy −3 ≤ 2x + 1 < 9? - Minimum score for a target average
Dario scored 84 and 91 on his first two tests. What is the minimum score he needs on a third test for his three-test ave…
Hard (315)
- Linear inequalities
For how many integer values of x is −2 < (x − 5)/3 ≤ 1 true? - Systems with infinitely many solutions
The system 2x + 3y = 6 and 4x + 6y = k has infinitely many solutions. What is the value of k? - Absolute value inequalities
Which of the following is the complete solution set to |x − 4| < 6? - Systems of linear inequalities
A student has $40 to spend on notebooks costing $4 each and pens costing $2 each, and wants at least 12 items total. If … - Linear inequalities in one variable (comparing two linear models)
What is the least whole number of minutes of international calling in a month for which the total monthly cost of Plan A… - Systems of two linear equations in a mixture context
How many liters of the 30% acid solution did the technician use? - Building and applying a linear function from two data points
Assuming the candle continues to burn at this rate, how many hours after it is lit will the candle's height be 6.0 centi… - Build and solve a linear equation from three related lengths
What is the length, in miles, of the Summit Trail? - Solve a linear equation with fractions on both sides
What value of n satisfies the equation? - Choose a constant so a linear equation has no solution
For what value of k is there no value of s for which the two expressions are equal? - Build a linear equation from fractional parts of a total
How many textiles are in the entire collection? - Choose a constant so a linear equation has infinitely many solutions
For what value of a do the two expressions give the same amount of water for every value of w? - Build and solve an equation comparing two multi-day rate plans
How many miles did she drive? - Write equation of perpendicular line through a point
Which equation represents the new trail in the xy-plane? - Find missing coordinate using perpendicular slope
A second route is represented by a line that passes through the points (-3, 8) and (5, k) and is perpendicular to the su… - Determine coefficient making two lines perpendicular
What is the value of k? - Find y-intercept of a parallel line
What is the y-coordinate of the y-intercept of the line representing the second corridor? - Build linear equation from two data points
Which equation gives the altitude a, in meters, of the balloon t minutes after it is released? - Find x-intercept of a perpendicular line
What is the x-coordinate of the x-intercept of the line representing the second transect? - Finding the slope from a point
What is the value of m? - Value of a constant for infinitely many solutions
In the equation 4(x + 2) = 4x + k, k is a constant. For which value of k does the equation have infinitely many solution… - Testing a point against a system of inequalities
Which of the following points in the xy-plane is a solution to the system? - Constant for a dependent system
For what value of k does the system have infinitely many solutions? - Constant for a system with no solution
For what value of k does the system have no solution? - Line parallel to a given line
Which equation represents the line in the xy-plane that passes through the point (2, 1) and is parallel to the line y = … - Solving a compound inequality
Which of the following is equivalent to −1 < 2x + 3 ≤ 9? - Solving a linear model for the input
The balance of a loan, in dollars, after m monthly payments is modelled by B(m) = 150 − 12m. After how many payments wil… - Equation with parentheses on both sides
What value of x satisfies 5(x − 2) = 2(x + 4) + 3? - Coin problem as a system
A jar contains 25 coins, all dimes and quarters, worth $4.00 in total. How many quarters are in the jar? - When two linear models meet
Candle A is 20 centimetres tall and burns down at 2 centimetres per hour. Candle B is 14 centimetres tall and burns down… - Standard form from slope and a point
A line in the xy-plane has slope −2 and passes through the point (1, 5). Which of the following is an equation of the li… - Rectangle from perimeter and a relation
The perimeter of a rectangle is 44 centimetres, and its length is 4 centimetres more than twice its width. What is the a… - Where a linear model reaches a target
A hiker starts a descent at an elevation of 1,200 metres and descends at a steady 150 metres per hour. After how many ho… - Identifying an identity
Which of the following equations is true for EVERY value of x? - Word-problem inequality with a whole-number answer
A print shop charges a $15 setup fee plus $4 per poster. A club has a budget of $110 for posters. What is the greatest n… - Two numbers from their sum and difference
The sum of two numbers is 15 and their difference is 3. What is the product of the two numbers? - Slope from two function values, then the intercept
For a linear function f, f(12) = 13 and f(18) = 17. What is the value of f(0)? - Perpendicular line's equation
Line k in the xy-plane has equation y = −(1/4)x + 2. Which of the following is an equation of a line perpendicular to li… - Greatest whole number under a budget
A van rental costs $45 per day plus $0.50 per kilometre driven. A customer rents the van for one day and can spend at mo… - Rearranging a conversion formula
The formula C = (5/9)(F − 32) converts a temperature F in degrees Fahrenheit to C in degrees Celsius. Which equation giv… - Slope of a perpendicular line
In the xy-plane, the line y = mx + 4 is perpendicular to the line y = 2x − 1. What is the value of m? - Consecutive integers under a limit
The sum of three consecutive integers is at most 48. What is the greatest possible value of the largest of the three int… - Second equation for infinitely many solutions
A system of two linear equations in x and y has infinitely many solutions. One of the equations is 3x − y = 7. Which of … - Time for a battery to reach a level
A phone's battery drops from 100% to 40% in 5 hours, losing charge at a constant rate. At this rate, how many hours afte… - Fractions on both sides
If (x + 4)/2 = (x − 1)/3, what is the value of x? - System with a halved variable
If x/2 + y = 7 and x − y = 2, what is the value of x? - Extending a linear function from two points
The graph of the linear function f in the xy-plane passes through the points (1, 3) and (3, 11). What is the value of f(… - Distance at which two fares are equal
One taxi company charges a $3 pick-up fee plus $2 per kilometre. A second company charges an $8 pick-up fee plus $1.50 p… - Two lines through the same point
In the xy-plane, the lines y = ax + 3 and y = 2x + b, where a and b are constants, both pass through the point (1, 5). W… - Heads and legs
A farmer keeps chickens and cows. Together the animals have 20 heads and 56 legs. How many cows are there? - Value of a line-defined function at another input
The graph of the linear function f in the xy-plane has slope −3 and passes through the point (2, 4). What is the value o… - Where a line through two points meets the x-axis
In the xy-plane, the line through the points (−2, 5) and (4, −1) crosses the x-axis at point P. What is the x-coordinate… - Minimum sales to reach a target
A school play sells adult tickets for $10 and child tickets for $6. Twenty adult tickets have been sold, and the school … - Third point on a line
In the xy-plane, the points (1, 2), (3, 8) and (5, k) lie on the same line. What is the value of k? - Minimum score for a target average
A student's scores on three tests are 72, 85 and 79. What is the least score the student can get on a fourth test so tha… - Price of one item from two purchases
Three apples and two pears cost $2.60, and one apple and four pears cost $2.20. What is the cost, in dollars, of one pea… - Zero of a linear function from slope and intercept
The linear function f has a slope of −2, and f(0) = 8. For what value of x is f(x) = 0? - Intercept of a perpendicular line
In the xy-plane, line n is perpendicular to the line y = 4x and passes through the point (8, 1). What is the y-intercept… - Greatest length under a perimeter limit
A rectangle's width is 3 centimetres less than its length, and its perimeter is at most 30 centimetres. What is the grea… - Substitution giving a zero
If 3x + 2y = 12 and y = x − 4, what is the value of y? - Working back from a known value at a constant rate
Each time x increases by 1, the linear function g decreases by 4. If g(3) = 10, what is the value of g(0)? - Line through two points with the same x
The points (2, −3) and (2, 7) both lie on line m in the xy-plane. Which statement about line m is true? - Eliminating a variable with matching coefficients
If 2x + 5y = 1 and 3x − 5y = 14, what is the value of x + y? - Intercept from a known crossing point
The functions f and g are defined by f(x) = 2x + b and g(x) = −x + 7, where b is a constant. If the graphs of f and g in… - Point not on a line
Line L in the xy-plane has a slope of 4 and a y-intercept of 6. Which of the following points is NOT on line L? - Longest plot from a fixed length of fence
A gardener has 60 metres of fencing to enclose a rectangular plot, one side of which is 12 metres. What is the greatest … - Two numbers from a sum and a relation
The sum of two numbers is 30, and twice the smaller number exceeds the larger number by 3. What is the smaller number? - Equation of a line parallel to a given line
Which equation represents the line in the xy-plane that passes through (0, −2) and is parallel to the line y = 4x + 7? - Solving a compound inequality
Which of the following describes all values of x that satisfy −3 < 2x − 5 ≤ 7? - Constant that makes a system have no solution
The system 3x − ky = 7 and 6x − 8y = 5 has no solution, where k is a constant. What is the value of k? - Fixed cost from two totals
A photographer charges a fixed booking fee plus a constant amount per hour. A 3-hour session costs $60 and a 6-hour sess… - Inequality from a word constraint
A lift can carry at most 600 kilograms. A delivery worker who weighs 80 kilograms rides with n boxes that weigh 25 kilog… - x + y from a system
If 2x + 3y = 19 and x + 4y = 17, what is the value of x + y? - Perimeter equation for a rectangle
A rectangle's length is 6 centimetres more than its width w. Its perimeter is 60 centimetres. Which equation can be used… - Graph features from standard form
The graph of 5x + 2y = 20 is a line in the xy-plane. Which statement about the line is true? - Rate of change from a table in context
The table shows the amount of money in a savings jar at the start of several weeks. The amount changes by the same numbe… - Class size from two fractional groups
In a class, one quarter of the students come by bus and one third walk. Together, the students who come by bus or walk n… - Inequality from a rate comparison
Plan A charges $0.10 per text message with no monthly fee. Plan B charges a $6 monthly fee plus $0.04 per text. For how … - Difference of the solution values
If 3x + 2y = 23 and 5x − 2y = 17, what is the value of x − y? - Which value fails an inequality
Which of the following values of x is NOT a solution of the inequality 3(x − 2) < 5x + 4? - Linear function from two input-output pairs in context
A plumber charges a fixed call-out fee plus an hourly rate. A 2-hour job costs $35 and a 6-hour job costs $95. Which fun… - Line through a point with the same slope as a given line
In the xy-plane, line m has the equation y = −2x + 5. Which equation represents the line that passes through (3, 1) and … - Number of solutions of a system
How many solutions does the system 3x + y = 7 and 6x + 2y = 10 have? - Solving an inequality with x on both sides
Which of the following describes all solutions of −4x + 9 ≥ x − 6? - Linear function from a table with negative slope
The table gives values of a linear function g. Which equation defines g? - Equation with a fraction on one side
If (3x − 4)/4 = 5, what is the value of x? - Line through the origin and a system's solution
The solution (x, y) to the system 2x − y = 2 and 4x + y = 16 lies on the line y = kx, where k is a constant. What is the… - Solving an inequality with a fractional coefficient
Which of the following describes all solutions of x/2 − 3 > 1? - Intercept meaning from two data points
A plant nursery's weekly sales S, in dollars, depend linearly on the number of sunny days d that week. In a week with 3 … - Equation of a horizontal or vertical line
Which equation represents the line in the xy-plane that passes through (5, −2) and (5, 7)? - Solution value from a system with a negative
If 2x + 3y = 5 and x − 2y = 6, what is the value of y? - Inequality requiring a flip
Which of the following describes all solutions of 7 − 3x ≤ 1? - Slope as a rate with units
A tank holds 60 litres of water and drains completely in 5 minutes at a constant rate. Which function gives the volume V… - Equation with nested distribution
What value of x satisfies 5(3x − 4) − 2x = 71? - Choosing the system that models a situation
Two large candles and three small candles cost $16 together, and a large candle costs $3 more than a small one. If L is … - Solving an inequality with distribution on one side
Which of the following describes all solutions of 2(x + 3) > 4x − 2? - Linear function from two data points in context
A courier charges a flat fee plus a rate per kilometre. A 2-kilometre delivery costs $50 and an 8-kilometre delivery cos… - y-intercept of a perpendicular line through a point
In the xy-plane, line ℓ is perpendicular to the line y = 2x − 5 and passes through the point (4, 1). What is the y-coord… - Value of k for infinitely many solutions
The system 4x − 6y = 10 and 2x − 3y = k has infinitely many solutions. What is the value of k? - Inequality with variables on both sides
Which of the following describes all solutions of 5 − 2x < 3x − 10? - Extending a linear pattern from a table
The table shows the number of subscribers to a newsletter at the end of several months. If the pattern continues linearl… - Equation of a line from a graph description
A line in the xy-plane has a y-intercept of −4 and passes through (2, 2). Which equation represents the line? - Product of the solution values
If 3x + 4y = 18 and 2x − y = 1, what is the value of xy? - Solving an inequality with a negative coefficient and negative constant
Which of the following describes all solutions of 4 − 3x > −11? - Function from an initial value and a later value
A candle is 14 centimetres tall when lit and 2 centimetres tall after burning for 6 hours at a constant rate. Which func… - Line parallel to a given line through a point
Which equation represents the line in the xy-plane that passes through (−2, 3) and is parallel to the line 3x + y = 4? - Sum of the solution values from a system with substitution
If 5x − 3y = 7 and x + 2y = 4, what is the value of x + y? - Inequality with a fractional coefficient
Which of the following describes all solutions of (2x)/3 + 1 ≤ 5? - When a linear model reaches zero, from two values
A phone's battery is at 90% at 8 a.m. and at 60% at 2 p.m., draining at a constant rate. At what time will it reach 0%? - Which line is perpendicular
Which of the following lines is perpendicular to the line 2x + 3y = 6 in the xy-plane? - Price per kilogram from two purchases
At a market stall, 5 kilograms of apples and 2 kilograms of pears cost $17 in total, and 3 kilograms of apples cost $5 m… - Equation of a line from a graph's description
A line in the xy-plane crosses the y-axis at (0, 5) and the x-axis at (10, 0). Which equation represents the line? - Difference of the solutions from a system
If 3x − 2y = 6 and x + y = 7, what is the value of x − y? - Comparing two car parks' charges
Car park P charges $3 per hour, with a $5 voucher taken off each visit. Car park Q charges $4 per hour with no voucher. … - Inequality with a negative coefficient
Which of the following describes all solutions of 3 − 4x ≥ −9? - Time to reach zero from two readings
A water butt held 80 litres at 6 a.m. and 50 litres at noon, draining at a constant rate. At what time will it be empty? - Equation of a line through two points
Which equation represents the line in the xy-plane that passes through (−1, 1) and (3, 7)? - Product of the solutions
If 2x + 3y = 11 and x − y = 3, what is the value of xy? - Inequality with distribution and x on both sides
Which of the following describes all solutions of 2(x − 4) ≥ 3x − 14? - Model from two data points
A window cleaner charges a fixed fee plus a rate per window. Cleaning 2 windows costs $38 and cleaning 6 windows costs $… - Value on a line between two known points
In the xy-plane, a line passes through (1, 2) and (7, 10). What is the y-coordinate of the point on the line whose x-coo… - Difference of the solutions
If 4x − y = 5 and x + 2y = 8, what is the value of x − y? - Inequality with x on both sides
Which of the following describes all solutions of 9 − 2x > 3x − 6? - Predicting from a linear trend
A reservoir held 20 million litres at the start of a rainy season and 50 million litres after 3 weeks, filling at a cons… - Sum of a line's intercepts
In the xy-plane, a line passes through (−2, 7) and (4, 1). What is the sum of the line's x-intercept and y-intercept? - Value of a combination of the solutions
If 2x − 3y = 4 and x + 2y = 9, what is the value of 3x − y? - Inequality with x on both sides and a negative coefficient
Which of the following describes all solutions of 7 − 3x ≤ 2x − 8? - Time to reach zero from two readings
A candle was 45 centimetres tall when lit and 15 centimetres tall after 6 hours, burning at a constant rate. After how m… - Ages: a multiple of an earlier age
Nadia is now three times as old as she was 8 years ago. How old is Nadia now? - Last whole minute above a threshold
The water level in a tank, in centimetres, t minutes after a drain is opened is 40 − 1.5t. What is the greatest whole nu… - Which line is parallel to a given line
Which of the following lines is parallel to the line 4x − 2y = 6 in the xy-plane? - Predicting from a linear trend
A queue for a ride had 60 people at 10 a.m. and 96 people at 1 p.m., growing at a constant rate. If the rate continues, … - Ages with a past comparison
Twice Maya's current age equals three times her age seven years ago. How old is Maya now? - Testing values against an inequality with x on both sides
For which of the following values of x is 7 − 2x greater than 3x + 22? - Slope from standard form with a negative
What is the slope of the line 5x − 2y = 8 in the xy-plane? - Predicting from a linear trend in context
A community garden had 20 plots in use when it opened and 50 plots in use three years later, with the number rising at a… - Fractional parts of an unknown number
Two thirds of a number is 12 more than one quarter of the same number. What is the number? - x-intercept from a slope and a point
A line in the xy-plane has slope −2/3 and passes through the point (6, 1). At what value of x does the line cross the x-… - Slope that makes two lines meet on the x-axis
In the xy-plane, the lines 2x + 3y = 12 and y = mx + 1 intersect at a point on the x-axis, where m is a constant. What i… - Area of the triangle a line makes with the axes
In the xy-plane, the graph of 3x + 4y = 24 and the two coordinate axes form a triangle. What is the area of the triangle… - Two-stage problem: solve a system, then apply a change
A café sells coffee at $3 a cup and tea at $2 a cup. On Monday it sold 80 cups in total for $220. On Tuesday it sold twi… - Two-variable system from training times
Leo's training session of 3 laps and 4 sprints takes 20 minutes, and a session of 5 laps and 2 sprints takes 24 minutes.… - Solving a compound inequality with a negative coefficient
Which of the following describes all values of x that satisfy −7 < 3 − 2x ≤ 5? - Perimeter equation with a described relationship
A rectangle's length is 4 centimetres less than three times its width, and its perimeter is 64 centimetres. What is the … - Slope of a line from standard form
The graph of 6x + 4y = 12 in the xy-plane is a line. What is the slope of the line? - Two-variable word problem with a difference
A plumber's bill for one job was $780 for 12 hours of skilled work and 8 hours of unskilled work. The skilled rate is $1… - Inequality with a bounded quantity
A lift can carry at most 630 kilograms. A delivery worker who weighs 80 kilograms rides with boxes of 25 kilograms each.… - Checking values against a linear function defined by slope and a point
A linear function f has a slope of −2, and f(3) = 10. Which of the following must be true? - Coefficients of a line from its intercepts
In the xy-plane, the graph of ax + by = 24 has x-intercept 6 and y-intercept −8, where a and b are constants. What is th… - Two-digit number from its digits
The sum of the digits of a two-digit number is 11. When the digits are reversed, the new number is 27 greater than the o… - Value satisfying two inequalities at once
Which of the following values of x satisfies both 2x − 3 > 5 and 10 − x ≥ 3? - Difference of two fractions of a number
Two thirds of a number exceeds three fifths of the same number by 3. What is the number? - Identifying a linear function from three table values
A student claims that the table below shows values of a linear function f. x | f(x) 0 | 12 4 | 6 10 | 3 Which statemen… - y-intercept of a line parallel to a given line through a point
In the xy-plane, line m is parallel to the line 3x + 2y = 8 and passes through the point (4, 5). What is the y-intercept… - Interpreting the solution of a system in context
A baker uses 2 eggs for each loaf of brioche and 3 eggs for each sponge cake. One morning she uses 18 eggs to make x loa… - Point in the solution set of a system of inequalities
Which of the following points is a solution to the system y > x − 2 and y ≤ −x + 6 in the xy-plane? - Linear function from a functional relationship
A linear function f satisfies f(x + 4) = f(x) + 10 for every value of x, and f(2) = 7. What is the value of f(10)? - Product of a line's slope and y-intercept
The graph of x − 2y = −6 in the xy-plane is a line. What is the product of the line's slope and its y-intercept? - y-intercept of a line reflected across the x-axis
In the xy-plane, line ℓ has equation 2x − 3y = 12, and line m is the reflection of line ℓ across the x-axis. What is the… - Two numbers from a sum and a division with remainder
The sum of two positive integers is 40. When the larger is divided by the smaller, the quotient is 3 and the remainder i… - Speed of a current from a round trip
A boat travels 24 kilometres downstream in 2 hours and makes the return trip upstream in 3 hours. The boat's speed in st… - Fixed fee plus unit price, then a new total
An online bookshop charges a fixed delivery fee plus the same price for each book. An order of 3 books costs $41.50 and … - Greatest value satisfying an inequality with distribution
What is the greatest value of x that satisfies 5 − 2(x + 1) ≥ 3x + 8? - Equation with two fractions subtracted
If (x + 4)/3 − (x − 2)/5 = 4, what is the value of x? - Three fractional parts of a number
Half of a number plus one third of the number is 14 more than one quarter of the number. What is the number? - x-intercept of a line built from another line's features
In the xy-plane, line ℓ has equation 3x + 5y = 30. Line k has the same y-intercept as line ℓ and twice its slope. What i… - Slope of a line through the origin and a midpoint
In the xy-plane, the midpoint of the line segment from (1, 2) to (5, 8) lies on the line y = mx, where m is a constant. … - Point on a line whose x-coordinate is twice its y-coordinate
In the xy-plane, a point on the line y = 3x − 7 has an x-coordinate that is twice its y-coordinate. What is the y-coordi… - y-intercept of a perpendicular through the second of two points
In the xy-plane, line ℓ passes through the points (2, 3) and (6, 11). Line m is perpendicular to ℓ and passes through (6… - Mixing two ingredients to a target price
A grocer mixes nuts that cost $8 per kilogram with raisins that cost $3 per kilogram to make 10 kilograms of a mix worth… - Two unknown parameters from a common point
In the xy-plane, the lines y = ax + 2 and y = 3x + b intersect at the point (2, 8), where a and b are constants. What is… - Equation of a line after a vertical shift
In the xy-plane, the graph of 2x − 3y = 6 is shifted 4 units upward. Which of the following is an equation of the shifte… - Two constants from a shared point on two lines
In the xy-plane, the lines ax + by = 12 and 2ax − by = 6 both pass through the point (2, 1), where a and b are constants… - Daily wages from two crew totals
On one day a builder pays 4 carpenters and 3 painters a total of $1,070; on another day, 2 carpenters and 5 painters cos… - Distance from the origin to an intersection point
In the xy-plane, the lines y = x + 1 and y = −2x + 10 intersect at point P. What is the distance from P to the origin? - Constant for a parallel line with a given intercept gap
In the xy-plane, the lines 2x + 5y = 20 and 2x + 5y = c, where c > 20, are parallel, and their y-intercepts are 3 units … - Greatest value of a linear expression over an interval
If −2 ≤ x < 5, what is the greatest possible value of 3 − 2x? - Quadrant a line does not pass through
In the xy-plane, a line passes through the points (3, −2) and (−1, 6). Which quadrant does the line NOT pass through? - x-intercept of a line after finding its slope from a point
In the xy-plane, the line y = kx + 2 passes through the point (−2, 8), where k is a constant. What is the x-intercept of… - Constant that makes a system have infinitely many solutions
For what value of k does the system 3x − y = 2 and 6x − 2y = k have infinitely many solutions? - Greatest difference of two bounded integers
The integers x and y satisfy 2 < x < 7 and 1 < y < 3. What is the greatest possible value of x − y? - Least hours to reach an earnings target with overtime
A worker earns $15 per hour for the first 40 hours in a week and $22.50 per hour for each hour beyond 40. What is the le… - Cost price from a markup and a discount
A shop sets its price by adding 40% to the cost of an item. During a sale, 25% is taken off the shop's price, and a cust… - Slope after finding a coefficient from a point
In the xy-plane, the line kx + 2y = 8 passes through the point (2, 1), where k is a constant. What is the slope of the l… - Area of a triangle formed by three lines
In the xy-plane, the lines y = 2x, y = −2x, and y = 8 form a triangle. What is the area of the triangle? - Two pipes filling a tank together
One pipe can fill a tank in 6 hours, and a second pipe can fill the same tank in 3 hours. How many hours will the two pi… - Distance from a round trip at two speeds
Sara cycles from home to a park at 12 kilometres per hour and walks back along the same route at 4 kilometres per hour. … - Rectangle that becomes a square after resizing
A rectangle has a perimeter of 44 centimetres. If its length is decreased by 2 centimetres and its width is increased by… - Value in one solution set but not another
Which of the following values of x satisfies 3(x − 2) ≤ x + 4 but does NOT satisfy 2x + 1 > 7? - Parameter values that give a positive solution
For which values of the constant k does the equation 3x + k = 5 have a positive solution for x? - Parameter from perpendicular lines through the origin
In the xy-plane, the line through the origin and (3, 4) is perpendicular to the line through the origin and (a, 3), wher… - Equation with two fractions
If (2x − 1)/3 = (x + 4)/2, what is the value of x? - Equation with decimal coefficients
What value of x satisfies 0.3(x − 20) = 0.5x − 12? - Largest of three consecutive even integers
The sum of three consecutive even integers is 78. What is the largest of the three integers? - Strengthening a mixture
A 5-litre drink is 20% juice. How many litres of pure juice must be added so that the drink becomes 50% juice? - Two pipes filling a tank
One pipe can fill a tank in 6 hours, and a second pipe can fill it in 3 hours. If both pipes are used together, how many… - Age from a future and past comparison
In 5 years, Ravi will be twice as old as he was 4 years ago. How old is Ravi now? - First side of a triangle from its perimeter
A triangle has a perimeter of 54 centimetres. Its second side is twice as long as its first side, and its third side is … - Hours worked with an overtime rate
Ana is paid $12 an hour for the first 35 hours she works in a week and $18 an hour for each hour after that. Last week s… - Unwinding a chain of operations
A number is doubled, 7 is subtracted from the result, and that result is divided by 3 to give 5. What is the number? - Tank capacity from two fractions
A tank is one quarter full. After 30 litres of water are added, it is two thirds full. What is the capacity of the tank,… - Third of three stepped numbers
The sum of three numbers is 120. The second number is 5 more than the first, and the third is 5 more than the second. Wh… - Miles from a taxi fare
A taxi charges $3.50 plus $2.25 for each mile. A ride cost $21.50. How many miles long was the ride? - Unknown from an average
The average (arithmetic mean) of 4, 9, x, and 2x is 10. What is the value of x? - Input that gives a target output
The linear function f has slope −3 and f(2) = 11. For what value of x is f(x) = −4? - Boat hire cost from two known prices
The cost of hiring a boat is a linear function of the number of hours. Hiring the boat for 2 hours costs $45, and hiring… - Parallel line through a point
Which of the following defines a linear function whose graph in the xy-plane is parallel to the graph of y = 3x − 2 and … - Extending a table beyond its last row
The table shows values of the linear function g. x | g(x) 0 | 20 3 | 14 6 | 8 What is the value of g(10)? - When a descending lift reaches the ground
A lift descends at a constant rate. It is 120 metres above the ground 10 seconds after it starts and 60 metres above the… - Cost price behind a markup and a discount
A shop marks a coat up by 25% above its cost price and later sells it at 20% off the marked price, for $96. What was the… - Smallest of three consecutive integers from a condition
Twice the smallest of three consecutive integers is 6 more than the largest. What is the smallest of the three integers? - Cupcakes sold at the higher price
A tray of 24 cupcakes was sold out. Some were sold at $2 each and the rest at $1.50 each, for $42 in total. How many wer… - Number removed from a list, from two averages
The average (arithmetic mean) of five numbers is 12. When one of the numbers is removed, the average of the remaining fo… - Films rented from a monthly bill
A streaming service charges $8 a month plus $3 for each film rented. In a month when the bill was $26, how many films we… - Longest side of a triangle from its perimeter
The sides of a triangle have lengths 2x − 1, x + 4, and 3x. Its perimeter is 27. What is the length of the longest side? - Tank contents from a steady leak
A tank leaks at a constant rate. It held 500 litres at 8:00 a.m. and 380 litres at 10:00 a.m. How many litres will it ho… - Value at zero from two values
The linear function g satisfies g(1) = 3 and g(4) = 12. What is the value of g(0)? - Interpreting a rate of sale
The function N(t) = 250 − 15t models the number of tickets still unsold t hours after sales open. Which of the following… - When two batteries show the same charge
Phone A's battery is at 80% and loses 10 percentage points per hour. Phone B's battery is at 50% and loses 4 percentage … - Value of a parallel linear function
The linear function f has a graph that passes through (2, 5) and is parallel to the graph of y = −3x + 1. What is the va… - Function value from two intercepts
The graph of a linear function has x-intercept 6 and y-intercept −4. What is the value of the function at x = 3? - Crates that fit under a weight limit
A delivery van's load must not exceed 1,200 kilograms. It already carries 400 kilograms, and each crate to be added weig… - Counting integers in a compound inequality
How many integer values of x satisfy 7 < 3x − 2 ≤ 16? - Greatest integer length under a perimeter limit
A rectangle has a width of 5 units and a perimeter of less than 40 units. What is the greatest possible integer value of… - Least third score for a target average
A student's first two test scores are 70 and 85. What is the least score on a third test that would make the average of … - Number of shelves from a nested expression
A carpenter cuts a board of length 60 units into pieces: three pieces of length 2n − 4 each and two pieces of length n e… - Linear function from a fixed increase
For a linear function f, f(x + 2) − f(x) = 10 for every value of x, and f(1) = 3. What is the value of f(6)? - x-intercept of a line from a point and slope
In the xy-plane, a line with slope −3 passes through the point (2, 7). At what value of x does the line cross the x-axis… - Shifting a line to pass through a point
In the xy-plane, line ℓ has the equation 4x + 5y = 12. Line m is parallel to ℓ and passes through the point (2, 4). Line… - Coefficients from two intercepts
The graph of ax + by = 24 in the xy-plane has an x-intercept of 6 and a y-intercept of −3, where a and b are constants. … - Two-part order from a total and a difference
A florist sold roses at $5 each and tulips at $3 each. In one order, the number of roses was 4 more than the number of t… - Largest integer x allowed by two inequalities
The system y > 2x − 3 and y < x + 2 has solutions (x, y) in the xy-plane. What is the largest integer value of x for whi… - Crates that fit under a weight limit
A truck can carry at most 2,000 kilograms. It is already loaded with 30 boxes that weigh 40 kilograms each. What is the … - Number from a third and a half
One third of a number, increased by 5, is equal to one half of the same number, decreased by 1. What is the number? - Speed needed on the second half of a trip
A cyclist rode 60 kilometres at an average speed of 20 kilometres per hour for the whole trip. For the first 30 kilometr… - Input that gives a target output
For the linear function k, k(0) = −4, and the graph of k passes through the point (6, 8). For what value of x is k(x) = … - Slope of a line reflected across the x-axis
In the xy-plane, line ℓ has the equation y = (3/4)x + 2. Line m is the reflection of line ℓ across the x-axis. What is t… - Area of the triangle a line makes with the axes
In the xy-plane, the line 3x + 4y = 24 forms a triangle with the x-axis and the y-axis. What is the area of that triangl… - Difference of the solution of a system
If 5x + 2y = 31 and x + 2y = 11, what is the value of x − y? - Largest width under a perimeter limit
A rectangle has width w and a length three times its width. Its perimeter must be at most 64. What is the largest possib… - Number from fractional parts summing to a value
One third of a number plus one half of the same number equals 25. What is the number? - Starting value from two readings
A taxi meter shows $20 after 3 kilometres and $35 after 6 kilometres, and the fare is a linear function of distance. Wha… - Slope from standard form
In the xy-plane, what is the slope of the line 3x + 5y = 15? - Point on a line with equal coordinates
In the xy-plane, the line 2x + 3y = 12 contains exactly one point whose x- and y-coordinates are equal. What is the x-co… - Price of an eraser from two purchases
Two notebooks and three erasers cost $9. Four notebooks and one eraser cost $13. What is the price, in dollars, of one e… - Priya's age from a relation and a sum
Priya is 4 years older than her cousin Ravi. Three times Ravi's age plus Priya's age equals 28. How old is Priya? - Maximum plants within a budget
A gardener has $170 to spend and buys 4 shrubs at $20 each. With the remaining money, what is the greatest number of $6 … - Greatest integer in a solution set
What is the greatest integer x for which 4 − 2x > −6? - Equation with a bracket on the right
What value of x satisfies 5x − 2(x + 1) = 7? - Number of members from a fraction and a difference
Two thirds of the members of a club came to the annual meeting. If 10 more had come, the number present would have been … - Fixed charge from two readings
A plumber's total charge is a linear function of the hours worked. A 2-hour job costs $20 and a 6-hour job costs $50. Wh… - Input for a target output of a linear function
For the linear function g, g(x) = 3x − 7. For what value of x is g(x) equal to 20? - Most guests within a party budget
A party venue charges a fixed $45 plus $20 per guest. A host has at most $200 to spend. What is the greatest number of g… - Number from a half of a difference
Half of the difference between three times a number and 4 is 25. What is the number? - Marbles in one of three jars
Three jars hold 100 marbles in total. The first jar holds 10 more than the second, and the third holds the same as the s… - Starting fee from two totals
A courier's charge is a linear function of distance. A 4-kilometre delivery costs $14 and an 8-kilometre delivery costs … - Weeks until a savings goal from a decreasing balance
A gift card has $100 on it, and its holder spends $6 from it every week. After how many weeks will the balance first be … - Constant from an x-intercept
In the xy-plane, the line 3x − 4y = c has an x-intercept of 3, where c is a constant. What is the y-intercept of the lin… - Product of x and y from two equations
If 3x − 2y = 11 and x + 4y = 13, what is the value of xy? - Bags of two sizes from a total weight
A shop packs rice in 3-kilogram and 5-kilogram bags. One order contained 24 bags weighing 80 kilograms in total. How man… - Most sessions within a budget
A tutor charges a $30 registration fee plus $45 per session. A family has at most $400 to spend. What is the greatest nu… - Greatest integer under an inequality with a negative coefficient
What is the greatest integer x for which 5 − 2x ≥ −3? - Number from a quarter and a difference
A quarter of three times a number is 18 less than three times the number. What is the number? - Number from a bracketed relation
Four times the result of subtracting 3 from a number equals three times the number. What is the number? - Later value from two known values
A linear function g has g(1) = 10 and g(5) = 18. What is the value of g(9)? - Coordinates of intercepts from a standard-form line
In the xy-plane, the line 6x + 4y = 9 has x-intercept a and y-intercept b. What is the value of a · b? - Constant from parallel lines through a point
In the xy-plane, line k is parallel to the line y = −2x + 9 and passes through the point (3, −1). What is the y-intercep… - Coins of two values in a parking meter
A parking meter accepts only 20-cent and 50-cent coins. At the end of a day it holds 26 coins worth $9.10 in total. How … - Most plants after buying pots
A gardener buys 4 pots at $12 each and then as many plants as possible at $5 each, spending no more than $90 in total. H… - Greatest integer for an inequality with subtraction
What is the greatest integer x for which 10 − 3x > 1? - Number where two fractional expressions agree
A quarter of a number, plus 3, equals a third of the same number, minus 1. What is the number? - Starting balance from two later balances
A savings jar's contents grow by the same amount each week. After 2 weeks it holds $22 and after 8 weeks it holds $46. H… - Slope of a line built from two other lines' intercepts
In the xy-plane, line m has the same y-intercept as the line 5x + 2y = 20 and the same x-intercept as the line x + y = 8… - Large bags from a mixed order
A shop sells flour in 4-kilogram and 3-kilogram bags. An order of 11 bags weighed 39 kilograms. How many 4-kilogram bags… - Most lessons within a budget
A driving school charges a $60 registration fee plus $15 per lesson. A learner has at most $200 to spend. What is the gr… - Minutes until two travellers meet
A cyclist and a walker start 8 kilometres apart and travel toward each other along the same road, the cyclist at 15 kilo… - Number of pages from a fraction read
After reading two thirds of a book and then 10 more pages, Ines has read 40 pages. How many pages does the book have? - Value of a linear function at a negative input
For the linear function f, f(x) = 9 − 2x. What is the value of f(−2)? - Slope of a line through two intercepts
In the xy-plane, a line passes through (5, 0) and (0, 10). What is the slope of the line? - Large boxes in a delivery
A delivery contains 35 boxes weighing 90 kilograms in total. Each large box weighs 3 kilograms and each small box weighs… - Most pens after buying notebooks
Ravi buys 8 pencils at $2 each and then as many pens as he can at $3 each, spending at most $50 in total. How many pens … - Input giving a required output
For a linear function h, h(2) = 7 and h(5) = 16. For what value of x is h(x) = 1? - Equation of a line from a table
The table gives three points on a line: when x = 1, y = 7; when x = 2, y = 4; when x = 3, y = 1. Which equation represen… - Fixed fee from two rental prices
A rental company charges a fixed fee plus a rate for each day. A 3-day rental costs 95 dollars and a 7-day rental costs … - Greatest integer in a two-sided inequality
If 5 − 2x ≥ 3x − 10 and x is an integer, what is the greatest possible value of x? - Minutes used from a phone bill
A phone plan costs 20 dollars a month, which includes 300 minutes of calls, plus 5 cents for each minute over 300. In a … - Value at zero from a table of a linear function
The table gives values of a linear function f: f(2) = 11, f(5) = 20, and f(8) = 29. What is the value of f(0)? - Larger of two numbers from two relations
The sum of two numbers is 40. Three times the smaller number minus the larger number is 8. What is the larger number? - Number from a doubled and a third relation
When a number is doubled and 7 is subtracted, the result equals 3 more than one third of the number. What is the number? - Point on a parallel line through the origin
In the xy-plane, line l passes through the points (4, −1) and (8, 5). Line m passes through the origin and is parallel t… - Solving a compound inequality
Which of the following gives all values of x that satisfy −4 ≤ 2x + 6 < 10? - Smallest of three consecutive integers
The sum of three consecutive integers is 3 less than 4 times the smallest of them. What is the smallest integer? - Time for a battery to drain to a level
A phone's battery drains at a constant rate, from 100 percent at 8 am to 40 percent at noon. How many hours after noon w… - Constants from a known intersection
In the xy-plane, the lines y = mx + 3 and y = 2x + b intersect at the point (2, 7), where m and b are constants. What is… - Value from an average of three expressions
The average of x, 2x, and 3x + 6 is 12. What is the value of x? - Fare for a longer ride from two fares
A taxi fare is a linear function of the distance travelled. A 5-kilometre ride costs 11 dollars, and a 9-kilometre ride … - Y-intercept after reflecting a line
In the xy-plane, the line y = 2x − 3 is reflected across the x-axis. What is the y-intercept of the reflected line? - Solving an inequality with the variable on both sides
Which of the following describes all values of x that satisfy 3 − 2x > 4x + 15? - Equation with x over 3 and x over 4
If x/3 − 2 = x/4 + 1, what is the value of x? - Constant from two points on a line
The points (2, a) and (a, 8) both lie on the line y = x + 3 in the xy-plane. What is the value of a? - Number from a sum and three times a difference
The sum of a number and 12 is equal to three times the difference between the number and 4. What is the number? - Slope constant for perpendicular lines
In the xy-plane, the lines y = 2x + 1 and y = kx + 5 are perpendicular. What is the value of k? - Difference of outputs from a difference of inputs
For a linear function f, f(4) − f(1) = 18. What is the value of f(9) − f(2)? - Sum of a line's intercepts
The graph of f(x) = 3x + k passes through the point (2, 11). What is the sum of the x-intercept and the y-intercept of t… - Two-step: find a, then the x-intercept
The graph of ax + 3y = 21 passes through the point (2, 5). What is the x-intercept of the graph? - x-intercept from a slope and a point
A line with slope −4/3 passes through the point (6, 1). The line crosses the x-axis at (a, 0). What is the value of a? (… - Interpolating between two points
A line passes through the points (−2, 9) and (4, −3). What is the y-coordinate of the point on the line where x = 1? - Constant that makes a system inconsistent
For what value of k does the system 6x + ky = 12 and 3x + 4y = 5 have no solution? - Two printers, staggered start
Printer A prints 40 pages per minute and printer B prints 55 pages per minute. Printer A runs alone for 4 minutes, and t… - Value of a combination from a system
The solution (x, y) of the system 2x + 3y = 19 and 5x − y = 22 also satisfies 4x − 3y = n. What is the value of n? - Counting bills in a wallet
A wallet holds only $5 bills and $10 bills — 13 bills worth $95 in total. How many $10 bills are in the wallet? - Largest integer under a linear cap
What is the greatest integer k for which 6k + 5 < 50? - Minimum booths for required seating
A restaurant floor has exactly 18 seating units: tables that seat 4 and booths that seat 6. If the floor must seat at le… - Extreme value of a difference from ranges
If 3 < x < 8 and 2 < y < 5, what is the greatest possible integer value of x − y? - Point satisfying a system of inequalities
Which point (x, y) satisfies both y > 2x − 3 and y ≤ −x + 6?
Very hard (315)
- Systems with no solution
For what value of c does the system 3x − 2y = 8 and 9x + cy = 5 have no solution? - Systems of linear equations
In the system 5x + 4y = 32 and 3x − 2y = 6, what is the value of 8x + 2y? - Absolute value inequalities with unknown constants
The solution set of the inequality |ax − b| ≤ 6, where a and b are constants and a > 0, is 3 ≤ x ≤ 9. What is the value … - Linear functions from a constant difference condition
The function f is linear, and for every value of x, f(x + 2) − f(x) = 6. If f(5) = 4, what is the value of f(0)? - Systems of linear equations with an added constraint on the solution
In the system of equations 2x + 3y = 12 and 5x − 2y = k, where k is a constant, the solution (x, y) satisfies x = y. Wha… - Conditions for a system to have infinitely many solutions
In the xy-plane, the system of equations kx + 6y = 12 and 2x + (k − 1)y = 6, where k is a constant, has infinitely many … - Build and solve fractional linear equation from context
What is the value of t? - Model two-rate total with one linear equation
How many centimeters long is the upper section of the core? - Find parameter making a linear equation have no solution
What is the value of k? - Find parameter giving infinitely many solutions
If the two expressions give the same damage for every value of L, what is the value of c? - Solve equal-cost equation then compute requested total
What is that total cost? - Solve linear equation with fractional parts of unknown
What is the value of c? - Comparing two linear models
For what number of gigabytes do the two plans cost the same amount? - Perpendicular line through a point
Line k is perpendicular to the line y = (2/3)x + 1 and passes through the point (4, −1). What is the y-intercept of line… - Solving a system by substitution
If (x, y) is the solution to the system, what is the value of x + y? - Inequality with two costs
A car rental costs $30 per day plus $0.20 per mile driven. A customer rents the car for 2 days and can spend at most $10… - Intersection of two lines
In the xy-plane, the lines y = 2x − 3 and y = −x + 6 intersect at the point (a, b). What is the value of a + b? - Finding a coordinate from a slope
In the xy-plane, the line through the points (k, 4) and (2, −2) has slope 3. What is the value of k? - Value on a line through two points
A line in the xy-plane passes through the points (2, 7) and (6, 19). What is the y-coordinate of the point on the line w… - Ordered pair satisfying two inequalities
Which ordered pair (x, y) satisfies both inequalities? - Two equations for the same line
In the xy-plane, the equations 2x − y = 4 and 4x − 2y = k represent the same line. What is the value of k? - Condition for no solution
The equation 3(2x − 5) = 6x + k, where k is a constant, has no solution. Which of the following must be true? - Interpreting the slope of a constraint line
A cinema sells adult tickets for $12 and child tickets for $8. The equation 12a + 8c = 480 gives the combinations of a a… - Compound inequality with a subtracted variable
Which of the following is the solution set of −2 ≤ (4 − x)/3 < 1? - Parallel line through a point
In the xy-plane, line p passes through the points (0, 1) and (2, 5). Line q is parallel to line p and passes through the… - Equation requiring careful distribution
What value of x satisfies 3(2x + 1) − x = 7x − 7? - Integer solutions of a compound inequality
How many integer values of x satisfy −3 ≤ 2x − 1 < 5? - Recognising a system with no solution
Which of the following systems of equations has NO solution? - Evaluating a shifted function
The functions f and g are defined by f(x) = 2x + 1 and g(x) = f(x − 3). What is the value of g(5)? - Adding pure juice to a mixture
A 12-litre drink is 25% juice by volume. How many litres of pure juice must be added so that the drink is 40% juice? - Constant that makes an identity
The equation a(x − 3) = 4x − 12, where a is a constant, is true for every value of x. What is the value of a? - Coefficients from the intercepts
In the xy-plane, the line ax + by = 12, where a and b are constants, has an x-intercept of 4 and a y-intercept of −6. Wh… - Constant from a known intersection
In the xy-plane, the lines 3x + 2y = 12 and kx − 4y = 8, where k is a constant, intersect at a point whose x-coordinate … - Constant that makes an equation an identity
The equation 2(4x − 1) − 5x = 3x + c, where c is a constant, is true for every value of x. What is the value of c? - Slope that makes a system inconsistent
For what value of the constant k does the system y = kx + 1 and y = 3x − 2 have NO solution? - Clearing two different denominators
If (2x − 1)/3 − (x + 2)/4 = 1, what is the value of x? - Standard-form equation from two intercepts
Which of the following is an equation of the line in the xy-plane that passes through the points (3, 0) and (0, −2)? - Constants from a known solution
The ordered pair (2, −1) is the solution to the system ax + y = 5 and x + by = 5, where a and b are constants. What is t… - Solving f(2x) for a linear f
The function f is linear, with f(0) = −5 and a slope of 3. For what value of x is f(2x) = 19? - Constant that makes an identity
The equation 2(3x − k) = 6x − 10, where k is a constant, is true for every value of x. What is the value of k? - Constant that makes two lines parallel
For what value of the constant a are the lines ax + 3y = 6 and 2x + y = 2 parallel in the xy-plane? - Constant from a known solution
The equation 5x − 4 = 2x + b, where b is a constant, has the solution x = 3. What is the value of b? - Distance between a line's intercepts
In the xy-plane, the line 3x − 4y = 12 crosses the x-axis at point P and the y-axis at point Q. What is the distance bet… - Constant for a consistent dependent system
A system consists of the equations 2x + 3y = 7 and 4x + 6y = c, where c is a constant. If the system has at least one so… - Constant for infinitely many solutions
The equation 6x + 9 = 3(2x + b), where b is a constant, has infinitely many solutions. What is the value of b? - Slope of a line with an unknown coefficient
In the xy-plane, the line ax + 2y = 8, where a is a constant, passes through the point (2, 1). What is the slope of the … - Coefficient for infinitely many solutions
The system 3x + ky = 6 and 6x + 4y = 12, where k is a constant, has infinitely many solutions. What is the value of k? - Counting solutions of a simplifying equation
How many solutions does the equation 3(x − 2) − 2(x − 3) = x have? - Slope that is also a coordinate
In the xy-plane, the line y = kx + 3, where k is a positive constant, passes through the point (k, 7). What is the value… - Condition for no solution
The system of equations 2x − y = 5 and 4x − 2y = c, where c is a constant, has no solution. Which of the following must … - Value of a constant giving no solution
In the equation 4(x + k) = 4x + 12 − 2k, k is a constant. For which value of k does the equation have NO solution? - Inequality graph: which point is in the solution set
Which ordered pair (x, y) satisfies BOTH inequalities y > x − 2 and y ≤ −x + 4? - Value of a constant for infinitely many solutions
In the equation 6x − 2(x + c) = 4x − 10, c is a constant. For what value of c does the equation have infinitely many sol… - Perpendicular line through a point
Which equation represents the line in the xy-plane that passes through (2, 1) and is perpendicular to the line 2x − y = … - Comparing rates of two linear functions
Function f is defined by f(x) = 4x − 3. Function g is linear, with g(0) = 5 and g(2) = 9. Which statement is true? - Inequality with a fraction and a negative
Which of the following describes all solutions to 5 − (x/3) ≥ 2? - System with infinitely many solutions
The system 2x − 5y = 8 and 6x + ky = 24 has infinitely many solutions, where k is a constant. What is the value of k? - Equation with no solution
Which of the following equations has NO solution? - x-intercept of a line through two points
In the xy-plane, a line passes through (2, 3) and (4, −1). What is the x-coordinate of the point where the line crosses … - System of inequalities: describing the solution region
Which of the following points satisfies the system y ≤ x + 1 and y ≥ −x + 3 and x ≤ 4? - Value of a parameter from a parallel condition
The graph of f(x) = kx + 3 is parallel to the line through (1, 2) and (4, 11). What is the value of k? - Equation whose solution is a given value
For which of the following equations is x = −2 the solution? - Two-variable inequality with a context
A bakery has 20 kilograms of flour. A loaf uses 0.5 kilograms and a cake uses 0.8 kilograms. If the bakery makes x loave… - Finding a function value from the slope and another value
For a linear function h, h(3) = 10 and the graph of h has slope −4. What is the value of h(7)? - Identifying a line from its intercepts in standard form
Which of the following lines has x-intercept 3 and y-intercept −6 in the xy-plane? - Inequality with two variables from a budget
A florist has a budget of $120 for roses at $3 each and lilies at $4 each, and needs at least 10 lilies. If r roses and … - Finding where two linear models cross
Company A's cost to print n flyers is 40 + 0.05n dollars. Company B's is 10 + 0.11n dollars. For what number of flyers d… - Value of an expression after solving
If 3(2x + 1) − 5 = 22, what is the value of 4x + 6? - Which point satisfies a system of two inequalities with a strict boundary
Which ordered pair (x, y) satisfies BOTH y > 2x − 3 and y ≤ 5 − x? - Parameter from a function's graph passing through a point
The graph of the linear function g(x) = kx − 7 passes through the point (3, 5). What is the value of g(−1)? - Line through two points: value of a missing coordinate
In the xy-plane, the points (1, 4), (3, 10), and (k, 16) lie on the same line. What is the value of k? - Graphical solution: which region
In the xy-plane, which point is in the solution set of the system y ≥ x − 1 and y ≤ −2x + 8? - Finding an input from a function defined by two points
For a linear function f, f(0) = 12 and f(4) = 0. For what value of x is f(x) = −6? - Equation with exactly one solution
Which of the following equations has exactly one solution? - Interpreting a two-variable inequality's boundary point
A delivery van can carry at most 800 kilograms. Crates weigh 20 kilograms and sacks weigh 30 kilograms. If c crates and … - Where one linear function is twice another
Functions f and g are defined by f(x) = 3x + 8 and g(x) = 2x − 1. For what value of x is f(x) equal to twice g(x)? - Constant that makes an equation an identity
In the equation 5(x − 2) = 5x + k, k is a constant. If the equation is true for every value of x, what is the value of k… - System of inequalities: identifying a point in the region
Which ordered pair (x, y) satisfies BOTH x + y ≤ 6 and y ≥ 2x − 4? - Parameter from a function's value
The linear function f is defined by f(x) = ax + 5, and f(4) = 17. What is the value of f(10)? - Value of a constant for a given solution
In the equation 3(x − k) = 2x + 1, k is a constant. If x = 7 is the solution, what is the value of k? - System of inequalities in context: which combination is allowed
A bakery has at most 12 hours of oven time and at most 20 kilograms of flour today. A batch of bread needs 2 hours and 4… - Difference of two outputs from the slope
A linear function f satisfies f(2) = 9 and f(5) = 21. What is the value of f(8) − f(6)? - Time from a drain-then-fill sequence
A tank is drained at 3 litres per minute for m minutes and then filled at 5 litres per minute for m + 4 minutes. At the … - Value of a constant so a point lies on a line
In the xy-plane, the line with equation kx − 3y = 12 passes through the point (2, −2). What is the value of k? - Number of solutions of a system
How many solutions does the system 2x − 4y = 8 and x − 2y = 4 have? - Second point on a line from a first
The line 4x − 5y = 17 passes through (3, −1) and through (−2, k). What is the value of k? - Value of a constant for no solution
The system 3x + 2y = 12 and 6x + 4y = k has no solution. Which of the following could be the value of k? - Time from a two-stage draining process
A tank holds 60 litres. Pump A removes 4 litres per minute. After m minutes, pump B is switched on and adds 1 litre per … - Constant so that two lines are parallel
In the xy-plane, the lines 2x + ky = 7 and 6x − 9y = 4 are parallel. What is the value of k? - Value of a constant for infinitely many solutions
The system 5x − 2y = 10 and kx − 6y = 30 has infinitely many solutions. What is the value of k? - Value of a constant that removes all solutions
In the equation 2(3x + a) = 6x + 9, a is a constant. For which value of a does the equation have NO solution? - Constant so that a line passes through a given point
The line with equation 3x + ky = 24 passes through the point (4, 3) in the xy-plane. What is the y-coordinate of the poi… - Interpreting the number of solutions of a system in context
Two phone plans are compared. Plan A costs 20 + 0.05m dollars for m minutes; Plan B costs 20 + 0.05m dollars as well, af… - Constant that gives a specified solution
In the equation 4(x + c) = 2x + 26, c is a constant. If x = 3 is the solution, what is the value of c? - Which value of a constant gives a specified solution
In the equation 5(x − 2) = 3x + k, k is a constant. For which value of k is the solution x = 9? - Which point satisfies a system of inequalities
Which ordered pair (x, y) satisfies BOTH 2x + y ≤ 10 and y ≥ x − 1? - Number of solutions of a system with proportional coefficients
How many solutions does the system 3x + 6y = 9 and x + 2y = 4 have? - Constant giving infinitely many solutions
In the equation 3(2x − c) = 6x − 15, c is a constant. For which value of c does the equation have infinitely many soluti… - Point strictly inside a region
Which ordered pair (x, y) satisfies BOTH y < 3x − 2 and x + y ≤ 6? - Interpreting parallel lines in context
Two savings accounts are compared. Account A starts with $200 and gains $15 a month. Account B starts with $260 and gain… - Change in y for a change in x along a line
In the xy-plane, the points (a, 6) and (a + 3, 4) both lie on the line 2x + 3y = 10. What is the value of a? - Choosing a system that models a situation
A gardener buys x bags of compost at $6 each and y bags of bark at $9 each, spending $105 in total. She buys twice as ma… - Mixture of two solutions
A chemist mixes a 50% acid solution with an 80% acid solution to make 60 millilitres of a 60% acid solution. How many mi… - Slope from a general pair of points
The graph of a linear function passes through the point (2, 5) and, for every positive value of h, through the point (2 … - Parameter appearing in both points on a line
In the xy-plane, a line with slope 2 passes through the points (a, 3) and (4, a), where a is a constant. What is the val… - x-intercept of a line whose intercepts are in a given ratio
In the xy-plane, line ℓ has an x-intercept that is twice its y-intercept, and ℓ passes through the point (2, 1). What is… - Time at which one candle is twice the height of another
Two candles of the same height are lit at the same time. One burns down completely in 4 hours and the other in 6 hours, … - Slope of a linear function that swaps two values
A linear function f satisfies f(a) = b and f(b) = a, where a and b are distinct constants. What is the slope of the grap… - Intercept of a linear function whose value doubles over an interval
The graph of a linear function f passes through the point (2, 5), and f(4) is twice f(2). What is the value of f(0)? - Linear function forced through the origin by a scaling property
A linear function f satisfies f(2x) = 2f(x) for every value of x, and f(3) = 7.5. What is the value of f(10)? - Intercept in terms of a parameter
The graph of a linear function f has slope 2 and passes through the point (k, k), where k is a nonzero constant. Which e… - Initial value from two later readings of a linear model
A tank drains at a constant rate. Two minutes after the drain opens it holds 180 litres, and seven minutes after it hold… - Input where one linear function is twice another
The functions f and g are defined by f(x) = 3x − 4 and g(x) = −2x + 11. For what value of x is f(x) equal to 2g(x)? - Parameter that reverses an inequality's solution set
For which values of the constant k is the solution set of kx + 3 > 3 exactly the set of all x less than 0? - Constant that produces a given solution set
The solution set of the inequality a(x − 2) ≤ 4 is all x ≥ 0, where a is a constant. What is the value of a? - Feasible distances under a budget and a minimum
A van hire costs $25 per day plus $0.40 per kilometre. A courier hires the van for 3 days, must drive at least 200 kilom… - Least value of a linear combination over bounded variables
If 2 ≤ x ≤ 5 and −3 ≤ y ≤ 1, what is the least possible value of x − 2y? - Point on a line equidistant from both axes
In the xy-plane, point P lies on the line 3x − 4y = 12, is in quadrant IV, and is the same distance from the x-axis as f… - Positive constant making two lines parallel but distinct
In the xy-plane, the lines kx + 2y = 6 and 2x + ky = 8 are parallel and distinct, where k is a positive constant. What i… - x-intercept from a slope and a point, expressed through intercept parameters
In the xy-plane, a line with slope −2 passes through the point (1, 4) and crosses the x-axis at (p, 0) and the y-axis at… - Chaining two systems through a shared constant
The system 2x + 3y = a and 4x + 6y = 10 has infinitely many solutions, where a is a constant. The system 2x + 3y = a and… - Difference of outputs from another difference
For the linear function f, f(7) − f(2) = 15. What is the value of f(11) − f(3)? - Composition of a linear function with itself
The function g is defined by g(x) = −2x + c, where c is a constant. If g(g(1)) = 3, what is the value of c? - Intercepts in a fixed ratio
In the xy-plane, the graph of a linear function passes through (2, 5), and its y-intercept is three times its x-intercep… - Missing table value from non-adjacent rows
The table gives three values of the linear function f. x | f(x) 1 | 7 4 | ? 10 | 34 What is the missing value f(4)? - Two constants from one meeting point
The functions h and p are defined by h(x) = kx + 4 and p(x) = 2x + j, where k and j are constants. In the xy-plane, the … - Sum of integer solutions of a compound inequality
What is the sum of all integer values of x that satisfy 3 ≤ 2x − 1 ≤ 9? - Whole-number maximum under a budget
A hall costs $40 to book plus $12 for each hour it is used, and it can be booked only for a whole number of hours. What … - Point satisfying a strict system
Which of the following points (x, y) satisfies both y > x + 1 and y < −x + 5? - Least integer in a compound inequality with a negative coefficient
What is the least integer value of x that satisfies −2 < 4 − 3x ≤ 10? - System of inequalities with no solution
Which of the following systems of inequalities has no solution? - Triangle cut off by a line and the axes
In the xy-plane, the line 3x − 4y = 24 and the two axes bound a triangle. What is the area of that triangle? - Unknown coordinate from a perpendicular
In the xy-plane, the line through (1, 2) and (5, k) is perpendicular to the line 2x + y = 7. What is the value of k? - Constant for infinitely many solutions
The system ax + 6y = 12 and 2x + 3y = 6, where a is a constant, has infinitely many solutions. What is the value of a? - Cost of a third combination
Three pens and two notepads cost $11. Five pens and four notepads cost $20. How much, in dollars, do two pens and three … - Constant from a double application
The linear function f is defined by f(x) = mx + b, where m > 0. If f(f(x)) = 4x + 9 for all x, what is the value of b? - Extrapolating a linear function
For the linear function f, f(2) = 7 and f(6) = 19. What is the value of f(10)? - Perpendicular function's constant term
The linear function f is defined by f(x) = (1/3)x + 2. The graph of the linear function g is perpendicular to the graph … - Distance at which two hire plans cost the same
A bike-hire company offers two plans. Plan A costs $30 plus $2 per kilometre ridden. Plan B costs $10 plus $6 per kilome… - Intercept in terms of a parameter
For a nonzero constant a, the graph of the linear function f passes through the points (a, 2a) and (3a, 8a). Which expre… - Years until a value is reached
A machine's value V, in dollars, t years after purchase is modelled by V(t) = 12,000 − 900t. After how many years will i… - Slope equal to the y-intercept
In the xy-plane, the line through (2, 3) and (6, k) has a slope equal to its y-intercept. What is the value of k? - Reflection of a line across the x-axis
In the xy-plane, line m is the reflection of the line y = 2x − 3 across the x-axis. What is the y-coordinate of the poin… - Meeting point with a perpendicular through a given point
In the xy-plane, line ℓ has equation y = 2x + 1. Line m is perpendicular to ℓ and passes through (0, 5). What is the x-c… - Constant making a line pass through a point
In the xy-plane, the line 3x + cy = 6, where c is a constant, passes through the point (4, −3). What is the value of c? - Intercept from an enclosed area
In the xy-plane, the line y = −2x + b, where b is a positive constant, forms a triangle with the two axes. If the area o… - Counting integers in an absolute-value band
How many integer values of x satisfy 2 ≤ |x − 3| ≤ 5? - Minimum sales for a target profit
A stall sells candles for $12 each. It costs $200 to hire the stall plus $7 to make each candle. What is the least numbe… - Range of a coordinate inside a region
In the xy-plane, the point (k, 3) lies in the region where y > x and y < 2x. Which of the following gives all possible v… - Greatest integer after distributing a negative
What is the greatest integer value of x that satisfies −3(x − 2) > 2x − 4? - Equivalent inequality
Which of the following inequalities has the same solution set as 4 − x ≥ 2x + 1? - Equation with two fractions and subtraction
What value of x satisfies (x + 4)/2 − (x − 4)/3 = 5? - Constant that rescues an equation from having no solution
The equation 5x − 2(x + p) = 3x + 6, where p is a constant, has no solution unless p takes one particular value. What is… - Constant giving a system no solution
The system kx + 2y = 7 and 3x + y = 4, where k is a constant, has no solution. What is the value of k? - Ages from a sum and a past relationship
The ages of a mother and her daughter add up to 32. Four years ago, the mother was twice as old as the daughter. How old… - Distance from a round trip at two speeds
A cyclist rides from home to a town at 12 kilometres per hour and returns along the same road at 18 kilometres per hour.… - Starting amount from fractional spending
Kai spent one third of his money on a book and then $12 on lunch. He then had exactly half of his original money left. H… - Consecutive odd integers with a condition on the largest
The sum of three consecutive odd integers is 3 more than twice the largest of them. What is the smallest of the three in… - Original price after a cut and a rise
A jacket's price was reduced by 20%, and the reduced price was then increased by 10%, giving a final price of $88. What … - Solving a literal equation
If a(x − b) = c, where a ≠ 0, which of the following expresses x in terms of a, b, and c? - Time to reach a level with inflow and outflow
A tank holds 200 litres. Water drains out at 4 litres per minute while a pipe adds water at 1.5 litres per minute. After… - Age from a present ratio and a future ratio
Mira is three times as old as her son. In 12 years she will be twice as old as he is then. How old is her son now? - Reflecting a linear function across the y-axis
The graph of the linear function g has slope 4 and y-intercept −2. The graph of the function h is the reflection of the … - When a draining tank is empty
The depth of water in a tank decreases linearly. It is 40 centimetres at t = 2 minutes and 25 centimetres at t = 8 minut… - Interpreting a small negative slope
The function T(d) = 15 − 0.0065d models the air temperature T, in degrees Celsius, at a height of d metres above a town.… - Zero of a linear function from two values
For the linear function f, f(−2) = 9 and f(4) = −3. For what value of x is f(x) = 0? - Slope constant from equal outputs
The linear functions f and g are defined by f(x) = 2x + 5 and g(x) = kx − 1, where k is a constant. If f(3) = g(3), what… - Minutes until a battery reaches a level
A phone's battery charge decreases linearly. It is 100% at 8:00 and 64% at 10:24 the same morning. How many minutes afte… - Value at zero from a constant step
The linear function f satisfies f(x + 1) − f(x) = −3 for every value of x, and f(4) = 10. What is the value of f(0)? - Coffees sold from two days' takings
A café sells coffee for $3 a cup and tea for $2 a cup. On Monday its takings from these drinks were $260. On Tuesday it … - Two constants for one line written twice
In the xy-plane, the equations ax + 3y = 9 and 2x + by = 6, where a and b are constants, describe the same line. What is… - Product of the coordinates of an intersection
In the xy-plane, the lines 2x + y = 8 and x − 2y = −1 intersect at a single point. What is the product of the coordinate… - Speed of a current from two journeys
A boat travels 28 kilometres downstream in 2 hours and returns the same 30 kilometres upstream in 3 hours. What is the s… - Conditions for infinitely many solutions
The system y = mx + 4 and y = 2x + b, where m and b are constants, has infinitely many solutions. Which of the following… - Rectangle whose area survives a reshaping
A rectangle has a perimeter of 40 centimetres. If its length is decreased by 3 centimetres and its width is increased by… - Cars in a mixed car park
A car park contains only cars and motorbikes. There are 30 vehicles with a total of 84 wheels. How many cars are in the … - Unknown coordinate from two perpendicular segments
In the xy-plane, the line through (1, 2) and (4, k) is perpendicular to the line through (0, 0) and (3, −1). What is the… - Third point from two intercepts
In the xy-plane, a line has x-intercept 4 and y-intercept −2. The point (6, k) lies on the line. What is the value of k? - Constant making two lines meet on the x-axis
In the xy-plane, the lines y = 2x + b and y = −x + 7, where b is a constant, intersect at a point on the x-axis. What is… - Where two temperature scales agree
The Fahrenheit temperature F and the Celsius temperature C are related by F = 1.8C + 32. At what temperature are the two… - Slope through a midpoint
In the xy-plane, the line y = mx + 3, where m is a constant, passes through the midpoint of the segment joining (2, 5) a… - Line through the origin bisecting a rectangle
In the xy-plane, a rectangle has vertices (1, 2), (5, 2), (5, 6), and (1, 6). A line through the origin divides the rect… - Sharing an x-intercept with a given line
In the xy-plane, line ℓ has the equation 5x − 2y = 20. Line m has the same x-intercept as ℓ and a y-intercept of 5. If l… - Counting integers satisfying two inequalities
How many integers x satisfy both 3 − 2x ≥ x − 9 and x > −1? - Maximum boxes with a fixed load
A van can carry at most 800 kilograms. It must carry 8 crates that each weigh 60 kilograms, and the rest of its load wil… - Maximum of a sum over a triangular region
In the xy-plane, a region consists of all points (x, y) satisfying y ≤ −x + 6, y ≥ 2, and x ≥ 1. What is the greatest po… - Sign of a constant from a solution set
For a nonzero constant k, the solution set of the inequality kx + 3 > 3 is x < 0. Which of the following must be true? - Sum of the extreme integer solutions
What is the sum of the least and the greatest integer values of x that satisfy −1 ≤ (2x + 1)/3 < 3? - Counting production levels that make a profit
A workshop can make at most 60 chairs a week. Each chair sells for $15 and costs $6 in materials, and the workshop has f… - Length of an absolute-value solution interval
The solutions of |3x − 6| ≤ 9 form an interval on the number line. What is the length of that interval? - Distance from a time saved on the return
A train travels from town A to town B at 80 kilometres per hour and returns at 120 kilometres per hour. The return journ… - When one candle is twice the length of another
Two candles are the same length. One burns out completely in 4 hours and the other in 6 hours, each at a steady rate. Af… - Blending two coffees to a target price
A shop blends coffee costing $12 per kilogram with coffee costing $18 per kilogram to make 10 kilograms of a blend worth… - Number from its half, third, and quarter
The half, the third, and the quarter of a number add up to 26. What is the number? - Condition for an equation to have no solution
The equation 5x + 3 = 5x + c, where c is a constant, has no solution. Which of the following must be true? - Number of girls from class averages
In a class, the 20 boys have an average test mark of 60 and the girls have an average mark of 70. The average mark of th… - Linear function from a doubling relation
The linear function g satisfies g(1) = 4 and g(3) = 2·g(1). What is the value of g(5)? - Distance at which a tank runs dry
A car's fuel gauge shows 42 litres after 100 kilometres and 30 litres after 250 kilometres, and the fuel level falls lin… - Perpendicular linear function's value
The linear function L satisfies L(0) = 8, and its graph in the xy-plane is perpendicular to the graph of y = 4x. What is… - Meaning of a model's starting value
A diving club models the length of rope left on a drum, in metres, after d dives by M(d) = 1,500 − 25d. What does the va… - Fixed charge from two fares
A taxi fare is a linear function of the distance travelled. A 3-kilometre ride costs $11 and a 7-kilometre ride costs $2… - Starting altitude of a descending hiker
A hiker descends at a constant rate. She is at an altitude of 1,900 metres after 2 hours and 1,300 metres after 5 hours.… - Constant giving two lines the same x-intercept
In the xy-plane, the line kx + 3y = 12, where k is a constant, has the same x-intercept as the line 2x − y = 8. What is … - x-intercept of a parallel line through a point
In the xy-plane, line ℓ has the equation 3x − 4y = 24. Line m is parallel to ℓ and passes through (0, 3). What is the x-… - Sum of two prices from two receipts
A shop sells mugs at m dollars each and plates at p dollars each. One receipt shows 4 mugs and 3 plates for $17; another… - Time for two vehicles to be a given distance apart
A train and a bus leave the same station at the same time and travel in opposite directions along a straight route, the … - Months of spending before a reserve is breached
A club's rules say its fund must always stay above $500. The fund holds $2,000 and the club spends $125 from it every mo… - Constant that fixes a solution set
For what value of k is the solution set of 2x + k ≥ 3x − 1 exactly x ≤ 5? - Sum of integer solutions of an absolute-value inequality
What is the sum of all integer values of x that satisfy |x + 3| < 2? - Area of a region defined by three inequalities
In the xy-plane, the region satisfying y ≥ 2x − 4, y ≤ 4, and x ≥ 0 is a triangle. What is its area? - Smallest weight at which one courier is cheaper
Courier A charges $5 plus $2 per kilogram. Courier B charges $9 plus $1.20 per kilogram. For parcels weighing a whole nu… - Counting possible purchases within a budget range
Chairs cost $30 each. A school will spend at least $600 and at most $800 on chairs, and it must spend a whole number of … - Sum of the intercepts of a line
In the xy-plane, a line has slope −2 and x-intercept 5. What is the sum of its x-intercept and its y-intercept? - Intercept of a perpendicular partner line
In the xy-plane, the lines y = ax + 2 and y = 3x + b, where a and b are constants, are perpendicular and intersect at a … - Intercept from a fixed ratio and a point
In the xy-plane, a line crosses the x-axis at (a, 0) and the y-axis at (0, 2a), where a ≠ 0, and passes through the poin… - Perimeter of a triangle from an intercept-form line
In the xy-plane, the line x/4 + y/3 = 1 and the two axes enclose a triangle. What is the perimeter of that triangle? - Smaller number from a sum-to-difference ratio
The sum of two numbers is three times their difference, and the larger number is 12. What is the smaller number? - Class size from fractions of two groups
In a class, three quarters of the boys and half of the girls play a musical instrument. If 18 boys and 12 girls play an … - Rectangle length from two perimeters
A rectangle has a perimeter of 36. If its length were doubled and its width halved, the perimeter would be 42. What is t… - Number of two-dollar coins in a jar
A jar contains only $1 coins and $2 coins. There are 50 coins in the jar, worth $80 in total. How many $2 coins are ther… - Constant from a known solution
The equation (x − a)/3 = (x + 2)/5 has the solution x = 13, where a is a constant. What is the value of a? - Sum of two values of a linear function
The graph of the linear function f passes through the points (−2, 4) and (4, −2). What is the value of f(0) + f(1)? - Vertical gap between parallel lines
In the xy-plane, the lines y = 2x + 3 and y = 2x − 5 are parallel. For any value of x, what is the vertical distance bet… - Product of an intersection point's coordinates
In the xy-plane, the lines 3x + 2y = 12 and x = 2y intersect at a single point. What is the product of the x- and y-coor… - Maximum of a linear expression under constraints
Real numbers x and y satisfy x + y ≤ 10, x ≥ 2, and y ≥ 3. What is the greatest possible value of 2x + y? - Total hours from pay with overtime
A worker is paid $12 per hour for the first 40 hours in a week and $18 per hour for each hour beyond 40. In one week the… - When two tanks hold the same amount
Tank A holds 500 litres and is draining at 20 litres per minute. Tank B holds 200 litres and is filling at 10 litres per… - y-intercept from a value and a difference
For a linear function g, g(1) = 5 and g(3) − g(1) = 8. What is the y-coordinate of the y-intercept of the graph of g? - x-intercept of a perpendicular line through a point
In the xy-plane, lines p and q are perpendicular and intersect at (2, 3). Line p has slope 2. At what value of x does li… - Distance between a line's intercepts
In the xy-plane, a line passes through the points (−6, 0) and (0, 8). What is the distance between the line's x-intercep… - Constant so that a line passes through an intersection
In the xy-plane, the lines x + y = 9 and x − y = 1 intersect at a point P. For what value of c does the line y = 2x + c … - Integers satisfying two inequalities
How many integers x satisfy both 2x − 3 < 7 and 5 − x < 3? - Greatest width under a length condition
A rectangle has a perimeter of 60 centimetres, and its length is at least twice its width. What is the greatest possible… - Capacity of a bus from a fraction and a count
A bus is three quarters full. When 12 more passengers board, every seat is taken. How many seats does the bus have? - Total from two fractions and a remainder
A charity spent one quarter of its funds on rent and one third on salaries, leaving $25,000. How much money, in dollars,… - Prediction from two readings of a linear meter
A water meter's reading is a linear function of the number of days since it was installed. On day 1 it read 5 units and … - Distance from a slope and a target value
The function d(t) = −2t + 20 gives the distance, in kilometres, between a walker and her home t hours after she sets off… - Intercepts from a line and its triangle
In the xy-plane, the line 4x + 3y = 24 crosses the x-axis at point P and the y-axis at point Q. What is the length of se… - Combined price of a ride and a game
At a fair, 3 rides and 2 games cost $16, and 1 ride and 4 games cost $12. What is the total cost, in dollars, of 1 ride … - Greatest count under a two-item budget
Pens cost $2 and notebooks cost $3. Mira buys exactly 5 notebooks and some pens, spending at most $30 in total. What is … - Product of two numbers from their mean and difference
The mean of two numbers x and y is 7, and x is 4 more than y. What is the value of xy? - Slope from an equation with unknown coefficients
In the xy-plane, the line ax + by = 0 passes through the point (6, 4), where a and b are nonzero constants. What is the … - Line through the x-intercept of another line
In the xy-plane, line m passes through the point (4, 5) and through the x-intercept of the line 4x − 9 = 0. What is the … - Value of a combination from a system
If 2x + 3y = 22 and x − y = 1, what is the value of 3x − 2y? - Number of each ticket type from two totals
A theatre sold 50 tickets for a show, some at $12 and the rest at $8, taking $480 in total. How many $8 tickets were sol… - Integers satisfying two inequalities at once
How many integers x satisfy both 3x − 2 ≥ 7 and x + 4 < 10? - Greatest length under a perimeter limit
A rectangle has a width of 7 centimetres and a whole-number length. Its perimeter must be at most 40 centimetres. What i… - Amount from shares described in words
A sum of $85 is split among three people. The second person receives twice as much as the first, and the third receives … - Time for two linear quantities to match
A candle 100 millimetres tall burns down 4 millimetres per hour. A second candle is 60 millimetres tall and burns down 1… - Input where a decreasing linear function turns negative
For the linear function f, f(3) = 5 and f(8) = −5. For what value of x is f(x) = 0? - Change in output over an interval of a linear function
For the linear function f, f(x) = 4x − 3. By how much does f(x) change as x increases from 2 to 5? - Largest of three numbers from their mean and relations
The mean of three numbers is 10. The first number is twice the second, and the third is 6 more than the second. What is … - Integers satisfying two strict inequalities
How many integers x satisfy both 2x + 1 > 5 and 3x − 4 < 11? - Total from two fractional shares that match
Two fifths of the tickets for a show plus 6 more tickets is the same number as half of the tickets. How many tickets are… - Time until a falling quantity reaches zero
A candle is 40 centimetres tall and burns down at 2.5 centimetres per hour. After how many hours will it be completely b… - Slope from the intercepts of a line
In the xy-plane, a line crosses the x-axis at (4, 0) and the y-axis at (0, 6). What is the slope of the line? - Counting integers between two bounds
How many integers x satisfy both 4 − x > 1 and 2x + 5 ≥ 3? - Group size from a fraction and a remainder
Three fifths of the members of a choir are sopranos, and the remaining 12 members are altos. How many members does the c… - Equation with two fractional expressions
If (2x + 5)/3 − (x − 1)/2 = 4, what is the value of x? - Constant that makes an equation an identity
The equation 3(x + a) − 2(x − 4) = x + 20 is true for every value of x. What is the value of a? - Evaluating a line through two points
The graph of the linear function f passes through the points (2, 5) and (6, −3) in the xy-plane. What is the value of f(… - Defining a linear function from a constant change
The function g is linear, and g(x) − g(x − 1) = −4 for every value of x. If g(3) = 2, which of the following defines g? - Y-intercept of a perpendicular line
Line l has the equation 3x − 4y = 24. Line m is perpendicular to l and passes through the point (6, 1). What is the y-in… - Finding a coordinate on a line through two points
In the xy-plane, a line passes through the points (−2, 7) and (4, −2). If the point (k, 1) also lies on the line, what i… - Coins of two kinds from a count and a total
A jar holds only 5-cent coins and 10-cent coins. There are 30 coins with a total value of 2 dollars and 30 cents. How ma… - Constants for a dependent system
The system ax + 3y = 12 and 4x + 6y = k, where a and k are constants, has infinitely many solutions. What is the value o… - Child tickets from a count and a total
A theatre sold 300 tickets for one performance. Adult tickets cost 12 dollars and child tickets cost 8 dollars, and the … - Constant that makes two lines parallel
In the xy-plane, the lines 2x − 5y = 7 and kx + 10y = 3 are parallel. What is the value of k? - Largest integer in a compound inequality
If −3 < 2 − x ≤ 4, what is the largest integer value of x? - Point satisfying a system of inequalities
Which of the following points (x, y) satisfies both y > 2x − 1 and y ≤ −x + 5? - Least sales to reach a profit target
A company earns 4 dollars for each item it sells and has fixed costs of 1,250 dollars per week. What is the least number… - X-intercept of a parallel line
In the xy-plane, line p passes through the points (1, 2) and (5, 10). Line q is parallel to p and passes through (0, −3)… - Y-intercept from an x-intercept
The graph of 3x + 2y = c in the xy-plane, where c is a constant, has an x-intercept of 8. What is the y-intercept of the… - Constant giving infinitely many solutions
For what value of k does the equation 4(x − 2) − 3(x + k) = x + 1 have infinitely many solutions? - Equation with the unknown in a denominator
If 3/(x + 2) = 1/4, what is the value of x? - Hours worked with overtime pay
A worker is paid 18 dollars per hour for the first 40 hours in a week and 27 dollars per hour for each hour beyond 40. I… - Linear function from a functional relation
A linear function f satisfies f(x + 2) = f(x) + 6 for all values of x, and f(1) = 4. What is the value of f(−3)? - Coefficient from two points on a line
The graph of ax + by = 10 in the xy-plane passes through the points (1, 2) and (3, 1), where a and b are constants. What… - Point of the form (k, 2k) on a line
In the xy-plane, a line passes through the points (2, 7) and (−4, 1). The point (k, 2k) also lies on the line. What is t… - Mixing two salt solutions
A chemist mixes a 10 percent salt solution with a 40 percent salt solution to make 300 millilitres of a 30 percent salt … - Sum of two prices from two orders
Three pencils and two pens cost 4.10 dollars, and two pencils and three pens cost 4.90 dollars. What is the total cost, … - System of inequalities for vans and trucks
A company must ship at least 200 boxes using vans that carry 30 boxes each and trucks that carry 50 boxes each. It can u… - Least integer x for a point in a system of inequalities
The point (k, 3) satisfies both y < 2x − 1 and y ≥ −x + 4. What is the least possible integer value of k? - Linear function from a difference and an intercept
The linear function f satisfies f(4) − f(1) = 9 and f(0) = −2. What is the value of f(6)? - Linear function from its two intercepts
The graph of the linear function g in the xy-plane has x-intercept 6 and y-intercept −4. Which of the following defines … - Equation with three distributed products
If 2(3x − 1) − 5(x + 2) = 3(x − 4), what is the value of x? - Coefficient for a perpendicular line
In the xy-plane, the line ax + 2y = 8, where a is a constant, is perpendicular to the line y = 4x − 1. What is the value… - Greatest number of crates under a weight limit
A truck can carry at most 2,000 kilograms. It is loaded with crates weighing 60 kilograms each and boxes weighing 25 kil… - Time to fill a leaking tank
A tank is filled by a pipe at 8 litres per minute while a leak drains it at 3 litres per minute. Starting from empty, af… - Linear function perpendicular to a given line
The linear function f satisfies f(1) = 3, and the graph of f is perpendicular to the line y = (1/2)x + 7. What is the va… - Constant for a system with no solution
For what value of k does the system 3x − y = 4 and kx + 2y = 7 have no solution? - Water added to dilute a solution
A 200-millilitre solution is 15 percent salt. How many millilitres of pure water must be added so that the solution beco… - Sum of the intercepts of a line
In the xy-plane, a line with slope −2 passes through the point (3, 4) and crosses the axes at (a, 0) and (0, b). What is… - Greatest side length under a fencing constraint
A gardener has 60 metres of fencing to enclose three sides of a rectangular plot against a wall. The side parallel to th… - Cost price from a mark-up and a sale
A shop marks up a coat by 40 percent above its cost, then sells it in a sale at 20 percent off the marked price for 84 d… - Constant from a slope between two parametrised points
In the xy-plane, the line through the points (k, 3) and (2k, 9) has slope 2, where k is a positive constant. What is the… - Weekend hours from a week's pay
A worker is paid 15 dollars per hour on weekdays and 22.50 dollars per hour at weekends. In one week she worked 40 hours… - Constant for a parallel line a fixed distance above
In the xy-plane, the line y = 2x + c is parallel to the line y = 2x − 5 and lies 3 units above it. What is the value of … - Class size from two relations between boys and girls
In a class, the number of girls is 6 more than the number of boys. If the number of boys were doubled, there would be 4 … - Total respondents from fractions and a remainder
In a survey, 3/8 of the respondents chose option A, 1/4 chose option B, and the remaining 60 respondents chose option C.… - Slope from a composed value
The linear function g is defined by g(x) = mx + 3, where m is a constant. If g(g(0)) = 11, what is the value of m? - Lengths satisfying a perimeter and an area condition
A rectangle has length L and width 4. Its perimeter must be at most 30, and its area must be at least 32. Which of the f… - Least number of standard tickets for a revenue target
A theatre sells standard tickets at 20 dollars and premium tickets at 50 dollars, and it can sell at most 500 tickets in… - Slope hidden in a scaling identity
For a linear function h, h(3t) − h(t) = 8t for every value of t, and h(2) = 9. What is the value of h(7)? - Line midway between two parallel lines
Line m lies exactly midway between the parallel lines y = 2x + 3 and y = 2x − 7 at every value of x. What is the y-coord… - Where two pricing plans cost the same
A ride with Carrier A costs $3.50 plus $2.25 per mile. The same ride with Carrier B costs $6.00 plus $1.75 per mile. For… - Equal intercepts condition
In the xy-plane, the graph of cx + 4y = 12 has an x-intercept equal to its y-intercept. What is the value of c? - Intercept relationship through a point
A line passes through the point (3, −2), and its x-intercept is twice its y-intercept (both nonzero). What is the y-coor… - Self-referencing constant on a line
The graph of 2x − 3y = c passes through the point (c, c − 4). What is the value of c? - Inconsistency condition with fractions
For what value of c does the system cx + 2y = 10 and 3x + 6y = 21 have no solution? - Difference of coordinates
If (x, y) is the solution to the system x − 2y = 3 and 4x + y = 30, what is the value of x − y? - River current from two trip times
A boat travels 36 kilometers downstream in 2 hours and makes the return trip upstream in 3 hours, the boat's own speed a… - Recognizing a dependent system
How many solutions (x, y) does the system 3x − y = 4 and 6x − 2y = 8 have? - Recovering a constant from a solution set
The solutions of the inequality 2(x − c) > 10 are exactly the values x > 9. What is the value of c? - Maximum heavy boxes under a weight limit
A van will carry exactly 35 boxes, each weighing either 12 kilograms or 20 kilograms, and the total weight must not exce…
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