A backpack with a regular price of $65 is marked down 20%. What is the sale price?Common Core State Standards for Mathematics, 7.RP.A.3: use proportional relationships to solve multistep ratio and percent problems
A hose fills 2 1/2 gallons of a tank in 1/3 minute. What is the unit rate in gallons per minute?Common Core State Standards for Mathematics, 7.RP.A.1: compute unit rates associated with ratios of fractions
A jacket costs $48 before tax. Sales tax is 7.5%. What is the total cost?Common Core State Standards for Mathematics, 7.RP.A.3: use proportional relationships to solve multistep ratio and percent problems
A lemonade recipe uses 2/3 cup of honey for every 1/4 cup of lemon juice. How many cups of honey are used for each cup of lemon juice?Common Core State Standards for Mathematics, 7.RP.A.1: compute unit rates associated with ratios of fractions
A library had 250 members last year and has 290 this year. What is the percent increase?Common Core State Standards for Mathematics, 7.RP.A.3: use proportional relationships to solve multistep ratio and percent problems
Show all 80 questions (75 more)
Ratios and Proportional Relationships, continued
A meal costs $36. Dana leaves an 18% tip. How much is the tip?Common Core State Standards for Mathematics, 7.RP.A.3: use proportional relationships to solve multistep ratio and percent problems
A painter covers 3/5 of a wall in 3/4 hour. At this rate, how much of the wall is painted in 1 hour?Common Core State Standards for Mathematics, 7.RP.A.1: compute unit rates associated with ratios of fractions
A printer prints 18 pages each minute. Which equation gives the number of pages p printed in m minutes?Common Core State Standards for Mathematics, 7.RP.A.2.c: represent proportional relationships by equations
A proportional relationship includes the pair x = 8, y = 6. Which equation describes it?Common Core State Standards for Mathematics, 7.RP.A.2.c: represent proportional relationships by equations
Each table lists three pairs of x and y. In which table is y proportional to x?Common Core State Standards for Mathematics, 7.RP.A.2.a: decide whether two quantities are in a proportional relationship
The equation d = 55t gives the distance d, in miles, that a train travels in t hours. What does the 55 stand for?Common Core State Standards for Mathematics, 7.RP.A.2.b: identify the constant of proportionality (unit rate)
The graph of a proportional relationship between gallons of gas used and miles driven passes through (1, 32). What does this point mean?Common Core State Standards for Mathematics, 7.RP.A.2.d: explain what a point on the graph of a proportional relationship means
The graph of a relationship is a straight line that crosses the y-axis at (0, 4). Is the relationship proportional?Common Core State Standards for Mathematics, 7.RP.A.2.a: decide whether two quantities are in a proportional relationship
Leo estimates that a board is 50 inches long. It measures 40 inches. What is the percent error of his estimate?Common Core State Standards for Mathematics, 7.RP.A.3: use proportional relationships to solve multistep ratio and percent problems
Maya puts $400 in an account that pays 3% simple interest each year. How much interest does the account earn in 5 years?Common Core State Standards for Mathematics, 7.RP.A.3: use proportional relationships to solve multistep ratio and percent problems
Ribbon is sold by length: 4 yards cost $10, 6 yards cost $15 and 10 yards cost $25. What is the constant of proportionality in dollars per yard?Common Core State Standards for Mathematics, 7.RP.A.2.b: identify the constant of proportionality (unit rate)
The Number System 17
A bank takes a fee of $4.50 from an account each week. What is the total change in the balance after 8 weeks?Common Core State Standards for Mathematics, 7.NS.A.3: solve problems involving the four operations with rational numbers
A diver is 12 feet below the surface of a lake and then rises 12 feet. Where is the diver now?Common Core State Standards for Mathematics, 7.NS.A.1.a: describe situations in which opposite quantities combine to make 0
A hiker starts at an elevation of −30 feet, climbs 125 feet, then goes down 48 feet. What is the hiker's elevation now?Common Core State Standards for Mathematics, 7.NS.A.3: solve problems involving the four operations with rational numbers
A stock price changes by −3/4 dollar on Monday and by +1 1/2 dollars on Tuesday. What is the total change over the two days?Common Core State Standards for Mathematics, 7.NS.A.3: solve problems involving the four operations with rational numbers
A submarine goes down 15 meters each minute. Which number shows its change in depth after 4 minutes?Common Core State Standards for Mathematics, 7.NS.A.2.a: the rules for multiplying signed numbers
The temperature at dawn is −7°F. It then drops 5 degrees. What is the new temperature?Common Core State Standards for Mathematics, 7.NS.A.1.b: understand p + q as a distance |q| from p on the number line
What is (−3/4) × (8/15)?Common Core State Standards for Mathematics, 7.NS.A.2.c: apply properties of operations to multiply and divide rational numbers
What is (−7)(−12)?Common Core State Standards for Mathematics, 7.NS.A.2.a: the rules for multiplying signed numbers
What is 3/4 + (−5/8) + 1/4?Common Core State Standards for Mathematics, 7.NS.A.1.d: apply properties of operations to add and subtract rational numbers
What is the distance between −14 and 9 on a number line?Common Core State Standards for Mathematics, 7.NS.A.1.c: understand subtraction of rational numbers as adding the additive inverse
What is −4.5 ÷ (−0.9)?Common Core State Standards for Mathematics, 7.NS.A.2.c: apply properties of operations to multiply and divide rational numbers
What is −9 + 15?Common Core State Standards for Mathematics, 7.NS.A.1.b: understand p + q as a distance |q| from p on the number line
Which expression has no value?Common Core State Standards for Mathematics, 7.NS.A.2.b: integers can be divided when the divisor is not zero
Which expression has the same value as 6 − (−9)?Common Core State Standards for Mathematics, 7.NS.A.1.c: understand subtraction of rational numbers as adding the additive inverse
Which fraction has a decimal form that repeats and never ends?Common Core State Standards for Mathematics, 7.NS.A.2.d: convert a rational number to a decimal using long division
Which fraction is equal to −(3/4)?Common Core State Standards for Mathematics, 7.NS.A.2.b: integers can be divided when the divisor is not zero
Which is the decimal form of 5/8?Common Core State Standards for Mathematics, 7.NS.A.2.d: convert a rational number to a decimal using long division
Expressions and Equations 17
A coat with a price of p dollars is marked 30% off. Which expression gives the sale price?Common Core State Standards for Mathematics, 7.EE.A.2: rewriting an expression in different forms shows how its quantities are related
A shelf 28 1/2 inches wide holds a row of 6 equal boxes with no gaps. How wide is each box?Common Core State Standards for Mathematics, 7.EE.B.3: solve multi-step problems with positive and negative rational numbers in any form
Ben has $80 and saves $15 each week. He needs at least $200 for a bike. What is the least number of whole weeks he must save?Common Core State Standards for Mathematics, 7.EE.B.4.b: solve word problems leading to inequalities of the form px + q > r or px + q < r
Nora pays a $25 sign-up fee plus $12 for each dance class. She has paid $133 in all. How many classes has she taken?Common Core State Standards for Mathematics, 7.EE.B.4.a: solve word problems leading to equations of the form px + q = r and p(x + q) = r
The perimeter of a rectangle is written 2l + 2w. Which form shows that the perimeter is twice the sum of the length and the width?Common Core State Standards for Mathematics, 7.EE.A.2: rewriting an expression in different forms shows how its quantities are related
Sam buys 3 1/2 pounds of apples at $1.80 per pound and pays with a $10 bill. How much change does he get?Common Core State Standards for Mathematics, 7.EE.B.3: solve multi-step problems with positive and negative rational numbers in any form
Six gift bags each hold the same number of stickers and 2 pencils. The bags hold 54 items in all. How many stickers are in each bag?Common Core State Standards for Mathematics, 7.EE.B.4.a: solve word problems leading to equations of the form px + q = r and p(x + q) = r
The temperature is −4.5°C at 6 a.m. and rises 1.5 degrees each hour for 5 hours. What is the temperature then?Common Core State Standards for Mathematics, 7.EE.B.3: solve multi-step problems with positive and negative rational numbers in any form
What value of x makes (2/3)x − 4 = 10 true?Common Core State Standards for Mathematics, 7.EE.B.4.a: solve word problems leading to equations of the form px + q = r and p(x + q) = r
What value of x makes 4x + 7 = 39 true?Common Core State Standards for Mathematics, 7.EE.B.4.a: solve word problems leading to equations of the form px + q = r and p(x + q) = r
What value of x makes 5(x − 3) = 40 true?Common Core State Standards for Mathematics, 7.EE.B.4.a: solve word problems leading to equations of the form px + q = r and p(x + q) = r
Which expression is equivalent to (5x + 2) − (2x − 7)?Common Core State Standards for Mathematics, 7.EE.A.1: add, subtract, factor and expand linear expressions with rational coefficients
Which expression is equivalent to 1/3(9x − 12) + 2x?Common Core State Standards for Mathematics, 7.EE.A.1: add, subtract, factor and expand linear expressions with rational coefficients
Which expression is equivalent to 6(2x − 3) + 7x?Common Core State Standards for Mathematics, 7.EE.A.1: add, subtract, factor and expand linear expressions with rational coefficients
Which expression is equivalent to 28x + 42?Common Core State Standards for Mathematics, 7.EE.A.1: add, subtract, factor and expand linear expressions with rational coefficients
Which values of x make 4x − 9 > 19 true?Common Core State Standards for Mathematics, 7.EE.B.4.b: solve word problems leading to inequalities of the form px + q > r or px + q < r
Which values of x make −3x + 4 < 19 true?Common Core State Standards for Mathematics, 7.EE.B.4.b: solve word problems leading to inequalities of the form px + q > r or px + q < r
Geometry 16
A circle has a circumference of 18π centimeters. What is its area?Common Core State Standards for Mathematics, 7.G.B.4: know the formulas for the area and circumference of a circle and use them
A circle has a diameter of 12 inches. What is its area? Use 3.14 for π.Common Core State Standards for Mathematics, 7.G.B.4: know the formulas for the area and circumference of a circle and use them
A circle has a radius of 5 centimeters. What is its circumference? Use 3.14 for π.Common Core State Standards for Mathematics, 7.G.B.4: know the formulas for the area and circumference of a circle and use them
A drawing at a scale of 1 inch to 4 feet shows a wall 6 inches long. How long is the same wall in a drawing at a scale of 1 inch to 8 feet?Common Core State Standards for Mathematics, 7.G.A.1: solve problems involving scale drawings of geometric figures
A figure is a rectangle 12 meters by 5 meters with a triangle on top. The triangle has a base of 12 meters and a height of 6 meters. What is the area of the whole figure?Common Core State Standards for Mathematics, 7.G.B.6: solve problems involving area, volume and surface area
A plane cuts a right rectangular pyramid from its top point straight down to the base, at a right angle to the base. What shape is the cut face?Common Core State Standards for Mathematics, 7.G.A.3: describe the two-dimensional figures that result from slicing three-dimensional figures
A rectangular prism measures 6 inches by 4 inches by 2 inches. What is its surface area?Common Core State Standards for Mathematics, 7.G.B.6: solve problems involving area, volume and surface area
A right rectangular prism is sliced by a plane parallel to its base. What shape is the cross-section?Common Core State Standards for Mathematics, 7.G.A.3: describe the two-dimensional figures that result from slicing three-dimensional figures
A scale drawing of a room uses 1 centimeter for 2 meters. The drawing is 4 centimeters by 3 centimeters. What is the actual area of the room?Common Core State Standards for Mathematics, 7.G.A.1: solve problems involving scale drawings of geometric figures
Angles A and B are complementary. Angle A measures (4x + 10) degrees and angle B measures (2x + 8) degrees. What is the measure of angle A?Common Core State Standards for Mathematics, 7.G.B.5: use facts about supplementary, complementary, vertical and adjacent angles
The base of a triangular prism is a right triangle with legs of 6 centimeters and 8 centimeters. The prism is 10 centimeters long. What is its volume?Common Core State Standards for Mathematics, 7.G.B.6: solve problems involving area, volume and surface area
How many triangles of different sizes can be drawn with angles of 40°, 60° and 80°?Common Core State Standards for Mathematics, 7.G.A.2: draw geometric shapes with given conditions, with a focus on triangles
On a road map, 2 centimeters stand for 15 kilometers. Two towns are 7 centimeters apart on the map. How far apart are the towns?Common Core State Standards for Mathematics, 7.G.A.1: solve problems involving scale drawings of geometric figures
Two straight lines cross. One of the four angles measures 68°. What is the measure of an angle next to it?Common Core State Standards for Mathematics, 7.G.B.5: use facts about supplementary, complementary, vertical and adjacent angles
Two supplementary angles measure 3x degrees and (2x + 20) degrees. What is the value of x?Common Core State Standards for Mathematics, 7.G.B.5: use facts about supplementary, complementary, vertical and adjacent angles
Which set of three side lengths cannot form a triangle?Common Core State Standards for Mathematics, 7.G.A.2: draw geometric shapes with given conditions, with a focus on triangles
Statistics and Probability 14
A bag holds 5 red, 3 blue and 12 green marbles. One marble is drawn without looking. What is the probability that it is blue?Common Core State Standards for Mathematics, 7.SP.C.7.a: develop a uniform probability model and use it to find probabilities
A forecast gives the probability of snow tomorrow as 0.02. Which word describes snow tomorrow?Common Core State Standards for Mathematics, 7.SP.C.5: the probability of a chance event is a number between 0 and 1
A library wants to learn which kind of book its members like best. Which sample is most likely to represent all of the members?Common Core State Standards for Mathematics, 7.SP.A.1: a sample supports a generalization only if it is representative of the population
A plastic spoon is dropped 60 times and lands bowl up 42 times. Based on these results, what is the probability that it lands bowl up?Common Core State Standards for Mathematics, 7.SP.C.7.b: develop a probability model from observed frequencies
A player makes half of her free throws. Which simulation models one free throw?Common Core State Standards for Mathematics, 7.SP.C.8.c: design and use a simulation to generate frequencies for compound events
A spinner lands on blue with a probability of 3/10. About how many times should it land on blue in 250 spins?Common Core State Standards for Mathematics, 7.SP.C.6: approximate a probability from long-run relative frequency
A spinner with 4 equal sections is spun and a coin is flipped. How many outcomes are in the sample space?Common Core State Standards for Mathematics, 7.SP.C.8.b: represent sample spaces for compound events with lists, tables and tree diagrams
A survey about a new skate park asks only people who are at the current skate park. Why is the result a weak guide to what the town thinks?Common Core State Standards for Mathematics, 7.SP.A.1: a sample supports a generalization only if it is representative of the population
Cards numbered 1 to 8 lie face down, and one is picked without looking. What is the probability of picking a multiple of 3?Common Core State Standards for Mathematics, 7.SP.C.7.a: develop a uniform probability model and use it to find probabilities
Class A has a mean quiz score of 82 and class B has a mean of 76. The mean absolute deviation of each class is 3. The difference between the means is how many times the mean absolute deviation?Common Core State Standards for Mathematics, 7.SP.B.3: express the difference between two centers as a multiple of a measure of variability
In a random sample of 40 students, 14 walk to school. The school has 500 students. What is the best estimate of the number who walk?Common Core State Standards for Mathematics, 7.SP.A.2: use data from a random sample to draw inferences about a population
Random samples of two tomato plots are measured. Plot A has a median height of 30 inches and plot B has 24 inches. Both have an interquartile range of 4 inches. Which conclusion fits the data?Common Core State Standards for Mathematics, 7.SP.B.4: use measures of center and variability to compare two populations
Three random samples of 40 shoppers each find 22, 25 and 19 who bring their own bags. What do the three results show?Common Core State Standards for Mathematics, 7.SP.A.2: use data from a random sample to draw inferences about a population
Two fair coins are flipped. What is the probability of getting exactly one head?Common Core State Standards for Mathematics, 7.SP.C.8.a: the probability of a compound event is the fraction of outcomes in the sample space
How this list was compiled: Our own questions. Outline: the Common Core State Standards for Mathematics, grade 7, https://www.thecorestandards.org/Math/Content/7/introduction/, with the five domain pages (Ratios and Proportional Relationships, The Number System, Expressions and Equations, Geometry, Statistics and Probability), read 2026-10-10 there and in the standards’ own file, https://learning.ccsso.org/wp-content/uploads/2022/11/ADA-Compliant-Math-Standards.pdf; thecorestandards.org is an unofficial site that carries the same text by domain. Each question names the standard it practices and links to that domain page. Every answer is arithmetic or reasoning on the numbers the question prints, and each one was worked out again on 2026-10-10. Questions on circles say to use 3.14 for pi or keep pi in the answer. Licence: Own work. Questions, answer choices and explanations were written for this site. Nothing is copied or reworded from a state test, a released form, a sample item, a textbook or another practice test, and no example printed in the standards is used as a question.
How it works
Unofficial seventh grade math practice: 80 questions written for this page to the five domains of the Common Core grade 7 standards. It follows no state's test, so no test length or pass mark is implied.
Read the full guide
What the 80 questions cover
The Number System and Expressions and Equations have 17 questions each, Ratios and Proportional Relationships 16, Geometry 16, and Statistics and Probability 14.
Where seventh grade changes
A percent problem gains a second step, such as tax and then the total. A subtraction can end below zero. An inequality reverses when both sides are divided by a negative number. Those three ideas sit behind many of the wrong choices here, and each explanation ends with its standard, such as 7.RP.A.3 or 7.EE.B.4.b.
For a percent change, divide the change by the starting amount, not the new one.
The area of a circle uses the radius. If a question gives the diameter, halve it first.
Questions and answers
Is this a common core 7th grade math practice test?
Its questions are written to the Common Core grade 7 standards, and each one names the standard it practices. The questions are our own; the standards' authors did not write or review them.
Is there a 7th grade common core math practice test PDF?
The page prints as a paper test, and choosing Save as PDF in the print window keeps it as a file. The answer key is optional and prints after the questions.
Is this grade 7 math practice test for a state test?
It follows the Common Core grade 7 standards and no single test. For one test's own design, try the STAAR, MCAS, NC EOG or Smarter Balanced grade 7 pages.
What math do 7th graders learn in Common Core?
The standards name four critical areas: proportional relationships; operations with rational numbers and linear equations; scale drawings, area, surface area and volume; and drawing inferences about populations from samples. Probability is taught as well.