• 96 questions

Pre-Algebra Practice Test

Unofficial pre-algebra math practice in six topics, from integers to first equations, each answer worked out.

Which of these integers is the greatest?

Pick an answer, then press Check answer. Then you see Correct or Not quite, with the reason. Keys: A to D pick, Enter checks.

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Unofficial practice questions, not affiliated with any school, district or testing agency. Bank checked October 9, 2026.

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All 96 questions

Integers and order of operations 16

  • At dawn the temperature was −7°F. By noon it had risen 12 degrees. What was the temperature at noon? Common Core State Standards for Mathematics, 6.NS.C.5: positive and negative numbers describe quantities having opposite directions or values
  • Evaluate (4 + 6) · 3 − 5. Common Core State Standards for Mathematics, 5.OA.A.1: evaluate numerical expressions with parentheses, brackets or braces
  • Evaluate (−8)(7). Common Core State Standards for Mathematics, 7.NS.A.2: multiply and divide rational numbers
  • Evaluate (−9)(−6). Common Core State Standards for Mathematics, 7.NS.A.2: multiply and divide rational numbers
  • Evaluate 6 + 18 ÷ 3. Common Core State Standards for Mathematics, 6.EE.A.2.c: evaluate expressions at specific values of their variables, in the conventional order of operations
  • Evaluate 8 − 15. Common Core State Standards for Mathematics, 7.NS.A.1: add and subtract rational numbers
  • Evaluate 24 ÷ (8 − 2) + 7. Common Core State Standards for Mathematics, 5.OA.A.1: evaluate numerical expressions with parentheses, brackets or braces
  • Evaluate 40 − 4 · (2 + 5). Common Core State Standards for Mathematics, 5.OA.A.1: evaluate numerical expressions with parentheses, brackets or braces
  • Evaluate |−15| + |6|. Common Core State Standards for Mathematics, 6.NS.C.7.c: absolute value as distance from 0 on the number line
  • Evaluate −6 − 11. Common Core State Standards for Mathematics, 7.NS.A.1: add and subtract rational numbers
Show all 96 questions (86 more)

Integers and order of operations, continued

  • Evaluate −13 − (−20). Common Core State Standards for Mathematics, 7.NS.A.1.c: subtraction as adding the additive inverse; distance on the number line as the absolute value of a difference
  • Evaluate −14 + 9. Common Core State Standards for Mathematics, 7.NS.A.1: add and subtract rational numbers
  • Evaluate −45 ÷ (−5). Common Core State Standards for Mathematics, 7.NS.A.2: multiply and divide rational numbers
  • Evaluate −72 ÷ 8. Common Core State Standards for Mathematics, 7.NS.A.2: multiply and divide rational numbers
  • What is the distance between −4 and 9 on a number line? Common Core State Standards for Mathematics, 7.NS.A.1.c: subtraction as adding the additive inverse; distance on the number line as the absolute value of a difference
  • Which of these integers is the greatest? Common Core State Standards for Mathematics, 6.NS.C.7.a: inequality statements as the relative position of two numbers on a number line

Fractions, decimals and percents 16

  • 15 is 20% of what number? Common Core State Standards for Mathematics, 6.RP.A.3.c: find a percent of a quantity as a rate per 100, and find the whole from a part and the percent
  • 27 is what percent of 90? Common Core State Standards for Mathematics, 6.RP.A.3.c: find a percent of a quantity as a rate per 100, and find the whole from a part and the percent
  • Evaluate 0.4 · 0.7. Common Core State Standards for Mathematics, 6.NS.B.3: add, subtract, multiply and divide multi-digit decimals
  • Evaluate 2/3 + 1/4. Common Core State Standards for Mathematics, 5.NF.A.1: add and subtract fractions with unlike denominators
  • Evaluate 3/4 ÷ 3/8. Common Core State Standards for Mathematics, 6.NS.A.1: compute quotients of fractions
  • Evaluate 3/5 · 10/9. Common Core State Standards for Mathematics, 5.NF.B.4: multiply a fraction or whole number by a fraction
  • Evaluate 4.8 + 3.75. Common Core State Standards for Mathematics, 6.NS.B.3: add, subtract, multiply and divide multi-digit decimals
  • Evaluate 5/6 − 1/2. Common Core State Standards for Mathematics, 5.NF.A.1: add and subtract fractions with unlike denominators
  • Evaluate 6.2 − 1.85. Common Core State Standards for Mathematics, 6.NS.B.3: add, subtract, multiply and divide multi-digit decimals
  • Evaluate 7.2 ÷ 0.9. Common Core State Standards for Mathematics, 6.NS.B.3: add, subtract, multiply and divide multi-digit decimals
  • What is 35% of 140? Common Core State Standards for Mathematics, 6.RP.A.3.c: find a percent of a quantity as a rate per 100, and find the whole from a part and the percent
  • What is the greatest common factor of 56 and 98? Common Core State Standards for Mathematics, 6.NS.B.4: greatest common factor and least common multiple of two whole numbers
  • What is the least common multiple of 10 and 12? Common Core State Standards for Mathematics, 6.NS.B.4: greatest common factor and least common multiple of two whole numbers
  • Write 0.6 as a fraction in lowest terms. Common Core State Standards for Mathematics, 7.NS.A.2.d: convert a rational number to a decimal
  • Write 5/8 as a decimal. Common Core State Standards for Mathematics, 7.NS.A.2.d: convert a rational number to a decimal
  • Write 7/20 as a percent. Common Core State Standards for Mathematics, 6.RP.A.3.c: find a percent of a quantity as a rate per 100, and find the whole from a part and the percent

Ratios, rates and proportions 16

  • A $60 jacket is marked 25% off. 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 car travels 240 miles in 4 hours at a steady speed. What is its unit rate? Common Core State Standards for Mathematics, 6.RP.A.3.b: solve unit rate problems, including unit pricing and constant speed
  • A class has 12 boys and 18 girls. What is the ratio of boys to girls in simplest form? Common Core State Standards for Mathematics, 6.RP.A.1: use ratio language to describe a ratio relationship between two quantities
  • A diner leaves a 15% tip on a $32 meal. 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 hiker walks 3/4 mile in 1/2 hour. What is her unit rate? Common Core State Standards for Mathematics, 7.RP.A.1: compute unit rates associated with ratios of fractions
  • A price rises from $40 to $50. 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
  • A recipe uses 2 cups of flour for 3 dozen cookies. How much flour is needed for 9 dozen cookies? Common Core State Standards for Mathematics, 6.RP.A.3.a: make tables of equivalent ratios and find missing values
  • A sales tax of 6% is added to a $45 purchase. How much is the tax? Common Core State Standards for Mathematics, 7.RP.A.3: use proportional relationships to solve multistep ratio and percent problems
  • In a proportional relationship, x-values of 2, 4 and 6 pair with y-values of 7, 14 and 21. What is the constant of proportionality, y/x? Common Core State Standards for Mathematics, 7.RP.A.2.b: identify the constant of proportionality (unit rate)
  • On a map, 1 centimeter stands for 15 kilometers. Two lakes are 4.5 centimeters apart on the map. How far apart are the lakes? Common Core State Standards for Mathematics, 7.RP.A.2.c: represent proportional relationships by equations
  • Six oranges cost $7.50. At that rate, what does one orange cost? Common Core State Standards for Mathematics, 6.RP.A.3.b: solve unit rate problems, including unit pricing and constant speed
  • Solve the proportion 3/8 = 9/n. Common Core State Standards for Mathematics, 7.RP.A.2.c: represent proportional relationships by equations
  • Solve the proportion x/15 = 4/5. Common Core State Standards for Mathematics, 7.RP.A.2.c: represent proportional relationships by equations
  • There are 12 inches in a foot. How many inches are in 3.5 feet? Common Core State Standards for Mathematics, 6.RP.A.3.d: use ratio reasoning to convert measurement units
  • What is the constant of proportionality in the equation y = 7x? Common Core State Standards for Mathematics, 7.RP.A.2.b: identify the constant of proportionality (unit rate)
  • Which pair of ratios forms a proportion? Common Core State Standards for Mathematics, 7.RP.A.2.a: decide whether two quantities are in a proportional relationship

Exponents and square roots 16

  • √50 lies between which two whole numbers? Common Core State Standards for Mathematics, 8.NS.A.2: use rational approximations of irrational numbers
  • Evaluate (−2)⁵. Common Core State Standards for Mathematics, 7.NS.A.2: multiply and divide rational numbers
  • Evaluate 2⁵. Common Core State Standards for Mathematics, 6.EE.A.1: write and evaluate numerical expressions involving whole-number exponents
  • Evaluate 4⁻². Common Core State Standards for Mathematics, 8.EE.A.1: know and apply the properties of integer exponents
  • Evaluate 5³. Common Core State Standards for Mathematics, 6.EE.A.1: write and evaluate numerical expressions involving whole-number exponents
  • Evaluate 7⁰. Common Core State Standards for Mathematics, 8.EE.A.1: know and apply the properties of integer exponents
  • Evaluate 10⁴. Common Core State Standards for Mathematics, 6.EE.A.1: write and evaluate numerical expressions involving whole-number exponents
  • Evaluate √81. Common Core State Standards for Mathematics, 8.EE.A.2: square roots of small perfect squares and cube roots of small perfect cubes
  • Evaluate √121. Common Core State Standards for Mathematics, 8.EE.A.2: square roots of small perfect squares and cube roots of small perfect cubes
  • Evaluate ∛27. Common Core State Standards for Mathematics, 8.EE.A.2: square roots of small perfect squares and cube roots of small perfect cubes
  • Which choice gives every value of x that makes x² = 64 true? Common Core State Standards for Mathematics, 8.EE.A.2: square roots of small perfect squares and cube roots of small perfect cubes
  • Write (2³)² as a single power of 2. Common Core State Standards for Mathematics, 8.EE.A.1: know and apply the properties of integer exponents
  • Write 0.00056 in scientific notation. Common Core State Standards for Mathematics, 8.EE.A.4: perform operations with numbers expressed in scientific notation
  • Write 3.2 × 10⁴ in standard form. Common Core State Standards for Mathematics, 8.EE.A.4: perform operations with numbers expressed in scientific notation
  • Write 3² · 3³ as a single power of 3. Common Core State Standards for Mathematics, 8.EE.A.1: know and apply the properties of integer exponents
  • Write 5⁶ ÷ 5² as a single power of 5. Common Core State Standards for Mathematics, 8.EE.A.1: know and apply the properties of integer exponents

The coordinate plane 16

  • A rectangle has corners at (0, 0), (7, 0), (7, 3) and (0, 3). What is its area? Common Core State Standards for Mathematics, 6.G.A.3: draw polygons in the coordinate plane and find side lengths from coordinates
  • A rectangle has corners at (−2, 1), (4, 1), (4, 5) and (−2, 5). What is its perimeter? Common Core State Standards for Mathematics, 6.G.A.3: draw polygons in the coordinate plane and find side lengths from coordinates
  • From the point (−3, 2), move 5 units right and 4 units down. Where do you land? Common Core State Standards for Mathematics, 6.NS.C.6.c: find and position pairs of integers on a coordinate plane
  • How far apart are points A and B? (Picture: A coordinate grid from −5 to 5 with two marked points at the same height, 2 units above the horizontal axis. A is 3 units left of the vertical axis and B is 4 units right of it.) Common Core State Standards for Mathematics, 6.NS.C.8: graph points in all four quadrants and find distances between points that share a coordinate
  • In which quadrant is the point (5, −9)? Common Core State Standards for Mathematics, 6.NS.C.6.b: signs of the numbers in an ordered pair and the quadrants of the coordinate plane
  • In which quadrant is the point (−1, −7)? Common Core State Standards for Mathematics, 6.NS.C.6.b: signs of the numbers in an ordered pair and the quadrants of the coordinate plane
  • In which quadrant is the point (−6, 2)? Common Core State Standards for Mathematics, 6.NS.C.6.b: signs of the numbers in an ordered pair and the quadrants of the coordinate plane
  • The point (3, 5) is reflected across the x-axis. Where does it land? Common Core State Standards for Mathematics, 6.NS.C.6.b: signs of the numbers in an ordered pair and the quadrants of the coordinate plane
  • The point (−2, 6) is reflected across the y-axis. Where does it land? Common Core State Standards for Mathematics, 6.NS.C.6.b: signs of the numbers in an ordered pair and the quadrants of the coordinate plane
  • Start at the origin. Move 4 units left and 7 units up. Where are you? Common Core State Standards for Mathematics, 6.NS.C.6.c: find and position pairs of integers on a coordinate plane
  • Three corners of a rectangle are (1, 1), (1, 5) and (7, 5). What is the fourth corner? Common Core State Standards for Mathematics, 6.G.A.3: draw polygons in the coordinate plane and find side lengths from coordinates
  • What are the coordinates of point P? (Picture: A coordinate grid from −5 to 5 with one marked point, P. It is 4 units left of the vertical axis and 3 units above the horizontal axis.) Common Core State Standards for Mathematics, 6.NS.C.6.c: find and position pairs of integers on a coordinate plane
  • What are the coordinates of point Q? (Picture: A coordinate grid from −5 to 5 with one marked point, Q. It is on the vertical axis, 3 units below the horizontal axis.) Common Core State Standards for Mathematics, 6.NS.C.6.c: find and position pairs of integers on a coordinate plane
  • What is the distance between the points (4, 6) and (4, −3)? Common Core State Standards for Mathematics, 6.NS.C.8: graph points in all four quadrants and find distances between points that share a coordinate
  • Which of these four points is on the x-axis? Common Core State Standards for Mathematics, 6.NS.C.6.c: find and position pairs of integers on a coordinate plane
  • Which of these four points is on the y-axis? Common Core State Standards for Mathematics, 6.NS.C.6.c: find and position pairs of integers on a coordinate plane

First expressions and one-step equations 16

  • Eight pencils cost $2.40 in all. The equation 8p = 2.40 gives the price p of one pencil. What is p? Common Core State Standards for Mathematics, 6.EE.B.7: solve equations of the form x + p = q and px = q
  • Evaluate 7n when n = 9. Common Core State Standards for Mathematics, 6.EE.A.2.c: evaluate expressions at specific values of their variables, in the conventional order of operations
  • Evaluate 20 − 2a when a = 6. Common Core State Standards for Mathematics, 6.EE.A.2.c: evaluate expressions at specific values of their variables, in the conventional order of operations
  • Evaluate x + 12 when x = 30. Common Core State Standards for Mathematics, 6.EE.A.2.c: evaluate expressions at specific values of their variables, in the conventional order of operations
  • Jo has b books and buys 6 more. Which expression gives how many books she has now? Common Core State Standards for Mathematics, 6.EE.B.6: use variables to represent numbers and write expressions when solving a problem
  • Simplify 2c + 7c. Common Core State Standards for Mathematics, 6.EE.A.3: apply the properties of operations to generate equivalent expressions
  • Solve 5n = 60. Common Core State Standards for Mathematics, 6.EE.B.7: solve equations of the form x + p = q and px = q
  • Solve a/6 = 7. Common Core State Standards for Mathematics, 6.EE.B.7: solve equations of the form x + p = q and px = q
  • Solve x + 8 = 21. Common Core State Standards for Mathematics, 6.EE.B.7: solve equations of the form x + p = q and px = q
  • Solve y − 14 = 30. Common Core State Standards for Mathematics, 6.EE.B.7: solve equations of the form x + p = q and px = q
  • Which expression is equivalent to 2(n + 6)? Common Core State Standards for Mathematics, 6.EE.A.3: apply the properties of operations to generate equivalent expressions
  • Which expression means "4 times a number y"? Common Core State Standards for Mathematics, 6.EE.A.2.a: write expressions that record operations with numbers and with letters standing for numbers
  • Which expression means "9 more than a number x"? Common Core State Standards for Mathematics, 6.EE.A.2.a: write expressions that record operations with numbers and with letters standing for numbers
  • Which expression means "a number n divided by 3"? Common Core State Standards for Mathematics, 6.EE.A.2.a: write expressions that record operations with numbers and with letters standing for numbers
  • Which inequality means "x is greater than 5"? Common Core State Standards for Mathematics, 6.EE.B.8: write an inequality of the form x > c or x < c for a constraint or condition
  • Which value of x makes 3x = 27 true? Common Core State Standards for Mathematics, 6.EE.B.5: use substitution to determine whether a number makes an equation or inequality true

How this list was compiled: Our own questions. The six topics follow the grade 6 to grade 8 standards of the Common Core State Standards for Mathematics for the number system, ratios and proportional relationships, and expressions and equations, with three grade 5 standards on order of operations and fractions and one grade 6 geometry standard on polygons in the coordinate plane (https://www.thecorestandards.org/Math/, read 2026-10-09). Each question names the standard it practices and links to that standard's page. Every answer is arithmetic on what the question prints, worked out a second time on 2026-10-09. Licence: Own work. Questions, answer choices, explanations and the three grid pictures were written and drawn for this site. Nothing is copied or reworded from a state test, a placement test, a released form, a textbook or another practice test.

How it works

This free pre-algebra practice test has 96 questions of our own, 16 in each topic. Answer on screen or print it with a key. It is not a state or school test.

Read the full guide

A test of 20, scored by topic

Exam mode draws 20 questions and scores each topic, so it works as a pre algebra diagnostic test: the result names the topic where you missed most. The 20 is our number, not any exam's.

Where the topics come from

They follow grades 6 to 8 of the Common Core State Standards for Mathematics, read October 9, 2026: the number system, ratios and proportional relationships, and expressions and equations. Each question names its standard.

  • Work each question on paper first; the numbers were chosen to come out without a calculator.
  • Two negatives multiply or divide to a positive; one negative and one positive give a negative.

Questions and answers

What is on a pre-algebra test?

Each school writes its own pre algebra exam. This page covers integers and order of operations, fractions, decimals and percents, ratios and proportions, exponents and roots, the coordinate plane and one-step equations. Five of the six topics are number work.

Is this a pre-algebra practice test with answers?

Yes. Every question shows the right answer and its steps as soon as you choose. On paper or as a PDF, Print the question sheet lists 20 questions, and one tick adds the answer key.

Is this a pre-algebra practice test for 7th grade?

It suits 7th grade well: most questions practice grade 6 and grade 7 standards. The exponent rules, roots and scientific notation are grade 8 standards, so a 7th grader may leave that topic for later.

Can I use this as a pre-algebra pretest?

As practice, yes. Take the 20-question test before the course and again after it, and compare the scores by topic. A school's own pretest or placement test is written and scored by the school, and this page copies none.

Can I take a pre-algebra quiz on one topic?

Yes. Choose a topic and answer its 16 practice pre algebra questions, with the working after each answer.

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