• 60 questions

ACT Math Practice Test

Unofficial ACT math prep: questions sorted by the reporting categories ACT publishes for its mathematics section.

See all 60 with answers
Vectors u = ⟨3, −2⟩ and v = ⟨−1, 5⟩. What is 2u + v?

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

Print covers the next 45 questions. Share this set copies a link to the same questions in the same order.

Exam mode: 45 questions, 50 minutes.

More options

Unofficial practice questions, not affiliated with ACT Education Corp. Bank checked October 7, 2026.

Next step ACT practice test: all four sectionsACT English practice test

All 60 questions with answers

Number and quantity 7

  • For i² = −1, what is (3 + 2i)(1 − 4i)? Answer: 11 − 10i. Source: ACT, Mathematics Test Description: Preparing for Higher Math: Number & Quantity (10–12% of the section), complex numbers. The answer is worked out from the numbers in the question.
  • For x ≠ 0, which expression is equal to (x³)⁴ · x⁻⁵? Answer: x⁷. Source: ACT, Mathematics Test Description: Preparing for Higher Math: Number & Quantity (10–12% of the section), integer exponents. The answer is worked out from the numbers in the question.
  • Matrix A has rows (2, 1) and (0, 3). Matrix B has rows (1, 4) and (2, 0). What is the entry in row 1, column 2 of the product AB? Answer: 8. Source: ACT, Mathematics Test Description: Preparing for Higher Math: Number & Quantity (10–12% of the section), matrices. The answer is worked out from the numbers in the question.
  • The number √50 lies between which two consecutive whole numbers? Answer: 7 and 8. Source: ACT, Mathematics Test Description: Preparing for Higher Math: Number & Quantity (10–12% of the section), real numbers. The answer is worked out from the numbers in the question.
Show all 60 questions (56 more)

Number and quantity, continued

  • Vectors u = ⟨3, −2⟩ and v = ⟨−1, 5⟩. What is 2u + v? Answer: ⟨5, 1⟩. Source: ACT, Mathematics Test Description: Preparing for Higher Math: Number & Quantity (10–12% of the section), vectors. The answer is worked out from the numbers in the question.
  • What is the value of 3⁻²? Answer: 1/9. Source: ACT, Mathematics Test Description: Preparing for Higher Math: Number & Quantity (10–12% of the section), integer exponents. The answer is worked out from the numbers in the question.
  • Which number is equal to 8^(2/3)? Answer: 4. Source: ACT, Mathematics Test Description: Preparing for Higher Math: Number & Quantity (10–12% of the section), rational exponents. The answer is worked out from the numbers in the question.

Algebra 11

  • Adult tickets cost $9 and child tickets cost $5. A family buys 2 adult tickets and some child tickets and pays $43 in all. How many child tickets did the family buy? Answer: 5. Source: ACT, Mathematics Test Description: Preparing for Higher Math: Algebra (17–20% of the section), linear equations in context. Also a Modeling question. The answer is worked out from the numbers in the question.
  • The equation x² − 6x + k = 0 has exactly one real solution. What is k? Answer: 9. Source: ACT, Mathematics Test Description: Preparing for Higher Math: Algebra (17–20% of the section), quadratic equations. The answer is worked out from the numbers in the question.
  • For what value of x is 2^(x + 1) = 32? Answer: 4. Source: ACT, Mathematics Test Description: Preparing for Higher Math: Algebra (17–20% of the section), exponential equations. The answer is worked out from the numbers in the question.
  • For x ≠ −2 and x ≠ −3, which expression is equal to (x² − 9)/(x² + 5x + 6)? Answer: (x − 3)/(x + 2). Source: ACT, Mathematics Test Description: Preparing for Higher Math: Algebra (17–20% of the section), rational expressions. The answer is worked out from the numbers in the question.
  • If 2x + y = 11 and x − y = 4, what is x? Answer: 5. Source: ACT, Mathematics Test Description: Preparing for Higher Math: Algebra (17–20% of the section), systems of equations. The answer is worked out from the numbers in the question.
  • Solve 7x − 9 = 3x + 15. Answer: x = 6. Source: ACT, Mathematics Test Description: Preparing for Higher Math: Algebra (17–20% of the section), linear equations. The answer is worked out from the numbers in the question.
  • Solve √(x + 6) = 5. Answer: x = 19. Source: ACT, Mathematics Test Description: Preparing for Higher Math: Algebra (17–20% of the section), radical equations. The answer is worked out from the numbers in the question.
  • What are the solutions of x² − 7x + 10 = 0? Answer: x = 2 and x = 5. Source: ACT, Mathematics Test Description: Preparing for Higher Math: Algebra (17–20% of the section), quadratic equations. The answer is worked out from the numbers in the question.
  • What is the slope of the line 4x − 2y = 10? Answer: 2. Source: ACT, Mathematics Test Description: Preparing for Higher Math: Algebra (17–20% of the section), graphs of linear equations. The answer is worked out from the numbers in the question.
  • Which expression is equal to (x + 4)(x − 9)? Answer: x² − 5x − 36. Source: ACT, Mathematics Test Description: Preparing for Higher Math: Algebra (17–20% of the section), polynomial expressions. The answer is worked out from the numbers in the question.
  • Which values of x satisfy −3x + 4 > 19? Answer: x < −5. Source: ACT, Mathematics Test Description: Preparing for Higher Math: Algebra (17–20% of the section), linear inequalities. The answer is worked out from the numbers in the question.

Functions 11

  • A culture of bacteria is modeled by P(t) = 500 · 2^(t/3), where t is the time in hours. By the model, how many bacteria are there after 9 hours? Answer: 4,000. Source: ACT, Mathematics Test Description: Preparing for Higher Math: Functions (17–20% of the section), exponential functions. Also a Modeling question. The answer is worked out from the numbers in the question.
  • A function is defined as f(x) = x + 5 when x < 2 and f(x) = x² when x ≥ 2. What is f(2) + f(−1)? Answer: 8. Source: ACT, Mathematics Test Description: Preparing for Higher Math: Functions (17–20% of the section), piecewise functions. The answer is worked out from the numbers in the question.
  • For real numbers, what is the domain of f(x) = √(x − 7)? Answer: x ≥ 7. Source: ACT, Mathematics Test Description: Preparing for Higher Math: Functions (17–20% of the section), radical functions. The answer is worked out from the numbers in the question.
  • The graph of a linear function f passes through (0, −2) and (3, 4). What is f(5)? Answer: 8. Source: ACT, Mathematics Test Description: Preparing for Higher Math: Functions (17–20% of the section), linear functions. The answer is worked out from the numbers in the question.
  • How is the graph of y = (x − 4)² + 3 related to the graph of y = x²? Answer: It is moved 4 units right and 3 units up. Source: ACT, Mathematics Test Description: Preparing for Higher Math: Functions (17–20% of the section), translating functions. The answer is worked out from the numbers in the question.
  • How many real zeros does f(x) = x(x − 3)(x² + 4) have? Answer: 2. Source: ACT, Mathematics Test Description: Preparing for Higher Math: Functions (17–20% of the section), polynomial functions. The answer is worked out from the numbers in the question.
  • If f(x) = (2x − 1)/3, which expression is f⁻¹(x)? Answer: (3x + 1)/2. Source: ACT, Mathematics Test Description: Preparing for Higher Math: Functions (17–20% of the section), inverse functions. The answer is worked out from the numbers in the question.
  • If f(x) = 2x + 3 and g(x) = x², what is g(f(1))? Answer: 25. Source: ACT, Mathematics Test Description: Preparing for Higher Math: Functions (17–20% of the section), composition of functions. The answer is worked out from the numbers in the question.
  • If f(x) = 2x² − 3x + 4, what is f(−3)? Answer: 31. Source: ACT, Mathematics Test Description: Preparing for Higher Math: Functions (17–20% of the section), function notation. The answer is worked out from the numbers in the question.
  • What is log₂ 64? Answer: 6. Source: ACT, Mathematics Test Description: Preparing for Higher Math: Functions (17–20% of the section), logarithmic functions. The answer is worked out from the numbers in the question.
  • What is the x-coordinate of the vertex of the parabola y = x² − 8x + 5? Answer: 4. Source: ACT, Mathematics Test Description: Preparing for Higher Math: Functions (17–20% of the section), features of graphs. The answer is worked out from the numbers in the question.

Geometry 11

  • A circle has a diameter of 10. What is its area? Answer: 25π. Source: ACT, Mathematics Test Description: Preparing for Higher Math: Geometry (17–20% of the section), circles. The answer is worked out from the numbers in the question.
  • A circle has the equation (x − 2)² + (y + 5)² = 49. What are its center and radius? Answer: Center (2, −5), radius 7. Source: ACT, Mathematics Test Description: Preparing for Higher Math: Geometry (17–20% of the section), equations of conic sections. The answer is worked out from the numbers in the question.
  • A rectangular box measures 4 by 5 by 6. What is its total surface area? Answer: 148. Source: ACT, Mathematics Test Description: Preparing for Higher Math: Geometry (17–20% of the section), surface area of solids. The answer is worked out from the numbers in the question.
  • In a circle of radius 12, how long is an arc whose central angle is 60°? Answer: 4π. Source: ACT, Mathematics Test Description: Preparing for Higher Math: Geometry (17–20% of the section), circles. The answer is worked out from the numbers in the question.
  • In a right triangle, the side opposite angle A is 8 units long and the hypotenuse is 17. What is cos A? Answer: 15/17. Source: ACT, Mathematics Test Description: Preparing for Higher Math: Geometry (17–20% of the section), trigonometric ratios. The answer is worked out from the numbers in the question.
  • The legs of a right triangle are 10 and 24 units long. How long is the hypotenuse? Answer: 26. Source: ACT, Mathematics Test Description: Preparing for Higher Math: Geometry (17–20% of the section), right triangles. The answer is worked out from the numbers in the question.
  • Triangles ABC and DEF are similar, with AB matching DE and BC matching EF. If AB = 6, BC = 9 and DE = 10, what is EF? Answer: 15. Source: ACT, Mathematics Test Description: Preparing for Higher Math: Geometry (17–20% of the section), similarity. The answer is worked out from the numbers in the question.
  • Two angles of a triangle measure 38° and 79°. What is the measure of the third angle? Answer: 63°. Source: ACT, Mathematics Test Description: Preparing for Higher Math: Geometry (17–20% of the section), triangles. The answer is worked out from the numbers in the question.
  • What is the distance between the points (−2, 1) and (4, 9)? Answer: 10. Source: ACT, Mathematics Test Description: Preparing for Higher Math: Geometry (17–20% of the section), coordinate geometry. The answer is worked out from the numbers in the question.
  • What is the measure of each interior angle of a regular hexagon? Answer: 120°. Source: ACT, Mathematics Test Description: Preparing for Higher Math: Geometry (17–20% of the section), polygons. The answer is worked out from the numbers in the question.
  • What is the volume of a right circular cylinder with radius 3 and height 7? Answer: 63π. Source: ACT, Mathematics Test Description: Preparing for Higher Math: Geometry (17–20% of the section), volume of solids. The answer is worked out from the numbers in the question.

Statistics and probability 8

  • A bag holds 5 red, 3 blue and 2 green marbles. One marble is drawn at random. What is the probability that it is not blue? Answer: 7/10. Source: ACT, Mathematics Test Description: Preparing for Higher Math: Statistics & Probability (12–15% of the section), probability. The answer is worked out from the numbers in the question.
  • A line of best fit relating hours studied, x, to test score, y, is y = 6x + 52. By this model, how many points higher is the predicted score for 5 hours of study than for 2 hours? Answer: 18. Source: ACT, Mathematics Test Description: Preparing for Higher Math: Statistics & Probability (12–15% of the section), relationships in bivariate data. Also a Modeling question. The answer is worked out from the numbers in the question.
  • A school wants to estimate what share of all its students walk to school. Which sample is most likely to give an unbiased estimate? Answer: 50 students picked at random from the full enrollment list. Source: ACT, Mathematics Test Description: Preparing for Higher Math: Statistics & Probability (12–15% of the section), data collection methods. The answer is worked out from the numbers in the question.
  • How many different 3-letter arrangements can be made from the letters A, B, C, D and E if no letter is used twice? Answer: 60. Source: ACT, Mathematics Test Description: Preparing for Higher Math: Statistics & Probability (12–15% of the section), counting. The answer is worked out from the numbers in the question.
  • The mean score of 20 students on a quiz is 78. A 21st student takes the quiz and scores 99. What is the new mean? Answer: 79. Source: ACT, Mathematics Test Description: Preparing for Higher Math: Statistics & Probability (12–15% of the section), center of a distribution. The answer is worked out from the numbers in the question.
  • Two fair six-sided dice are rolled. What is the probability that the two numbers add to 9? Answer: 1/9. Source: ACT, Mathematics Test Description: Preparing for Higher Math: Statistics & Probability (12–15% of the section), sample spaces. The answer is worked out from the numbers in the question.
  • What is the mean of 4, 9, 7, 12 and 8? Answer: 8. Source: ACT, Mathematics Test Description: Preparing for Higher Math: Statistics & Probability (12–15% of the section), center of a distribution. The answer is worked out from the numbers in the question.
  • What is the median of 3, 11, 5, 8, 20 and 6? Answer: 7. Source: ACT, Mathematics Test Description: Preparing for Higher Math: Statistics & Probability (12–15% of the section), center of a distribution. The answer is worked out from the numbers in the question.

Integrating essential skills 12

  • A car travels 150 miles in 2.5 hours. At the same speed, how far does it travel in 4 hours? Answer: 240 miles. Source: ACT, Mathematics Test Description: Integrating Essential Skills (20% of the section), rates. The answer is worked out from the numbers in the question.
  • A cube has a volume of 64 cubic centimeters. What is its total surface area, in square centimeters? Answer: 96. Source: ACT, Mathematics Test Description: Integrating Essential Skills (20% of the section), volume and surface area. The answer is worked out from the numbers in the question.
  • A full tank holds 240 gallons. Water drains out at 8 gallons a minute while a hose adds 3 gallons a minute. How many minutes pass before the tank is empty? Answer: 48. Source: ACT, Mathematics Test Description: Integrating Essential Skills (20% of the section), rates in chains of steps. Also a Modeling question. The answer is worked out from the numbers in the question.
  • A recipe uses 3 cups of flour to make 8 servings. How many cups of flour are needed for 20 servings? Answer: 7.5. Source: ACT, Mathematics Test Description: Integrating Essential Skills (20% of the section), proportional relationships. The answer is worked out from the numbers in the question.
  • A rectangle has a perimeter of 36, and its length is twice its width. What is its area? Answer: 72. Source: ACT, Mathematics Test Description: Integrating Essential Skills (20% of the section), area. The answer is worked out from the numbers in the question.
  • A shop mixes 12 pounds of nuts that cost $8 a pound with 18 pounds of nuts that cost $3 a pound. What does the mix cost per pound? Answer: $5.00. Source: ACT, Mathematics Test Description: Integrating Essential Skills (20% of the section), average and median. The answer is worked out from the numbers in the question.
  • A store raises the price of a $50 item by 20%, then takes 20% off the new price. What is the final price? Answer: $48. Source: ACT, Mathematics Test Description: Integrating Essential Skills (20% of the section), percentages in chains of steps. The answer is worked out from the numbers in the question.
  • A tent priced at $140 is on sale for 15% off. What is the sale price? Answer: $119. Source: ACT, Mathematics Test Description: Integrating Essential Skills (20% of the section), percentages. The answer is worked out from the numbers in the question.
  • On a map, 1 inch stands for 12 miles. Two towns are 3.5 inches apart on the map. How far apart are the towns? Answer: 42 miles. Source: ACT, Mathematics Test Description: Integrating Essential Skills (20% of the section), proportional relationships. The answer is worked out from the numbers in the question.
  • The price of a book rises from $40 to $46. What is the percent increase? Answer: 15%. Source: ACT, Mathematics Test Description: Integrating Essential Skills (20% of the section), percentages. The answer is worked out from the numbers in the question.
  • Which number is equal to 4.2 × 10⁻³? Answer: 0.0042. Source: ACT, Mathematics Test Description: Integrating Essential Skills (20% of the section), expressing numbers in different ways. The answer is worked out from the numbers in the question.
  • Which percent is equal to 0.035? Answer: 3.5%. Source: ACT, Mathematics Test Description: Integrating Essential Skills (20% of the section), expressing numbers in different ways. The answer is worked out from the numbers in the question.

How this list was compiled: Our own questions, written to ACT's published description of the mathematics section (https://www.act.org/content/act/en/products-and-services/the-act/test-preparation/description-of-math-test.html, read 2026-10-06): Preparing for Higher Math 80% (Number & Quantity 10–12%, Algebra 17–20%, Functions 17–20%, Geometry 17–20%, Statistics & Probability 12–15%) and Integrating Essential Skills 20%; Modeling questions are counted inside those categories. The bank holds 7, 11, 11, 11, 8 and 12 questions. Every answer is arithmetic, algebra or geometry on what the question itself prints, and each was worked out a second time on 2026-10-07. Section length (45 questions, 50 minutes; 41 scored and 4 field-test questions) from https://www.act.org/content/act/en/products-and-services/the-act.html and https://www.act.org/content/act/en/products-and-services/the-act/scores/understanding-your-scores.html, read 2026-10-06. Licence: Questions, choices and explanations are original work of this site.

How it works

This free ACT math practice test has 60 questions of our own, spread like ACT's published reporting categories, each with its working. It is unofficial and is not affiliated with, endorsed by or sponsored by ACT Education Corp.

Read the full guide

The six categories

ACT's description of the mathematics section, read October 6, 2026, gives each of six categories a share: number and quantity (10–12%), algebra, functions and geometry (17–20% each), statistics and probability (12–15%) and integrating essential skills (20%). This bank holds 7, 11, 11, 11, 8 and 12 questions.

Timing

The real section has 45 questions in 50 minutes; ACT's score page counts 41 as scored and 4 as field-test questions. Exam mode uses the same 45 and 50, for a full ACT math practice test.

Reading the notation

Whole-number powers are written x² or x⁻⁵. Other exponents use a caret, as in 2^(x + 1) or 8^(2/3). √ means a square root, log₂ a base-2 logarithm, i the imaginary unit and ⟨3, −2⟩ a vector.

  • ACT takes no points off for a wrong answer, so answer every question.
  • A calculator is allowed on the math section only, and ACT says every problem can be solved without one.

Questions and answers

Is this ACT math practice test the real exam?

No. Every question is our own, written to ACT's published description of the section. None is copied or reworded from a real test or an official sample question, and a score here does not predict a score there.

Is this an ACT math practice test with answers?

Yes. In practice mode each answer is marked at once and the working is shown under it. Exam mode holds the answers back until the end, then lists every question you missed with its working.

Is there a printable ACT math practice test, or an ACT mathematics practice test PDF?

Yes. Print the question sheet puts these questions on paper, with an answer key if you tick it. Choose Save as PDF in the print window to keep the file.

How is the ACT math section scored?

ACT counts the questions you answer right and converts that number to a score from 1 to 36. The math score is also one of the three that are averaged into the Composite, with English and reading.

More tests

Show 7 more

Browse Civics and Law