• 100 questions

ALEKS Math Placement Test Practice

Fractions, equations, factoring, functions, logarithms and trigonometry: unofficial practice with every answer worked out.

What is 3/8 + 5/6?

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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Exam mode: 25 questions, no time limit.

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Unofficial practice questions, not affiliated with McGraw Hill. Bank checked October 7, 2026.

The real test: ALEKS PPL Placement Assessment

Questions
25 or fewer. The assessment is adaptive, so the questions depend on your answers.
Question kind
Open response: no answer choices to pick from.
Covers
314 topics; students are placed anywhere from Basic Math to Calculus.
Time
The page for high schools says the whole assessment takes 90 minutes to complete.
Attempts
Up to five.
Learning module
A personalized Prep and Learning Module, with 12 months of access.

Checked October 7, 2026 against McGraw Hill's ALEKS Placement, Preparation and Learning page and its ALEKS PPL page for high schools. Rules change, so confirm with the agency itself before your test.

McGraw Hill's ALEKS PPL page

All 100 questions

Real numbers: fractions, percents, signed numbers 10

  • 18 is what percent of 45? McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Real Numbers, Percents and Proportions
  • A jacket priced at $80 is marked 35% off. What is the sale price? McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Real Numbers, Percents and Proportions
  • After a 20% discount, a pair of shoes costs $60. What was the original price? McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Real Numbers, Percents and Proportions
  • On a map, 2 inches stand for 25 miles. How many miles do 7 inches stand for? McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Real Numbers, Percents and Proportions
  • Solve the proportion x/12 = 15/20. McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Real Numbers, Percents and Proportions
  • What is 3/8 + 5/6? McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Real Numbers, Fractions
  • What is 5/6 ÷ 10/9? McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Real Numbers, Fractions
  • What is 6 − 2(3 − 5)²? McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Real Numbers, Signed Numbers
  • What is −8 − (−3) + (−6)? McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Real Numbers, Signed Numbers
  • Which of these fractions is the greatest? McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Real Numbers, Fractions
Show all 100 questions (90 more)

Equations and inequalities 9

  • A gym charges a $40 sign-up fee plus $25 a month. Dana has paid $265 in all. How many months has she paid for? McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Equations and Inequalities, Linear Equations
  • Solve 3(x + 2) ≤ 5x − 4. McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Equations and Inequalities, Linear Inequalities
  • Solve 4x − 9 = 19. McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Equations and Inequalities, Linear Equations
  • Solve 5(x − 2) = 3x + 8. McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Equations and Inequalities, Linear Equations
  • Solve P = 2L + 2W for W. McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Equations and Inequalities, Linear Equations
  • Solve x/3 + x/4 = 14. McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Equations and Inequalities, Linear Equations
  • Solve |2x − 1| = 7. McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Equations and Inequalities, Absolute Value Equations and Inequalities
  • Solve |x + 2| < 5. McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Equations and Inequalities, Absolute Value Equations and Inequalities
  • Solve −2x + 5 > 11. McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Equations and Inequalities, Linear Inequalities

Exponents and polynomials 15

  • Expand (3x − 4)². McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Exponents and Polynomials, Polynomial Expressions
  • Factor 4x³ − 36x completely. McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Exponents and Polynomials, Factoring
  • Factor 6x² + 7x − 3. McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Exponents and Polynomials, Factoring
  • Factor x² − 5x − 24. McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Exponents and Polynomials, Factoring
  • How many real solutions does 2x² − 3x + 5 = 0 have? McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Exponents and Polynomials, Quadratic Equations
  • Multiply (2x − 3)(x + 5). McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Exponents and Polynomials, Polynomial Expressions
  • Simplify (2x³)⁴. McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Exponents and Polynomials, Properties of Exponents
  • Simplify (3a²b)(−4ab³). McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Exponents and Polynomials, Properties of Exponents
  • Simplify (3x² − 5x + 2) − (x² + 4x − 6). McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Exponents and Polynomials, Polynomial Expressions
  • Simplify (x⁵y²)/(x²y⁶), written with positive exponents. McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Exponents and Polynomials, Properties of Exponents
  • Solve (x − 4)² = 9. McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Exponents and Polynomials, Quadratic Equations
  • Solve x² + 2x − 15 = 0. McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Exponents and Polynomials, Quadratic Equations
  • Solve x² − 6x + 7 = 0. McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Exponents and Polynomials, Quadratic Equations
  • What is (3 × 10⁴)(5 × 10⁻⁷) in scientific notation? McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Exponents and Polynomials, Scientific Notation
  • What is 4⁻²? McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Exponents and Polynomials, Properties of Exponents

Lines and systems 11

  • A cafe sells coffee for $3 and tea for $2. One morning it sells 50 drinks for $128. How many coffees did it sell? McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Lines and Systems, Systems of Linear Equations
  • Solve the system x + y = 7 and 2x − y = 8. McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Lines and Systems, Systems of Linear Equations
  • Solve the system y = 2x − 1 and 3x + 2y = 12. McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Lines and Systems, Systems of Linear Equations
  • What is the slope of a line perpendicular to y = (2/5)x − 1? McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Lines and Systems, Equations of Lines
  • What is the slope of the line 3x + 4y = 8? McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Lines and Systems, Equations of Lines
  • What is the slope of the line through (−2, 5) and (4, −4)? McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Lines and Systems, Equations of Lines
  • Which equation is the line through (0, −3) and (4, 5)? McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Lines and Systems, Equations of Lines
  • Which equation is the line with slope −2 through the point (3, 1)? McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Lines and Systems, Equations of Lines
  • Which line is parallel to y = 3x − 4 and passes through (2, 1)? McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Lines and Systems, Equations of Lines
  • Which point is a solution of the inequality y < 3x − 4? McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Lines and Systems, Graphing Linear Inequalities
  • Which point lies on the line 2x − 3y = 12? McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Lines and Systems, Ordered Pairs

Functions and graphs 12

  • A function is defined by f(x) = 2x + 1 when x < 3 and f(x) = x² − 4 when x ≥ 3. What is f(3)? McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Functions and Graphs, Sets, Relations, and Functions
  • A relation contains the pairs (1, 4), (2, 5), (3, 4) and (5, 7). What is its range? McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Functions and Graphs, Sets, Relations, and Functions
  • The graph of y = x² is shifted 4 units left and 1 unit up. Which equation is the new graph? McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Functions and Graphs, Graphs and Transformations
  • The graph of y = |x| is reflected over the x-axis and then moved up 3 units. Which equation is the new graph? McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Functions and Graphs, Graphs and Transformations
  • If f(x) = 3x − 1 and g(x) = x² + 2, what is f(g(2))? McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Functions and Graphs, Combining Functions; Composite Functions; Inverse Functions
  • If f(x) = x² − 3x + 2, what is f(−2)? McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Functions and Graphs, Sets, Relations, and Functions
  • What are the x-intercepts of y = x² − x − 12? McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Functions and Graphs, Graphs and Transformations
  • What are the zeros of f(x) = x(x − 2)(x + 5)? McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Functions and Graphs, Polynomial Functions
  • What is the intersection of the intervals [−2, 5) and (1, 8]? McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Functions and Graphs, Sets, Relations, and Functions
  • What is the inverse of f(x) = 4x + 8? McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Functions and Graphs, Combining Functions; Composite Functions; Inverse Functions
  • What is the vertex of the parabola y = (x + 1)² − 4? McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Functions and Graphs, Graphs and Transformations
  • What is the vertex of the parabola y = x² + 4x − 1? McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Functions and Graphs, Graphs and Transformations

Rational expressions 10

  • Add 3/x + 2/(x + 1). McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Rational Expressions, Rational Expressions
  • For which value of x is (x + 2)/(x − 5) undefined? McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Rational Expressions, Rational Expressions
  • Simplify (6x²)/(5y) × (10y²)/(3x). McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Rational Expressions, Rational Expressions
  • Simplify (x² − 9)/(x² + 5x + 6). McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Rational Expressions, Rational Expressions
  • Simplify the complex fraction (1/2 + 1/3)/(1/4). McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Rational Expressions, Rational Expressions
  • Solve 1/x + 1/3 = 1/2. McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Rational Expressions, Rational Equations
  • Solve 6/x = 3/(x − 2). McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Rational Expressions, Rational Equations
  • What is the remainder when x² + 3x − 5 is divided by x − 2? McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Rational Expressions, Rational Expressions
  • Which line is the vertical asymptote of f(x) = 3/(x + 4)? McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Rational Expressions, Rational Functions
  • y varies inversely with x, and y = 12 when x = 3. What is y when x = 9? McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Rational Expressions, Applications of Rational Expressions

Radical expressions 9

  • Rationalize the denominator of 10/√5. McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Radical Expressions, Radical Expressions
  • Simplify (3 + √2)(3 − √2). McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Radical Expressions, Radical Expressions
  • Simplify √12 + √27. McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Radical Expressions, Radical Expressions
  • Simplify √98. McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Radical Expressions, Radical Expressions
  • Solve √(x + 6) = x. McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Radical Expressions, Radical Equations
  • Solve √(x − 3) = 5. McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Radical Expressions, Radical Equations
  • What is 8^(4/3)? McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Radical Expressions, Higher Roots and Rational Exponents
  • What is the domain of f(x) = √(2x − 6)? McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Radical Expressions, Radical Functions
  • Which power of x equals √(x³), for positive x? McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Radical Expressions, Higher Roots and Rational Exponents

Exponentials and logarithms 7

  • A culture starts with 300 bacteria and doubles every 4 hours. How many bacteria are there after 20 hours? McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Exponentials and Logarithms, Applications with Exponential Equations
  • Solve 5^(x − 1) = 125. McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Exponentials and Logarithms, Logarithmic and Exponential Equations
  • Solve log₂ (x − 1) = 3. McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Exponentials and Logarithms, Logarithmic and Exponential Equations
  • What is log₃ 81? McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Exponentials and Logarithms, Properties of Logarithms
  • Which equation says the same thing as 2⁵ = 32? McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Exponentials and Logarithms, Properties of Logarithms
  • Which line is the horizontal asymptote of f(x) = 2^x + 3? McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Exponentials and Logarithms, Exponential and Logarithmic Functions
  • Which single logarithm equals log₂ x + 3 log₂ y? McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Exponentials and Logarithms, Properties of Logarithms

Geometry 7

  • A circle has a diameter of 10 m. What is its area, in terms of π? McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Geometry, Perimeter, Area, and Volume
  • A cylinder has a radius of 3 cm and a height of 8 cm. What is its volume, in terms of π? McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Geometry, Perimeter, Area, and Volume
  • A rectangle has a perimeter of 34 cm and a length of 12 cm. What is its area? McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Geometry, Perimeter, Area, and Volume
  • A triangle has a base of 16 in and a height of 11 in. What is its area? McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Geometry, Perimeter, Area, and Volume
  • The two legs of a right triangle measure 8 and 15. How long is the hypotenuse? McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Geometry, Coordinate Geometry
  • What is the distance between the points (−3, 2) and (5, 8)? McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Geometry, Coordinate Geometry
  • What is the surface area of a closed rectangular box that is 4 ft by 3 ft by 2 ft? McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Geometry, Perimeter, Area, and Volume

Trigonometry 10

  • A circle has radius 10. How long is the arc cut off by a central angle of 3π/5 radians? McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Trigonometry, Angles on the Unit Circle
  • A ladder makes a 60° angle with the ground, and its foot is 4 feet from the wall. How long is the ladder? McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Trigonometry, Right Triangle Trigonometry
  • A right triangle has a 30° angle and a hypotenuse of 10. How long is the side opposite the 30° angle? McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Trigonometry, Right Triangle Trigonometry
  • Convert 210° to radians. McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Trigonometry, Angles on the Unit Circle
  • In a right triangle, the side opposite angle A is 7 and the hypotenuse is 25. What is cos A? McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Trigonometry, Right Triangle Trigonometry
  • Simplify (1 − cos² x)/sin x. McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Trigonometry, Trigonometric Identities
  • What are the amplitude and period of y = 3 sin(2x)? McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Trigonometry, Graphing Trigonometric Functions
  • What is cos 135°? McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Trigonometry, Unit Circle Trigonometry
  • What is sin(5π/6)? McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Trigonometry, Unit Circle Trigonometry
  • Which values of x between 0 and 2π solve sin x = 1/2? McGraw Hill ALEKS, curriculum of the course Prep for Calculus 1: Trigonometry, Trigonometric Equations

How this list was compiled: Our own questions. Topic areas: McGraw Hill publishes the curriculum of its ALEKS course Prep for Calculus 1 at https://www.aleks.com/about_aleks/course_products?cmscache=detailed&detailed=ghighedmath35_prepcalculus#ghighedmath35_prepcalculus (281 topics in ten areas; read 2026-10-07). Facts about the Placement Assessment: McGraw Hill, ALEKS Placement, Preparation and Learning, https://www.mheducation.com/highered/digital-products/aleksppl.html (read 2026-10-07). Every answer is worked out from the numbers in the question, and the printed choices are read back and compared with it. Licence: Own work. Questions, answer choices and explanations were written for this site. Nothing is copied or reworded from an ALEKS assessment, an ALEKS learning module or another practice test.

How it works

This ALEKS practice test has 100 questions of our own in ten topic areas. It is unofficial and not affiliated with, endorsed by or sponsored by McGraw Hill, the publisher of ALEKS.

Read the full guide

How it differs from the real assessment

McGraw Hill's ALEKS PPL pages, read October 7, 2026, describe an assessment that adapts to each answer. This ALEKS placement test practice is multiple choice in a fixed order, so it shows the topics, not the format.

The ten topic areas

McGraw Hill's ALEKS PPL page lists no topics for the assessment. The areas here are those of its published curriculum for the ALEKS course Prep for Calculus 1, from real numbers to trigonometry.

Mixed rounds, easier first

The ALEKS practice questions go round the ten areas, easier ones first, so a round of ten mixes the areas. Exam mode draws 25, the real assessment's upper figure.

  • Work each answer on paper before you look at the choices: the real assessment gives none.
  • A wrong choice here is usually a common slip, such as adding the tops and the bottoms of two fractions.
  • Check a radical or rational equation in the original. Squaring or clearing a denominator can add an answer that fails.

Questions and answers

What are ALEKS math placement test questions like?

They have no answer choices: McGraw Hill calls its Placement Assessment open-response, and says it determines what a student knows across 314 topics in 25 questions or less.

How do you pass the ALEKS math placement test?

McGraw Hill's page names no pass mark: it says the assessment places students into courses from Basic Math to Calculus. The score a course needs comes from the school: Louisiana State University, for one, requires minimum ALEKS PPL scores for some of its math courses.

Is there an ALEKS practice test PDF?

After a round, Print makes a sheet of these questions, with an answer key if you tick it, and a browser's print window can save it as a PDF. It is our own ALEKS PPL practice test, not a McGraw Hill document.

What are the ALEKS practice modules?

McGraw Hill's page describes a personalized Prep and Learning Module with 12 months' access, alongside up to five assessment attempts. The module is part of ALEKS PPL itself. This page is separate, unofficial practice.

How long does the ALEKS math placement test take?

McGraw Hill's page for high schools says the whole assessment takes 90 minutes to complete. Ask your school whether it sets a time limit or a proctor.