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Free ALEKS Practice Test

Math Placement Test Prep — Open-Response Practice

Last updated: September 2026

ALEKS PPL is an adaptive math placement test used by colleges to determine which math course you're ready for — from basic math through Calculus. Unlike most tests, ALEKS questions are open-response: you type your exact answer rather than choosing from options. Use these free practice problems, with full worked solutions, to build confidence before your placement test.

Practice Set
8 Open-Response Qs
Exam Duration
Untimed (Avg. 60–90 Min)
Access Level
Instant & Unrestricted

How ALEKS PPL Works

ALEKS (Assessment and LEarning in Knowledge Spaces) PPL is McGraw Hill's adaptive, open-response mathematics placement assessment used by colleges and universities nationwide to evaluate math readiness and assign accurate course placements.

  • The test is adaptive: each question is chosen based on how you answered the previous one — correct answers lead to harder questions, incorrect answers lead to easier ones, so the test zeroes in on your actual skill level.
  • Typically 20-30 questions, reaching a placement in 25 questions or fewer, usually taking about 60-90 minutes (untimed, but most colleges recommend budgeting up to 2-3 hours).
  • All questions are open-response — you type your answer directly rather than selecting from multiple choices, and ALEKS provides an on-screen calculator only on certain problems (personal calculators generally aren't allowed).
  • There's no pass/fail — your result is a score from 0-100 representing the percentage of in-scope topics you've mastered, which your specific college then maps to a course placement (the same score can mean different course placements at different schools, so check your school's specific cutoff chart).
  • Most colleges allow multiple attempts (commonly up to 5), and provide access to a personalized "Prep and Learning Module" between attempts to target your weak areas before retesting.
  • ALEKS covers roughly 300+ topics across 8 broad math areas: real numbers/arithmetic, algebraic expressions/equations, geometry, functions, exponents, logarithms, and trigonometry.

Because each answer directly shapes the next question, taking your time on early problems and entering exact notation prevents the adaptive algorithm from prematurely down-scoring your skill level.

What the ALEKS Placement Assessment Covers

01

Real Numbers & Arithmetic

Operations with integers, fractions, decimals, percentages, signed numbers, order of operations (PEMDAS), absolute values, and ratio/proportion computations.

02

Algebraic Expressions & Polynomials

Simplifying algebraic expressions, evaluating variable expressions, operations on polynomials, factoring quadratic and higher-degree terms, and rational expressions.

03

Linear & Quadratic Equations & Inequalities

Solving linear equations, single-variable inequalities, systems of linear equations, absolute value equations, and solving quadratic equations via factoring, square roots, and quadratic formula.

04

Functions & Graphical Modeling

Function notation, evaluating functions, domain and range, finding intercepts and slopes, graphing linear and nonlinear functions, piece-wise functions, and graph transformations.

05

Exponents, Radicals & Logarithms

Integer and rational exponent rules, simplifying and combining radical expressions, rationalizing denominators, and solving exponential and logarithmic equations.

06

Geometry & Measurement

Perimeter, circumference, area, surface area, volume, Pythagorean theorem, properties of similar and congruent triangles, and Cartesian coordinate geometry.

07

Trigonometry & Precalculus

Unit circle radian and degree measures, fundamental trigonometric ratios, trigonometric identities, solving right and oblique triangles, and graphing trigonometric functions.

08

Word Problems & Mathematical Modeling

Translating verbal descriptions into algebraic equations, rate/time/distance problems, percentage and mixture problems, and geometric optimization scenarios.

ALEKS scores range from 0 to 100 representing topic mastery percentage. Course placement cutoffs vary by college (e.g., typically 30+ for College Algebra, 46+ for Precalculus, and 76+ for Calculus I). Check your institution's specific placement chart.

Why Open-Response Changes Your Strategy

Without multiple-choice options to use as a sanity check or fall back on process of elimination, you need to be confident in your actual computed answer and comfortable with correct mathematical notation/formatting for typed answers (e.g., fractions, exponents) — this is a different skill from recognizing a correct answer among choices.

Free ALEKS Practice Problems — Open-Response Format

8 Open-Response Problems • Worked Solutions
Problem 1 of 8Arithmetic & Pre-Algebra
Open-Response Math
Problem Statement

Evaluate the following numerical expression and express your answer as a fully simplified fraction in lowest terms: 5/6 - (2/3) · (1/4 + 3/8)

Simulate typing into ALEKS. You must compute the exact numerical or algebraic expression without multiple-choice cues.
Problem 2 of 8Arithmetic & Pre-Algebra
Open-Response Math
Problem Statement

A chemistry lab technician needs to produce 240 milliliters of a 15% acid solution by mixing a 10% acid solution with a 25% acid solution. How many milliliters of the 25% acid solution must be used?

Simulate typing into ALEKS. You must compute the exact numerical or algebraic expression without multiple-choice cues.
Problem 3 of 8Algebra & Equations
Open-Response Math
Problem Statement

Solve the rational equation for x: 3 / (x - 2) + 1 / (x + 2) = 8 / (x^2 - 4) If there is a unique solution, enter the value of x. If there are multiple solutions, separate them with commas. If there is no solution, type "no solution".

Simulate typing into ALEKS. You must compute the exact numerical or algebraic expression without multiple-choice cues.
Problem 4 of 8Algebra & Equations
Open-Response Math
Problem Statement

Solve the quadratic equation for x: 2x^2 - 7x - 15 = 0 Enter all solutions separated by a comma (e.g., "-3/2, 5"). If solutions are fractions, leave them as simplified improper fractions.

Simulate typing into ALEKS. You must compute the exact numerical or algebraic expression without multiple-choice cues.
Problem 5 of 8Functions & Exponents
Open-Response Math
Problem Statement

Consider the functions f(x) = 4 / (x - 3) and g(x) = 2x + 1. (a) Find the simplified formula for the composite function (f ∘ g)(x). (b) State the value of x that must be excluded from the domain of (f ∘ g)(x).

Simulate typing into ALEKS. You must compute the exact numerical or algebraic expression without multiple-choice cues.
Problem 6 of 8Functions & Exponents
Open-Response Math
Problem Statement

Solve the logarithmic equation for x: log₂(x + 6) + log₂(x) = 4 If there are multiple solutions, separate them with a comma. If a solution is extraneous, do not include it.

Simulate typing into ALEKS. You must compute the exact numerical or algebraic expression without multiple-choice cues.
Problem 7 of 8Geometry & Trigonometry
Open-Response Math
Problem Statement

A circle has a diameter with endpoints at A(-3, 4) and B(5, -2) in the Cartesian coordinate plane. (a) Find the exact radius of the circle. (b) Write the standard equation of the circle in the form (x - h)^2 + (y - k)^2 = r^2.

Simulate typing into ALEKS. You must compute the exact numerical or algebraic expression without multiple-choice cues.
Problem 8 of 8Geometry & Trigonometry
Open-Response Math
Problem Statement

Let θ be an angle in standard position in Quadrant III such that sin(θ) = -5/13. Find the exact values of cos(θ) and tan(θ). Express your answers as simplified fractions.

Simulate typing into ALEKS. You must compute the exact numerical or algebraic expression without multiple-choice cues.

How to Prepare for ALEKS PPL

1

Take Advantage of Unproctored Practice Attempts

Most colleges provide up to 5 ALEKS placement attempts, with the first 1–2 designated as unproctored diagnostic sessions. Use these early attempts to familiarize yourself with the open-response interface, math palette, and pacing without score anxiety.

2

Master ALEKS Mathematical Syntax & Exact Notation

ALEKS requires precise mathematical notation. Practice typing fractions (a/b), exponents (x^n), radicals, and solution sets. Avoid decimal approximations unless explicitly requested, as formatting errors count as incorrect answers even with correct underlying math.

3

Review Forgotten Arithmetic & Pre-Algebra Foundations

Because ALEKS is adaptive, early mistakes on basic arithmetic, fractions, or linear equations immediately anchor the test to lower difficulty levels. Brushing up on foundational algebra ensures you unlock higher-level calculus readiness questions.

4

Commit Seriously to the Prep and Learning Module

Between testing attempts, ALEKS unlocks a personalized Prep and Learning Module built directly around your specific missed topics. Spending 5–10 dedicated hours working through these interactive modules is the most effective way to jump course cutoffs.

5

Know Your Target College's Cutoff Score Chart

Placement cutoffs vary significantly by institution and major (e.g., typically 30+ for College Algebra, 46+ for Precalculus, and 76+ for Calculus I). Check your specific school's score-to-course chart in advance so you know the exact target score needed for your degree plan.

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