FREE ALEKS Study Guide 2026: All 8 Topic Areas

This free ALEKS study guide covers everything the ALEKS math placement assessment measures — all eight official topic areas, from arithmetic and algebra through functions, exponents, logarithms, geometry, and trigonometry — organized into six focused study modules.^[3]

It’s interactive, not a wall of text: every module has built-in checkpoint quizzes, flashcards, and practice questions, so you learn by doing — not just reading.

First, the part that surprises people: ALEKS is not a pass/fail test, and it’s not multiple choice. It is an adaptive, open-response assessment — you type and build your own answers — and it reports a single 0–100 score equal to the percentage of math topics you’ve mastered.^[1]

Your college maps that number to a course using its owncut scores, so “how high do I need?” depends on the class you want to place into. Read a module, test yourself at each checkpoint, then drill gaps with our free practice test and flashcards. This guide is a high-yield overview of every ALEKS topic — not a full textbook.

ALEKS Placement Assessment Snapshot

There is no single number you must hit — your 0–100 placement score simply maps to a course at your school.^[1] Here’s roughly how schools tend to use the score (your institution’s actual cut scores may differ — always confirm them):

ALEKS itself is adaptive and doesn’t publish fixed per-area weights — the chart above reflects the mix across our free practice question set so you can see where to focus, not an official ALEKS blueprint.

Module 1 · Real Numbers

The foundation of every other topic. ALEKS Real Numbers covers integers, fractions, decimals, percentages, ratios, and proportional reasoning — and getting fluent here pays off everywhere, because the harder algebra problems still come down to clean arithmetic.^[3]

1.1 Integers & Order of Operations

Work confidently with signed numbers (adding, subtracting, multiplying, and dividing positives and negatives) and evaluate multi-step expressions using the Order of operations. Know the difference between a Rational number and an Irrational number.

1.2 Fractions, Decimals & Percents

Convert fluidly among the three forms, and master Percent problems: percent of a number, percent change, and finding the whole. A percent is just a decimal in disguise — divide by 100.

1.3 Ratios & Proportions

A Ratio compares two quantities; a Proportion sets two ratios equal. Solve proportions by cross-multiplying — the workhorse for unit conversions, scaling, similar figures, and “is/of” percent problems.

Module 2 · Equations & Inequalities

Solving for the unknown is the heart of ALEKS algebra. This module covers linear equations, inequalities, systems, and quadratic equations — the skills that unlock most of the rest of the assessment.^[3]

2.1 Linear Equations

Solve a Linear equation by isolating the variable with inverse operations, keeping both sides balanced. Clear fractions and combine like terms first, then undo addition/subtraction, then multiplication/division.

2.2 Linear Inequalities

Solve an Inequality exactly like an equation, with one twist: flip the inequality symbol whenever you multiply or divide both sides by a negative number. The solution is a range, often shown on a number line.

2.3 Systems of Equations

A System of equations asks for the values that satisfy two equations at once — graphically, the point where two lines cross. Solve by substitution or elimination.

2.4 Quadratic Equations

A Quadratic equation has the form a x squared + b x + c = 0. Solve it by Factoring when it factors cleanly, or by the Quadratic formula when it doesn’t. The Discriminant tells you how many real solutions to expect.

Module 3 · Linear & Quadratic Functions

Functions describe how one quantity depends on another. ALEKS tests graphs and function basics, linear functions (slope and intercepts), and parabolas — reading them, writing them, and graphing them.^[3]

3.1 Functions & Graphs

A Function assigns exactly one output to each input. On a graph it passes the Vertical line test. Learn to read coordinates, evaluate f(x), and find a function’s domain and range.

3.2 Linear Functions

A linear function graphs as a straight line, y = mx + b, where the Slope m is the rise over run and the Y-intercept b is where it crosses the y-axis. Slope is one of the most-tested ALEKS ideas.

3.3 Parabolas

A quadratic function graphs as a Parabola. Find its Vertex (the x-coordinate is negative b over 2a), its direction (up if a is positive, down if negative), and its intercepts.

Module 4 · Exponents, Polynomials & Expressions

This module groups three closely related ALEKS topic areas — Exponents & Polynomials, Rational Expressions, and Radical Expressions — because they all build on the same algebra of powers and roots.^[3] Master the exponent rules and everything else follows.

4.1 Exponents & Polynomial Arithmetic

An Exponent is repeated multiplication; the laws of exponents tell you how to combine them. A Polynomial is a sum of power terms — add, subtract, and multiply them by combining like terms and using the distributive property (FOIL for two binomials).

4.2 Factoring & Polynomial Equations

Factoring reverses multiplication. Pull out the greatest common factor first, then factor trinomials into two binomials, recognize special patterns (difference of squares), and solve polynomial equations with the zero-product property.

4.3 Rational Expressions

A Rational expression is a fraction of polynomials. Simplify by factoring and canceling common factors, and always note the values that make the denominator zero — those are excluded, and they cause extraneous solutions.

4.4 Radical Expressions

A Radical is a root. Simplify by pulling out perfect-square (or perfect nth-power) factors, and remember that a rational exponent is a root: x to the one-half power is the square root of x.

Drill this module: because ALEKS asks you to produce these algebra answers (not pick them), the fastest way to lock them in is reps. Run the exponents, polynomials & radicals flashcards and the matching practice questions until each move is automatic.

Module 5 · Exponentials & Logarithms

The higher-level algebra on ALEKS: function composition and inverses, properties of logarithms, and logarithmic equations.^[3] The key insight is that exponentials and logarithms are inverses — they undo each other.

5.1 Functions, Composition & Inverses

Composition feeds one function’s output into another, f(g(x)). An Inverse function undoes a function: swap x and y and solve. An Exponential function and a Logarithm are a classic inverse pair.

5.2 Properties of Logarithms

A Logarithm answers “what exponent?”: log base b of x = y means b to the y power equals x. Three properties let you expand or condense logs — turning products into sums and powers into multipliers.

5.3 Logarithmic Equations

Solve a logarithmic equation by rewriting it in exponential form, or by condensing both sides to a single log and matching the insides. Always check for solutions that would force a log of a non-positive number — those are extraneous.

Module 6 · Geometry & Trigonometry

The most concrete ALEKS area: perimeter, area and volume, coordinate geometry, and trigonometry (ratios, identities, and equations).^[3] Much of it is choosing the right formula and substituting carefully.

6.1 Perimeter, Area & Volume

Know the core formulas and apply them with the right units. Perimeter is the distance around; Area is surface covered (square units); Volume is space filled (cubic units).

6.2 Coordinate Geometry

Geometry on the coordinate plane connects to algebra. The distance between two points is the Pythagorean theorem in disguise; the midpoint is the average of the coordinates; and slope measures steepness.

6.3 Trigonometry

ALEKS trig starts with the right-triangle ratios — SOH-CAH-TOA — and extends to identities and solving simple trigonometric equations. Identify the sides relative to your angle, then apply the matching ratio.

How to Use This ALEKS Study Guide

Because ALEKS is adaptive and your goal is to place into the highest math course you can, the smartest plan is targeted, not exhaustive:

• Take a baseline first. A quick run through our practice test shows which topic areas are shaky so you don’t waste time on what you already know.
• Study the weak modules in depth. Read the module, then take its end-of-module checkpoint to confirm the sub-topics actually stuck.
• Drill the open-response algebra. Module 4 (exponents, polynomials, rational & radical) is where you must produce answers — grind the flashcards until the moves are automatic.
• Check off as you go. Mark each section done in the Study Guide Contents — it raises your exam-readiness score.
• Use the real Prep & Learning Module. After your actual ALEKS attempt, the personalized module is the biggest lever — put in the hours before retaking.
• Mind the rules. Wait at least 48 hours between attempts, and confirm your school’s cut score for the course you want.

ALEKS Glossary

The high-yield ALEKS math terms across all eight topic areas in one place — hover any dotted term in the guide, or flip the whole deck here as a self-grading flashcard set.

Area

The amount of surface a two-dimensional figure covers, measured in square units.

Composition

Combining functions by using one's output as the next one's input, written f(g(x)).

Discriminant

The expression b squared minus 4ac in the quadratic formula; it tells how many real solutions exist.

Exponent

A small raised number showing how many times to multiply a base by itself (2 to the 3rd = 8).

Exponential function

A function where the variable is in the exponent, such as y = 2 to the x; models growth and decay.

Extraneous solution

An answer that appears valid algebraically but fails the original equation (often makes a denominator zero).

Factoring

Rewriting an expression as a product of simpler factors, the reverse of multiplying out.

Function

A rule that assigns exactly one output to each input; written f(x).

Hypotenuse

The longest side of a right triangle, opposite the right angle.

Inequality

A statement comparing two expressions with <, >, ≤, or ≥; its solution is a range of values.

Inverse function

A function that undoes another; swap x and y and solve. Its graph reflects across y = x.

Irrational number

A number that cannot be written as a fraction, such as the square root of 2 or pi; its decimal never repeats or ends.

Linear equation

An equation whose variables are only to the first power; its graph is a straight line (e.g., 2x + 3 = 11).

Logarithm

The inverse of an exponential: log base b of x = y means b to the y power equals x.

Natural log

The logarithm with base e (about 2.718), written ln.

Order of operations

The sequence for evaluating an expression — Parentheses, Exponents, Multiplication/Division, Addition/Subtraction (PEMDAS).

Parabola

The U-shaped graph of a quadratic function; it has a vertex and an axis of symmetry.

Percent

A part per hundred; convert to a decimal by dividing by 100 (25% = 0.25).

Perimeter

The total distance around the outside of a two-dimensional figure.

Polynomial

A sum of terms made of variables raised to whole-number powers, like 3x squared − 5x + 2.

Proportion

An equation stating that two ratios are equal; solved by cross-multiplying.

Pythagorean theorem

In a right triangle, a squared + b squared = c squared, where c is the hypotenuse.

Quadratic equation

An equation with a squared variable, a x squared + b x + c = 0; its graph is a parabola.

Quadratic formula

x = (−b ± the square root of (b squared − 4ac)) ÷ 2a — solves any quadratic equation.

Radical

An expression with a root symbol, such as the square root of 12; a fractional exponent means a root.

Ratio

A comparison of two quantities by division, written a to b, a:b, or a/b.

Rational expression

A fraction whose numerator and denominator are polynomials; the denominator can't be zero.

Rational number

A number that can be written as a fraction of two integers, such as 3/4, −2, or 0.25.

Slope

The steepness of a line: rise over run, the change in y divided by the change in x; the m in y = mx + b.

SOH-CAH-TOA

The trig ratios: Sine = Opposite/Hypotenuse, Cosine = Adjacent/Hypotenuse, Tangent = Opposite/Adjacent.

System of equations

Two or more equations solved together; the solution satisfies all of them at once.

Vertex

The turning point of a parabola — its highest or lowest point.

Vertical line test

A graph is a function if no vertical line crosses it more than once.

Volume

The amount of space a three-dimensional solid occupies, measured in cubic units.

Y-intercept

The point where a graph crosses the y-axis (where x = 0); the b in y = mx + b.

ALEKS Study Guide FAQ

References

1. 1.McGraw Hill. “ALEKS PPL: Placement, Preparation and Learning.” mheducation.com. ↑
2. 2.McGraw Hill. “ALEKS Placement, Preparation and Learning (Product).” mheducation.com. ↑
3. 3.University of Oregon Testing Center. “What topics are covered during the ALEKS PPL Assessment?.” uoregon.edu. ↑
4. 4.McGraw Hill. “ALEKS — Adaptive Learning & Assessment.” aleks.com. ↑

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