SAT Algebra Study Guide
Prepare for SAT Math. Study linear equations, linear functions, systems and inequalities. Choose a lesson below, or try mixed practice to check your skills.
All lessons
5 lessons
About this guide
Five complete lessons, 75 worked examples, 25 topic-practice exercises and 30 mixed-practice questions. Written explanation tasks include model answers for self-review.
How to use this guide
Algebra is not a collection of unrelated tricks. Most of this domain comes from three ideas: equal quantities stay equal under valid operations; a linear relationship has a constant rate of change; and a solution must satisfy every stated condition. Harder questions often hide these familiar ideas behind an unfamiliar form, an unknown coefficient, or a target that is not simply x.
This guide follows the five Algebra sections in the larger SAT Math outline. Each contains concept lessons, exactly 15 worked examples, and a five-question exit check. There are 75 worked examples, 25 exit-check questions, and a separate 30-question mixed practice set. Full answers are provided for every question.
A study cycle that makes the explanations useful
Learn the relationship. Read the lesson, then reproduce the essential rule without looking. Include its condition: a slope formula needs different x-coordinates; division by a parameter requires a nonzero denominator.
Attempt before reading. Leave the worked solution closed and solve the shaded question. Write down the target first. When stuck, open the worked solution, read the recognition cue, then close it and try again. The title and cue are learning supports; the mixed practice removes them.
Explain the choice. Do not stop at a correct answer. Explain why substitution, elimination, a slope comparison, a graph, or a direct expression was the appropriate tool. An unexplained calculator result is incomplete learning.
Retrieve and transfer. Re-solve missed questions after a gap. Then use the exit checks and mixed practice without notes. Record whether an error came from a concept, translation, algebra, a graph, the calculator, or the final target.
The difficulty progression
Foundation examples isolate a relationship or a common operation. Standard examples combine representations, introduce context, or require a deliberate method choice. Challenge examples emphasize parameters, hidden structure, feasibility, and reasoning about an entire set of solutions. These are editorial labels, not predictions of a question’s official difficulty.
Two useful routes through the guide
Build from the beginning: read Sections 1–5 in order, attempt each example, and complete the exit checks.
Repair a weakness: use the skills map in Review and reference, study the linked examples, and then attempt mixed practice. Do not treat a strong result on one small set as a score prediction.
Navigation. Use the guide contents for lessons and review materials. The skills map links to individual worked examples.
What this Algebra guide covers
The official Algebra domain contains linear equations in one variable, linear equations in two variables, linear functions, systems of two linear equations in two variables, and linear inequalities in one or two variables. This guide uses one section for each area.[1]
College Board places Algebra at approximately 35% of SAT Math; its student overview lists 13–15 Algebra questions. The weight is a guide to emphasis, not a promise about the number of questions on a particular subtopic.[2][3]
Section | Central question |
|---|---|
1. One-variable equations | Which number makes the relationship true, and when is there one solution, no solution, or every real number? |
2. Two-variable equations | Which ordered pairs lie on the line, and what do its slope, intercepts, and coefficients mean? |
3. Linear functions and models | How does an output change with its input, and how can a table, graph, or context reveal the rule? |
4. Systems of linear equations | Which values satisfy both constraints, and can the requested expression be found without solving for everything? |
5. Linear inequalities | Which values are allowed, and what do boundaries, overlap, and whole-number restrictions change? |
The boundary with other SAT Math domains
This is the Algebra volume, not the Advanced Math volume. Quadratics, exponential functions, higher-degree polynomials, radical equations, rational equations with variable denominators, and absolute-value equations belong primarily in Advanced Math. Percentages and units appear here when they supply the context for a linear relationship; broad statistics and probability belong in Problem-Solving and Data Analysis.[2]
Digital testing and calculator context
The standard Math section has 44 questions in two 35-minute modules. Performance on the first module influences the difficulty of the second. Questions include multiple choice and student-produced responses.[3][4]
Calculators are permitted throughout Math. Bluebook includes Desmos graphing and scientific options. Current policy prohibits handheld calculators with computer algebra system (CAS) functionality; check the official policy again before your test. This guide’s methods do not require symbolic solving software.[5]
Do not confuse the graphing tool with the mathematical argument
A graph can identify an intersection quickly. Algebra explains why a parameter gives no solution or infinitely many solutions. Use both, but choose intentionally. The calculator workshop in Review and reference shows how to check numeric answers without surrendering control of the problem.
What the reference sheet will not do for you. The official sheet is geometry-focused; it does not supply the slope, line-form, system-classification, or inequality rules in this guide. Learn or be able to derive them.[6]