SAT Essential Foundations Study Guide
Prepare for SAT Math. Build confidence with arithmetic, algebraic notation, graphs and word problems. 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, a 24-exercise starting check, 25 topic-practice exercises and 30 mixed-practice questions. Written explanation tasks include model answers for self-review.
How to use this guide
This volume is the entry point to the four content-domain books: Algebra, Advanced Math, Problem-Solving and Data Analysis, and Geometry and Trigonometry. It teaches the prerequisites those books use repeatedly. It is not a fifth official SAT content domain.
You do not need to read every lesson before starting harder material. A student who is comfortable with arithmetic but misreads functions should spend more time in Section 4 than in Section 2. A student who understands a worked solution but cannot begin a new question needs more independent attempts, not another rereading.
A practical route through the book
Orient. Read Sections 1.1–1.3, then take the diagnostic without opening its solutions.
Locate. Use the diagnostic skill map to identify the earliest step that needs repair.
Learn. Attempt each worked example before reading its explanation. Say why the method is valid.
Retrieve. Complete the section-exit questions with the lesson closed. Revisit missed skills later.
Transfer. Finish with the mixed sets and then move into the appropriate domain volume.
What the labels mean
Foundation examples isolate one essential idea. Standard examples connect two or more ideas. Challenge examples expose a subtle distinction or require a less obvious representation; they do not assume advanced coursework. Section 1 also contains two explicitly labeled Planning scenarios. Those teach pacing and diagnostic interpretation, not mathematical test content.
Worked examples show a complete method. Diagnostic questions are for locating gaps before instruction. Section exits check a newly learned skill. Mixed practice removes topic hints. Every diagnostic, exit, and mixed question has an explanation in the solutions section.
How to review one mistake
Do not stop at “I made a careless error.” Identify the first line that became wrong. Was the issue a missing fact, a misread condition, an invalid operation, a calculator entry, a graph scale, or the final response format? Write a specific replacement habit, then solve a fresh question that uses it. A correct guess is still a review item.
The readiness thresholds in this guide are suggested learning decisions, not validated cut scores. No result in this booklet can be converted into an SAT scaled score. Use an official full-length adaptive Bluebook practice test for a more realistic test baseline.[7]
Use the guide contents, lesson sections, example references and source notes to navigate. Leave worked solutions closed until you have attempted the problem.