FREE SAT Study Guide 2026: Digital SAT, Reading, Writing & Math

This free SAT study guide teaches to the Digital SAT — every content domain the College Board tests, organized the way the exam is built.^[1] The test moved fully digital and adaptive in spring 2024, so this guide covers the current format: two sections (Reading and Writing, then Math), each split into two modules, and a 400–1600 score.

It’s interactive, not a wall of text: every domain has a built-in checkpoint quiz, hover-able glossary terms, worked math examples, and concept questions, so you learn by doing.

Read it domain by domain, test yourself at each checkpoint, then round out your free SAT prep with our practice questions and flashcards.

SAT Exam Snapshot

Because the test is multistage adaptive, your work on the first module of each section decides how hard — and how high-scoring — the second module can be.^[1] Spend your study time across all eight domains, but know that Algebra and Advanced Math dominate the Math section and that grammar rules in Standard English Conventions are some of the fastest points to win:

College Board reports domain shares as approximate ranges within each section, so the exact mix shifts slightly each form.^[4] This guide teaches all eight domains — the four Reading and Writing domains first, then the four Math domains — as eight study modules.

1 · Craft and Structure (Reading & Writing)

About 28% of Reading and Writing. These questions test how you read closely — vocabulary in context, why a text is built the way it is, and how two related texts connect. Every answer must be supported by the passage in front of you.^[2]

Words in Context

Words in Context questions give a short passage with a blank (or an underlined word) and ask for the choice that best fits the surrounding meaning. The trick is to predict your own word first, before you read the choices, then pick the closest match. A choice can be a perfect synonym yet still be wrong if its tone or connotation clashes with the passage.

Text Structure & Purpose

These ask why the author wrote something or how a part functions — for example, whether a sentence introduces a counterargument, gives an example, or states the main claim. Name the role of the line in your own words (define, contrast, illustrate, qualify) before checking the choices.

Cross-Text Connections

Cross-Text Connections give you two short passageson the same topic and ask how their authors relate — does Text 2 support, challenge, or extend Text 1? Pin down each author’s viewpoint separately, then describe the relationship.

2 · Information and Ideas (Reading & Writing)

About 26% of Reading and Writing. This domain is comprehension and reasoning: finding the main point, locating the evidence that backs a claim (in text or in a graph), and drawing a conclusion the passage supports.^[2]

Central Ideas & Details

A central-idea question asks for the main point of the passage; a detail question asks for a specific fact it states. The central idea is the claim the whole text supports — broader than any single detail, but never beyond what the passage says.

Command of Evidence

Command of evidence questions come in two flavors. Textual evidence asks which quotation best supports a claim; quantitative evidence gives a graph or table and asks which choice the data backs. For data questions, read the axis labels and units before the choices.

Inferences

An inference is a conclusion the passage impliesbut doesn’t state. The correct choice is the one the text most directly supports — not the most interesting or most extreme one. If a choice needs information the passage never gives, eliminate it.

3 · Expression of Ideas (Reading & Writing)

About 20% of Reading and Writing. This domain is about effective writing — combining information to meet a goal, and choosing the transition that fits the logic between two ideas.^[2]

Rhetorical Synthesis

Rhetorical synthesisquestions give you a set of bulleted notes and a stated goal (“emphasize a contrast,” “introduce the study to an unfamiliar audience”) and ask for the sentence that uses the notes to meet it. Read the goal first, then find the choice that actually accomplishes it.

Transitions

Transition questions test logic, not vocabulary. Decide the relationship between the two ideas, then pick the matching word:

4 · Standard English Conventions (Reading & Writing)

About 26% of Reading and Writing. Grammar, punctuation, and sentence structure — and some of the fastest, most learnable points on the whole test, because the rules are finite.^[2]

Boundaries (Punctuation)

“Boundaries” questions test how you join and separate clauses. The key idea is whether each side is an independent clause (a complete sentence):

Form, Structure & Sense (Grammar)

This covers subject-verb agreement, verb tense, pronoun agreement, and modifiers. The most common traps:

5 · Algebra (Math)

About 35% of the Math section — the single biggest Math domain. Linear equations, functions, systems, and inequalities. Get fluent here and you bank a third of the Math points.^[3]

Linear Equations & Functions

A linear equation graphs as a straight line. In slope-intercept form $y = mx + b$, the slope $m$ is the rise over run and $b$ is the y-intercept. The slope between two points is $m = \dfrac{y_2 - y_1}{x_2 - x_1}$.

Systems of Equations

Solve a system by substitution or elimination; the solution is where the lines cross. A system has no solution when the lines are parallel (same slope, different intercept) and infinitely many when the two equations are multiples of each other.

Inequalities

Solve inequalities like equations, with one rule: flip the inequality sign when you multiply or divide by a negative number. Systems of inequalities define a shaded region; a solution is any point inside it.

6 · Advanced Math

About 35% of the Math section. Nonlinear equations and functions — quadratics, exponentials, polynomials — and the algebra of equivalent expressions. This is where the harder adaptive-module questions live.^[3]

Quadratics & Nonlinear Functions

A quadratic has the form $ax^2 + bx + c = 0$. Solve it by factoring when it’s clean, or with the quadratic formula:

$x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

The discriminant $b^2 - 4ac$ tells you how many real solutions there are: positive → two, zero → one, negative → none. The graph of a quadratic is a parabola whose vertex is its maximum or minimum.

Equivalent Expressions

These ask you to rewrite an expression — factor, expand, or combine — into an equivalent form. Know the key patterns:

Function Notation & Graphs

Function notation writes a rule as $f(x)$; $f(3)$ means evaluate at $x = 3$. An exponential function $y = a \cdot b^x$ grows by a constant percent (when $b > 1$) or decays (when $0 < b < 1$) — the contrast with a line that adds a constant amount is heavily tested.

7 · Problem-Solving & Data Analysis

About 15% of the Math section. Real-world quantitative reasoning — ratios, rates, percentages, units, and reading data — plus basic statistics and probability.^[3]

Ratios, Rates & Percentages

Set up a proportion for ratio and rate problems, and watch your units. Percent change is the change divided by the original value, times 100.

Data, Statistics & Probability

Know the measures of center and spread: the mean is the average, the median is the middle value, and a larger standard deviation means more spread. The median resists outliers, so a single extreme value pulls the mean but not the median.

8 · Geometry & Trigonometry

About 15% of the Math section. Area and volume, lines and angles, triangles (including right-triangle trig), and circles. The SAT provides a reference sheet of formulas, but speed comes from knowing the core ones cold.^[3]

Area, Volume, Lines & Angles

Know the workhorses: area of a rectangle $= lw$, triangle $= \tfrac{1}{2}bh$, circle $= \pi r^2$. Angles on a straight line sum to 180°, around a point to 360°, and a triangle’s interior angles sum to 180°. When parallel lines are cut by a transversal, corresponding and alternate angles are equal.

Triangles & Right-Triangle Trig

The Pythagorean theorem $a^2 + b^2 = c^2$ gives the sides of a right triangle, and SOH-CAH-TOA gives the trig ratios:

Memorize the special right triangles — the 45-45-90 (sides $1 : 1 : \sqrt{2}$) and the 30-60-90 (sides $1 : \sqrt{3} : 2$) — and that complementary angles satisfy $\sin\theta = \cos(90^\circ - \theta)$.

Circles

Circle facts the SAT tests: circumference $= 2\pi r$, area $= \pi r^2$, and the equation of a circle centered at $(h, k)$ with radius $r$ is $(x - h)^2 + (y - k)^2 = r^2$. Arc length and sector area are simple fractions of the whole, set by the central angle.

How to Use This Study Guide

A study guide is a map, not the whole territory — use it alongside official College Board practice in Bluebook and our free tools. Because the Digital SAT is adaptive, the goal is steady accuracy across both modules, so spaced, mixed practice beats one long cram.

SAT Glossary

Quick definitions for the terms you’ll see most across the Digital SAT:

Central idea

The main point a passage is making. Central Ideas and Details questions ask you to identify it or a specific supporting detail.

Comma splice

A punctuation error in which two independent clauses are joined by only a comma. Fix it with a period, semicolon, or comma plus a conjunction.

Command of evidence

A skill that asks you to identify the textual quotation or quantitative data point that best supports a given claim or conclusion.

Desmos calculator

The graphing calculator built into the SAT Math section. It is available on every Math question.

Digital SAT

The current SAT, taken on a computer in the Bluebook app since spring 2024. It has a Reading and Writing section and a Math section, each split into two adaptive modules.

Discriminant

The expression b² − 4ac inside the quadratic formula. It tells you the number of real solutions: positive = two, zero = one, negative = none.

Exponential function

A function y = a · bˣ where a is the starting value and b is the growth (b > 1) or decay (0 < b < 1) factor; the quantity changes by a constant percent each step.

Function notation

Writing a rule as f(x), where f(x) is the output for input x. f(3) means evaluate the function at x = 3.

Independent clause

A group of words with a subject and verb that can stand alone as a complete sentence.

Inference

A logical conclusion the passage supports but does not state outright. The correct inference is the one the text most strongly implies.

Median

The middle value of an ordered data set. Unlike the mean, it is not pulled toward outliers.

Module

Half of an SAT section. Each section has two modules; Reading and Writing has 27 questions per module (32 minutes), Math has 22 questions per module (35 minutes).

Multistage adaptive testing

A design where the difficulty of a section's second module depends on how you performed on the first. Stronger first-module performance unlocks a harder, higher-scoring second module.

Percent change

The change in a quantity divided by its original value, times 100. Always divide by the starting amount.

Pythagorean theorem

For a right triangle with legs a and b and hypotenuse c, a² + b² = c².

Quadratic equation

An equation of the form ax² + bx + c = 0. It can be solved by factoring, completing the square, or the quadratic formula.

Quadratic formula

x = (−b ± √(b² − 4ac)) ÷ (2a), which solves any quadratic ax² + bx + c = 0.

Rhetorical synthesis

An Expression of Ideas task that gives you bulleted notes and asks you to combine them into a single sentence that meets a stated goal.

Slope

The steepness of a line: the change in y divided by the change in x (rise over run). In y = mx + b, the slope is m.

Slope-intercept form

The linear equation y = mx + b, where m is the slope and b is the y-intercept (where the line crosses the y-axis).

SOH-CAH-TOA

The right-triangle trig memory aid: sine = opposite/hypotenuse, cosine = adjacent/hypotenuse, tangent = opposite/adjacent.

Special right triangles

The 30-60-90 and 45-45-90 triangles, whose side ratios (1 : √3 : 2 and 1 : 1 : √2) appear often on the SAT.

Standard deviation

A measure of how spread out data is around its mean. A larger standard deviation means more spread.

Student-produced response

A 'grid-in' Math question with no answer choices — you enter your own numeric answer.

Subject-verb agreement

The rule that a verb must match its subject in number — a singular subject takes a singular verb, a plural subject a plural verb.

System of equations

Two or more equations solved together; the solution is the point that satisfies all of them — where the graphs intersect.

Transition

A word or phrase (however, therefore, for example) that signals the logical relationship between ideas — contrast, cause, addition, or example.

Words in Context

A Reading and Writing question type asking you to choose the word or phrase that best completes a passage based on its surrounding meaning.

Free SAT Study Materials & Resources

Everything you need to prepare for the SAT is free here — no paywall, no sign-up. This guide is the foundation; pair it with the rest of our free SAT study materials for active recall, timed practice, and last-minute review:

• SAT Practice Test — exam-style questions across all eight domains, with explanations.
• SAT Flashcards — active-recall decks for the high-yield grammar rules, math formulas, and reading skills.

SAT Study Guide FAQ

References

1. 1.College Board. “How the SAT Is Structured — SAT Suite.” College Board. ↑
2. 2.College Board. “The Reading and Writing Section — SAT Suite.” College Board. ↑
3. 3.College Board. “The Math Section — SAT Suite.” College Board. ↑
4. 4.College Board. “What Are Content Domains? — SAT Suite.” College Board. ↑
5. 5.College Board. “Understanding SAT Scores.” College Board. ↑
6. 6.College Board. “SAT Registration Fees.” College Board. ↑
7. 7.College Board. “Assessment Framework for the Digital SAT Suite.” College Board. ↑

Sources for the concept answers

Every answer in the SAT concept questions above is drawn from an official primary source:

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