The visual guide to
SAT®
15 units, 321 topics. Each topic is explained in writing, drawn as a lesson you can watch, and checked with practice questions.
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Each unit is as wide as its share of its test section. Striped units aren't weighted on the exam.Filled: topics you've opened.
Unit 1Math: Algebra
- Solving a Linear Equation in One Variable
- Strategic Use of Structure in One-Variable Equations
- Building a One-Variable Equation from a Context
- Using One-Variable Equations in Context
- Interpreting Parts of a One-Variable Equation
- When a One-Variable Equation Has No Solution or Infinitely Many
- Evaluating a Linear Function and Reversing It
- Modelling a Relationship with a Linear Function
- Using Linear Functions to Solve Problems in Context
- Interpreting an Input-Output Pair, Constant, or Term
- Reading the Graph of a Linear Function in Context
- Table, Equation, and Graph of a Linear Function
- Connecting a Table, an Equation, and a Graph in Context
- Given an Input, Finding and Interpreting the Output
- Writing a Linear Function's Rule from Two Pairs
- Creating and Using a Linear Equation in Two Variables
- Modelling a Constraint on Two Quantities
- Interpreting Parts of a Two-Variable Equation
- Reading the Graph of Ax + By = C in Context
- Equation, Table, and Graph of a Line
- Two-Variable Representations in Context
- Given One Quantity, Finding the Other
- Writing the Equation of a Line from Points or a Slope
- Writing a Line Parallel or Perpendicular to Another
- Solving a System by Substitution and Elimination
- Strategic Use of Structure in a System
- Creating and Using a System in Context
- Modelling Two Constraints with a System
- Systems with No Solution or Infinitely Many Solutions
- A System and Its Graph
- A System and Its Graph in Context
- Creating and Using Linear Inequalities in Context
- Solving a One-Variable Inequality
- Modelling Constraints with Inequalities
- Interpreting Parts of a Linear Inequality
- Which Side of the Boundary Line to Shade
- Interpreting a Point in the xy-Plane as a Solution
- Table, Algebra, and Graph of an Inequality
- Student-Produced Responses: Entering Your Answer
- Student-Produced Responses with More Than One Answer
Unit 2Math: Advanced Math
- Making Strategic Use of Algebraic Structure
- Adding, Subtracting, and Multiplying Polynomials
- Factoring Out a Common Factor
- Difference of Two Squares
- Factoring a Trinomial as the Product of Two Binomials
- Factoring Beyond the Basic Cases
- Rewriting Simple Rational Expressions
- Rational Exponents and Radical Form
- Solving a Quadratic Given in Factored Form
- Solving a Quadratic in Standard Form by Factoring
- Solving a Quadratic Given in Vertex Form
- What Completing the Square Actually Is
- Completing the Square to Solve a Quadratic
- The Quadratic Formula
- Choosing the Most Efficient Method
- The Discriminant and the Number of Real Solutions
- Linear Absolute Value Equations
- Simple Rational Equations
- Radical Equations
- Extraneous Solutions
- Polynomial Equations Written in Factored Form
- Systems of a Linear and a Nonlinear Equation
- Relating a System's Solutions to Its Graphs
- Solving a Formula for the Variable of Interest
- Creating and Using Quadratic Functions in Context
- Creating and Using Exponential Functions in Context
- Identifying the Right Model for a Relationship
- Exponential Growth Versus Quadratic Growth
- Interpreting an Input/Output Pair, Intercept, or Initial Value
- Interpreting a Constant, Variable, Factor, or Term in Context
- Interpreting a Point on the Graph
- Interpreting Parts of a Graph Beyond a Single Point
- Connecting a Table, an Equation, and a Graph
- Graphs of Polynomial and Simple Rational Functions
- Transformations of Nonlinear Graphs
- Connecting Representations in a Context
- The Most Suitable Form of a Quadratic
- The Most Suitable Form of an Exponential
- Zeros, x-Intercepts, and the y-Intercept
- Function Notation and Evaluating
- Finding the Input for a Given Output
Unit 3Math: Problem-Solving and Data Analysis
- Ratios, Rates, and Unit Rates
- Proportional Relationships in Scale Drawings and Science
- Derived Units from Products and Quotients
- One-Step Unit Conversion
- Multistep and Multidimensional Unit Conversion
- Scale Factor in a Proportional Relationship
- Percents in Context: Discounts, Taxes, and Tips
- Simple and Compound Interest
- Percent Increase and Percent Decrease
- Percent Change and the Growth Factor
- Percentages At or Above 100 Percent
- Frequency Tables and Histograms
- Dot Plots and Box Plots
- Calculating Mean, Median, and Range
- Comparing Distributions with Different Means
- Comparing Distributions with Different Standard Deviations
- Outliers and Their Effect on Mean and Median
- Reading a Scatterplot Without Predicting
- Making Predictions from a Line of Best Fit
- Fitting Linear Models to Data
- Fitting Quadratic and Exponential Models
- Reading a Graph of a Modeled Relationship
- Comparing Linear and Exponential Growth
- Probability from a One-Way Data Display
- Two-Way Tables and Conditional Probability
- Area Models and Other Probability Representations
- Finding an Unknown Frequency from a Probability
- Sample Statistics as Estimates of a Population
- Interpreting Margin of Error
- Sample Size and the Width of the Margin of Error
- Random Samples and Which Population a Result Extends To
- Random Assignment and Causal Claims
- Observational Studies versus Experiments
Unit 4Math: Geometry and Trigonometry
- Area and Perimeter of Plane Figures
- Composite Figures and Shaded Regions
- Surface Area and Volume of Solids
- Real Objects Modeled by Geometric Figures
- Scale Factor: Lengths, Areas, and Volumes
- Selecting and Applying the Right Formula
- Vertical Angles and Angles on a Line
- Parallel Lines Cut by a Transversal
- The Triangle Angle Sum Theorem
- Congruence of Triangles
- Similarity of Triangles
- Dilation: Lengths Scale, Angles Stay
- Sufficiency: Which Statement Would Prove It
- The Pythagorean Theorem
- Special Right Triangles: 30-60-90 and 45-45-90
- Right Triangle Trigonometry (SOH-CAH-TOA)
- Why Similarity Makes the Trig Ratios Work
- Sine and Cosine of Complementary Angles
- Radii, Diameters, and Tangent Lines
- Central and Inscribed Angles
- Arc Length and Sector Area
- Converting Between Degrees and Radians
- The Unit Circle and Radian Problems
- The Equation of a Circle in the xy-Plane
- Completing the Square to Find Center and Radius
- Changing the Equation, Moving the Graph
- The Distance Formula in Circle Problems
- The Math Reference Sheet: What It Gives You
Unit 5Reading and Writing: Information and Ideas
- Determining the Central Idea of a Text
- Where the Central Idea Hides
- Central Idea vs. Supporting Detail
- Too Narrow, Too Broad, Just Right
- True but Unsupported Answer Choices
- Interpreting the Key Details
- Matching Evidence to the Exact Claim
- Evidence Traps: True, Related, Useless
- Quotation Evidence in Literature and Poetry
- Which Finding Would Support the Hypothesis
- Reading the Axes, Units and Labels First
- Testing Each Choice Against the Claim
- Combining the Text's Claim with the Graph's Numbers
- Completing the Text with a Logical Conclusion
- One Step Beyond the Evidence, Not Two
- The Connector That Constrains the Ending
- The Restatement Trap
- Working a Short Passage in 71 Seconds
- Reading the Question Before the Passage
- Science and Social Science with No Outside Knowledge
Unit 6Reading and Writing: Craft and Structure
- Words in Context: The Two Question Forms
- Predicting Your Own Word Before Reading the Choices
- Contrast Signals That Flip a Word's Meaning
- Cause, Result and Continuation Signals
- Restatement, Lists and Appositives as Built-In Definitions
- Why the Most Common Meaning Is Usually the Trap
- Secondary and Tertiary Dictionary Senses
- Connotation as the Tiebreaker Between Two Defensible Words
- Words That Shift Meaning with Part of Speech
- Tier-Two Academic Vocabulary: What Is Actually Tested
- Precision: Choosing Between Two Words That Both Fit
- Word Meaning in Literary and Older Texts
- What a Text Says vs. What a Text Is Doing
- Main Purpose of a Whole Text
- The Function of a Single Underlined Sentence
- Problem-Solution and Claim-Counterclaim Shapes
- Chronological, General-to-Specific and Cause-Effect Shapes
- Definition-then-Example and the Case in Point
- Purpose Verbs and What Separates Them
- Answers That Get the Content Right and the Function Wrong
- Purpose and Structure in Literary Narrative
- How the Paired-Text Question Works
- Isolating Each Author's Claim Before Comparing
- How One Author Would Respond to the Other
- Agreement on the Facts, Disagreement on the Reading
- Disagreement About the Facts Themselves
- One Text Extending Rather Than Contradicting the Other
- The Trap That Gets Text 2 Right and Text 1 Wrong
- Pacing the Craft and Structure Block
Unit 7Reading and Writing: Expression of Ideas
- Where Expression of Ideas Sits in the Module
- The Stated Goal Is the Whole Scoring Criterion
- Reading the Goal Before the Notes
- How Many Notes a Correct Answer Uses
- Goal: Emphasize a Similarity
- Goal: Emphasize a Difference
- Goal: Introduce a Topic to an Unfamiliar Audience
- Goal: Describe or Identify Something
- Goal: Explain the Purpose of a Study
- Goal: Present the Findings
- Goal: Summarize the Steps in a Procedure
- Goal: Make and Support a Generalization
- Matching the Goal Verb to a Sentence Shape
- True but Aimed at the Wrong Goal
- The Fact That Was Never in the Notes
- Claims Neither Note Supports
- Scope Errors: Too Narrow or Too Broad
- The Longest Choice Trap
- Vague Choices That Dodge the Goal
- Naming the Relationship Before Looking at the Choices
- Covering the Blank and Predicting Your Own Word
- Same Direction or Opposite Direction First
- Reading Both Sides of the Blank
- Addition Transitions
- Contrast Transitions
- Cause and Effect Transitions
- Example Transitions
- Sequence and Time Transitions
- Concession Transitions
- Emphasis Transitions
- Similarity Transitions
- Clarification and Restatement Transitions
- Specifying and Restrictive Transitions
- Summary and Conclusion Transitions
- The Relationship Families as One Wheel
- However Versus Therefore
- Moreover Versus Nevertheless
- Indeed Versus However
- Nonetheless and the Concession Trap
- Right Relationship, Wrong Register
- Two Choices From the Same Family
Unit 8Reading and Writing: Boundaries — Between Sentences
- What Makes a Sentence Complete
- The Period, the Question Mark, and the Exclamation Point
- The Semicolon as a Sentence Boundary
- Comma Splices
- Fused Sentences and Run-Ons
- The Four Legal Repairs for a Fused Pair
- Participial Fragments
- Subordinate-Clause Fragments
- Appositive and Noun-Phrase Fragments
- Conjunctive Adverbs and the Splice They Hide
Unit 9Reading and Writing: Boundaries — Within Sentences
- The Comma Plus a Coordinating Conjunction
- Commas in a Series
- The Semicolon in a Complex Series
- What Must Come Before a Colon
- What a Colon Can Introduce
- The Single Dash as a Colon Substitute
- Paired Dashes and Parentheses
- Paired Commas Around an Interrupter
- Why You Cannot Mix the Pair
- Restrictive versus Nonrestrictive Modifiers
- Relative Clauses and Whether They Take a Comma
- The Comma and the Dependent Clause
- No Comma Between a Subject and Its Verb
- When No Punctuation Is the Answer
Unit 10Reading and Writing: Form, Structure, and Sense — Agreement
- Finding the Real Subject
- The Prepositional Phrase Between Subject and Verb
- Inverted Sentences and There Is versus There Are
- Compound Subjects Joined by And
- Compound Subjects Joined by Or and Nor
- Collective Nouns as Subjects
- Indefinite Pronouns as Subjects
- A Nonrestrictive Clause Between Subject and Verb
- The Number Of versus A Number Of
- Pronoun-Antecedent Agreement in Number
- Collective and Indefinite Antecedents
- Ambiguous Antecedents
Unit 11Reading and Writing: Form, Structure, and Sense — Verbs and Verbals
- Finite Verbs versus Verbals
- A Participle Is Not a Predicate
- The Sentence With No Main Verb at All
- Having Met versus Met
- Gerunds versus Infinitives
- When a Verbal Is the Right Choice
- The Simple Tenses on a Timeline
- The Progressive Aspect
- The Perfect Aspect
- The Past Perfect and the Earlier Past
- Sequence of Tenses Across Clauses
- Tense Consistency in a Narrative
Unit 12Reading and Writing: Form, Structure, and Sense — Modifiers, Genitives, and Plurals
- The Introductory Participial Phrase
- Dangling Modifiers
- Misplaced Only and the Other Limiting Words
- Misplaced Prepositional Phrases
- Squinting Modifiers
- The Two Ways to Repair a Dangler
- Modifier Placement in the Answer Choices
- Plural versus Possessive
- Singular Possessive versus Plural Possessive
- Irregular Plurals and Their Possessives
- Its versus It's
- Their, They're, There and Your, You're
- The Compound Possessive
Unit 13Reading and Writing: Standard English Conventions — Strategy and Scope
Unit 14Test Mechanics: How the Digital SAT Actually Works
- The Two-Module Adaptive Design
- Why Module 1 Is Not a Warm-Up
- No Penalty for a Wrong Answer
- Mark for Review and the Question Menu
- Free Navigation and the One-Way Door
- Embedded Pretest Questions
- The Score Scale and How Raw Becomes Scaled
- What Happened to Subscores and Cross-Test Scores
- The Time Budget Per Question
- Superscoring and Retaking the SAT
- The Bluebook Testing Environment
Unit 15Test Mechanics: The Tools and the Traps
- Desmos: Graphing a System Instead of Solving It
- Desmos: Zeros, Vertices, and Key Points
- Desmos: Sliders for an Unknown Parameter
- When Reaching for Desmos Is Slower Than Algebra
- What Is on the Math Reference Sheet
- What Is Not on the Reference Sheet
- Student-Produced Response Entry Rules
- Plugging In the Answer Choices
- Picking Numbers for Variables in the Answers
- What the Digital SAT No Longer Tests