SAT Concept Library

The SAT tests 183 specific skills.
Here they all are.

Every concept comes with a plain-English explanation, a sample question, and targeted practice questions. Find out exactly which skills are costing you points.

Math121 concepts

Linear Equations in One Variable

Solve a basic linear equation

24+ questions

Linear Equations in One Variable

Solve a linear equation involving fractions

24+ questions

Linear Equations in One Variable

Set up and solve a linear equation from a word problem

47+ questions· High frequency

Linear Equations in One Variable

Solve equations with variables on both sides

12+ questions

Linear Equations in One Variable

Identify equations with no solution or infinitely many solutions

28+ questions

Linear Equations in One Variable

Solve absolute value equations

21+ questions

Linear Equations in Two Variables

Write and interpret slope-intercept form (y = mx + b)

44+ questions· High frequency

Linear Equations in Two Variables

Work with standard form (Ax + By = C)

26+ questions

Linear Equations in Two Variables

Write an equation given a point and slope

24+ questions

Linear Equations in Two Variables

Calculate slope from two points

32+ questions· High frequency

Linear Equations in Two Variables

Identify parallel and perpendicular lines from their slopes

36+ questions· High frequency

Linear Equations in Two Variables

Find x- and y-intercepts of a line

38+ questions· High frequency

Linear Equations in Two Variables

Interpret the graph of a linear equation in context

35+ questions· High frequency

Linear Functions

Interpret slope as rate of change in a real-world context

36+ questions· High frequency

Linear Functions

Interpret the y-intercept as an initial value

35+ questions· High frequency

Linear Functions

Build a linear function from a real-world description

24+ questions

Linear Functions

Evaluate a linear function for a given input

24+ questions

Linear Functions

Write a linear equation from a table of values

24+ questions

Systems of Linear Equations

Solve a system using substitution

35+ questions· High frequency

Systems of Linear Equations

Solve a system using elimination

32+ questions· High frequency

Systems of Linear Equations

Set up a system of equations from a word problem

41+ questions· High frequency

Systems of Linear Equations

Determine when a system has no solution or infinitely many solutions

28+ questions

Systems of Linear Equations

Interpret the intersection of two lines graphically

35+ questions· High frequency

Linear Inequalities

Solve a linear inequality in one variable

24+ questions

Linear Inequalities

Graph the solution of an inequality on a number line

26+ questions

Linear Inequalities

Solve compound inequalities (and / or)

20+ questions

Linear Inequalities

Identify the solution region for a linear inequality in two variables

24+ questions

Linear Inequalities

Set up an inequality from a real-world constraint

26+ questions

Equivalent Expressions

Distribute and use FOIL to expand expressions

41+ questions· High frequency

Equivalent Expressions

Factor out the greatest common factor

34+ questions· High frequency

Equivalent Expressions

Factor a quadratic trinomial

43+ questions· High frequency

Equivalent Expressions

Recognize and factor difference of squares

38+ questions· High frequency

Equivalent Expressions

Complete the square to rewrite a quadratic

28+ questions

Equivalent Expressions

Apply exponent rules (product, quotient, power rules)

37+ questions· High frequency

Equivalent Expressions

Simplify rational expressions

22+ questions

Equivalent Expressions

Add, subtract, and multiply polynomials

28+ questions

Equivalent Expressions

Simplify radical expressions and convert between radical and exponent form

22+ questions

Nonlinear Equations

Solve a quadratic equation by factoring

45+ questions· High frequency

Nonlinear Equations

Solve a quadratic equation using the quadratic formula

45+ questions· High frequency

Nonlinear Equations

Solve a quadratic by taking the square root

28+ questions

Nonlinear Equations

Use the discriminant to determine the number of solutions

28+ questions

Nonlinear Equations

Solve a system with one linear and one quadratic equation

23+ questions

Nonlinear Equations

Solve rational equations (check for extraneous solutions)

37+ questions· High frequency

Nonlinear Equations

Solve radical equations (check for extraneous solutions)

24+ questions

Nonlinear Functions

Interpret vertex form of a quadratic f(x) = a(x−h)² + k

38+ questions· High frequency

Nonlinear Functions

Interpret standard form of a quadratic f(x) = ax² + bx + c

31+ questions· High frequency

Nonlinear Functions

Find zeros (x-intercepts) of a quadratic

31+ questions· High frequency

Nonlinear Functions

Determine if a parabola opens up or down and find the vertex

30+ questions· High frequency

Nonlinear Functions

Interpret exponential growth and decay functions

33+ questions· High frequency

Nonlinear Functions

Build an exponential function from a real-world description

26+ questions· High frequency

Nonlinear Functions

Evaluate and interpret function notation f(x), f(a+b), etc.

40+ questions· High frequency

Nonlinear Functions

Evaluate composite functions f(g(x))

20+ questions

Nonlinear Functions

Apply and interpret transformations (shifts, reflections, stretches)

31+ questions· High frequency

Nonlinear Functions

Describe end behavior of polynomial and exponential functions

18+ questions

Ratios, Rates, and Proportions

Set up and solve a proportion

38+ questions· High frequency

Ratios, Rates, and Proportions

Convert between units using dimensional analysis

22+ questions

Ratios, Rates, and Proportions

Use ratios in scale drawings or similar figures

23+ questions

Ratios, Rates, and Proportions

Solve rate problems (speed, distance, time; work rate)

34+ questions· High frequency

Ratios, Rates, and Proportions

Find part-to-whole and part-to-part ratios

32+ questions· High frequency

Percentages

Find what percent one number is of another

27+ questions· High frequency

Percentages

Find a percent of a number

30+ questions· High frequency

Percentages

Calculate percent increase or decrease

39+ questions· High frequency

Percentages

Apply successive (stacked) percent changes

21+ questions

Percentages

Set up and solve a percent problem from a word problem

26+ questions

One-Variable Data and Statistics

Calculate and interpret the mean

41+ questions· High frequency

One-Variable Data and Statistics

Calculate and interpret the median

36+ questions· High frequency

One-Variable Data and Statistics

Identify the mode

10+ questions

One-Variable Data and Statistics

Calculate the range

16+ questions

One-Variable Data and Statistics

Interpret standard deviation (not calculate)

20+ questions

One-Variable Data and Statistics

Determine how an outlier affects mean, median, and range

25+ questions

One-Variable Data and Statistics

Describe distribution shape: symmetric, skewed, bimodal

17+ questions

One-Variable Data and Statistics

Read and interpret dot plots and histograms

30+ questions· High frequency

One-Variable Data and Statistics

Read and interpret box plots (quartiles, IQR)

18+ questions

Two-Variable Data and Scatterplots

Read a scatterplot and identify individual data points

29+ questions· High frequency

Two-Variable Data and Scatterplots

Interpret the slope and intercept of a line of best fit

32+ questions· High frequency

Two-Variable Data and Scatterplots

Use a line or curve of best fit to make predictions

23+ questions

Two-Variable Data and Scatterplots

Identify positive, negative, or no correlation

30+ questions· High frequency

Two-Variable Data and Scatterplots

Distinguish correlation from causation

22+ questions

Two-Variable Data and Scatterplots

Interpret residuals (difference between actual and predicted values)

12+ questions

Probability

Calculate basic probability (favorable / total outcomes)

28+ questions· High frequency

Probability

Use the complement rule (P(not A) = 1 − P(A))

20+ questions

Probability

Calculate conditional probability P(A given B)

30+ questions· High frequency

Probability

Read and use a two-way frequency table to find probabilities

35+ questions· High frequency

Probability

Determine if events are independent

19+ questions

Statistical Inference

Distinguish between a sample and a population

30+ questions· High frequency

Statistical Inference

Explain why random sampling enables generalization

16+ questions

Statistical Inference

Interpret margin of error in context

37+ questions· High frequency

Statistical Inference

Distinguish observational studies from experiments

15+ questions

Statistical Inference

Explain when an experiment (vs. observation) supports causation

14+ questions

Lines and Angles

Identify complementary and supplementary angles

22+ questions

Lines and Angles

Use the vertical angles theorem

42+ questions· High frequency

Lines and Angles

Find angle measures formed by parallel lines and a transversal (alternate interior, corresponding, co-interior)

26+ questions· High frequency

Lines and Angles

Apply the triangle angle sum theorem (angles sum to 180°)

24+ questions· High frequency

Lines and Angles

Use the exterior angle theorem

42+ questions· High frequency

Triangles

Identify similar triangles and set up proportions

33+ questions· High frequency

Triangles

Identify congruent triangles (SSS, SAS, ASA, AAS)

16+ questions

Triangles

Apply the Pythagorean theorem

42+ questions· High frequency

Triangles

Use 30-60-90 triangle ratios

27+ questions

Triangles

Use 45-45-90 triangle ratios

27+ questions

Triangles

Apply the triangle inequality theorem

20+ questions

Right Triangles and Trigonometry

Define sine, cosine, and tangent in a right triangle (SOH-CAH-TOA)

36+ questions· High frequency

Right Triangles and Trigonometry

Use trig ratios to find a missing side

25+ questions· High frequency

Right Triangles and Trigonometry

Use inverse trig to find a missing angle

25+ questions· High frequency

Right Triangles and Trigonometry

Apply the cofunction identity (sin θ = cos(90°−θ))

13+ questions

Right Triangles and Trigonometry

Set up a trig equation from a word problem (angle of elevation/depression)

47+ questions· High frequency

Area and Volume

Find the area of a rectangle or square

18+ questions

Area and Volume

Find the area of a triangle

27+ questions

Area and Volume

Find the area and circumference of a circle

38+ questions· High frequency

Area and Volume

Find the area of composite (combined) shapes

18+ questions

Area and Volume

Find the area of a sector or length of an arc

18+ questions

Area and Volume

Find the volume of a rectangular prism

29+ questions· High frequency

Area and Volume

Find the volume of a cylinder

25+ questions

Area and Volume

Find the volume of a cone, sphere, or pyramid

16+ questions

Area and Volume

Relate surface area and volume to scale factor

15+ questions

Circles

Write and interpret the standard equation of a circle (x−h)²+(y−k)²=r²

20+ questions

Circles

Find the center and radius from the equation of a circle

38+ questions· High frequency

Circles

Complete the square to rewrite a circle equation in standard form

18+ questions

Circles

Relate central angles to arcs (in degrees and radians)

15+ questions

Circles

Apply the inscribed angle theorem

42+ questions· High frequency

Circles

Identify properties of a tangent line to a circle

15+ questions

Coordinate Geometry

Use the distance formula and midpoint formula in the coordinate plane

22+ questions· High frequency

Reading & Writing62 concepts

Central Ideas and Details

Identify the main purpose or central idea of a passage

44+ questions· High frequency

Central Ideas and Details

Identify details that support a central claim

36+ questions· High frequency

Central Ideas and Details

Choose the best summary of a passage or paragraph

34+ questions· High frequency

Central Ideas and Details

Match a passage to its best title or thesis

22+ questions

Command of Evidence (Textual)

Find textual evidence that supports a given claim

46+ questions· High frequency

Command of Evidence (Textual)

Identify evidence that weakens or complicates an argument

25+ questions

Command of Evidence (Textual)

Identify evidence that strengthens an argument

33+ questions· High frequency

Command of Evidence (Textual)

Explain what a quoted passage accomplishes

24+ questions

Command of Evidence (Textual)

Match an author's claim to the evidence they use

22+ questions

Command of Evidence (Quantitative)

Interpret data from a chart, graph, or table

36+ questions· High frequency

Command of Evidence (Quantitative)

Determine whether data supports, refutes, or is neutral to a claim

36+ questions· High frequency

Command of Evidence (Quantitative)

Complete a sentence or argument using information from a graph

28+ questions

Command of Evidence (Quantitative)

Identify trends or patterns in quantitative data

22+ questions

Inferences

Infer the author's perspective, attitude, or opinion

24+ questions

Inferences

Draw a logical conclusion from the passage

39+ questions· High frequency

Inferences

Infer a character's motivation or feeling (literary passages)

21+ questions

Inferences

Identify what is implied but not directly stated

33+ questions· High frequency

Words in Context

Determine the meaning of a word or phrase as used in the passage

48+ questions· High frequency

Words in Context

Distinguish between words with similar denotations but different connotations

29+ questions· High frequency

Words in Context

Interpret figurative language (metaphor, simile, idiom)

20+ questions

Words in Context

Choose a word that matches the tone or register of the passage

27+ questions· High frequency

Words in Context

Choose the best replacement for an underlined word or phrase

34+ questions· High frequency

Text Structure and Purpose

Identify how a passage is organized (compare/contrast, cause/effect, etc.)

20+ questions

Text Structure and Purpose

Explain the function of a specific paragraph within the passage

22+ questions

Text Structure and Purpose

Explain what a specific sentence or detail does in context

29+ questions

Text Structure and Purpose

Explain why an author made a specific structural or stylistic choice

18+ questions

Text Structure and Purpose

Explain the purpose of the opening or closing of a passage

16+ questions

Cross-Text Connections

Determine whether two authors agree or disagree, and on what

20+ questions

Cross-Text Connections

Predict how Author 1 would respond to Author 2's claim

18+ questions

Cross-Text Connections

Identify an assumption both authors share

33+ questions· High frequency

Cross-Text Connections

Describe how two texts approach the same topic differently

19+ questions

Rhetorical Synthesis

Synthesize multiple bullet-point notes into a single coherent sentence

36+ questions· High frequency

Rhetorical Synthesis

Choose a sentence that best accomplishes a stated rhetorical goal

38+ questions· High frequency

Rhetorical Synthesis

Choose phrasing that best emphasizes a particular point

25+ questions

Rhetorical Synthesis

Introduce an example or counterexample effectively

18+ questions

Transitions

Choose a transition word/phrase showing contrast (however, although, etc.)

38+ questions· High frequency

Transitions

Choose a transition showing cause and effect (therefore, as a result, etc.)

40+ questions· High frequency

Transitions

Choose a transition showing addition or continuation (furthermore, also, etc.)

31+ questions· High frequency

Transitions

Choose a transition showing sequence or time (first, subsequently, etc.)

20+ questions

Transitions

Choose a transition showing concession (even though, granted, etc.)

16+ questions

Transitions

Choose a transition introducing an example (for instance, specifically, etc.)

26+ questions· High frequency

Transitions

Choose a transition showing elaboration or clarification (in other words, that is, to clarify, etc.)

22+ questions

Sentence Boundaries

Identify and fix comma splices

40+ questions· High frequency

Sentence Boundaries

Identify and fix run-on sentences

22+ questions

Sentence Boundaries

Identify and fix sentence fragments

29+ questions

Sentence Boundaries

Use semicolons correctly to join independent clauses

39+ questions· High frequency

Sentence Boundaries

Use periods to correctly separate independent clauses

39+ questions· High frequency

Sentence Boundaries

Use colons correctly to introduce lists or explanations

22+ questions

Sentence Boundaries

Use em dashes correctly for emphasis or interruption

23+ questions

Form, Structure, and Sense (Grammar)

Ensure subjects and verbs agree in number

52+ questions· High frequency

Form, Structure, and Sense (Grammar)

Ensure pronouns agree with their antecedents

44+ questions· High frequency

Form, Structure, and Sense (Grammar)

Use correct pronoun case (I vs. me, who vs. whom)

28+ questions· High frequency

Form, Structure, and Sense (Grammar)

Maintain consistent verb tense within a passage

26+ questions

Form, Structure, and Sense (Grammar)

Choose the correct verb form (infinitive, gerund, participle)

24+ questions

Form, Structure, and Sense (Grammar)

Place modifiers correctly to avoid dangling or misplaced modifiers

36+ questions· High frequency

Form, Structure, and Sense (Grammar)

Use parallel structure in lists and comparisons

38+ questions· High frequency

Form, Structure, and Sense (Grammar)

Use apostrophes correctly for possession vs. contraction

25+ questions

Form, Structure, and Sense (Grammar)

Use commas to set off nonessential (non-restrictive) clauses

37+ questions· High frequency

Form, Structure, and Sense (Grammar)

Use commas correctly in a series or list

28+ questions

Form, Structure, and Sense (Grammar)

Distinguish between adjectives and adverbs

20+ questions

Form, Structure, and Sense (Grammar)

Use comparatives and superlatives correctly

22+ questions

Form, Structure, and Sense (Grammar)

Eliminate wordiness and redundancy to produce the most concise correct sentence

38+ questions· High frequency

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