SAT Practice
Complete Prep System

Central Ideas and Details

The SAT asks you to identify the main idea of passages and distinguish it from supporting details. The central idea is what the passage is MOSTLY about — not a minor supporting fact.

• Main idea questions often use phrases like "mainly," "primarily," or "best describes."
• Eliminate answers that are too narrow (just one detail) or too broad (beyond scope).
• The central idea is often stated in the first or last paragraph but may be implied.

Making Inferences

Inferences are logical conclusions drawn from evidence in the text, NOT personal opinion.

• Inference answers must be directly supported by specific text evidence.
• Avoid answers with absolute words like "always," "never," or "all" unless clearly supported.
• Look for "implies," "suggests," or "can be inferred."

Evidence-Based Questions

Paired questions ask you to (1) answer a question about the text, then (2) identify which part of the passage best supports that answer.

Quantitative Reasoning

Some passages include a graph, chart, or table. You must interpret data AND connect it to the passage text.

• Read axis labels, titles, and data points carefully.
• The correct answer will be supported by BOTH the text and the data.

Words in Context (Vocabulary)

The SAT tests how words function in specific passages, not just definitions. You must find the best meaning given the surrounding sentences.

• Replace the word with each answer choice and re-read the sentence.
• Focus on tone: is the word positive, negative, or neutral in context?
• Common trap: a commonly known definition that doesn't fit the context.

Text Structure and Purpose

Structure questions ask how a passage is organized or why the author includes a specific detail.

• Common structures: compare/contrast, problem/solution, cause/effect, chronological, claim/evidence.
• For function questions, ask: what job does this paragraph/sentence do in the argument?

Author's Point of View and Purpose

• What is the author's attitude toward the subject? Look for charged language and rhetorical choices.
• Purpose = why the author wrote this (to inform, persuade, critique, analyze, entertain).
• Dual-passage questions: compare what two authors agree/disagree on and how their approaches differ.

Cross-Text Connections

Paired passages require you to understand how the two texts relate.

Rhetorical Synthesis

These questions give you bullet-point notes and ask you to write a sentence that achieves a specific goal (introduce, compare, argue, conclude).

• Read the goal carefully. If it says "compare," the answer must address both items.
• If it says "support the claim," the answer must present evidence, not just restate the claim.
• Eliminate answers that include information NOT in the notes.

Transitions

Transition questions ask you to pick the word or phrase that best connects ideas between two sentences.

• Adding info: furthermore, in addition, also, moreover
• Contrasting: however, although, on the other hand, nevertheless
• Cause/Effect: therefore, as a result, consequently, thus
• Clarifying: in other words, specifically, that is

Organization and Flow

Some questions ask where to place a sentence within a paragraph or passage.

• Look for logical order: each sentence should connect to the one before and after it.
• Introductory sentences introduce; concluding sentences summarize or generalize.

Sentence Boundaries

You must correctly identify and fix run-ons, comma splices, and sentence fragments.

• Run-on: Two independent clauses joined without proper punctuation.
• Comma splice: Two independent clauses joined only with a comma.
• Fragment: A group of words missing a subject or verb, or a dependent clause alone.

Punctuation Rules

• Commas with nonessential clauses: set off with commas if removing the clause doesn't change the core meaning.
• Semicolons join two independent clauses; use them where a period could go.
• Colons introduce a list, explanation, or elaboration after an independent clause.
• Dashes can replace commas, semicolons, or colons for emphasis.
• Apostrophes: possession (cat's = belonging to one cat), contractions (it's = it is).

Agreement and Pronouns

• Subject-verb agreement: singular subjects take singular verbs.
• Watch out for interruptive phrases between subject and verb.
• Pronoun-antecedent agreement: pronouns must match their noun in number and gender.
• Avoid pronoun ambiguity — make sure it's clear what the pronoun refers to.

Modifiers

Misplaced modifiers are a common SAT trap. Modifying phrases must be next to the word they modify.

Linear Equations

• Parallel lines have the SAME slope; perpendicular lines have NEGATIVE RECIPROCAL slopes.
• A linear equation has one solution, no solution (parallel), or infinitely many solutions (same line).

Linear Inequalities

• Solving is the same as equations, except flip the inequality sign when multiplying/dividing by a negative.
• Graphically: < and > use dashed lines; ≤ and ≥ use solid lines.

Systems of Equations

Methods: substitution, elimination, graphing.

Functions and Graphs

• f(x) notation: f(3) means substitute x = 3 into the function.
• x-intercept = set y = 0; y-intercept = set x = 0.
• Transformations: f(x) + k shifts up; f(x + h) shifts left; -f(x) reflects over x-axis.

Quadratic Equations

• Discriminant b² - 4ac: if >0 = two real solutions; if =0 = one solution; if <0 = no real solutions.
• Sum of roots = -b/a; Product of roots = c/a.

Polynomial Functions

• Degree determines end behavior and max number of roots.
• Factor theorem: (x - r) is a factor if f(r) = 0.
• Remainder theorem: dividing f(x) by (x - a) gives remainder f(a).

Exponential Functions

Rational and Radical Equations

• When solving radical equations, isolate the radical and square both sides. CHECK for extraneous solutions.
• For rational equations, find common denominator. CHECK for excluded values (denominator = 0).

Key Geometry Formulas (Provided on Test)

Coordinate Geometry

Trigonometry

Arc Length and Sector Area

Ratios, Rates, and Proportions

• Set up proportions as fractions: a/b = c/d → cross multiply.
• Unit rates: find "per one" by dividing. Convert units carefully.

Percentages

Statistics

• Mean = sum of values ÷ number of values.
• Median = middle value (sorted). Mode = most frequent value.
• Range = max - min. Standard deviation measures spread.
• A larger standard deviation = more spread out data.

Data Interpretation

• Scatterplot best-fit lines: positive slope = positive correlation.
• Two-way tables: find row/column totals. Conditional probability uses a subset row/column.

Probability

Digital SAT Module Timing

Pacing Rules

• Spend no more than 90 seconds per Reading/Writing question. If stuck, mark it and move on.
• For Math, attempt all "easy" questions first, then return to harder ones.
• Leave 3-5 minutes at the end to review flagged questions.
• Never leave a question blank — there is NO penalty for guessing.

Energy Management

• The 10-minute break between Reading/Writing and Math is mandatory — use it.
• If you're confused, skip and come back. Spending 5 minutes on one question costs you points elsewhere.

Process of Elimination (POE)

On every question, your goal is to eliminate wrong answers, not just find the right one.

• Eliminate answers that are too extreme, too vague, or unsupported by the text.
• Eliminate answers that are factually true but don't answer the specific question asked.
• On grammar questions, eliminate answers that create new grammatical errors.
• On math, plug in your answer choices — especially for word problems.

Trap Answer Types

• True but irrelevant: Stated in passage but doesn't answer the question.
• Too extreme: Uses "always," "never," "all," "none" without full support.
• Opposite: Means the reverse of what is correct.
• Half right: First part is correct, second part is wrong.
• Out of scope: Introduces information not in the passage.