- Main idea
- The central point a passage conveys — what the whole text is mostly about.
- Supporting detail
- A fact, example, statistic, or reason that explains, proves, or develops the main idea.
- Inference
- A logical conclusion drawn from text evidence plus reasoning — implied, not stated outright.
- Author's purpose
- The reason a text was written — to inform, persuade, entertain, or explain.
- Tone
- The author's attitude toward the subject, shown through word choice (e.g., formal, critical, hopeful).
- Mood
- The feeling or atmosphere a text creates in the reader.
- Point of view
- The perspective from which a text is written and the author's stance toward the subject.
- Vocabulary in context
- The meaning of a word as it is used in a specific sentence, found from context clues.
- Context clues
- Surrounding words and ideas that reveal the meaning of an unfamiliar word.
- Connotation
- The emotional or implied meaning of a word, beyond its literal definition.
- Denotation
- The literal, dictionary meaning of a word.
- Fact
- A statement that can be verified or proven true.
- Opinion
- A belief, judgment, or interpretation that cannot be proven.
- Text structure
- How a passage is organized — e.g., cause/effect, compare/contrast, sequence, problem/solution.
- Cause and effect
- A text structure showing how one event leads to another.
- Compare and contrast
- A text structure that examines similarities and differences.
- Sequence
- A text structure that presents events or steps in order.
- Problem and solution
- A text structure that states a problem and proposes a way to solve it.
- Summary
- A brief restatement of a passage's main idea and key points in your own words.
- Paraphrase
- Restating someone else's idea in your own words and sentence structure.
- Theme
- The underlying message or insight about life that a literary text conveys.
- Figurative language
- Language that means more than the literal words — metaphor, simile, personification, idiom.
- Simile
- A comparison using 'like' or 'as' (e.g., 'brave as a lion').
- Metaphor
- A direct comparison stating one thing is another (e.g., 'time is money').
- Personification
- Giving human qualities to a non-human thing.
- Idiom
- A common expression whose meaning differs from its literal words (e.g., 'break a leg').
- Hyperbole
- Deliberate exaggeration for emphasis or effect.
- Symbolism
- Using an object or image to represent a larger idea.
- Topic sentence
- The sentence (often first) that states the main idea of a paragraph.
- Thesis (in reading)
- The central claim or controlling idea a whole text argues or explains.
- Claim
- A debatable statement an author argues for.
- Evidence
- Facts, examples, and reasoning used to support a claim.
- Anecdotal evidence
- A single personal story or example — weak support for a broad claim.
- Bias
- A one-sided perspective that can distort an author's argument.
- Counterargument
- A point that opposes the author's claim, often addressed to strengthen the argument.
- Evaluate an argument
- Judge whether the evidence is sufficient and relevant to the claim.
- Synthesis
- Combining ideas from two or more sources into a coherent understanding.
- Primary source (reading)
- A firsthand or original account of an event or topic.
- Secondary source (reading)
- A source that analyzes or interprets primary sources.
- Drawing conclusions
- Using stated facts plus reasoning to reach a logical judgment.
- Implicit meaning
- Meaning that is suggested or implied rather than stated directly.
- Explicit meaning
- Meaning that is stated directly in the text.
- Generalization
- A broad statement drawn from specific examples; valid only if well supported.
- Audience
- The readers a text is written for, which shapes its language and content.
- Rhetoric
- The author's use of language to inform or persuade an audience.
- Graphic / data in reading
- Charts, tables, and graphs that must be read and tied back to the passage.
- Paired passages
- Two passages on a related topic that you compare and synthesize.
- Objective summary
- A summary free of personal opinion or judgment.
- Word relationships
- How words relate in meaning — synonyms, antonyms, analogies.
- Transition words
- Words like 'however,' 'therefore,' and 'meanwhile' that signal connections between ideas.
- Subject-verb agreement
- A singular subject takes a singular verb; a plural subject takes a plural verb.
- Verb tense
- The form of a verb that shows when an action happens; keep it consistent unless time changes.
- Pronoun-antecedent agreement
- A pronoun must match its antecedent in number and gender.
- Pronoun clarity
- Every pronoun must clearly refer to one specific noun.
- Antecedent
- The noun a pronoun refers back to.
- Parallel structure
- Items in a list or comparison share the same grammatical form.
- Modifier
- A word or phrase that describes another word.
- Misplaced modifier
- A modifier positioned so it seems to describe the wrong word.
- Dangling modifier
- A modifier with no clear word in the sentence to describe.
- Run-on sentence
- Two independent clauses joined without proper punctuation or a conjunction.
- Comma splice
- Joining two independent clauses with only a comma — an error.
- Sentence fragment
- An incomplete sentence missing a subject, verb, or complete thought.
- Independent clause
- A clause that can stand alone as a complete sentence.
- Dependent clause
- A clause that cannot stand alone and depends on an independent clause.
- Coordinating conjunction
- FANBOYS: for, and, nor, but, or, yet, so — join equal elements.
- Subordinating conjunction
- A word like 'because,' 'although,' or 'when' that begins a dependent clause.
- Active voice
- The subject performs the action (e.g., 'The teacher graded the tests').
- Passive voice
- The subject receives the action (e.g., 'The tests were graded').
- Comma
- Separates items, sets off intro/nonessential phrases, and joins clauses with a conjunction.
- Semicolon
- Joins two closely related independent clauses without a conjunction.
- Colon
- Introduces a list, explanation, or quotation after a complete clause.
- Apostrophe
- Shows possession (dog's) or contraction (it's) — never a plain plural.
- Its vs. it's
- 'Its' = possessive; 'it's' = 'it is' or 'it has.'
- Their / there / they're
- 'Their' = possessive; 'there' = place; 'they're' = 'they are.'
- Your vs. you're
- 'Your' = possessive; 'you're' = 'you are.'
- Capitalization
- Capitalize proper nouns and the first word of a sentence.
- Word choice (diction)
- Choosing precise, appropriate, standard English words.
- Wordiness
- Using more words than needed; concise writing is usually better.
- Redundancy
- Unnecessary repetition of an idea (e.g., 'free gift').
- Conciseness
- Expressing ideas clearly in as few words as needed.
- Standard English conventions
- The accepted rules of grammar, usage, punctuation, and mechanics.
- Argumentative essay
- An essay that takes a clear position on an issue and defends it with reasons and evidence.
- Source-based essay
- An informative/explanatory essay that synthesizes and cites two provided sources.
- Thesis statement
- A single sentence stating the central claim or focus of an essay.
- Introduction
- The opening paragraph that hooks the reader and states the thesis.
- Body paragraph
- A paragraph that develops one main point with evidence and explanation.
- Topic sentence (writing)
- The sentence that states the main point of a body paragraph.
- Conclusion
- The closing paragraph that restates the thesis and ties the ideas together.
- Transitions
- Words and phrases that connect ideas and guide the reader between points.
- Counterargument (writing)
- An opposing view the writer acknowledges, often to refute it.
- Plagiarism
- Using another's words or ideas without credit.
- Citation
- A reference that credits a source so readers can identify and locate it.
- Quotation
- Another's exact words, set in quotation marks and cited.
- Paraphrasing
- Restating a source's idea in your own words and structure, with a citation.
- In-text citation
- A brief note in the text pointing to a full reference (e.g., author and page).
- Primary source (research)
- A firsthand or original document (e.g., a diary, data set, or interview).
- Secondary source (research)
- A source that analyzes or interprets primary sources.
- Credible source
- A relevant, current, accurate source from an authority with little bias.
- Evaluating sources
- Judging a source's relevance, credibility, currency, and bias.
- Integrating evidence
- Smoothly blending quotation or paraphrase into your own writing, then citing it.
- Revision
- Improving content, organization, and clarity of writing.
- Editing
- Correcting grammar, punctuation, spelling, and mechanics.
- Audience and purpose
- Whom you write for and why — they shape tone and word choice.
- Spelling (commonly confused)
- Watch homophones: accept/except, affect/effect, then/than.
- Affect vs. effect
- 'Affect' is usually a verb (to influence); 'effect' is usually a noun (a result).
- Then vs. than
- 'Then' = time/sequence; 'than' = comparison.
- Slope
- Rise over run: the change in y over the change in x; the m in y = mx + b.
- Slope formula
- slope = (y₂ − y₁) / (x₂ − x₁)
- Y-intercept
- Where a line crosses the y-axis (x = 0); the b in y = mx + b.
- Slope-intercept form
- y = mx + b, where m is the slope and b is the y-intercept.
- Horizontal line slope
- A horizontal line has slope 0.
- Vertical line slope
- A vertical line has an undefined slope.
- Order of operations
- PEMDAS: Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction.
- PEMDAS example
- 4 + 3 × 2 = 4 + 6 = 10 (multiply before adding).
- Percent
- A part per hundred; 25% means 25 out of 100.
- Percent to decimal
- Divide by 100 (or move the decimal 2 places left): 25% = 0.25.
- Percent of a number
- Convert to a decimal and multiply: 20% of 80 = 0.20 × 80 = 16.
- Percent change
- (new − old) / old × 100.
- Ratio
- A comparison of two quantities by division (e.g., 3 to 4, or 3:4).
- Proportion
- An equation stating two ratios are equal; solve by cross-multiplying.
- Cross-multiplying
- For a/b = c/d, set a × d = b × c.
- Unit rate
- A ratio comparing a quantity to one unit (e.g., miles per hour).
- Integer
- A whole number or its negative, including 0 (…, −2, −1, 0, 1, 2, …).
- Absolute value
- A number's distance from 0; always non-negative. |−5| = 5.
- Negative × negative
- A negative times a negative equals a positive.
- Negative × positive
- A negative times a positive equals a negative.
- Exponent
- Repeated multiplication: 2³ = 2 × 2 × 2 = 8.
- Square root
- √ undoes squaring: √25 = 5.
- Exponent product rule
- xᵃ × xᵇ = xᵃ⁺ᵇ.
- Prime number
- A whole number greater than 1 with exactly two factors: 1 and itself (e.g., 2, 3, 5, 7).
- Composite number
- A whole number greater than 1 with more than two factors (e.g., 4, 6, 9).
- Factor
- A number that divides another evenly (3 is a factor of 12).
- Multiple
- The product of a number and an integer (12 is a multiple of 3).
- LCM
- Least common multiple — the smallest number that is a multiple of two numbers.
- GCF
- Greatest common factor — the largest number that divides two numbers evenly.
- Rounding
- Look at the next digit: 5 or more rounds up, less than 5 rounds down.
- Place value
- The value of a digit based on its position (ones, tens, hundreds…).
- Fraction addition
- Find a common denominator, then add the numerators.
- Fraction multiplication
- Multiply numerators and denominators straight across.
- Mixed number
- A whole number plus a fraction (e.g., 2½).
- Linear equation
- An equation whose graph is a straight line; variables to the first power.
- Solving equations
- Use inverse operations to isolate the variable on one side.
- Inequality
- Solve like an equation, but flip the sign when multiplying/dividing by a negative.
- Expression
- A combination of numbers, variables, and operations with no equals sign.
- Variable
- A symbol (like x) that stands for an unknown number.
- Function
- A rule where each input has exactly one output; f(x) is the output for x.
- Coordinate plane
- A grid of x (horizontal) and y (vertical) axes meeting at the origin (0, 0).
- Distributive property
- a(b + c) = ab + ac.
- Perimeter
- The distance around a shape; add all the side lengths.
- Rectangle area
- Area = length × width.
- Triangle area
- Area = ½ × base × height.
- Circle area
- Area = πr², where r is the radius.
- Circumference
- Circumference = 2πr (or πd).
- Rectangular solid volume
- Volume = length × width × height.
- Cylinder volume
- Volume = πr²h.
- Pythagorean theorem
- In a right triangle, a² + b² = c², where c is the hypotenuse.
- Hypotenuse
- The longest side of a right triangle, opposite the right angle.
- Radius vs. diameter
- The radius is half the diameter; diameter = 2 × radius.
- Angles on a line
- Angles on a straight line add up to 180°.
- Angles in a triangle
- The interior angles of a triangle sum to 180°.
- Full turn
- A full rotation is 360°.
- Similar figures
- Same shape, proportional sides; corresponding angles are equal.
- Congruent figures
- Same shape and same size.
- Mean
- The average — add all values and divide by how many there are.
- Median
- The middle value when data are in order (average the two middle if even count).
- Mode
- The value that appears most often in a data set.
- Range
- The difference between the highest and lowest values.
- Outlier
- A value far from the rest; it affects the mean more than the median.
- Probability
- Favorable outcomes ÷ total outcomes — a number from 0 to 1.
- Probability of 0
- An impossible event has probability 0.
- Probability of 1
- A certain event has probability 1.
- Reading a graph
- Use the title, axes, labels, legend, and units to interpret data.
- Bar graph
- Compares amounts across categories with rectangular bars.
- Line graph
- Shows change over time with points connected by lines.
- Pie chart
- Shows parts of a whole as slices of a circle.
- Scientific notation
- A number written as a × 10ⁿ, with 1 ≤ a < 10 (e.g., 3.2 × 10⁴).
- Estimation
- Rounding to check whether an answer is reasonable.
- Explicit vs. implicit
- Explicit is stated directly; implicit is suggested and must be inferred.
- Argument
- A claim supported by reasons and evidence.
- Logical fallacy
- A flaw in reasoning that weakens an argument.
- Relevant evidence
- Support that directly relates to and backs the claim.
- Sufficient evidence
- Enough support to reasonably establish a claim.
- Compare sources
- Identify agreement, disagreement, and differing emphasis between two texts.
- Author's assumption
- An unstated belief the author treats as true.
- Connotative meaning
- The feelings or associations a word carries beyond its definition.
- Chronological order
- A sequence structure that presents events in time order.
- Main idea vs. theme
- Main idea is the central point; theme is the broader life message.
- Restating the main idea
- A correct summary covers the whole passage, not just one detail.
- Persuasive text
- Writing intended to convince the reader of a position.
- Informational text
- Writing intended to explain or inform; about 75% of test passages.
- Reading for detail
- Locating a specific fact or statement in the passage.
- Tone words
- Word choices that reveal attitude (e.g., 'sadly,' 'fortunately').
- Fact-based question
- Answer is stated directly in the passage.
- Inference question
- Answer is implied; reason from the text's evidence.
- Vocabulary strategy
- Plug each choice into the sentence and keep the original meaning.
- Best title
- A good title captures the passage's main idea, not a single detail.
- Quantitative information
- Numbers, charts, or graphs you interpret alongside the text.
- Comma after intro phrase
- Use a comma after an introductory word, phrase, or clause.
- Nonessential clause
- Set off with commas; removing it doesn't change the core meaning.
- Essential clause
- No commas; it's needed to identify the noun.
- Joining clauses correctly
- Use a period, semicolon, or comma + conjunction — not a lone comma.
- Verb agreement with phrases
- Ignore words between the subject and verb when checking agreement.
- Compound subject (and)
- Subjects joined by 'and' usually take a plural verb.
- Compound subject (or/nor)
- With 'or'/'nor,' the verb agrees with the nearer subject.
- Consistent point of view
- Don't shift between first, second, and third person without reason.
- Sentence variety
- Mixing sentence lengths and types improves writing quality.
- Concise revision
- Cut wordiness while keeping meaning; shorter and correct beats long and fancy.
- Formal vs. informal tone
- Match tone to audience and purpose; the essays expect standard English.
- Outline
- A plan that organizes an essay's thesis and main points before drafting.
- Hook
- An opening line that grabs the reader's attention.
- Evidence in an essay
- Specific reasons, examples, or source material that supports a point.
- Synthesis (writing)
- Combining ideas from both sources into one coherent explanation.
- Objective stance
- Presenting information without inserting personal opinion (source-based essay).
- Proofreading
- A final pass to catch grammar, spelling, and punctuation errors.
- Homophone
- Words that sound alike but differ in meaning/spelling (to/two/too).
- Accept vs. except
- 'Accept' = to receive; 'except' = to leave out.
- Subject of a sentence
- Who or what the sentence is about; it performs the verb.
- Predicate
- The part of a sentence containing the verb and what's said about the subject.
- Apostrophe for plurals
- Wrong — apostrophes don't make plurals (apple's ≠ apples).
- Citing a quotation
- Provide the source so a reader can find the exact wording.
- Bias in sources
- A one-sided slant that reduces a source's credibility.
- Current source
- Up-to-date information is usually more credible than outdated material.
- Decimal to percent
- Multiply by 100 (move the point 2 places right): 0.4 = 40%.
- Fraction to decimal
- Divide the numerator by the denominator: 3/4 = 0.75.
- Equivalent fractions
- Fractions equal in value (1/2 = 2/4 = 3/6).
- Simplifying fractions
- Divide numerator and denominator by their GCF.
- Decimal place value
- Tenths, hundredths, thousandths to the right of the point.
- Adding negatives
- −3 + (−5) = −8; same sign, add and keep the sign.
- Subtracting integers
- Subtracting is adding the opposite: 4 − (−3) = 4 + 3 = 7.
- Squaring a number
- Multiply it by itself: 6² = 36.
- Perfect square
- A number that is an integer squared (1, 4, 9, 16, 25…).
- Word problem strategy
- Identify the question, assign a variable, translate, then solve.
- Average word problem
- To find a missing value given an average, multiply the average by the count.
- Direct proportion
- As one quantity grows, the other grows at the same rate.
- Scale factor
- The ratio by which a figure is enlarged or reduced.
- Coordinate point
- Written (x, y): x is horizontal, y is vertical.
- Origin
- The point (0, 0) where the x- and y-axes meet.
- Quadrants
- The four regions of the coordinate plane, numbered I–IV.
- X-axis
- The horizontal axis on the coordinate plane.
- Y-axis
- The vertical axis on the coordinate plane.
- Function notation
- f(x) means the output of function f for input x.
- Evaluate a function
- Substitute the input value and compute: if f(x)=2x+1, f(3)=7.
- Combining like terms
- Add or subtract terms with the same variable: 3x + 2x = 5x.
- Equation vs. expression
- An equation has an equals sign; an expression does not.
- Surface area
- The total area of all faces of a solid.
- Volume
- The amount of space a solid occupies, measured in cubic units.
- Diameter
- A straight line through a circle's center; twice the radius.
- Right angle
- An angle of exactly 90°.
- Acute angle
- An angle less than 90°.
- Obtuse angle
- An angle greater than 90° but less than 180°.
- Supplementary angles
- Two angles that add up to 180°.
- Complementary angles
- Two angles that add up to 90°.
- Mean from a total
- Mean = total sum ÷ number of values.
- Median (even count)
- Average the two middle values.
- Probability (and)
- For independent events, multiply their probabilities.
- Theoretical probability
- What should happen based on equally likely outcomes.
- Data display
- A chart, table, or graph used to organize and show data.
- Comparing data sets
- Compare center (mean/median) and spread (range) between sets.
- Reasonable answer
- Estimate first to check that a computed answer makes sense.
- Units in measurement
- Keep all measurements in the same unit before calculating.
