- Central idea
- The main point a passage makes — the claim every sentence supports; broader than any one detail but never beyond what the text says.
- Supporting detail
- A specific fact, example, or statement in a passage that backs up the central idea; a detail question asks for one stated fact, not the main point.
- Command of evidence
- Identifying the textual quotation or quantitative data point that best supports a given claim or conclusion.
- Textual evidence
- A specific quotation or line from a passage that supports a claim; the right choice must directly back the claim, not just be true.
- Quantitative evidence
- A value read from a graph or table that supports a claim; check axis labels and units before choosing.
- Inference
- A logical conclusion a passage implies but does not state outright; the correct inference is the one the text most strongly supports.
- Main idea vs. detail
- The main idea is the overall point of a passage; a detail is one specific piece of information that supports it.
- Reading for the claim
- Pinning down exactly what a passage argues before evaluating answer choices, so each choice is judged against the text's actual point.
- Two-way table (reading)
- A data display crossing two categories; read the correct row and column, and watch for 'given that' conditional wording.
- Eliminating unsupported choices
- Crossing out any answer that needs information the passage never gives — a key move on inference and evidence questions.
- Trend (data passage)
- The overall direction a graph shows (rising, falling, steady); evidence answers must match the trend actually displayed.
- Conclusion (Information & Ideas)
- The logical endpoint a passage's information leads to; choose the conclusion the text best supports, not the most dramatic one.
- Words in Context
- Choosing the word or phrase that best completes a passage based on the surrounding meaning, tone, and logic — not the dictionary definition.
- Connotation
- The emotional or tonal shade of a word beyond its literal meaning; a synonym with the wrong connotation is still wrong in context.
- Predict-then-match
- Covering the choices and predicting your own word first, then picking the closest match — the best Words in Context strategy.
- Text Structure & Purpose
- Why an author wrote a passage and how each part functions — whether a line states a claim, gives an example, or qualifies.
- Author's purpose
- The reason a writer includes a passage or line — to inform, persuade, illustrate, contrast, or qualify; name the role before checking choices.
- Cross-Text Connections
- A question pairing two short passages on one topic, asking how their authors relate — does Text 2 support, challenge, or extend Text 1?
- Point of view
- An author's stance or attitude toward the subject; cross-text questions require pinning down each author's viewpoint separately.
- Tone
- The author's attitude conveyed through word choice — e.g., cautious, critical, enthusiastic, ambivalent; supported only by the text.
- Simile
- A comparison using 'like' or 'as' — 'fierce like a lion.'
- Metaphor
- A direct comparison without 'like' or 'as,' stating one thing is another — 'a heart of stone.'
- Hyperbole
- Deliberate exaggeration for emphasis or effect, not meant to be taken literally.
- Symbol
- An object, person, or image that stands for a larger idea — e.g., an old diary representing memory or the past.
- Foreshadowing
- Hints or clues an author plants that suggest an event will happen later in the text.
- Parallel structure
- Using the same grammatical form for items in a series — 'reading, writing, and playing music' — for clarity and emphasis.
- Rhetorical synthesis
- An Expression of Ideas task: combine bulleted notes into one sentence that meets a stated goal (emphasize a contrast, introduce a topic).
- Stated goal (synthesis)
- The specific purpose a rhetorical-synthesis question gives; read it first, then pick the sentence that actually accomplishes it.
- Transition
- A word or phrase (however, therefore, for example) signaling the logical relationship between ideas — contrast, cause, addition, or example.
- Addition transitions
- furthermore, moreover, in addition, also — signal that the next idea adds to the previous one.
- Contrast transitions
- however, nevertheless, on the other hand, conversely — signal that the next idea opposes the previous one.
- Cause/effect transitions
- therefore, thus, consequently, as a result — signal that the next idea is a result of the previous one.
- Example transitions
- for example, for instance, specifically — signal that an illustration of the previous idea follows.
- Sequence transitions
- first, next, finally, subsequently — signal the order of steps or events.
- Conciseness
- Expressing an idea in as few words as needed without losing meaning; the PSAT rewards the most concise correct choice.
- Transition trap
- Using a contrast word where the ideas actually agree, or 'for example' where no example follows — name the relationship yourself first.
- Independent clause
- A group of words with a subject and verb that can stand alone as a complete sentence.
- Dependent clause
- A clause with a subject and verb that cannot stand alone (often starting with because, although, when); it needs an independent clause.
- Comma splice
- Joining two independent clauses with only a comma — an error; fix with a period, semicolon, or comma plus a conjunction.
- Semicolon
- Joins two complete, related sentences with no conjunction; can replace a period between closely linked independent clauses.
- FANBOYS
- The coordinating conjunctions — for, and, nor, but, or, yet, so; a comma + FANBOYS can join two independent clauses.
- Colon
- Introduces a list or explanation after a complete sentence — 'three items: a book, a pen, and a key.'
- Subject-verb agreement
- A verb must match its subject in number; ignore words between them and match the true subject ('the list of items is long').
- Pronoun agreement
- A pronoun must match its antecedent in number — a company is 'it,' not 'they.'
- Verb tense consistency
- Keeping verb tense consistent with the passage's timeline unless the meaning requires a shift.
- Dangling/misplaced modifier
- An opening modifier that does not describe the noun right after the comma; fix by putting the modified noun first — 'Walking to school, the students...'
- Sentence fragment
- A group of words punctuated as a sentence but missing a subject, a verb, or a complete thought; fix by attaching it to an independent clause.
- Run-on sentence
- Two independent clauses joined with no punctuation or conjunction; fix with a period, semicolon, or comma + FANBOYS.
- Its vs. it's
- 'Its' is possessive (the dog wagged its tail); 'it's' means 'it is' or 'it has.'
- Their / there / they're
- 'Their' = possessive; 'there' = a place; 'they're' = they are.
- Apostrophe (possession)
- Shows possession (the student's book) or a contraction (don't); not used to make a noun plural.
- Punctuating dialogue
- Place the comma or period inside the closing quotation mark — 'I will go,' said John.
- Nonessential information
- Detail that can be removed without changing the core meaning; set it off with a pair of commas, dashes, or parentheses.
- Slope
- The steepness of a line: change in y divided by change in x (rise over run). In y = mx + b, slope is m.
- Slope-intercept form
- y = mx + b, where m is the slope and b is the y-intercept (where the line crosses the y-axis).
- Slope between two points
- m = (y2 − y1) ÷ (x2 − x1), the change in y over the change in x.
- y-intercept
- The point where a line crosses the y-axis; in y = mx + b it is b, the value of y when x = 0.
- Parallel lines (slopes)
- Lines with equal slopes; they never intersect.
- Perpendicular lines (slopes)
- Lines whose slopes are negative reciprocals (their product is −1); they meet at a right angle.
- System of equations
- Two or more equations solved together; the solution is the point that satisfies all of them — where the graphs intersect.
- Substitution method
- Solve one equation for a variable, then substitute that expression into the other equation.
- Elimination method
- Add or subtract the equations of a system to cancel one variable, then solve for the other.
- System with no solution
- Occurs when the lines are parallel — same slope, different y-intercept; they never cross.
- System with infinite solutions
- Occurs when the two equations are multiples of each other — the same line; every point satisfies both.
- Inequality sign flip
- When you multiply or divide both sides of an inequality by a negative number, reverse the inequality sign.
- Linear equation
- An equation whose graph is a straight line, expressible as y = mx + b; it changes by a constant amount per step.
- Solving a one-variable equation
- Isolate the variable by doing the same operation to both sides — e.g., 3x + 7 = 22 gives 3x = 15, so x = 5.
- Absolute value equation
- |A| = b (b ≥ 0) means A = b or A = −b — two cases; |A| = (negative) has no solution.
- Quadratic equation
- An equation of the form ax² + bx + c = 0; solve by factoring, completing the square, or the quadratic formula.
- Quadratic formula
- x = (−b ± √(b² − 4ac)) ÷ (2a), which solves any quadratic ax² + bx + c = 0.
- Discriminant
- b² − 4ac inside the quadratic formula; positive = two real solutions, zero = one, negative = none.
- Factoring a quadratic
- Writing ax² + bx + c as a product of binomials; if it factors cleanly, factoring is faster than the formula.
- Sum and product of roots
- For ax² + bx + c = 0, the roots sum to −b/a and multiply to c/a.
- Parabola
- The U-shaped graph of a quadratic; its vertex is the maximum or minimum point.
- Vertex of a parabola
- The highest or lowest point of a quadratic's graph; the axis of symmetry passes through it at x = −b/(2a).
- Exponential function
- y = a · bˣ, where a is the starting value and b is the growth (b > 1) or decay (0 < b < 1) factor; changes by a constant percent.
- Exponential growth vs. decay
- Growth factor b > 1 (e.g., 5% growth makes b = 1.05); decay factor 0 < b < 1 (e.g., 5% decay makes b = 0.95).
- Linear vs. exponential
- Linear adds a constant amount each step; exponential multiplies by a constant percent each step.
- Function notation
- Writing a rule as f(x); f(3) means evaluate the function at x = 3.
- Difference of squares
- a² − b² = (a + b)(a − b).
- Perfect square trinomial
- (a + b)² = a² + 2ab + b²; (a − b)² = a² − 2ab + b².
- Exponent product rule
- xᵐ · xⁿ = xᵐ⁺ⁿ — add exponents when multiplying powers of the same base.
- Exponent power rule
- (xᵐ)ⁿ = xᵐⁿ — multiply exponents when raising a power to a power.
- Negative exponent
- x⁻ⁿ = 1 ÷ xⁿ — a negative exponent means reciprocal.
- Rational equation
- An equation with a variable in a denominator; solve by clearing fractions, then check for excluded values that make a denominator zero.
- Polynomial
- A sum of terms each with a variable raised to a whole-number power; degree is the highest exponent.
- Percent change
- Change ÷ original value × 100; always divide by the starting amount, not the new one.
- Percent increase shortcut
- To increase a number by 25%, multiply by 1.25; to decrease by 25%, multiply by 0.75.
- Ratio
- A comparison of two quantities (5 to 2); set up a proportion to scale it up or down.
- Proportion
- An equation stating two ratios are equal; cross-multiply to solve for the unknown.
- Unit rate
- A rate expressed per single unit — e.g., $3.00 for 12 oz is $0.25 per ounce.
- Mean
- The average: the sum of values divided by how many there are; sensitive to outliers.
- Median
- The middle value of an ordered data set; unlike the mean, it resists outliers.
- Mode
- The value that appears most often in a data set.
- Range (statistics)
- The difference between the maximum and minimum values in a data set.
- Standard deviation
- A measure of how spread out data is around the mean; a larger value means more spread.
- Probability
- Favorable outcomes ÷ total outcomes, always a number from 0 to 1.
- Skew (mean vs. median)
- Right-skewed: mean > median; left-skewed: mean < median; the skew points toward the mean.
- Correlation coefficient
- A value from −1 to 1 measuring the strength and direction of a linear relationship; its square (r²) is the fraction of variation explained.
- Two-way frequency table
- A table crossing two categories of data; read the correct row and column, and watch conditional 'given that' wording.
- Successive percent change
- Apply each change to the running total: a 25% rise then a 20% fall on a price of 50 gives 50 × 1.25 × 0.80 = 50 — back to the start.
- Pythagorean theorem
- For a right triangle with legs a and b and hypotenuse c, a² + b² = c².
- SOH-CAH-TOA
- Right-triangle trig: sin = opposite/hypotenuse, cos = adjacent/hypotenuse, tan = opposite/adjacent.
- 45-45-90 triangle
- An isosceles right triangle with side ratio 1 : 1 : √2; each leg equals the hypotenuse ÷ √2.
- 30-60-90 triangle
- A right triangle with side ratio 1 : √3 : 2 (short leg : long leg : hypotenuse).
- Pythagorean triple
- Whole-number right-triangle sides such as 3-4-5, 5-12-13, and 7-24-25.
- Complementary angles (trig)
- Two angles that sum to 90°; sin θ = cos(90° − θ).
- Triangle angle sum
- The interior angles of any triangle add to 180°.
- Angles on a straight line
- Angles on a straight line sum to 180°; angles around a point sum to 360°.
- Area of a triangle
- Area = ½ × base × height.
- Area of a circle
- Area = πr², where r is the radius.
- Circumference of a circle
- C = 2πr (or πd), where r is the radius and d the diameter.
- Equation of a circle
- (x − h)² + (y − k)² = r², a circle centered at (h, k) with radius r.
- Volume of a sphere
- V = (4/3)πr³, where r is the radius.
- Interior angle of a regular polygon
- Each interior angle = (n − 2) × 180° ÷ n, where n is the number of sides (e.g., a regular octagon = 135°).
- Similar triangles
- Triangles with equal corresponding angles and proportional sides; set up a ratio to find a missing length.
- Transversal angles
- When a transversal cuts parallel lines, corresponding and alternate angles are equal; co-interior angles sum to 180°.
- Equilateral triangle area
- Area = (√3 ÷ 4) × side²; for side 12, area ≈ 62.35 square units.
- PSAT/NMSQT
- The Preliminary SAT / National Merit Scholarship Qualifying Test — a digital practice SAT, given each October, that qualifies juniors for National Merit.
- Multistage adaptive testing
- A design where the difficulty of a section's second module depends on your first-module performance; doing well on Module 1 unlocks a harder, higher-scoring Module 2.
- Module (PSAT)
- Half of a PSAT section; each section has two modules — R&W is 27 questions × 32 min, Math is 22 questions × 35 min.
- PSAT score scale
- 320–1520 total, the sum of a Reading & Writing section score and a Math section score, each 160–760.
- Selection Index
- (Reading & Writing score × 2 + Math score) ÷ 10, ranging 48–228 — the number National Merit uses for recognition.
- National Merit Scholarship Program
- A scholarship competition juniors enter by taking the PSAT/NMSQT; high scorers become Commended Students, Semifinalists, and Finalists.
- Commended Student
- A National Merit recognition for scorers above the nationwide Commended cutoff (usually a Selection Index around 207–209) but below the state Semifinalist cutoff.
- Semifinalist (National Merit)
- A junior whose Selection Index meets the state-specific cutoff; Semifinalists may advance to Finalist and compete for scholarships.
- Bluebook app
- The College Board's digital testing application used to take the PSAT/NMSQT and SAT on a computer.
- Desmos calculator
- The graphing calculator built into the PSAT Math section; available on every Math question.
- No guessing penalty
- Wrong answers never cost points on the PSAT, so you should answer every question.
- PSAT vs. SAT
- The PSAT/NMSQT uses the same digital framework and content domains as the SAT, on a 320–1520 scale instead of 400–1600.
- Reading & Writing section
- 54 questions in two 32-minute modules; short passages, each with one multiple-choice question across four R&W domains.
- Math section (PSAT)
- 44 questions in two 35-minute modules; a mix of multiple-choice and student-produced (grid-in) responses, calculator allowed throughout.