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Your FREE ISEE Flashcards 2026 – 250+ Cards

Realistic, ISEE exam-style flashcards across Verbal, Quantitative, Reading, Math & Essay — flip, match, type, and quiz yourself.

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Click Study Flashcards above to open the flashcard hub — 250+ ISEE cards you can flip, match, type, or quiz yourself on. Every card is drawn from the five ISEE sections, so you study exactly what the exam tests.[1] Pair them with our free practice test and study guide.

ISEE Flashcard Study Modes

Flip mode moves you through one card at a time at your own speed. Match turns the same cards into a timed pairing game. Type shows a definition and asks you to produce the term, so a front like Unit rate has to come back from memory, not recognition. Quiz builds multiple-choice questions from the deck so you can check yourself under pressure.

Free ISEE flashcards from Career Employer — active recall for Verbal, Quantitative, Reading, and Math

Why Flashcards Work for the ISEE

Verbal Reasoning is the biggest block at 84 cards, and most of it is morphology: prefixes and roots that let you decode a synonym or sentence-completion word you have never seen. Expect fronts like Prefix: re-, Prefix: sub-, and Root: ’mal’, each pushing you toward meaning rather than memorized word lists.

Mathematics Achievement follows with 63 cards covering the computation and definitions behind the math section. You get procedure cards such as Divide fractions, concept cards like Types of angles, and the card that asks What is slope?, so the arithmetic and the vocabulary that frames it get drilled together.

Quantitative Reasoning holds 37 cards aimed at the number sense behind comparison questions. Prompts like What is a factor? and What is the median? pin down the vocabulary those items assume, while Compare exponents drills the side-by-side judgment the section is built on.

Reading Comprehension has 36 cards on the language used to ask about passages. Cards that ask What is an inference? and What is personification? sit beside structure cards like Cause-and-effect structure, so a question about device, tone, or organization is recognizable before you reread the passage.

Essay & Test Strategy closes the deck with 34 cards on the written prompt and on how the test itself works. Basic essay structure and Pacing strategy shape what you do during the sitting, while the card that asks How is the ISEE scored? covers the reporting you will see afterward.

That matters for the ISEE, which rewards instant recall of vocabulary, math formulas (the area of a circle, the Pythagorean theorem, percent change), and reading strategies. Used alongside our practice test and study guide, flashcards turn review time into measurable progress.[3]

ISEE Flashcards by Section

The cards are organized by the five ISEE sections. Weight your study toward the biggest sections — Mathematics Achievement is the largest, and two of the four scored sections are math, so vocabulary and math both deserve heavy review:[1]

ISEE flashcards by section (2026, Upper / Middle Level)
SectionWhat it coversQuestions
Verbal ReasoningSynonyms, sentence completion, word roots40
Quantitative ReasoningWord problems, quantitative comparisons, data37
Reading ComprehensionMain idea, inference, vocabulary, tone36
Mathematics AchievementNumbers, algebra, geometry, measurement, data47
Essay & test strategyStructure, scoring, guessing, pacingUnscored essay

How to Get the Most Out of These Flashcards

  • Start with Verbal Reasoning. At 84 cards it is the largest domain here, and the prefix and root fronts pay off across synonyms and sentence completions, so front-load them.
  • Type-drill the roots. Fronts like Root: ’aud’ and Root: ’dict’ reward exact recall, and typing the meaning back forces precision that a quick Flip-mode glance lets you fake.
  • Let Match handle the labels. Reading Comprehension terms such as the card that asks What is hyperbole? pair cleanly with short definitions, so the timed game builds speed at naming devices.
  • Switch when recall is stable. Once Quiz runs clean across Mathematics Achievement and Quantitative Reasoning, move to the practice test for pacing and stamina, then use the study guide on whatever it exposes.
  • Keep sessions small. With 254 cards, work one domain per sitting and revisit Essay & Test Strategy, the smallest at 34 cards, in short repeated passes instead of saving it for the end.

ISEE Flashcards FAQ

Hundreds of free ISEE flashcards, organized across all five sections — Verbal Reasoning, Quantitative Reasoning, Reading Comprehension, Mathematics Achievement, and Essay & test strategy. They're free to use with no account required.

ISEE flashcard bank

All 254 cards, by topic

A reference copy of every card in this deck. Each answer stays hidden until you choose to show it. To study with Flip, Match, Type and Quiz modes and track what you have mastered, use Study Flashcards at the top of the page.

Verbal Reasoning (84)

What is a synonym?
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A word that means the same (or nearly the same) as another. ISEE Verbal Reasoning synonym questions give a capitalized word and ask for the answer choice closest in meaning.

What is an antonym?
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A word that means the opposite of another (hot/cold, expand/contract). Watch for antonyms hiding among synonym answer choices as traps.

Synonym for ABUNDANT
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Plentiful. (More than enough; in great supply.) Antonym: scarce.

Synonym for BRITTLE
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Fragile. (Hard but easily broken or snapped.) Antonym: flexible.

Synonym for CANDID
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Frank, honest, and direct in speech.

Synonym for FRUGAL
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Thrifty; careful and economical with money or resources. Antonym: wasteful.

Synonym for MUNDANE
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Ordinary, everyday, dull. Antonym: extraordinary.

Synonym for ZEALOUS
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Eager, enthusiastic, and devoted to a cause.

Synonym for LENIENT
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Merciful; tolerant and not strict in punishment. Antonym: harsh.

Synonym for DOCILE
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Obedient; easy to manage or teach. Antonym: defiant.

Synonym for TRIVIAL
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Minor; of little importance. Antonym: significant.

Synonym for BENEVOLENT
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Kind and generous; wishing to do good. Antonym: cruel.

Synonym for METICULOUS
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Showing great care and attention to detail. Antonym: careless.

Synonym for TENACIOUS
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Persistent; holding firmly and not giving up.

Synonym for AMBIGUOUS
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Open to more than one interpretation; unclear or vague.

Synonym for OBSOLETE
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No longer in use; outdated.

Synonym for VIVID
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Bright, intense, and lifelike; producing a strong, clear image.

Synonym for RELUCTANT
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Unwilling or hesitant to do something. Antonym: eager.

Synonym for ABRUPT
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Sudden and unexpected; or curt in manner.

Synonym for SCARCE
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In short supply; rare or insufficient. Antonym: abundant.

Synonym for DILIGENT
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Hardworking and showing careful, persistent effort.

Synonym for CONCEAL
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To hide or keep secret. Antonym: reveal.

Synonym for FERTILE
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Producing abundant growth; rich and productive (soil, ideas). Antonym: barren.

Synonym for FEEBLE
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Weak; lacking strength. Antonym: robust.

Synonym for HOSTILE
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Unfriendly and aggressive; antagonistic. Antonym: friendly.

What is a sentence completion question?
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A Verbal Reasoning question with a sentence missing one (or sometimes two) words; you pick the word(s) that best fit the sentence's meaning and tone.

Sentence completion strategy: predict first
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Before reading the choices, cover them and predict a word that fits the blank. Then choose the answer closest to your prediction. This avoids being trapped by tempting wrong words.

Sentence completion: use context clues
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Look for signal words. 'Although / but / however' signal contrast; 'because / therefore / so' signal cause and effect; 'and / also' signal a similar idea. They tell you the direction of the blank.

What is a context clue?
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Information in the surrounding words or sentence that helps you figure out the meaning of an unknown word or the best word for a blank.

Synonym strategy: think of the word in a sentence
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If you know the capitalized word, put it in a sentence, then test which answer choice could replace it. If you do not know it, use word roots, prefixes, and suffixes.

Prefix: un-, in-, im-, dis-
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Mean 'not' or the opposite (unhappy, invisible, impossible, disagree). Spotting a negative prefix helps you decode an unfamiliar word.

Prefix: re-
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Means 'again' or 'back' (rewrite, return, replay).

Prefix: pre-
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Means 'before' (preview, prehistoric, predict).

Prefix: mis-
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Means 'wrongly' or 'badly' (misunderstand, misplace, mislead).

Root: 'bene'
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Means 'good' or 'well' (benefit, benevolent, beneficial).

Root: 'mal'
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Means 'bad' or 'evil' (malice, malfunction, malevolent).

Root: 'aud'
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Means 'hear' (audible, audience, auditory).

Root: 'spec / spect'
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Means 'look' or 'see' (inspect, spectator, spectacle).

Root: 'port'
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Means 'carry' (transport, portable, export).

Suffix: -ous
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Means 'full of' and makes an adjective (joyous, dangerous, courageous).

Suffix: - less
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Means 'without' (fearless, hopeless, careless).

Synonym for ELOQUENT
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Fluent, persuasive, and expressive in speaking or writing.

Synonym for INDIFFERENT
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Having no interest or concern; unconcerned. Antonym: passionate.

Synonym for PROVOKE
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To stir up or trigger a reaction; to deliberately annoy.

Synonym for SUBTLE
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Delicate; so slight as to be hard to notice. Antonym: obvious.

Synonym for VIGILANT
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Watchful and alert, especially for danger or problems.

Synonym for ARID
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Extremely dry; lacking moisture (an arid desert).

Synonym for QUERY
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A question or inquiry.

Synonym for NOVICE
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A beginner; someone new and inexperienced. Antonym: expert.

Synonym for INEVITABLE
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Certain to happen; unavoidable.

Two-blank sentence completion tip
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Some Upper Level sentences have two blanks. Solve the easier blank first, eliminate any choice that fails it, then test the remaining pairs for the second blank.

Synonym for COMPEL
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To force or strongly urge someone to do something.

Synonym for FUTILE
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Pointless; incapable of producing a useful result.

Synonym for LUMINOUS
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Giving off light; bright or glowing.

Synonym for PROFOUND
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Very deep or intense in meaning or feeling. Antonym: shallow.

Synonym for OPTIMISTIC
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Hopeful and confident about the future. Antonym: pessimistic.

Synonym for COURTEOUS
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Polite, respectful, and considerate. Antonym: rude.

Synonym for SOLITARY
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Alone; existing or done by one person. Antonym: accompanied.

Synonym for IMMENSE
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Extremely large or great in size. Antonym: tiny.

Synonym for HASTY
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Done in a hurry; rushed and often careless. Antonym: deliberate.

Synonym for GENEROUS
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Willing to give freely; unselfish. Antonym: stingy.

Synonym for PECULIAR
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Strange or unusual; odd.

Synonym for ANCIENT
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Very old; belonging to the distant past. Antonym: modern.

Synonym for TIMID
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Shy and lacking courage. Antonym: bold.

Synonym for GRADUAL
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Happening slowly, by small steps. Antonym: sudden.

Synonym for ESSENTIAL
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Absolutely necessary; extremely important.

Synonym for VACANT
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Empty; not occupied. Antonym: occupied.

Synonym for FLEXIBLE
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Able to bend easily; willing to change. Antonym: rigid.

Synonym for HUMBLE
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Modest; not proud or arrogant. Antonym: arrogant.

Synonym for RADIANT
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Shining brightly; glowing with light or joy.

Synonym for STUBBORN
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Unwilling to change one's mind; obstinate.

Synonym for ABOLISH
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To formally end or do away with (a law or system).

Synonym for VAGUE
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Unclear; not definite or precise. Antonym: specific.

Synonym for SUMMIT
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The highest point or top, especially of a mountain.

Root: 'dict'
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Means 'say' or 'speak' (dictate, predict, contradict).

Root: 'scrib / script'
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Means 'write' (describe, manuscript, scribble).

Root: 'tele'
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Means 'far' or 'distant' (telephone, telescope, television).

Root: 'geo'
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Means 'earth' (geography, geology, geometry).

Prefix: trans-
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Means 'across' or 'through' (transport, translate, transfer).

Prefix: sub-
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Means 'under' or 'below' (submarine, subway, substandard).

Suffix: -able / -ible
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Means 'capable of' (readable, flexible, possible).

Suffix: -tion / -sion
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Turns a verb into a noun meaning an act or state (action, decision, tension).

Synonym for PERSUADE
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To convince someone to do or believe something.

Synonym for ABUNDANCE
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A large quantity; plenty. Antonym: shortage.

Quantitative Reasoning (37)

What does ISEE Quantitative Reasoning test?
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Math reasoning and problem solving rather than computation. Lower Level has word problems only; Middle and Upper Levels add quantitative comparison questions.

What is a quantitative comparison question?
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A Middle/Upper Level Quantitative Reasoning format that gives Column A and Column B. You decide whether A is greater, B is greater, the two are equal, or the relationship cannot be determined.

The four quantitative-comparison answer choices
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(A) Column A is greater, (B) Column B is greater, (C) the two quantities are equal, (D) the relationship cannot be determined from the information given. They are the same on every QC question.

Quantitative comparison strategy: plug in numbers
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When a variable is involved, try several values — including 0, 1, a fraction, and a negative — for each column. If the comparison changes, the answer is (D).

Order of operations (PEMDAS)
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Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right). Example: 2 + 3 × 4 = 2 + 12 = 14.

What is the mean (average)?
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The sum of the values divided by how many values there are. Mean of 4, 9, 20 = 33 ÷ 3 = 11.

What is the median?
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The middle value of a data set when the numbers are put in order. For an even count, average the two middle numbers. The median resists outliers.

What is the mode?
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The value that appears most often in a data set. A set can have one mode, more than one, or none.

What is the range of a data set?
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The largest value minus the smallest value. Range of 4, 9, 20 = 20 − 4 = 16.

What is a factor?
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A whole number that divides evenly into another with no remainder. The factors of 12 are 1, 2, 3, 4, 6, 12.

What is a multiple?
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The product of a number and any whole number. Multiples of 6: 6, 12, 18, 24… The LCM of 6 and 15 is 30.

What is a prime number?
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A whole number greater than 1 whose only factors are 1 and itself (2, 3, 5, 7, 11, 13…). 2 is the only even prime.

What is probability?
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Favorable outcomes ÷ total outcomes, a number from 0 to 1. The probability of rolling a 3 on a fair die is 1/6.

What is a ratio?
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A comparison of two quantities, written a : b or a/b. A 3 : 2 ratio of boys to girls in 30 students means 18 boys and 12 girls.

What is a proportion?
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An equation stating two ratios are equal (a/b = c/d). Solve by cross-multiplying: a × d = b × c.

Estimate before computing
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On Quantitative Reasoning, estimate or round to eliminate choices quickly — you often do not need an exact answer to know which column is larger.

What is the perimeter of a shape?
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The total distance around it — the sum of all side lengths. A square with side 6 has perimeter 4 × 6 = 24.

What is the area of a rectangle?
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length × width. A rectangle 8 by 4 has area 32 and perimeter 2 × (8 + 4) = 24.

Interior angles of a triangle
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Always sum to 180°. An equilateral triangle has three equal 60° angles.

What is an exponent?
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A small raised number showing repeated multiplication. 2 to the 4th power = 2 × 2 × 2 × 2 = 16; 4 squared = 16, so they are equal.

What is a fraction of a number?
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Multiply the fraction by the number. Three-fourths of 60 = (3 ÷ 4) × 60 = 45.

Quantitative comparison: simplify both columns
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Do any safe operation to both columns (add the same number, divide both by the same positive value) to make them easier to compare — like balancing an equation.

Percent of a number
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Convert the percent to a decimal and multiply. 60% of 80 = 0.6 × 80 = 48. Note 60% of 80 equals 80% of 60.

What is an integer?
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A whole number and its opposites, including zero: …−2, −1, 0, 1, 2… No fractions or decimals.

Number between −1 and 0
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It is negative and smaller than 0, so it is less than any positive number and less than its own square (since squaring a fraction makes it closer to 0).

Quantitative comparison: when is the answer (D)?
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Choose (D), cannot be determined, when plugging in different allowed values changes which column is larger. If the relationship is not fixed, it's (D).

Compare fractions by cross-multiplying
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To compare a/b and c/d, cross-multiply: compare a×d with b×c. Whichever product is larger marks the larger fraction (for positive numbers).

Estimate a percent quickly
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10% of a number is the number with the decimal moved one place left; 1% moves it two places. Build other percents from these (20% = two 10%s; 5% = half of 10%).

Squaring a fraction between 0 and 1
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Makes it smaller, not larger. For example, one half squared is one quarter, which is less than one half. This is a common comparison trap.

Even and odd number rules
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even ± even = even; odd ± odd = even; even ± odd = odd. even × anything = even; odd × odd = odd.

Compare exponents
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Rewrite with the same base when you can. 2 to the 4th is 16 and 4 squared is 16, so they're equal. Watch that a bigger base doesn't always win once exponents differ.

Reasoning shortcut: look before you compute
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Many comparisons can be solved by reasoning (sign, size, parity) without finishing the arithmetic — the section rewards logic over calculation.

What is a whole-number factor count?
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List factor pairs to count factors. 16 = 1×16, 2×8, 4×4 → factors 1, 2, 4, 8, 16 (five). 10 = 1×10, 2×5 → four factors.

Reading a word problem
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Underline what is asked, list the given numbers, choose the operation that matches the words ('total' = add, 'left' = subtract, 'each' = multiply or divide), then solve.

Backsolving with answer choices
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When choices are numbers, plug them into the problem and see which one works. Start with a middle value to narrow up or down quickly.

Sequences and patterns
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Find the rule between terms (add a constant, multiply by a constant). 2, 5, 8, 11… adds 3 each time, so the next term is 14.

Logical reasoning with 'at least' / 'at most'
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'At least 5' means 5 or more (≥ 5); 'at most 5' means 5 or fewer (≤ 5). Reading these correctly prevents off-by-one errors.

Reading Comprehension (36)

What does ISEE Reading Comprehension test?
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Your ability to read short passages and answer questions about main idea, supporting details, inferences, vocabulary in context, tone, and the author's purpose or organization.

What is the main idea of a passage?
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The central point the whole passage supports — broader than any single detail but never beyond what the text actually says. Often found in the first or last sentence of a paragraph.

Main idea vs. supporting detail
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The main idea is the overall point; a supporting detail is a specific fact, example, or reason that backs it up. A main-idea answer that is too narrow (just one detail) is wrong.

What is an inference?
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A logical conclusion the passage strongly implies but does not state outright. The correct inference is the one the text best supports — not the most dramatic guess.

What is 'vocabulary in context'?
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Choosing the meaning a word has as it is used in the passage. A word can have several dictionary meanings; use the surrounding sentence to pick the right one.

What is the author's purpose?
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The reason the author wrote the passage — to inform, persuade, entertain, or describe. Ask what the writer wants the reader to think, feel, or do.

What is tone in reading?
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The author's attitude toward the subject, shown by word choice (wistful, critical, admiring, neutral, humorous). Look at the connotation of key words.

What is text organization (structure)?
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How a passage is arranged — for example chronological order, cause and effect, compare and contrast, or problem and solution. Questions may ask how one part functions.

Reading strategy: answer from the passage only
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Every correct answer must be supported by the text in front of you, not by outside knowledge. If a choice needs information the passage never gives, eliminate it.

Reading strategy: read the questions' scope
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Some questions ask about the whole passage (main idea, tone) and some about one line or word. For line questions, reread a sentence or two around the reference.

Reading strategy: watch extreme words
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Answer choices with 'always, never, all, none, only' are often too strong to be supported. Passages usually allow for exceptions, so extreme choices are frequently wrong.

What is a summary?
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A brief restatement of a passage's main points in your own words, leaving out minor details. A good summary captures the main idea, not every example.

What is a fact vs. an opinion?
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A fact can be proven true or false; an opinion expresses a belief, judgment, or feeling. ISEE passages may ask you to tell them apart.

What does 'connotation' mean?
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The feeling or association a word carries beyond its literal meaning. 'Thrifty' and 'cheap' have similar definitions but different connotations (positive vs. negative).

What does 'denotation' mean?
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The literal dictionary definition of a word, without emotional coloring. Contrast it with connotation.

What is a passage's 'purpose' question phrased like?
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Often 'The author wrote this passage mainly to…' or 'The primary purpose is to…'. Choose the verb (describe, argue, explain) that matches the whole passage.

Reading strategy: paraphrase before you choose
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Answer the question in your own words first, then find the choice that matches your paraphrase. This protects you from tempting but unsupported answers.

What is figurative language?
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Language that means more than its literal words — similes, metaphors, and personification. ISEE passages may use it, and questions may ask what it suggests.

What is a simile?
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A comparison using 'like' or 'as' (brave as a lion). Compare with a metaphor, which states one thing IS another.

What is a metaphor?
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A direct comparison that says one thing is another without 'like' or 'as' (the classroom was a zoo).

What types of passages appear on the ISEE?
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Both literary/narrative texts and informational/nonfiction texts on subjects such as science, history, and the humanities. You never need prior subject knowledge.

Reading strategy: use the time wisely
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There is no penalty for wrong answers, so never leave a reading question blank. If a passage is hard, answer the detail and vocabulary questions first, then the harder inference ones.

What is 'supporting evidence'?
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The specific words, sentences, or facts in the passage that justify an answer. Strong readers can point to the exact line that supports each choice.

How do you answer a 'detail' question?
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Find the specific line in the passage that states the fact, and choose the answer that matches it. Don't rely on memory — go back and reread the relevant sentence.

What is a passage's 'purpose'?
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Why the author wrote it: to inform, persuade, entertain, or describe. Match the verb to the whole passage, not just one paragraph.

How to handle a 'NOT / EXCEPT' question
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Three choices are true (or supported) and one is not — you want the odd one out. Check each choice against the passage and eliminate the supported ones.

Compare-and-contrast structure
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A passage that shows similarities and differences between two things. Signal words: 'like, similarly, both' (compare) and 'unlike, however, whereas' (contrast).

Cause-and-effect structure
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A passage that explains why something happened and what resulted. Signal words: 'because, since, as a result, therefore, leads to'.

Chronological (sequence) structure
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Events told in time order. Signal words: 'first, then, next, later, finally, in 1920'. Questions may ask what happened before or after an event.

Identifying the narrator's point of view
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First person uses 'I / we'; third person uses 'he / she / they'. Point of view affects what the reader knows and how events are described.

What is the theme of a literary passage?
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The deeper message or lesson about life — for example, 'perseverance pays off'. It's broader than the plot and not usually stated outright.

Reading strategy: skim then dig
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Read the passage for the gist first, then go back to specific lines for detail and vocabulary questions. Don't try to memorize every fact on the first read.

What is personification?
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Giving human qualities to something non-human ('the wind whispered'). It's a type of figurative language that questions may ask you to interpret.

What is hyperbole?
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Deliberate, obvious exaggeration for effect ('I've told you a million times'). It is not meant to be taken literally.

How do you find a word's meaning in context?
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Read the whole sentence, look for clues (a definition, an example, a contrast), and test each choice by substituting it back in. Keep the one that preserves the meaning.

Reading strategy: eliminate, don't just pick
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Cross out choices that are off-topic, too extreme, or unsupported by the text. The right answer is the one left standing that the passage supports.

Mathematics Achievement (63)

What does ISEE Mathematics Achievement test?
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Grade-level math knowledge aligned to school standards — numbers and operations, algebra, geometry, measurement, and data analysis and probability. It rewards computation and applying concepts.

Add fractions with unlike denominators
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Find a common denominator, rewrite each fraction, then add the numerators. 1/6 + 3/4 → 2/12 + 9/12 = 11/12.

Multiply two fractions
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Multiply the numerators and multiply the denominators, then simplify. 2/3 × 3/5 = 6/15 = 2/5.

Divide fractions
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Multiply by the reciprocal of the second fraction (flip and multiply). 1/2 ÷ 1/4 = 1/2 × 4/1 = 2.

Convert a fraction to a decimal
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Divide the numerator by the denominator. 7/20 = 7 ÷ 20 = 0.35.

Convert a fraction to a percent
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Convert to a decimal, then multiply by 100. 1/5 = 0.2 = 20%.

Find the percent of a number
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Multiply the decimal form of the percent by the number. 60% of 45 = 0.6 × 45 = 27.

What is percent change?
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The change divided by the ORIGINAL value, times 100. From 80 to 100: change 20 ÷ 80 = 0.25 = 25% increase. Always divide by the starting amount.

Prime factorization
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Writing a number as a product of primes. 84 = 2 × 2 × 3 × 7 (also written 2² × 3 × 7).

Greatest common factor (GCF)
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The largest number that divides two values evenly. GCF of 16 and 40 is 8.

Least common multiple (LCM)
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The smallest number both values divide into. LCM of 4 and 10 is 20; LCM of 9 and 12 is 36.

Solve a one-step equation
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Do the inverse operation to both sides. For x + 7 = 12, subtract 7: x = 5. For 3x = 15, divide by 3: x = 5.

Solve a two-step equation
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Undo addition/subtraction first, then multiplication/division. 2x + 3 = 11 → 2x = 8 → x = 4.

Combine like terms
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Add or subtract terms with the same variable. 3x + 5x = 8x; 4y + 2 − y = 3y + 2. Constants combine with constants.

Evaluate an algebraic expression
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Substitute the given value for the variable, then simplify using order of operations. If x = 4, then 2x + 1 = 2(4) + 1 = 9.

The distributive property
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a(b + c) = ab + ac. Example: 3(x + 5) = 3x + 15.

Area of a triangle
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½ × base × height. A triangle with base 10 and height 6 has area ½ × 10 × 6 = 30.

Area and circumference of a circle
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Area = π × r²; circumference = 2 × π × r. A radius of 5 gives area 25π and circumference 10π.

The Pythagorean theorem
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For a right triangle with legs a and b and hypotenuse c, a² + b² = c². A 3-4-5 triangle works: 3² + 4² = 9 + 16 = 25 = 5².

Volume of a rectangular prism (box)
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length × width × height. A box 3 by 4 by 5 has volume 60 cubic units.

What is a coordinate plane?
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A grid formed by a horizontal x-axis and vertical y-axis. A point is written (x, y); the origin is (0, 0).

What is slope?
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The steepness of a line: rise over run, the change in y divided by the change in x. In y = mx + b, the slope is m.

Rules for negative numbers
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A negative times a negative is positive; a negative times a positive is negative. Subtracting a negative is the same as adding: 5 − (−3) = 8.

Absolute value
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The distance of a number from 0 on the number line, always non-negative. |−7| = 7 and |7| = 7.

Rounding a number
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Look at the digit to the right of the rounding place; if it is 5 or more, round up, otherwise round down. 3.47 rounds to 3.5 (to the tenths).

Convert between units (measurement)
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Multiply or divide by the conversion factor. 1 foot = 12 inches, 1 meter = 100 cm, 1 hour = 60 minutes. 3 feet = 36 inches.

Mean from a total
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If 5 tests average 80, the total is 5 × 80 = 400. Use the total to find a missing score or a new average.

Number of factors of a number
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List the factor pairs. 28 = 1×28, 2×14, 4×7 → factors 1, 2, 4, 7, 14, 28, so 28 has 6 factors.

What is a square root?
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A square root (written √n) is the value that, multiplied by itself, gives n. For example, 36=6\sqrt{36}=6 because 6 × 6 = 36, and 81=9\sqrt{81}=9.

Convert a percent to a fraction
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Write the percent over 100 and simplify. 25% = 25/100 = 1/4; 60% = 60/100 = 3/5.

Ratio word problem
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Add the ratio parts to find the total share, then scale. A 3 : 2 ratio over 30 items: 3 + 2 = 5 parts, each part = 6, so 18 and 12.

Reading a bar graph or table
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Read the axis labels and units first, then find the value at the row/column you need. Watch the scale — bars may count by 2s, 5s, or 10s.

Mixed-number to improper fraction
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Multiply the whole number by the denominator, add the numerator, keep the denominator. 2 ¾ = (2×4 + 3)/4 = 11/4.

Average speed
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Distance ÷ time. A car going 120 miles in 2 hours averages 60 miles per hour. Keep units consistent.

Solve a proportion (word problem)
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Set the two ratios equal and cross-multiply. If 3 pens cost $1.50, then 10 pens cost x: 3/1.50 = 10/x → x = $5.00.

Exponent rules (basic)
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Multiply same bases: add exponents (x² × x³ = x⁵). Power of a power: multiply (x²)³ = x⁶. Anything to the 0 power = 1.

Perimeter vs. area
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Perimeter is the distance around (in units); area is the space inside (in square units). Don't confuse them on word problems.

Multiply decimals
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Multiply as whole numbers, then place the decimal point so the answer has as many decimal places as the two factors combined. 0.3 × 0.4 = 0.12.

Divide decimals
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Move the decimal point in the divisor to make it a whole number, move it the same number of places in the dividend, then divide. 1.2 ÷ 0.4 = 12 ÷ 4 = 3.

Convert a decimal to a percent
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Multiply by 100 (move the decimal two places right). 0.35 = 35%; 0.07 = 7%.

Simplify a fraction
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Divide the numerator and denominator by their greatest common factor. 6/15 = 2/5 (both divided by 3).

Find a percent of a number (word problem)
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Translate 'of' to multiply and the percent to a decimal. '15% of 60' = 0.15 × 60 = 9.

Solve an inequality
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Solve like an equation, but flip the inequality sign when you multiply or divide both sides by a negative number. −2x < 6 → x > −3.

Plot a point on the coordinate plane
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A point (x, y) is x units right (or left if negative) and y units up (or down if negative) from the origin (0, 0).

Find the slope from two points
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Slope = (change in y) ÷ (change in x). From (1, 2) to (3, 8): (8 − 2) ÷ (3 − 1) = 6 ÷ 2 = 3.

Area of a parallelogram
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base × height (the perpendicular height, not the slanted side).

Area of a trapezoid
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½ × (base 1 + base 2) × height — average the two parallel sides, then multiply by the height.

Surface area vs. volume
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Surface area is the total area of all faces (square units); volume is the space inside (cubic units). Don't confuse the two.

Volume of a cylinder
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π × r² × height — the area of the circular base times the height.

Perimeter of a circle (circumference)
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2 × π × r, or π × diameter. With radius 5, circumference = 10π ≈ 31.4.

Types of angles
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Acute < 90°, right = 90°, obtuse between 90° and 180°, straight = 180°. Complementary angles sum to 90°; supplementary angles sum to 180°.

Triangle angle sum
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The three interior angles of any triangle add to 180°. If two angles are 50° and 60°, the third is 70°.

Classify triangles by sides
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Equilateral = three equal sides (and three 60° angles); isosceles = two equal sides; scalene = no equal sides.

Ratio word problem (scaling)
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Add the parts to get the total share, find one part, then scale. A 2 : 3 ratio across 25: 2 + 3 = 5 parts, each = 5, so 10 and 15.

Unit rate
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A rate with a denominator of 1, like miles per hour or cost per item. $6 for 3 pens is $2 per pen.

Average of several numbers
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Add them and divide by how many there are. The average of 80, 90, and 100 is 270 ÷ 3 = 90.

Find a missing value given an average
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Multiply the average by the count to get the total, then subtract the known values. If four numbers average 50, their total is 200.

Exponent: anything to the power 0 or 1
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Any non-zero number to the 0 power equals 1; any number to the 1st power equals itself. 7⁰ = 1, 7¹ = 7.

Negative exponent
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A negative exponent means the reciprocal: 2⁻³ = 1 ÷ 2³ = 1/8.

Reading a pie (circle) chart
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Each slice is a fraction or percent of the whole; the whole circle is 100% (or 360°). A 25% slice is a right angle, 90°.

Mixed number arithmetic
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Convert to improper fractions to add, subtract, multiply, or divide, then convert back. 1 ½ + 2 ¼ = 3/2 + 9/4 = 6/4 + 9/4 = 15/4 = 3 ¾.

Estimate a square root
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Find the nearest perfect squares. 50\sqrt{50} is between 7 (since 72=497^2=49) and 8 (since 82=648^2=64), and closer to 7.

Distance, rate, and time
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distance = rate × time. So rate = distance ÷ time and time = distance ÷ rate. 150 miles at 50 mph takes 3 hours.

Essay & Test Strategy (34)

Is the ISEE essay scored?
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No. The essay is unscored, but a copy is sent to every school you apply to, so admissions officers read it as a writing sample. Treat it as if it matters — because it does.

What is the ISEE essay?
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A handwritten response to a single age-appropriate prompt, written in a set time at the end of the test. There are no answer choices — you plan and write an organized essay.

Basic essay structure
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Introduction with a clear thesis, two or three body paragraphs each with one main point and supporting details, and a short conclusion that restates your position.

What is a thesis statement?
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A single sentence near the start of your essay that states your main point or position. Everything in the essay should support it.

What is a topic sentence?
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The sentence that states the main idea of a paragraph, usually first. Each body paragraph needs one so the reader can follow your argument.

Essay strategy: plan before you write
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Spend the first few minutes outlining — pick a position, list two or three reasons with examples, then write. A planned essay is clearer than one written off the top of your head.

Essay strategy: answer the prompt
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Read the prompt carefully and address exactly what it asks. A well-written essay that drifts off topic still reads as not following directions.

Essay: use specific examples
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Support each point with concrete examples — from school, reading, history, or personal experience. Specific details are far more convincing than vague, general statements.

Essay: leave time to proofread
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Save a minute or two at the end to check spelling, punctuation, and capitalization, and to make sure every sentence is complete. Neat, error-free writing makes a better impression.

How is the ISEE scored?
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Each scored section gets a scaled score, a percentile rank (compared with other applicants of the same grade), and a stanine from 1 to 9. The essay is not scored.

What is a stanine?
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A score from 1 to 9 based on percentile rank. Stanines 1–3 are below average, 4–6 are average, and 7–9 are above average for your applicant grade group.

What is a percentile rank?
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The percent of students in the same-grade norm group you scored higher than. A 75th percentile means you scored better than about 75% of comparable applicants.

Is there a guessing penalty on the ISEE?
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No. Your score is based only on the number of questions you answer correctly, so you should answer every question, even if you have to guess.

Smart-guessing strategy
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Eliminate any answer choices you know are wrong, then guess among the rest. With no penalty for wrong answers, a guess is always better than a blank.

Pacing strategy
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Each section is timed, so don't get stuck. Answer the questions you find easy first, mark and skip hard ones, and circle back with the time that remains.

Who administers the ISEE?
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The Educational Records Bureau (ERB). The ISEE is used for admission to many independent (private) schools.

What are the ISEE levels?
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Primary (lower grades), Lower Level (applying to grades 5–6), Middle Level (applying to grades 7–8), and Upper Level (applying to grades 9–12). You take the level for the grade you're entering.

The five parts of the ISEE (in order)
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Verbal Reasoning, Quantitative Reasoning, Reading Comprehension, Mathematics Achievement, and an unscored Essay — in that order.

How often can you take the ISEE?
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Once per testing season. ERB defines three seasons (Fall, Winter, Spring), so a student may take it up to three times in a 12-month admissions cycle.

Essay: write legibly
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The essay is handwritten and read by admissions staff. Write neatly in print or cursor you can read — a great essay that can't be read can't help you.

Essay conclusion tip
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Restate your thesis in fresh words and briefly remind the reader of your strongest reason. Don't introduce a brand-new argument in the conclusion.

Transition words for essays
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Use them to connect ideas: 'first / next / finally' (sequence), 'for example' (illustration), 'however' (contrast), 'therefore' (result). They make your essay flow.

How many ISEE answer choices are there?
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Four answer choices per multiple-choice question. (The competing SSAT has five.)

Test-day strategy: bubble carefully
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On paper tests, keep your answer sheet aligned with the question number. If you skip a question, make sure you also skip its bubble so everything stays in order.

Should you leave questions blank on the ISEE?
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No. Because there is no penalty for wrong answers, never leave a question blank — guess on anything you can't finish.

Process of elimination
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Cross out choices you know are wrong to improve your guessing odds. Eliminating two of four choices turns a 25% guess into a 50% one.

Managing a timed section
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Don't spend too long on one hard question. Answer the easy ones first, mark and skip the rest, and return with your remaining time.

ISEE vs. SSAT: guessing
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The ISEE has no guessing penalty, so answer everything. The SSAT subtracts a quarter point for wrong answers on its Middle/Upper levels, so its strategy differs.

What does a percentile compare you to?
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Other students applying to independent schools in your same grade — a high-performing group — not the general population. That makes ISEE percentiles tougher than typical test percentiles.

Why does the level depend on the grade you're applying to?
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ISEE level is set by the grade you're entering, not your current grade, so the content matches the schoolwork of the grade you're competing to join.

Essay: read the prompt twice
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Make sure you understand exactly what the prompt asks before you plan. Answering a slightly different question is a common, avoidable mistake.

Essay: vary your sentences
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Mix short and longer sentences and use precise vocabulary. Strong, varied writing reads more maturely than a string of identical short sentences.

Night-before and morning-of tips
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Sleep well, eat a good breakfast, and bring required materials and ID. Arrive early so you're calm and focused when the test begins.

Can you change answers on the computer-based ISEE?
Show answer

Yes. The online and paper versions have the same questions, timing, and the ability to go back and change answers within a section.

References

  1. 1.Educational Records Bureau. “ISEE by ERB — Test Structure & Levels.” ERB. ↑
  2. 2.Educational Records Bureau. “Tips for Every Section of the ISEE.” ERB. ↑
  3. 3.Institute of Education Sciences (U.S. Dept. of Education). “Organizing Instruction and Study to Improve Student Learning (Practice Guide).” What Works Clearinghouse, IES. ↑
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