ISEE Lower Level cheat sheet

Synonym items: pick the answer closest in meaning to the stem word; a word that is only loosely related, opposite, or a different part of speech is wrong.

Antonym items: pick the answer most nearly opposite; beware answer choices that are merely unrelated to the stem word rather than truly opposite.

Use charge (positive, negative, neutral) to eliminate: a positive stem word cannot pair with a negative answer in a synonym item.

Use intensity to eliminate: a synonym must match strength, so a mild word does not equal an extreme one (warm is not scorching).

Sentence-completion logic: find the signal words (because, although, therefore, but) that fix whether the blank agrees with or contrasts the rest of the sentence.

Two-blank completions: test each answer pair against both blanks; one wrong blank is enough to eliminate the whole pair.

Prefix clues: un-, in-, dis-, non- negate; re- means again; pre- means before; mis- means wrongly; sub- means under.

Suffix clues: -less means without, -ful means full of, -able/-ible means capable of, -ist/-er means one who does or is.

Context clues in a stem sentence: a definition, example, or contrast stated nearby usually supplies the meaning the answer must match.

Estimate first: round each number to a convenient value, compute, then check which answer choice is nearest; exact computation is often unnecessary.

Percent of a number: part = percent × whole; convert the percent to a decimal first (35% = 0.35).

Percent increase or decrease = (change ÷ original) × 100; the original value, not the new value, is the denominator.

Average (mean) = sum of terms ÷ number of terms; to find a missing term, multiply the mean by the count and subtract the known terms.

Ratio problems: set up a proportion a/b = c/d and cross-multiply (a × d = b × c); keep units in matching positions.

Pattern sequences: check the difference between consecutive terms, then the ratio, then alternating or two interleaved patterns before predicting the next term.

Number properties: even × any integer is even; odd × odd is odd; the sum of two odd numbers is even; a number divisible by both 3 and 4 is divisible by 12.

Geometry estimates: area of a rectangle = length × width; area of a triangle = ½ × base × height; perimeter of a rectangle = 2(length + width).

Data interpretation: read axis labels and units before comparing; a taller bar drawn from a nonzero baseline can exaggerate a small difference.

Main idea = what the whole passage is about; a detail that appears in only one sentence is a supporting fact, not the main idea.

Primary purpose questions ask why the author wrote the passage (to explain, to persuade, to describe, to compare); answer with a verb phrase, not a topic.

Detail questions: the answer is stated in the passage; an answer that is true in real life but absent from the passage is wrong.

Inference answers must be supported by the text; if the passage does not imply it, the choice is out of scope.

Vocabulary-in-context: substitute each answer choice into the sentence and keep the one that preserves the sentence's meaning.

Tone and attitude: look for loaded adjectives and verbs; neutral, critical, admiring, and humorous are common labels.

Cause-and-effect questions: locate the words because, since, therefore, as a result, and led to, then check which event comes first.

Comparison passages: identify what both passages share and where they differ; a correct answer must be true of both passages when the question says so.

Sequence questions: track order words (first, then, after, finally) and reconstruct the timeline before choosing.

Order of operations: parentheses, exponents, multiplication and division left to right, then addition and subtraction left to right.

Fraction addition or subtraction requires a common denominator; multiply or divide fractions without one (a/b ÷ c/d = a/b × d/c).

Decimal place value: the first place after the point is tenths, the second hundredths, the third thousandths; line up decimal points when adding.

Convert units: 1 foot = 12 inches, 1 yard = 3 feet, 1 mile = 5,280 feet, 1 pound = 16 ounces, 1 hour = 60 minutes.

Perimeter of a polygon = sum of all side lengths; area of a square = side²; circumference of a circle = π × diameter (use π ≈ 3.14).

Volume of a rectangular prism = length × width × height; surface-area questions count the faces of the solid.

Mean, median, mode, range: median is the middle value of an ordered list; range = greatest minus least.

Integer rules: subtracting a negative adds (5 − (−3) = 8); a negative times a negative is positive; a negative times a positive is negative.

Solve one-step equations by doing the inverse operation to both sides (x + 7 = 12 → subtract 7 from both sides).