ISEE Middle Level cheat sheet

Synonyms: pick the answer closest in meaning to the stem word; a word with the same charge (positive/negative/neutral) but a different intensity is usually a trap.

Analogies: state the stem relationship as a precise sentence (e.g., 'A is a tool used by B'), then apply that same sentence to each option; reject options that fit a looser relationship.

Common analogy bridges: category/member, part/whole, cause/effect, function, degree, lack, characteristic, worker/tool, and synonym/antonym.

Sentence completion: the blank's logic is signaled by contrast words (although, despite, rather than) or continuation words (because, and, thus); predict a word before reading choices.

Two-blank sentences must be solved as a pair: both words must fit the sentence's logic and each other, so eliminate any option where only one blank works.

Prefixes worth decoding: bene- (good), mal- (bad), circum- (around), contra- (against), ob- (against/toward), super- (above), sub- (under), ante- (before), post- (after).

Roots worth decoding: dic/dict (say), spec (look), cred (believe), ject (throw), port (carry), tract (pull), voc (call), lum (light), path (feeling), chron (time).

A word's connotation can decide an answer even when two choices share a dictionary meaning; match the stem's tone before matching its definition.

Estimate before computing: QR answers are usually far apart, so rounding numbers and comparing magnitudes often eliminates four choices in seconds.

Percent change = (new − old) ÷ old × 100; a 20% increase followed by a 20% decrease returns to 96% of the original, not 100%.

Ratios: convert to parts. If a:b = 3:5 and the total is 64, one part = 64 ÷ 8 = 8, so the shares are 24 and 40.

Average = sum ÷ count; to find a missing value, use sum = average × count, then subtract the known values.

Probability of an event = favorable outcomes ÷ total equally likely outcomes; probabilities of all outcomes sum to 1.

For a sequence, check differences first, then ratios, then alternating or two-interleaved patterns before assuming a complex rule.

In a set of consecutive integers, mean = median = (first + last) ÷ 2, and count = last − first + 1.

When a problem gives answer choices with variables, substituting a convenient number (like 10 or 100) for the variable is a valid solving method.

Main idea = what the whole passage is about plus the author's point; a true detail from one paragraph is not automatically the main idea.

Primary purpose questions ask why the author wrote the passage (to explain, persuade, compare, or describe), which differs from the topic.

Tone and attitude answers must be supported by word choice; extreme words (outraged, mocking, indifferent) need strong textual evidence.

Inference answers must be logically forced by the text; a plausible real-world fact that the passage never implies is wrong.

Vocabulary-in-context: return to the sentence, substitute each choice, and keep the one that preserves the sentence's meaning, not the word's most common meaning.

Detail questions are answered by locating the relevant lines; the correct choice usually restates the text in different words rather than copying it.

Watch transition words: however, although, and yet signal a shift the author considers important; therefore and thus signal a conclusion worth noting.

For paired passage questions, identify each author's claim separately first, then classify the second author as agreeing, qualifying, or disagreeing.

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

Fractions: a/b + c/d needs a common denominator; to divide, multiply by the reciprocal (a/b ÷ c/d = a/b × d/c).

Percent problems: part = percent × whole; convert percents to decimals (35% = 0.35) before multiplying.

Area formulas: rectangle lw, triangle ½bh, circle πr², parallelogram bh, trapezoid ½(b₁ + b₂)h; circumference = 2πr.

Volume of a rectangular prism = lwh; volume of a cylinder = πr²h.

Slope = (y₂ − y₁) ÷ (x₂ − x₁); slope-intercept form is y = mx + b, where m is slope and b is the y-intercept.

Exponent rules: xᵃ · xᵇ = xᵃ⁺ᵇ, xᵃ ÷ xᵇ = xᵃ⁻ᵇ, (xᵃ)ᵇ = xᵃᵇ, and x⁰ = 1 for x ≠ 0.

Solve equations by undoing operations in reverse order; whatever is done to one side must be done to the other.

Mean, median, mode: median requires ordering the data first, and with an even count the median is the average of the two middle values.

The prompt asks for a writing sample scored on organization, development of ideas, and language use, not on a right or wrong position.

A workable structure: a short introduction stating a clear position, two body paragraphs each built on one reason with a specific example, and a brief conclusion.

Specific supporting detail (a named book, a personal experience, a concrete scenario) scores higher than repeated general statements.

Transition words (first, in addition, for example, however, as a result) make the structure visible to a reader on a first pass.

Sentence variety matters: mix shorter and longer sentences and avoid starting several consecutive sentences the same way.

Stay within the time budget by planning for about 2-3 minutes, writing for roughly 20 minutes, and reserving 2-3 minutes to check for errors.

Legible handwriting and clear paragraph indentation or spacing affect how easily a reader can follow the response.

A conclusion should restate the position in fresh words and add a final insight, not simply repeat the introduction verbatim.

An antonym question reverses the stem: find the choice opposite in meaning, and beware of choices that are merely unrelated rather than opposite.

Degree matters: hot/cold are opposites, but warm/cold is a weaker pair; choose the option matching the stem's intensity.

Words with multiple meanings (bank, fair, plain) must be read in the sense implied by the stem or sentence.

A choice that is a broader category of the stem word (dog → animal) is not a synonym and is usually a distractor.

In sentence completion, the blank's part of speech (noun, verb, adjective) must match the grammar of the sentence as well as the meaning.

Distance = rate × time; rearrange to rate = distance ÷ time or time = distance ÷ rate.

Simple interest = principal × rate × time; total amount = principal + interest.

A number is divisible by 3 if its digits sum to a multiple of 3, and by 9 if its digits sum to a multiple of 9.

A number is divisible by 4 if its last two digits form a multiple of 4; by 6 if it is divisible by both 2 and 3.

Prime numbers have exactly two factors; 1 is not prime, and 2 is the only even prime.

Percentage increase from a to b = (b − a) ÷ a × 100; percentage of a total = part ÷ total × 100.

Unit conversion: multiply when converting to a smaller unit and divide when converting to a larger unit (1 m = 100 cm, 1 hour = 60 minutes).