ISEE Upper Level cheat sheet

Synonym questions: pick the answer closest in meaning to the stem word; test each option by substituting it into a sentence containing the stem.

Two-blank sentence completion: read the whole sentence, predict both words, then eliminate options where either word fails; the two words must be logically consistent with each other.

Signal words such as "although," "despite," and "yet" reverse the expected meaning; "because," "thus," and "since" preserve it.

Contrast clues ("but," "rather than," "on the contrary") mean the blank opposes another word in the sentence; support clues ("indeed," "moreover") mean the blank restates it.

Eliminate answer choices with the wrong charge (positive vs. negative connotation) before judging precise meaning.

Prefix roots: bene- good, mal- bad, mis- wrong, anti- against, pro- forward/for, circum- around, retro- backward, hyper- over, hypo- under.

Roots worth memorizing: cred (believe), dict (say), duc/duct (lead), ject (throw), log/logue (word, reason), path (feeling), spec (look), ten (hold), vert (turn).

Extreme or absolute words ("always," "never," "all") are usually wrong in synonym and completion items unless the stem itself is absolute.

Analogies in this section follow the same bridge logic as sentence completion: state the relationship in a phrase, then apply that exact phrase to each option pair.

Percent change = (new - old) / old x 100; percent increase followed by equal percent decrease does not return to the original value.

Successive percent changes multiply: a 20% rise then a 25% fall gives 1.20 x 0.75 = 0.90, a net 10% loss.

Average (mean) = sum / count; if the mean of n numbers is m, the sum is n x m. Use this to find a missing value.

Rate problems: distance = rate x time; combined work rate adds reciprocals, 1/a + 1/b = 1/t.

Ratio a:b with total T means parts are aT/(a+b) and bT/(a+b).

Probability of independent events multiplies; probability of either of two mutually exclusive events adds.

Circle: area = pi r^2, circumference = 2 pi r. Triangle: area = (1/2) b h. Rectangle: area = lw, perimeter = 2(l + w).

Pythagorean theorem a^2 + b^2 = c^2 applies only to right triangles; common triples are 3-4-5, 5-12-13, 8-15-17, and 7-24-25.

Quantitative comparison: if both quantities are numbers, compute them; if variables appear, test values such as 0, 1, -1, and a fraction before deciding.

Main-idea questions ask for the author's central claim, not the topic; the correct answer covers the whole passage rather than one paragraph.

Tone and attitude answers must match the passage's language intensity; a mildly critical passage does not support "condemnatory."

Inference answers require only one small step from stated text; choices needing outside knowledge or two logical leaps are wrong.

Vocabulary-in-context: return to the sentence, substitute each option, and keep the one that preserves the sentence's logic and tone.

EXCEPT and NOT questions are answered by finding the three options the passage supports and selecting the remaining one.

Passage structure questions use signposts: "however" signals a shift, "for example" signals illustration, "therefore" signals conclusion.

Answers containing absolute language ("proves," "never," "all") are usually wrong unless the passage states the absolute directly.

When two answers seem right, the correct one is the more precisely supported; the distractor is true in general but not stated in the passage.

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

Slope = (y2 - y1) / (x2 - x1); parallel lines share a slope, perpendicular slopes are negative reciprocals.

Slope-intercept form y = mx + b; point-slope form y - y1 = m(x - x1).

Exponent rules: x^a x^b = x^(a+b), x^a / x^b = x^(a-b), (x^a)^b = x^(ab), x^0 = 1 for x not zero, x^(-a) = 1/x^a.

Factoring: difference of squares a^2 - b^2 = (a - b)(a + b); perfect square a^2 + 2ab + b^2 = (a + b)^2.

Quadratic formula: x = (-b +/- sqrt(b^2 - 4ac)) / 2a for ax^2 + bx + c = 0.

Sum of interior angles of a polygon with n sides = (n - 2) x 180 degrees; each exterior angle of a regular n-gon = 360/n degrees.

Volume: rectangular solid lwh, cylinder pi r^2 h, sphere (4/3) pi r^3, cone (1/3) pi r^2 h.

Absolute value equations |x| = k give two cases x = k and x = -k when k is positive; inequality |x| < k means -k < x < k.

Synonym questions: pick the answer closest in meaning to the stem word; test each option by substituting it into a sentence containing the stem.

Two-blank sentence completion: read the whole sentence, predict both words, then eliminate options where either word fails; the two words must be logically consistent with each other.

Signal words such as "although," "despite," and "yet" reverse the expected meaning; "because," "thus," and "since" preserve it.

Contrast clues ("but," "rather than," "on the contrary") mean the blank opposes another word in the sentence; support clues ("indeed," "moreover") mean the blank restates it.

Eliminate answer choices with the wrong charge (positive vs. negative connotation) before judging precise meaning.

Prefix roots: bene- good, mal- bad, mis- wrong, anti- against, pro- forward/for, circum- around, retro- backward, hyper- over, hypo- under.

Roots worth memorizing: cred (believe), dict (say), duc/duct (lead), ject (throw), log/logue (word, reason), path (feeling), spec (look), ten (hold), vert (turn).

Extreme or absolute words ("always," "never," "all") are usually wrong in synonym and completion items unless the stem itself is absolute.

Analogies in this section follow the same bridge logic as sentence completion: state the relationship in a phrase, then apply that exact phrase to each option pair.

Percent change = (new - old) / old x 100; percent increase followed by equal percent decrease does not return to the original value.

Successive percent changes multiply: a 20% rise then a 25% fall gives 1.20 x 0.75 = 0.90, a net 10% loss.

Average (mean) = sum / count; if the mean of n numbers is m, the sum is n x m. Use this to find a missing value.

Rate problems: distance = rate x time; combined work rate adds reciprocals, 1/a + 1/b = 1/t.

Ratio a:b with total T means parts are aT/(a+b) and bT/(a+b).

Probability of independent events multiplies; probability of either of two mutually exclusive events adds.

Circle: area = pi r^2, circumference = 2 pi r. Triangle: area = (1/2) b h. Rectangle: area = lw, perimeter = 2(l + w).

Pythagorean theorem a^2 + b^2 = c^2 applies only to right triangles; common triples are 3-4-5, 5-12-13, 8-15-17, and 7-24-25.

Quantitative comparison: if both quantities are numbers, compute them; if variables appear, test values such as 0, 1, -1, and a fraction before deciding.

Main-idea questions ask for the author's central claim, not the topic; the correct answer covers the whole passage rather than one paragraph.

Tone and attitude answers must match the passage's language intensity; a mildly critical passage does not support "condemnatory."

Inference answers require only one small step from stated text; choices needing outside knowledge or two logical leaps are wrong.

Vocabulary-in-context: return to the sentence, substitute each option, and keep the one that preserves the sentence's logic and tone.

EXCEPT and NOT questions are answered by finding the three options the passage supports and selecting the remaining one.

Passage structure questions use signposts: "however" signals a shift, "for example" signals illustration, "therefore" signals conclusion.

Answers containing absolute language ("proves," "never," "all") are usually wrong unless the passage states the absolute directly.

When two answers seem right, the correct one is the more precisely supported; the distractor is true in general but not stated in the passage.

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

Slope = (y2 - y1) / (x2 - x1); parallel lines share a slope, perpendicular slopes are negative reciprocals.

Slope-intercept form y = mx + b; point-slope form y - y1 = m(x - x1).

Exponent rules: x^a x^b = x^(a+b), x^a / x^b = x^(a-b), (x^a)^b = x^(ab), x^0 = 1 for x not zero, x^(-a) = 1/x^a.

Factoring: difference of squares a^2 - b^2 = (a - b)(a + b); perfect square a^2 + 2ab + b^2 = (a + b)^2.

Quadratic formula: x = (-b +/- sqrt(b^2 - 4ac)) / 2a for ax^2 + bx + c = 0.

Sum of interior angles of a polygon with n sides = (n - 2) x 180 degrees; each exterior angle of a regular n-gon = 360/n degrees.

Volume: rectangular solid lwh, cylinder pi r^2 h, sphere (4/3) pi r^3, cone (1/3) pi r^2 h.

Absolute value equations |x| = k give two cases x = k and x = -k when k is positive; inequality |x| < k means -k < x < k.

Synonym questions: pick the answer closest in meaning to the stem word; test each option by substituting it into a sentence containing the stem.

Two-blank sentence completion: read the whole sentence, predict both words, then eliminate options where either word fails; the two words must be logically consistent with each other.

Signal words such as "although," "despite," and "yet" reverse the expected meaning; "because," "thus," and "since" preserve it.

Contrast clues ("but," "rather than," "on the contrary") mean the blank opposes another word in the sentence; support clues ("indeed," "moreover") mean the blank restates it.

Eliminate answer choices with the wrong charge (positive vs. negative connotation) before judging precise meaning.

Prefix roots: bene- good, mal- bad, mis- wrong, anti- against, pro- forward/for, circum- around, retro- backward, hyper- over, hypo- under.

Roots worth memorizing: cred (believe), dict (say), duc/duct (lead), ject (throw), log/logue (word, reason), path (feeling), spec (look), ten (hold), vert (turn).

Extreme or absolute words ("always," "never," "all") are usually wrong in synonym and completion items unless the stem itself is absolute.

Analogies in this section follow the same bridge logic as sentence completion: state the relationship in a phrase, then apply that exact phrase to each option pair.

Percent change = (new - old) / old x 100; percent increase followed by equal percent decrease does not return to the original value.

Successive percent changes multiply: a 20% rise then a 25% fall gives 1.20 x 0.75 = 0.90, a net 10% loss.

Average (mean) = sum / count; if the mean of n numbers is m, the sum is n x m. Use this to find a missing value.

Rate problems: distance = rate x time; combined work rate adds reciprocals, 1/a + 1/b = 1/t.

Ratio a:b with total T means parts are aT/(a+b) and bT/(a+b).

Probability of independent events multiplies; probability of either of two mutually exclusive events adds.

Circle: area = pi r^2, circumference = 2 pi r. Triangle: area = (1/2) b h. Rectangle: area = lw, perimeter = 2(l + w).

Pythagorean theorem a^2 + b^2 = c^2 applies only to right triangles; common triples are 3-4-5, 5-12-13, 8-15-17, and 7-24-25.

Quantitative comparison: if both quantities are numbers, compute them; if variables appear, test values such as 0, 1, -1, and a fraction before deciding.

Main-idea questions ask for the author's central claim, not the topic; the correct answer covers the whole passage rather than one paragraph.

Tone and attitude answers must match the passage's language intensity; a mildly critical passage does not support "condemnatory."

Inference answers require only one small step from stated text; choices needing outside knowledge or two logical leaps are wrong.

Vocabulary-in-context: return to the sentence, substitute each option, and keep the one that preserves the sentence's logic and tone.

EXCEPT and NOT questions are answered by finding the three options the passage supports and selecting the remaining one.

Passage structure questions use signposts: "however" signals a shift, "for example" signals illustration, "therefore" signals conclusion.

Answers containing absolute language ("proves," "never," "all") are usually wrong unless the passage states the absolute directly.

When two answers seem right, the correct one is the more precisely supported; the distractor is true in general but not stated in the passage.

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

Slope = (y2 - y1) / (x2 - x1); parallel lines share a slope, perpendicular slopes are negative reciprocals.

Slope-intercept form y = mx + b; point-slope form y - y1 = m(x - x1).

Exponent rules: x^a x^b = x^(a+b), x^a / x^b = x^(a-b), (x^a)^b = x^(ab), x^0 = 1 for x not zero, x^(-a) = 1/x^a.

Factoring: difference of squares a^2 - b^2 = (a - b)(a + b); perfect square a^2 + 2ab + b^2 = (a + b)^2.

Quadratic formula: x = (-b +/- sqrt(b^2 - 4ac)) / 2a for ax^2 + bx + c = 0.

Sum of interior angles of a polygon with n sides = (n - 2) x 180 degrees; each exterior angle of a regular n-gon = 360/n degrees.

Volume: rectangular solid lwh, cylinder pi r^2 h, sphere (4/3) pi r^3, cone (1/3) pi r^2 h.

Absolute value equations |x| = k give two cases x = k and x = -k when k is positive; inequality |x| < k means -k < x < k.