ISEE Quantitative Reasoning flashcards

31 cards. Read the term and the definition here. The deck at the top of this page is optional.

Column A versus Column B

On the ISEE Quantitative Reasoning section, two quantities are compared. Choose A if Column A is greater, B if Column B is greater, C if they are equal, and D if the relationship cannot be determined.

Choosing answer D

Select 'cannot be determined' only when the unknown quantity can take values that make Column A larger, Column B larger, or the columns equal. Test positives, negatives, fractions, and zero first.

Percent change formula

Percent change equals the difference between the new and old values divided by the old value, then multiplied by 100. A decrease is expressed as a negative change.

Arithmetic mean

The arithmetic mean is the sum of all terms divided by the number of terms. Rearranging gives sum equals mean times count, which allows finding a missing term.

Ratio part value

In a ratio a to b, write the quantities as ax and bx. One part equals the total divided by a plus b, so each quantity can be computed from the total.

Distance, rate, time

Distance equals rate multiplied by time. For objects approaching each other, add their speeds; for objects moving the same direction, subtract the slower speed from the faster.

Probability complement rule

The probability that an event does not occur equals 1 minus the probability that it does occur, because all possible outcomes together have probability 1.

Simple interest formula

Simple interest equals principal times annual rate times time in years. The total amount owed or earned is the principal plus that interest.

Synonym question strategy

Choose the answer closest in meaning to the prompt word, matching its part of speech and tone. A word's secondary meaning often supplies the correct answer.

Analogy bridge sentence

Write a precise sentence linking the two prompt words, such as 'a hammer is a tool used by a carpenter.' Apply that same sentence to each answer pair and keep the one that fits.

Degree relationship analogies

Some pairs differ only in intensity, as warm relates to hot. The correct answer must show the same direction and comparable step of intensity.

Contrast signal words

Words such as although, despite, however, and rather than signal that the blank's meaning reverses the nearby clause, so predict a word opposite to the stated idea.

Continuation signal words

Words such as and, because, since, and therefore signal that the blank restates or follows logically from the nearby clause, so predict a word matching that idea.

Common Greek and Latin roots

Roots carry partial meaning: bene means good, mal means bad, circum means around, cred means believe, and the suffixes -ous and -ful mean full of.

Part-to-whole analogy

A relationship in which one item is a component of the other, such as a wheel to a car. The answer pair must preserve the same component-to-whole direction.

Category-to-member analogy

A relationship in which one word names a class and the other names something inside it, such as fruit to apple. The answer must show the same class-to-example direction.

Main idea questions

The correct answer summarizes the entire passage. Choices that are accurate but cover only one paragraph are distractors, even when the passage states them directly.

Vocabulary in context

Determine a word's meaning from the sentence and paragraph around it rather than from its most familiar dictionary definition, since passages often use secondary senses.

Valid inference

An inference is supported only when the passage's statements logically force the conclusion. Answers requiring outside knowledge or extra assumptions are incorrect.

Tone and attitude questions

Judge tone from word choice and connotation. Academic passages are usually measured or analytical, so extreme descriptors such as outraged or ecstatic rarely apply.

Author's purpose

Purpose describes why the author wrote the passage: to explain, to persuade, to compare, or to describe. It differs from the main idea, which states what the passage says.

Absolute language trap

Answer choices using all, never, always, or must are usually wrong unless the passage uses equally absolute wording. Qualified language more often matches academic prose.

Comparison passages

When two passages address one topic, identify where the authors agree and where they differ. Answers must reflect both passages, not just one of them.

Order of operations

Evaluate parentheses first, then exponents, then multiplication and division from left to right, and finally addition and subtraction from left to right.

Exponent rules

When multiplying like bases, add exponents; when dividing, subtract them; when raising a power to a power, multiply them. Any nonzero base to the zero power equals one.

Negative exponents

A base raised to a negative exponent equals the reciprocal of that base raised to the positive exponent, so x to the negative a equals one over x to the a.

Slope formula

The slope of a line through two points equals the change in y divided by the change in x. In slope-intercept form, y equals mx plus b, m is the slope.

Pythagorean theorem

In a right triangle, the square of the hypotenuse equals the sum of the squares of the two legs, written a squared plus b squared equals c squared.

Polygon interior angle sum

The interior angles of a polygon with n sides sum to n minus 2, multiplied by 180 degrees. Each exterior angle of a regular polygon measures 360 divided by n.

Circle area and circumference

The area of a circle equals pi times the radius squared, and its circumference equals 2 times pi times the radius. Diameter is twice the radius.

Solving linear systems

Solve two linear equations by substitution, replacing one variable with an equivalent expression, or by adding or subtracting equations to eliminate a variable.