ISEE Quantitative Reasoning key terms

A question format presenting two quantities, Column A and Column B, and asking you to decide which is larger, whether they are equal, or whether the relationship cannot be determined from the information given.

A judgment about whether the facts provided are enough to fix a single answer. If different valid cases give different results, the information is insufficient and the answer is 'cannot be determined'.

A single valid case that makes a general statement false. One counterexample is enough to disprove a claim, which is why testers check special values such as zero, one, and negatives.

Approximating a value to a convenient nearby number so arithmetic becomes quick. Useful when answer choices are spread far apart or when exact computation would waste time.

Replacing a number with a nearby value having fewer significant digits, based on the next digit. If that digit is 5 or more, increase the kept digit by one; otherwise leave it unchanged.

The rough scale of a number, usually expressed as the nearest power of ten. Comparing orders of magnitude quickly rules out answers that are far too large or far too small.

A comparison of two quantities by division, often written with a colon such as 3:5. It can be scaled by multiplying or dividing both parts by the same nonzero number.

An equation stating that two ratios are equal. Cross-multiplying converts a proportion into a simple linear equation, which is the standard method for solving for an unknown part.

A rate expressed per one unit of the second quantity, such as miles per hour or dollars per item. Dividing both quantities by the second quantity produces it.

Total distance divided by total time for a trip, which is not the same as the average of separate speeds unless the time intervals are equal.

A ratio out of one hundred. To convert a percent to a decimal, divide by 100; to find a percent of a number, multiply the number by the decimal form.

The difference between a new value and an original value, divided by the original value and expressed as a percent. The original value is always the denominator.

The arithmetic average: the sum of all values divided by how many values there are. It is pulled toward unusually large or small values.

The middle value when data are arranged in order; with an even count, it is the mean of the two middle values. It resists distortion by extreme values.

The value that appears most often in a data set. A set may have no mode or several modes, and the mode need not be near the mean.

The difference between the largest and smallest values in a data set. It measures spread rather than center, so it depends on only two data points.

An average in which each value counts according to an assigned weight. It equals the sum of value-times-weight products divided by the total of the weights.

A whole number, positive, negative, or zero, with no fractional part. Consecutive integers differ by exactly one, which allows them to be written as n, n+1, n+2.

A classification of integers by divisibility by two. Even numbers are multiples of two; odd numbers are not. Sums and products of these follow predictable parity rules.

An integer greater than one whose only positive divisors are one and itself. The number 1 is not prime, and 2 is the only even prime.

An integer that divides another integer with no remainder. Listing factor pairs of a number helps find its divisors and identify perfect squares.

The product of a given integer and any integer. Multiples of a number are infinite in count; the least common multiple of two numbers is the smallest shared one.

The property of dividing evenly with zero remainder. Short rules exist, such as a number being divisible by 3 when its digits sum to a multiple of 3.

A letter standing for an unknown or changing number. Expressions combine variables and constants with operations, while equations state that two expressions are equal.

A mathematical phrase built from numbers, variables, and operations, with no equals sign. It can be simplified or evaluated but not solved.

A statement that two expressions have equal value. Solving means finding every value of the variable that makes the statement true.

A statement comparing expressions with symbols such as less than, greater than, or their or-equal forms. Multiplying or dividing by a negative number reverses the direction of the symbol.

The rule that a factor outside parentheses multiplies each term inside them. It converts a product of a sum into a sum of products and back again when factoring.

Terms with identical variable parts, which may be combined by adding or subtracting their coefficients. Terms with different variable parts cannot be merged this way.

The steepness of a line, computed as the change in the vertical coordinate divided by the change in the horizontal coordinate between two points on the line.

The point where a graph crosses an axis. The vertical intercept occurs where the horizontal coordinate is zero, and it often represents a starting value in applied problems.

An equation whose graph is a straight line, typically written with a constant slope and a constant term. Its highest variable power is one.

A grid formed by a horizontal axis and a vertical axis intersecting at the origin. Points are located by ordered pairs giving horizontal position first, then vertical position.

The distance of a number from zero on the number line, always nonnegative. Equations containing it usually split into two separate cases to solve.

A compact way to write very large or very small numbers as a coefficient between one and ten multiplied by a power of ten. Exponents reveal the order of magnitude.

A small raised number showing how many times the base is used as a factor. A negative exponent indicates a reciprocal, and a zero exponent gives a value of one.

A value that, multiplied by itself, produces a given nonnegative number. Every positive number has two square roots, one positive and one negative.

The chance of an event, computed as the number of favorable outcomes divided by the total number of equally likely outcomes. Values range from zero to one.

A selection of items where order does not matter. Counting selections requires dividing out the arrangements of the chosen items, unlike counting ordered permutations.

How often a value or category occurs in a data set, often displayed in tables or bar graphs. Relative frequency divides the count by the total number of observations.