Kuwait University Mathematics Aptitude Test key terms

A counting number from the set 1, 2, 3, and so on. Some conventions include zero, so check the wording of the question before assuming.

Any whole number, positive, negative, or zero, written without a fractional or decimal part. Examples are -7, 0, and 12.

A number that can be written as a fraction of two integers with a nonzero denominator. Its decimal form either stops or repeats a block of digits.

A real number that cannot be written as a fraction of two integers. Its decimal expansion never stops and never settles into a repeating block, as with the square root of 2.

A whole number greater than 1 whose only positive divisors are 1 and itself. The first few are 2, 3, 5, 7, and 11.

An integer that divides another integer with no remainder. For example, 4 and 6 are factors of 24 because both divide 24 exactly.

The result of multiplying a given integer by any whole number. The multiples of 5 are 5, 10, 15, 20, and so on.

The largest positive integer that divides each of two or more given integers exactly. For 18 and 24 the value is 6.

The smallest positive integer that is a multiple of each of two or more given integers. For 4 and 6 the value is 12.

The distance of a number from zero on the number line, always zero or positive. It is written with vertical bars, as in the absolute value of -9, which is 9.

A statement comparing two quantities that are not necessarily equal, using the symbols <, >, ≤, or ≥. Solving one usually gives a range of values rather than a single number.

A continuous set of real numbers between two endpoints. Square brackets include an endpoint and round brackets exclude it, so [2, 5) contains 2 but not 5.

A comparison of two quantities by division, often written with a colon or as a fraction. A ratio of 3 to 4 means the first amount is three quarters of the second.

An equation stating that two ratios are equal. If two quantities are in proportion, scaling one by a constant scales the other by the same constant.

A number expressed as a fraction of 100, written with the percent sign. Thus 35% equals 0.35 and equals the fraction 35 over 100.

The difference between a new value and an original value, divided by the original value and multiplied by 100. It is positive for an increase and negative for a decrease.

A small raised number showing how many times a base is multiplied by itself. In 2 to the power 5, the exponent is 5 and the value is 32.

The result of raising a base to an exponent, or the whole expression written that way. Rules for combining powers include adding exponents when multiplying like bases.

A symbol or expression denoting a root of a number, such as a square root or cube root. The value under the radical sign is called the radicand.

A number that produces a given value when multiplied by itself. The principal square root is the nonnegative one, so the square root of 49 is 7.

A way of writing very large or very small numbers as a number between 1 and 10 multiplied by a power of 10. For instance, 0.0042 is written as 4.2 times 10 to the power -3.

An equation in which every variable appears to the first power only, so its graph is a straight line. A typical form is ax + b = c with a not equal to zero.

An equation whose highest power of the variable is two, usually written as ax squared plus bx plus c equals zero with a not equal to zero. It has up to two real solutions.

The quantity b squared minus 4ac taken from a quadratic equation. Its sign tells how many real solutions exist: positive gives two, zero gives one, negative gives none.

Two or more equations that must be satisfied at the same time by the same variables. A solution is a set of values satisfying every equation in the system.

An algebraic method of solving systems by expressing one variable in terms of others and inserting that expression into another equation, leaving a single equation in one variable.

A method of solving a system by adding or subtracting multiples of the equations so that one variable cancels, leaving an equation in fewer variables.

A rule that assigns exactly one output value to each allowed input value. The set of allowed inputs is its domain and the set of outputs is its range.

The set of all input values for which a function is defined. For a fraction, any input making the denominator zero must be excluded.

The set of all output values a function actually produces as its input runs through the domain. It is not the same as the domain.

A measure of how steep a line is, equal to the change in the vertical coordinate divided by the corresponding change in the horizontal coordinate between two points.

A point where a graph crosses an axis. The y-intercept is where the input is zero, and the x-intercept is where the output is zero.

A relationship in which one quantity is a constant multiple of another, written as y equals kx. Doubling the input doubles the output.

A relationship in which the product of two quantities stays constant, written as y equals k divided by x. Increasing one quantity decreases the other.

A list of numbers in which each term after the first is obtained by adding a fixed difference to the previous term, as in 3, 7, 11, 15.

A list of numbers in which each term after the first is obtained by multiplying the previous term by a fixed nonzero ratio, as in 2, 6, 18, 54.

The sum of the terms of a sequence. A finite series adds a limited number of terms, while an infinite series continues without end.

The arithmetic average, found by adding all values and dividing by how many there are. It is sensitive to unusually large or small values.

The middle value of a data set arranged in order. With an even number of values it is the mean of the two middle ones.

The value that occurs most often in a data set. A set may have no mode or several modes if values tie for the highest frequency.