ICAS Mathematics key terms

A whole number that divides another whole number exactly, leaving no remainder. For example, 3 and 4 are factors of 12 because 12 ÷ 3 = 4 exactly.

The result of multiplying a number by a whole number. The multiples of 5 are 5, 10, 15, 20 and so on; each one is obtained by adding another 5.

A whole number greater than 1 whose only whole-number factors are 1 and itself. The numbers 2, 3, 5, 7 and 11 are prime, while 1 and 9 are not.

The largest whole number that divides exactly into two or more given numbers. For 12 and 18 the common factors are 1, 2, 3 and 6, so the highest common factor is 6.

The smallest whole number that is a multiple of two or more given numbers. Listing multiples of 4 and 6 gives 4, 8, 12... and 6, 12, 18..., so the lowest common multiple is 12.

The number you multiply a given number by to get 1, found by turning a fraction upside down. The reciprocal of 3/4 is 4/3, and the reciprocal of 5 is 1/5.

A way of writing a number as a fraction of 100, shown with the symbol %. So 45% means 45 out of every 100, which is the same as 0.45 or 9/20.

A comparison of two or more quantities of the same kind, usually written with a colon. A ratio of 2:3 means that for every 2 of the first quantity there are 3 of the second.

A small number written above and to the right of a base that shows how many times the base is multiplied by itself. In 2⁴ the index 4 means 2 × 2 × 2 × 2 = 16.

The agreed order for working out an expression: brackets first, then indices, then multiplication and division from left to right, then addition and subtraction from left to right.

A letter or symbol that stands for a number whose value is unknown or can change. In the expression 3x + 5, the letter x is a variable.

The number written in front of a variable that multiplies it. In 7y the coefficient is 7, and in −4ab the coefficient is −4. A coefficient of 1 is normally left unwritten.

Terms in an algebraic expression that have exactly the same variable parts, so they can be added or subtracted. For example, 5x and −2x are like terms, but 5x and 5x² are not.

An equation in which each variable appears to the first power only, so its graph is a straight line. Solving it means finding the value of the variable that makes both sides equal.

A statement comparing two expressions that are not necessarily equal, using symbols such as < (less than), > (greater than), ≤ (less than or equal to) or ≥ (greater than or equal to).

An ordered list of numbers or terms that follows a rule. In 3, 6, 9, 12 the rule is to add 3 each time, and 3 is the first term of the sequence.

The single variable that a formula gives the value of, usually written on its own on the left. In A = πr², A is the subject; rearranging the formula can make r the subject instead.

Writing an expression as a product of simpler expressions, which is the reverse of expanding brackets. For example, 6x + 9 factorises to 3(2x + 3) because 3 is common to both terms.

The total distance around the outside edge of a flat shape, found by adding the lengths of all its sides. Perimeter is measured in units such as centimetres or metres.

The amount of flat surface enclosed by a two-dimensional shape, measured in square units such as cm². The area of a rectangle is its length multiplied by its width.

The amount of space inside a three-dimensional object, measured in cubic units such as cm³. The volume of a rectangular prism is length × width × height.

The perimeter of a circle, that is, the distance all the way around its curved edge. It equals π multiplied by the diameter, roughly 3.14 times the diameter.

Describing two shapes that are exactly the same size and shape, so one fits perfectly on top of the other. Matching sides and angles are equal, even if one shape is turned or flipped.

Describing two shapes that have equal matching angles and the same proportions but may be different sizes. Corresponding sides are in a fixed ratio called the scale factor.

The rule that in a right-angled triangle the square of the hypotenuse equals the sum of the squares of the other two sides, written a² + b² = c². It is used to find a missing side length.

Angles on opposite sides of a line that crosses two parallel lines, lying between the parallel lines. Alternate angles are equal in size and form a Z shape.

A way of moving or changing a shape on a plane: translation (slide), rotation (turn), reflection (flip) or enlargement (resize). The first three leave the shape congruent to the original.

The average of a set of numbers, found by adding all the values and dividing by how many there are. The mean of 2, 4 and 9 is 15 ÷ 3 = 5.

The middle value when a set of numbers is arranged in order from smallest to largest. With an even number of values, the median is halfway between the two middle values.

The value that occurs most often in a set of data. A data set may have one mode, several modes, or no mode if every value occurs the same number of times.

A simple measure of spread found by subtracting the smallest value in a data set from the largest. A large range means the values are spread widely apart.

A data value that is much smaller or much larger than the rest of the values in a set. Outliers can strongly affect the mean but have little effect on the median.

The set of all possible outcomes of an experiment. For a single roll of a fair six-sided die, the sample space is {1, 2, 3, 4, 5, 6}.

A number between 0 and 1 describing how likely an event is, where 0 means impossible and 1 means certain. It can be written as a fraction, a decimal or a percentage.

Two events that are the only possible outcomes and cannot happen at the same time, such as rain or no rain. Their probabilities add to 1, so P(not A) = 1 − P(A).