GCE O/L Mathematics key terms

A whole number with no fractional or decimal part, such as 7, 0 or -12. Integers can be positive, negative or zero, and are used for counting and for exact arithmetic.

A whole number greater than 1 whose only positive factors are 1 and itself, for example 2, 3, 7 and 13. The number 1 is not prime because it has only one factor.

A whole number that divides another number exactly, leaving no remainder. For example, the factors of 12 are 1, 2, 3, 4, 6 and 12.

The result of multiplying a number by a whole number. The multiples of 5 are 5, 10, 15, 20 and so on, continuing without end.

The largest whole number that divides exactly into two or more given numbers. For 18 and 24 the highest common factor is 6, found by listing factors or comparing prime factorisations.

The smallest whole number that is a multiple of two or more given numbers. For 4 and 6 the lowest common multiple is 12, useful when adding fractions with different denominators.

A way of writing very large or very small numbers as a number between 1 and 10 multiplied by a power of 10, such as 3.2 x 10^5 or 4.7 x 10^-3.

The result of dividing 1 by a number. The reciprocal of 4 is 1/4, and the reciprocal of 2/3 is 3/2. A number multiplied by its reciprocal always gives 1.

A number written as one whole number divided by another, such as 3/5, showing parts of a whole. The top number is the numerator and the bottom is the denominator.

A number written using place value columns to the right of a decimal point, such as 2.75, meaning 2 and 75 hundredths. Decimals can be terminating or recurring.

A fraction or proportion expressed out of 100. For example, 45% means 45 out of every 100, or the fraction 45/100, which simplifies to 9/20.

The change in a quantity expressed as a percentage of its original value, calculated by dividing the change by the original amount and multiplying by 100.

Interest calculated on the original amount plus any interest already added, so the total grows faster each period. It is found with repeated percentage multipliers, not by simple addition.

A single number used to carry out a percentage change in one step. For a 15% increase use 1.15; for a 15% decrease use 0.85.

A comparison of two or more quantities of the same kind, written as 3:5 or as a fraction. It shows how many parts of one quantity compare with another.

A statement that two ratios are equal, or a relationship where quantities change together at a constant rate. Direct proportion means both increase together; inverse proportion means one falls as the other rises.

How quickly one quantity changes compared with another, usually written as a quantity per unit, such as 60 kilometres per hour or 3 litres per minute.

The ratio between a measurement on a drawing or map and the real distance it represents, for example 1:25000. A scale factor enlarges or reduces a shape by multiplying lengths.

A combination of numbers, letters and operations with no equals sign, such as 4x + 7 or 3(a - 2). Letters stand for unknown or variable values.

A mathematical statement that two expressions are equal, such as 5x - 3 = 12. Solving it means finding the value or values of the unknown that make it true.

A rule written with letters showing how quantities are related, such as A = pi r^2 for the area of a circle or v = u + at for speed.

Replacing letters in an expression or formula with given numbers and then working out the result, following the normal order of operations.

Writing an expression as a product of simpler expressions. For example, 6x + 9 factorises to 3(2x + 3), and x^2 + 5x + 6 factorises to (x + 2)(x + 3).

To multiply out brackets and remove them, collecting like terms. For example, 3(2x + 5) expands to 6x + 15, and (x + 1)(x + 4) expands to x^2 + 5x + 4.

An equation in which the highest power of the unknown is 2, usually written ax^2 + bx + c = 0. It can be solved by factorising, completing the square or the quadratic formula.

Two or more equations that must be satisfied by the same values of the unknowns at the same time. They are solved by elimination or substitution.

A statement comparing expressions that are not necessarily equal, using the symbols <, >, <= or >=. For example, 2x + 1 < 9 means x < 4.

The steepness of a straight line, found by dividing the vertical change by the horizontal change between two points. A horizontal line has gradient 0.

The graph of an equation of the form y = mx + c, where m is the gradient and c is the y-intercept, the point where the line crosses the y-axis.

In a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides, written a^2 + b^2 = c^2. It is used to find missing lengths.

The longest side of a right-angled triangle, opposite the right angle. It is the side labelled c in Pythagoras' theorem and the denominator in sine and cosine ratios.

A ratio comparing two sides of a right-angled triangle, defined for an angle as sine (opposite over hypotenuse), cosine (adjacent over hypotenuse) or tangent (opposite over adjacent).

The angle measured upwards from the horizontal to a line of sight, used in problems involving heights of buildings or trees. The angle of depression is measured downwards.

A direction measured clockwise from north, written as a three-figure angle such as 045 or 210. Bearings are always between 000 and 360.

Shapes with the same angles whose matching sides are in the same ratio, so one is an enlargement of the other. Areas scale by the square of the length ratio.

The amount of surface inside a two-dimensional shape, measured in square units such as cm^2. Formulas include length x width for a rectangle and pi r^2 for a circle.

The amount of space a three-dimensional solid occupies, measured in cubic units such as cm^3. For a cuboid it is length x width x height.

The total area of all the outside faces of a three-dimensional solid, measured in square units. It is found by adding the areas of each face or using a net.

The average found by adding all values and dividing by how many there are. It uses every data value but can be pulled up or down by extreme values.

The middle value when data is arranged in order. With an even number of values it is the mean of the two middle values, so it is not affected by extreme values.

A simple measure of spread found by subtracting the smallest value from the largest. It shows how widely the data is spread but ignores all the middle values.

A running total of frequencies, showing how many data values are at or below each point. Its graph is used to estimate the median and quartiles.

A measure from 0 to 1 of how likely an event is. For equally likely outcomes it equals the number of favourable outcomes divided by the total number of outcomes.

Events that cannot happen at the same time, such as rolling a 3 and a 5 on one dice throw. Their probabilities add together to give the probability of either happening.

Events where the outcome of one does not affect the probability of the other, such as two separate dice throws. Their probabilities are multiplied to find both happening.

The estimated probability of an event found by dividing the number of times it happened by the total number of trials. With more trials it usually gets closer to the true probability.

A branching diagram showing all possible outcomes of two or more events, with probabilities written on the branches. Probabilities along a path are multiplied and separate paths are added.