CCEA GCSE Maths key terms

A whole number that divides exactly into another number with no remainder. For example, 1, 2, 3, 4, 6 and 12 are all factors of 12, and factor pairs list them together.

The result of multiplying a number by a whole number. Multiples of 7 include 7, 14, 21 and 28 and continue without end, so a number has infinitely many multiples but only finitely many factors.

The largest whole number that divides exactly into two or more given numbers. Find it by listing factors or by comparing prime factorisations and taking the lowest power of each shared prime.

The smallest number that is a multiple of two or more given numbers. Compare prime factorisations and take the highest power of every prime that appears; for 6 and 8 the LCM is 24.

A way of writing very large or very small numbers as A x 10^n, where A lies between 1 and 10 and n is an integer. For example, 4.2 x 10^-3 is 0.0042.

An expression containing the square root of a number that is not a perfect square, such as the root of 5. Surds are kept in exact form because their decimal values are irrational and never terminate or recur.

Any number that can be written as a fraction of two integers with a non-zero denominator. Terminating and recurring decimals are rational, while the square root of 2 and pi are not.

The range of values a quantity could have had before it was rounded, written as an inequality. A length given as 7 cm to the nearest centimetre has the error interval 6.5 <= x < 7.5.

Interest worked out on the original amount plus any interest already added, so the balance grows by a fixed multiplier each period. Use original amount x (1 + r/100)^n, where n is the number of periods.

A comparison of the sizes of two or more quantities, written with a colon such as 3 : 2. To share an amount in a given ratio, divide it by the total number of parts.

A relationship where one quantity increases as the other decreases, so their product stays constant. Doubling one quantity halves the other, as with speed and the time a journey takes.

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

Rewriting an expression as a multiplication of simpler expressions, the reverse of expanding brackets. For example, 6x + 9 becomes 3(2x + 3) and x^2 + 5x + 6 becomes (x + 2)(x + 3).

x = (-b +/- the square root of (b^2 - 4ac)) divided by 2a, which solves any equation of the form ax^2 + bx + c = 0. It works even when the expression will not factorise neatly.

The expression b^2 - 4ac taken from the quadratic formula. A positive value means two real roots, zero means one repeated root, and a negative value means there are no real roots.

Two or more equations that must be true at the same time, solved by elimination or substitution. The solution is the pair of values satisfying both, shown by the point where their graphs cross.

A statement comparing expressions with the symbols <, >, <= or >= instead of an equals sign. Its solution is a range of values, shown on a number line or by shading a region.

A rule, usually a formula written in n, that gives any term of a sequence from its position number. For linear sequences the rule has the form dn + c, where d is the common difference.

Writing a rule as f(x), read as f of x. The notation f(3) means the value of the function when x equals 3, and the inverse function f^-1 reverses its effect.

Rewriting a quadratic expression in the form (x + p)^2 + q. This reveals the turning point of the graph and can solve equations that do not factorise into whole-number brackets.

A measure of how steep a straight line is, found by dividing the vertical change by the horizontal change between two points. Parallel lines have equal gradients and perpendicular gradients multiply to -1.

In a right-angled triangle the square of the hypotenuse equals the sum of the squares of the other two sides, a^2 + b^2 = c^2. It finds a missing side and can test whether an angle is right.

A ratio linking an angle to two sides of a right-angled triangle: sine is opposite over hypotenuse, cosine is adjacent over hypotenuse and tangent is opposite over adjacent, remembered as SOHCAHTOA.

a/sin A = b/sin B = c/sin C, used in triangles that are not right-angled. It finds a side or angle when you know a matching side and angle pair, or two angles and one side.

a^2 = b^2 + c^2 - 2bc cos A, which applies to any triangle. Use it to find a third side from two sides and the included angle, or an angle from all three sides.

A fact about angles or lines in circles, such as the angle in a semicircle being 90 degrees or the angle at the centre being twice the angle at the circumference. You quote a theorem to justify each step.

Shapes with equal corresponding angles and sides in the same proportion. Lengths scale by one factor, areas by the square of that factor and volumes by its cube.

A direction measured clockwise from north, written as three digits such as 045 degrees. Bearings always start from the point you are at and range from 000 to 360 degrees.

A quantity with both size and direction, written as a column or a bold letter. Vectors add tip to tail, and the negative of a vector points in the opposite direction.

Frequency divided by class width, used to draw a histogram. The area of each bar, not its height, represents the frequency of that class, so unequal class widths are handled fairly.

A running total of frequencies up to the end of each class, plotted against upper class boundaries. The resulting curve estimates the median, the quartiles and how many values lie above or below a limit.

The difference between the upper quartile and the lower quartile, calculated as IQR = UQ - LQ. It measures the spread of the middle half of the data and is not affected by extreme values.

A straight line drawn through the middle of the points on a scatter graph. It summarises the trend and allows values to be estimated, but only within the range of the data collected.

Events that cannot happen at the same time, so the probability of one or the other is the sum of their individual probabilities. For example, rolling a 2 and rolling a 5 on one die.

A branching diagram showing the outcomes of two or more events. Multiply along the branches for combined outcomes and add between branches for different ways of getting the same overall result.

A sampling method where the sample is split in proportion to the sizes of groups in the population. Each group contributes a share equal to its population size divided by the total, times the sample size.

A logical argument showing a statement is always true, using known facts and algebra rather than examples. Writing expressions for consecutive numbers and simplifying them is a common technique.

A single case that shows a general statement is false. One counterexample is enough to disprove a conjecture, however many other cases appear to support it.

A statement believed to be true based on evidence but not yet proved. You test it with examples, then either prove it using algebra or find a counterexample to disprove it.