BGCSE Mathematics 0563 key terms

The value a digit has because of its position in a numeral; in 4729 the digit 7 stands for seven hundreds, not simply seven.

A way of writing very large or very small numbers as a number between 1 and 10 multiplied by a power of 10, for example 4.2 × 10^5.

The largest whole number that divides exactly into each of two or more given numbers, such as 6 for 24 and 42.

The smallest whole number that is a multiple of each of two or more given numbers, such as 12 for 4 and 6.

Any number that can be written as one integer divided by another non-zero integer, including fractions, terminating decimals and recurring decimals.

The digits of a number that carry meaning about its accuracy, counted from the first non-zero digit; rounding to three significant figures shortens a long answer.

A comparison of two or more quantities of the same kind, written with a colon such as 3 : 5 and usually simplified by dividing by a common factor.

The relationship in which two quantities increase or decrease together at the same rate, so that doubling one doubles the other and their quotient stays constant.

A relationship in which one quantity increases as the other decreases so that their product stays constant, for example more workers completing a job in fewer days.

A fraction or ratio expressed with a denominator of one hundred, so that 45% means 45 out of every 100.

Interest calculated only on the original sum invested or borrowed, using the formula I = PRT/100, and never on interest already earned.

Interest added to the principal at the end of each period so that later interest is earned on earlier interest as well as on the original amount.

The money left when the cost price of an item is subtracted from its selling price; when the result is negative the seller makes a loss.

The number multiplied by a variable in an algebraic term; in 7x the coefficient is 7 and in −3y² it is −3.

Rewriting an algebraic expression as a product of factors, for example turning x² + 5x + 6 into (x + 2)(x + 3).

An equation in which every variable appears to the first power only, so its graph is a straight line and it usually has a single solution for one unknown.

A statement comparing two expressions with the symbols <, >, ≤ or ≥, showing that one side is smaller or larger than the other rather than equal.

Two or more equations that must be satisfied by the same values of the variables at the same time, often solved by elimination or by substitution.

The single variable standing alone on one side of a formula, such as v in v = u + at; changing the subject means rearranging to isolate a different variable.

A measure of how steep a straight line is, found as the change in the vertical direction divided by the corresponding change in the horizontal direction.

A rule that assigns exactly one output value to each input value, often written f(x), and whose graph can be drawn on the Cartesian plane.

The point where a graph crosses an axis; the y-intercept of y = mx + c is the value c, occurring where x equals zero.

The smooth U-shaped curve that forms the graph of a quadratic function such as y = x² − 4x + 1.

The total distance around the outside edge of a plane shape, measured in units of length such as centimetres or metres.

The amount of flat surface enclosed by a boundary, measured in square units such as cm² and calculated with a formula for each shape.

The amount of space occupied by a solid, measured in cubic units such as cm³ and found by multiplying base area by height for a prism.

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.

The distance all the way around a circle, equal to π times the diameter or twice π times the radius.

The region of a circle enclosed between two radii and the arc joining their ends, shaped like a slice of pie.

In a right-angled triangle the ratio of the side opposite a given angle to the side adjacent to it; it equals sine divided by cosine.

A direction measured clockwise from north and written as a three-figure angle, so a bearing of 065° means 65 degrees clockwise from north.

The angle measured upward from a horizontal line to a line of sight pointing at an object above the observer.

A quantity that has both size and direction, represented by a directed line segment or by a column of two numbers.

A transformation that slides every point of a shape the same distance in the same direction, without turning or resizing it.

A transformation that changes the size of a shape by a scale factor from a fixed centre point while keeping the same shape and angles.

The average found by adding all the values in a data set and dividing the total by the number of 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 running total of frequencies up to a given class interval, used to plot a curve from which the median and quartiles can be read.

A number between 0 and 1 describing how likely an event is, found for equally likely outcomes by dividing favourable outcomes by all outcomes.

Events that cannot happen at the same time, so the probability that either one occurs is the sum of their separate probabilities.