BGCSE Scientific Mathematics 1237 key terms

The value a digit has because of its position in a number. In 4,072 the digit 4 stands for four thousands, while the 7 stands for seven tens.

A number written in digits with each digit in its correct place, such as 3,506. It is contrasted with word form and expanded form of the same number.

A number broken into the sum of its place values, for example 3,506 written as 3000 + 500 + 6. It shows the value contributed by each digit.

Replacing a number by a nearby number with fewer significant digits. You look at the first dropped digit: 5 or more rounds up, 4 or less keeps the digit unchanged.

Finding an answer close enough to the exact value by using rounded or simplified numbers. It is used to check whether a calculated result is reasonable.

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

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

A whole number greater than 1 whose only factors are 1 and itself. The first few primes are 2, 3, 5, 7, 11 and 13.

The largest number that divides two or more given numbers exactly. For 18 and 24 the common factors are 1, 2, 3 and 6, so the highest common factor is 6.

The smallest number that is a multiple of each of two or more given numbers. For 4 and 6 the multiples meet first at 12.

A position of a digit to the right of the decimal point. The first decimal place shows tenths, the second hundredths, and the third thousandths.

The digits of a number that carry meaning about its accuracy, counted from the first non-zero digit. Zeros used only to fix the size of a number are not significant.

A relationship in which one quantity doubles when the other doubles, so the ratio between them stays constant. Cost at a fixed price per item is a common example.

A comparison of two or more quantities of the same kind, often written with a colon such as 2:3. It tells how many parts of one quantity go with parts of another.

A fraction or ratio expressed as a number out of one hundred. For instance, 45% means 45 parts in every 100 parts of the whole.

Money paid for the use of borrowed money, or earned on savings. Simple interest is calculated only on the original amount each year.

A combination of numbers, letters and operation signs that has no equals sign, such as 3x + 5. The letters stand for unknown or variable values.

A letter or symbol that represents a number which may change or is not yet known. In the expression 2n + 1, the letter n is the variable.

The number that multiplies a variable in a term. In 7y the coefficient is 7, and in 3x + 4 the coefficient of x is 3.

Terms that contain exactly the same variables raised to the same powers, so they can be added or subtracted. For example, 5a and 9a are like terms but 5a and 5a squared are not.

Rewriting an expression in a shorter equivalent form by collecting like terms, removing brackets or cancelling common factors, without changing its value.

Writing an expression as a product of factors, the reverse of expanding brackets. For example, 6x + 9 factorises to 3(2x + 3).

Multiplying out brackets to remove them and write the expression as a sum of terms. Expanding 2(x + 4) gives 2x + 8.

A mathematical statement that two expressions are equal, containing an equals sign. For example, 4x - 1 = 11 is true only when x equals 3.

A value of the unknown that makes an equation or inequality true. Substituting it back into the original statement must give a correct numerical sentence.

Replacing letters in an expression or formula with given numbers and then calculating the result. For instance, substituting x = 2 into 3x + 1 gives 7.

A statement comparing two expressions that are not necessarily equal, using signs such as less than, greater than, or their or-equal-to forms. Solving it gives a range of values.

Two or more equations that must be satisfied by the same values of the unknowns at the same time. Their solution is the pair of values that fits every equation.

A rule written as an equation linking quantities, such as area equals length times width. Letters in a formula stand for measurable quantities.

The total distance around the outside edge of a flat shape. It is found by adding the lengths of all the sides, using matching units.

The amount of flat surface enclosed by a shape, measured in square units such as square centimetres. A rectangle's area is its length multiplied by its width.

The amount of space a solid occupies, measured in cubic units such as cubic metres. For a cuboid it is length times width times height.

The amount a container can hold, usually measured in litres or millilitres. One litre equals one thousand cubic centimetres.

The distance all the way round a circle, equal to pi multiplied by the diameter. It is the circle's equivalent of a perimeter.

The distance from the centre of a circle to any point on its edge, which is half the diameter. It is needed to calculate circumference and area of a circle.

The straight distance across a circle passing through its centre, equal to twice the radius. It is the longest chord of the circle.

The amount of turning between two straight lines that meet at a point, measured in degrees. A full turn is 360 degrees.

A flat shape with three straight sides and three interior angles. Its angles always add up to 180 degrees.

A closed flat shape bounded by straight sides, such as a pentagon or hexagon. It is named by the number of sides it has.

Straight lines in the same plane that never meet however far they are extended, staying the same distance apart. They are often marked with matching arrowheads.

Meeting at a right angle of 90 degrees. A vertical wall is perpendicular to a horizontal floor.

A balanced matching of parts of a shape. A line of symmetry divides a shape into two halves that fold exactly onto each other.

A change in the position, size or orientation of a shape on a grid. The main types are translation, reflection, rotation and enlargement.

A pair of numbers that fixes the position of a point on a grid, written as (x, y). The first number gives the horizontal position and the second the vertical.

A measure of how steep a straight line is, found by dividing the vertical change by the horizontal change between two points on it.

The straight-line picture produced by plotting an equation of the first degree, such as y = 2x + 1. Every point on the line satisfies the equation.

A rule that assigns exactly one output value to each allowed input value. A function may be shown as an equation, a table, a graph or a mapping.

The average found by adding all the values and dividing by how many there are. It uses every piece of data but can be pulled by extreme values.

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

The value that occurs most often in a set of data. A set may have one mode, several modes, or no mode at all.

The difference between the largest and smallest values in a set of data. It is a simple measure of how spread out the data are.

A table that records how often each value or group of values occurs in a set of data. It is often used to organise results before drawing a chart.

A number from 0 to 1 expressing how likely an event is, where 0 means impossible and 1 means certain. It can be found by dividing favourable outcomes by all equally likely outcomes.

The complete list or set of all possible outcomes of an experiment. For one roll of a fair die it contains the numbers 1 to 6.