Botswana BGCSE General Mathematics 1236 key terms

A way of writing very large or very small numbers as a number between 1 and 10 multiplied by a power of ten, for example 4.2 × 10⁵ or 6 × 10⁻³.

The small raised number showing how many times a base is multiplied by itself; in 3⁴ the index is 4, and 3⁴ means 3 × 3 × 3 × 3.

The result of dividing 1 by a given non-zero number. The reciprocal of 5 is one fifth, and any number multiplied by its reciprocal gives 1.

A comparison of two or more quantities of the same kind, written with a colon such as 3 : 5, showing how many times one amount contains the other.

A part expressed out of one hundred, so 45% means 45 parts in every 100 and is the same as the decimal 0.45 or the fraction 9/20.

The digits of a number that carry meaning for its accuracy, counted from the first non-zero digit; rounding to three significant figures keeps only the first three of these digits.

The set containing every element being considered in a particular problem, usually written ε; all the other sets in that problem are subsets of it.

A set whose members are all contained in another set. If A = {1, 2} and B = {1, 2, 3}, then A is a subset of B.

The set of all elements of the universal set that are not members of a given set A, written A′; if ε = {1, 2, 3, 4} and A = {1, 2}, then A′ = {3, 4}.

A rule that assigns to each input value exactly one output value, often written f(x); a single input may never produce two different outputs.

The function that undoes another function, so if f sends 3 to 7 then its inverse sends 7 back to 3; it is written f⁻¹.

A function formed by applying one function and then feeding its result into another, written fg(x) or f(g(x)), where g acts first and f acts second.

The number multiplying a variable in an algebraic term; in 7x² the coefficient is 7, and in −y the coefficient is understood to be −1.

Terms that contain exactly the same variables raised to the same powers, such as 3x² and −5x², which can be added or subtracted to give a single term.

To rewrite an expression as a product of factors, for example turning x² + 5x into x(x + 5), or 6x + 9 into 3(2x + 3).

The single variable that a formula is arranged to give, usually standing alone on one side; rearranging y = mx + c for x makes x the subject.

A rule or expression that produces any term of a sequence from its position number n, such as 3n + 1 for the sequence 4, 7, 10, 13, …

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

A statement comparing two expressions that are not necessarily equal, using symbols such as <, >, ≤ or ≥; its solution is a range of values rather than one number.

Describing two figures that are exactly the same shape and size, so one can be placed on the other with every matching side and angle equal.

Describing two figures with the same shape but not necessarily the same size; corresponding angles are equal and corresponding sides are in the same ratio.

A quantity with both size and direction, often drawn as an arrow or written as a column such as (3, −2); it can describe a translation from one point to another.

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

A straight line that touches a circle at exactly one point; a tangent is always perpendicular to the radius drawn to the point of contact.

A closed plane figure bounded by three or more straight line segments, such as a triangle, a pentagon or a hexagon; its interior angles add up to (n − 2) × 180°.

The distance all the way around a circle, found from the radius r using C = 2πr, or from the diameter d using C = πd.

A solid with the same uniform cross-section running along its whole length, such as a cuboid or a cylinder; its volume equals cross-sectional area multiplied by length.

The total area of all the flat faces and curved surfaces of a solid, measured in square units and found by adding the areas of each separate part.

The amount of space occupied by a solid, measured in cubic units and calculated differently for each shape, for example length × width × height for a cuboid.

The average found by adding all the values in a data set and dividing by how many values there are; for 2, 4 and 9 the mean is 5.

The middle value of a data set once the values are arranged in order of size; with an even number of values it is the mean of 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 at all if every value is different.

A running total of frequencies, made by adding each frequency to the total of all the ones before it; it is used to estimate the median and quartiles of grouped data.

A measure between 0 and 1 of how likely an event is; when outcomes are equally likely it equals the number of favourable outcomes divided by the total number of outcomes.

Events that cannot happen at the same time, so the probability that either one occurs is found by adding their separate probabilities together.

The longest side of a right-angled triangle, lying opposite the right angle; it is used as the denominator in the sine and cosine ratios.

The angle measured between the horizontal and the line of sight when an observer looks upward at an object that is above their own level.

A direction measured clockwise from due north and always written with three digits, so a bearing of 045° points north-east and 270° points due west.

A rule stating that in any triangle each side divided by the sine of its opposite angle is constant: a ÷ sin A = b ÷ sin B = c ÷ sin C.

A rule linking the three sides of a triangle to one angle, written a² = b² + c² − 2bc cos A, used when the sine rule cannot be applied.