JCE Mathematics (Syllabus 13) key terms

A whole number that can be positive, negative or zero, with no fractional or decimal part. Examples are -3, 0 and 7.

A number that can be written as a fraction a/b where a and b are integers and b is not zero. Its decimal form either stops or repeats a pattern.

A real number that cannot be written as a fraction of two integers. Its decimal form never stops and never repeats, for example the square root of two or pi.

An integer greater than one whose only positive divisors are one and itself. Examples are 2, 3, 5, 7 and 11. The number 1 is not prime.

The largest positive integer that divides two or more given numbers exactly. For 12 and 18 the common factors are 1, 2, 3 and 6, so the HCF is 6.

The smallest positive integer that is a multiple of two or more given numbers. For 4 and 6 the multiples first meet at 12, so the LCM is 12.

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 3.2 × 10^5.

A comparison of two or more quantities of the same kind, usually written with a colon such as 2:3. It shows how many times one quantity contains another.

A relationship in which two quantities increase or decrease together at the same rate. Doubling one quantity doubles the other, so their ratio stays constant.

Rules for combining powers with the same base, such as a^m × a^n = a^(m+n) and a^m ÷ a^n = a^(m-n). They also cover powers of powers, zero indices and negative indices.

The agreed sequence for evaluating expressions: work out brackets first, then indices, then multiplication and division from left to right, and finally addition and subtraction from left to right.

An irrational root left in exact form, such as √2 or 3√5, instead of being written as a decimal. Surds can often be simplified or combined using rules for roots.

A combination of numbers, variables and operation signs that represents a quantity, such as 3x + 2y - 7. It does not contain an equals sign.

The numerical factor multiplying a variable in a term. In the term 7x the numerical factor is 7, and in -4ab it is -4.

Terms that contain exactly the same variables raised to the same powers, so they can be added or subtracted. For example, 5x and -2x are like terms, but 5x and 5x² are not.

An equation in which the variable appears only to the first power, such as 3x + 5 = 20. Solving it means finding the value that makes both sides equal.

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

An equation whose highest power of the variable is two, usually written as ax² + bx + c = 0 where a is not zero.

Writing an expression as a product of simpler expressions that multiply together to give the original. For example, x² + 5x + 6 factorises to (x + 2)(x + 3).

The single variable that a formula is arranged to give, usually written alone on one side. Rearranging v = u + at to make t the subject gives t = (v - u)/a.

A measure of the turn between two lines or rays that meet at a point, usually given in degrees. A full turn is 360°, a straight line is 180° and a right angle is 90°.

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.

Shapes that have the same shape but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are in the same ratio.

A direction measured clockwise from north, written as a three-digit angle. For example, due east is written as 090° and due south as 180°.

The amount of space occupied by a solid object, measured in cubic units such as cm³. For a cuboid it is found by multiplying length, breadth and height.

The total area of all the faces of a three-dimensional solid, measured in square units. For a cube with edge length s it equals 6s².

The sum of all the values divided by the number of values. For the data 4, 6, 8 and 10 the mean is 28 ÷ 4 = 7.

The middle value when a set of data is arranged in order of size. If there is 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.

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

A number between 0 and 1 that measures how likely an event is to happen. It equals the number of favourable outcomes divided by the total number of equally likely outcomes.

The set of all possible outcomes of an experiment. For a single fair die the sample space is {1, 2, 3, 4, 5, 6}.

A rule that assigns exactly one output value to each input value. For example, the rule y = 2x + 1 gives one y for every chosen x.

The set of all input values for which a function is defined. For y = 1/x, zero must be excluded because division by zero is undefined.

The set of all output values that a function actually produces. For y = x² with real x, the output values are all numbers greater than or equal to zero.

A measure of how steep a straight line is, found by dividing the vertical change by the horizontal change between two points. It is often called the slope.

The point where a graph crosses the vertical y-axis, which occurs where x equals zero. For the line y = 3x + 2 the y-intercept is 2.

The straight-line graph produced by an equation of the form y = mx + c, where m is the gradient and c is the y-intercept.

The curved U-shaped graph of a quadratic function such as y = x². It has a vertex and a line of symmetry, and opens upwards when the coefficient of x² is positive.