NECO SSCE Mathematics key terms

A number that can be written exactly as a fraction of two integers, with a non-zero denominator. Whole numbers, terminating decimals and recurring decimals are all rational.

A real number that cannot be written as an exact fraction of two integers. Its decimal expansion never ends and never repeats; the square root of 2 and pi are examples.

The smallest positive integer that is a multiple of each of two or more given numbers. It is found by multiplying the highest power of every prime factor appearing.

The largest positive integer that divides each of two or more given numbers without a remainder. It is the product of the lowest powers of the prime factors they share.

A root of a number that cannot be evaluated exactly as a rational number, such as the square root of 3. Surds are simplified and combined using rules of roots.

Writing a number as A multiplied by ten raised to a whole-number power, where A is at least 1 and less than 10. Very large and very small quantities become easier to compare.

The digits of a number that carry meaning about its accuracy, counted from the first non-zero digit. Rounding to a given number of significant figures shortens answers sensibly.

A counting system that uses a fixed set of digits, with place values that are powers of the base. Base two uses only 0 and 1 while base ten uses 0 to 9.

A comparison of two or more quantities of the same kind, showing how many times one contains the other. Ratios simplify like fractions and are used to share amounts.

A fraction or ratio expressed as a number out of one hundred. It is used for profit and loss, discount, commission, simple interest and comparing quantities of different sizes.

Powers that show how many times a base is multiplied by itself. The laws of indices cover multiplication, division, negative and zero powers and powers of powers.

The number that multiplies a variable in an algebraic term, including its sign. In 7x the coefficient is 7, and in minus 3xy it is minus 3.

Writing an expression as a product of simpler expressions called factors. Common factors, difference of two squares and quadratic trinomials are the usual patterns tested.

An equation whose highest power of the unknown is two, written as ax squared plus bx plus c equals zero, where a is not zero. It has at most two roots.

Rewriting a quadratic expression as a squared bracket plus a constant, for example x plus 3 all squared minus 5. It solves quadratics and locates the turning point.

Two or more equations that must all be true for the same values of the unknowns. They are solved by elimination, substitution or by reading a graph.

The variable that is expressed in terms of all the other variables in a formula, standing alone on one side. Changing the subject uses inverse operations.

A statement that compares two expressions using less than, greater than, or their or-equal forms. Its solution is a range of values, and multiplying by a negative reverses the sign.

A sequence in which each new term is obtained by adding the same fixed number, called the common difference, to the previous term. The nth term and the sum of terms have standard formulas.

A sequence in which each term after the first is obtained by multiplying the previous term by a fixed constant called the common ratio. Its nth term and sum are examined.

The relationship between two or more quantities that change together, classed as direct, inverse, joint or partial. Each type is written as an equation with a constant of proportionality.

In a right-angled triangle the square of the hypotenuse equals the sum of the squares of the other two sides. It finds missing sides and tests whether an angle is right.

Triangles that are equal in both shape and size, so every corresponding side and angle matches. They are proved using SSS, SAS, ASA or RHS.

Figures with identical shape but possibly different size. Corresponding angles are equal and corresponding lengths are in the same ratio, called the scale factor.

A rule linking angles, chords, tangents and arcs in a circle, for example that the angle in a semicircle is a right angle or that angles in the same segment are equal.

The part of a circle enclosed by two radii and the arc between them. Its arc length and area are the same fraction of the whole circle as its central angle.

The set of all points that satisfy a stated geometric condition, such as all points a fixed distance from a given point, which form a circle.

The average obtained by adding all the observations and dividing by their number. For grouped data the class mid-points are multiplied by frequencies before dividing.

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

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

A graph of running totals of frequency plotted against upper class boundaries, also called an ogive. It estimates the median, quartiles and other percentiles.

A measure of the spread of data about the mean, equal to the square root of the variance. Small values mean the observations cluster near the mean.

The complete set of all possible outcomes of an experiment. The probability of an event is the number of favourable outcomes divided by the size of the sample space.

Events that cannot occur in the same trial. When two events are mutually exclusive, the probability that either one happens is the sum of their separate probabilities.

A direction written as three digits, measured clockwise from due north, such as 045 degrees. Back bearings differ by 180 degrees and scale drawings help solve problems.

In any triangle, each side divided by the sine of the angle opposite it gives the same value. It is used when a side and its opposite angle are known.

In any triangle, the square of a side equals the sum of the squares of the other two sides minus twice their product times the cosine of the included angle.

In a right-angled triangle, the side opposite a given acute angle divided by the side adjacent to it. Along with sine and cosine it forms the basic trigonometric ratios.

The angle at the centre of a circle subtended by an arc equal in length to the radius. One radian is about 57.3 degrees, and pi radians equal 180 degrees.

The angle between the horizontal and the line of sight of an observer looking upward at an object above their level. It is used with the tangent ratio to calculate unknown heights and distances.