MATSEC SEC Mathematics key terms

A whole number with no fractional or decimal part, such as 7, 0 or -12. Integers can be positive, negative or zero, and are used for counting and for describing positions on a number line.

A whole number greater than 1 whose only positive divisors are 1 and itself, for example 2, 3, 7 or 13. The number 1 is not prime because it has only one divisor.

A number that divides another number exactly, leaving no remainder. For instance, the factors of 12 are 1, 2, 3, 4, 6 and 12. Factors are used when simplifying fractions and factorising expressions.

The result of multiplying a number by a whole number. The multiples of 6 are 6, 12, 18, 24 and so on. The lowest common multiple of two numbers helps when adding fractions with different denominators.

The largest number that divides two or more given numbers exactly. The highest common factor of 18 and 24 is 6. It is used to simplify fractions and to factorise algebraic expressions fully.

The smallest number that is a multiple of two or more given numbers. For 4 and 6 the lowest common multiple is 12. It is used to find a common denominator when adding or subtracting fractions.

A way of writing very large or very small numbers as a number between 1 and 10 multiplied by a power of 10, such as 3.2 × 10^5. It makes the size of the number easy to compare and calculate with.

The rules for combining powers with the same base: multiply by adding indices, divide by subtracting them, and raise a power to a power by multiplying indices. A negative index gives a reciprocal, and a zero index gives 1.

A comparison of two or more quantities of the same kind, written with a colon such as 3 : 5. Ratios can be simplified like fractions and are used to share an amount in given proportions.

A statement that two ratios or fractions are equal, or a relationship where quantities change at the same rate. Direct proportion means both increase together; inverse proportion means one increases as the other decreases.

A fraction expressed as a part out of 100, written with the % symbol. To find a percentage of an amount, divide by 100 and multiply, or multiply by the decimal equivalent such as 0.15 for 15%.

Interest calculated on the original amount plus any interest already added, so the total grows faster each period. It is found using repeated percentage increase, often with the formula P(1 + r/100)^n.

Square roots of numbers that are not perfect squares, such as √2 or √5, left in root form because their decimal values never terminate. They can be simplified or combined using rules such as √a × √b = √(ab).

Any number that can be written as one integer divided by another non-zero integer, including fractions, terminating decimals and recurring decimals. Irrational numbers such as π or √2 cannot be written this way.

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

Two or more equations that must be true at the same time, solved together to find values satisfying all of them. Common methods are elimination, where equations are added or subtracted, and substitution.

An equation containing a squared variable as its highest power, usually written ax² + bx + c = 0. It can be solved by factorising, completing the square or using the quadratic formula.

The single variable that is expressed in terms of the others in a formula, usually alone on one side. Changing the subject means rearranging the formula using inverse operations, as when making r the subject of C = 2πr.

A rule that assigns exactly one output value to each input value, often written f(x). Its graph shows the relationship, and the set of allowed inputs is called the domain.

A measure of how steep a straight line is, found by dividing the vertical change by the horizontal change between two points. A positive gradient rises to the right; a negative one falls.

The point where a graph crosses the vertical axis, so it is the value of y when x equals zero. In the equation y = mx + c, the letter c gives the y-intercept.

An ordered list of numbers or terms that follows a rule, such as 2, 5, 8, 11. Each term is found from the position number using a term-to-term or position-to-term rule.

A formula that gives any term of a sequence directly from its position number n. For the sequence 3, 7, 11, 15 with constant difference 4, the nth term is 4n − 1.

A closed flat shape made of straight sides that do not cross. Polygons are named by their number of sides, such as triangles, quadrilaterals, pentagons and hexagons, and may be regular or irregular.

A polygon in which every side is the same length and every interior angle is equal, such as a square or an equilateral triangle. Regular polygons have symmetry and simple angle formulas.

An angle inside a polygon at one of its vertices. The interior angles of any polygon with n sides add up to (n − 2) × 180°, so a pentagon's angles total 540°.

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. It is used to find a missing side length.

The longest side of a right-angled triangle, opposite the right angle. It is the side labelled c in Pythagoras' theorem and is always opposite the 90° angle.

The use of the ratios sine, cosine and tangent to relate angles and side lengths in right-angled triangles. Remembered as SOH CAH TOA, it finds unknown sides or angles.

A direction measured clockwise from due north, written as a three-figure angle such as 045° or 210°. Bearings are used to describe the position of one point from another.

Describing two shapes that are exactly the same size and shape, so one fits exactly onto the other. Congruent triangles can be identified by conditions such as SSS, SAS, ASA and RHS.

Describing two shapes with the same angles and the same proportions between sides, though not necessarily the same size. Corresponding lengths share a constant scale factor.

A transformation that changes the size of a shape by a scale factor from a fixed centre point. A factor greater than 1 makes the shape larger; a factor between 0 and 1 makes it smaller.

A drawing in which all lengths are reduced or increased by the same ratio to represent a real object. The scale, such as 1 : 50, converts measurements on the drawing to actual lengths.

The amount of space a solid occupies, measured in cubic units such as cm³. For a cuboid it is length × width × height; a prism's volume is the cross-sectional area multiplied by its length.

The total area of all the outer faces of a solid, measured in square units. It is found by working out the area of each face and adding them together.

A solid with two identical circular ends joined by a curved surface. Its volume is πr²h and its total surface area is 2πr² + 2πrh, where r is the radius and h the height.

A measure of average found by adding all the values and dividing by how many there are. The mean uses every value, so it is affected strongly by very high or very low outliers.

The middle value when a set of data is arranged in order. If there is an even number of values, the median is the mean of the two middle ones. It is not affected by extreme values.

The value that appears most often in a set of data. A data set may have no mode, one mode, or several modes if values tie for most frequent.

The difference between the largest and smallest values in a data set. It is a simple measure of spread but depends only on the two extreme values.

The running total of frequencies up to a given value, used to find the median and quartiles of grouped data. Its graph, the cumulative frequency curve, rises steadily to the total frequency.

A chart for continuous grouped data in which the bars touch and the area of each bar represents frequency. Bars may have different widths, so frequency density is plotted on the vertical axis.

The number of times a value or category occurs in a data set. Frequencies are often shown in tables or charts and add up to the total number of observations.

A measure between 0 and 1 of how likely an event is, where 0 means impossible and 1 means certain. It can be found from equally likely outcomes or estimated from experimental data.

A branching diagram showing the possible outcomes of two or more events in sequence. Probabilities along a path are multiplied together, and paths giving the same result are added.

A graph plotting pairs of values as points to show whether two variables are related. A line of best fit can be drawn to describe the trend and allow estimates.

A description of how closely two variables are related, shown by how near the points in a scatter graph lie to a straight line. Correlation may be positive or negative, and does not prove cause.