Maths Dictionary

The size of a number, ignoring its sign; its distance from zero.

Example: |−7| = 7.

An angle smaller than 90°.

A series of equal payments made at regular intervals, such as a loan repayment or savings plan.

A part of the circumference of a circle.

The amount of surface a 2D shape covers, measured in square units.

A formula for the area of any triangle using two sides and the included angle.

Example: Area = ½·ab·sinC.

A sequence where each term differs from the previous by a constant common difference.

A line that a graph approaches ever more closely but never actually touches.

Example: y = 1⁄x has asymptotes on both axes.

The vertical line that divides a parabola into two mirror-image halves.

The number being raised to a power in an exponential expression.

Example: In 2⁵, the base is 2.

To cut exactly in half.

Example: A perpendicular bisector cuts a line in half at 90°.

The order of operations: Brackets, Of/Orders (powers), Division, Multiplication, Addition, Subtraction.

The grid formed by a horizontal x-axis and vertical y-axis, used to plot points and graphs.

A straight line joining two points on a circle (not necessarily through the centre).

The distance around the outside of a circle.

Example: C = 2πr.

The number multiplied by a variable in a term.

Example: In 7x, the coefficient is 7.

The constant amount added between consecutive terms of an arithmetic sequence.

Example: In 3, 7, 11, … the common difference is 4.

The constant amount each term is multiplied by in a geometric sequence.

Example: In 2, 6, 18, … the common ratio is 3.

Two angles that add up to 90°.

Rewriting a quadratic in the form (x + p)² + q, useful for solving and for finding the turning point.

Example: x² + 6x + 5 = (x + 3)² − 4.

Interest calculated on the principal plus all previously earned interest, so it grows faster than simple interest.

Exactly the same shape and size; identical figures.

Example: Two triangles with all matching sides and angles.

A term with a fixed value that contains no variable.

Example: In 3x + 8, the constant is 8.

A graph with no breaks, jumps or holes — you could draw it without lifting your pen.

An ordered pair (x, y) giving a point's position on the Cartesian plane.

In a right-angled triangle, the ratio of the adjacent side to the hypotenuse.

Example: cosθ = adjacent ⁄ hypotenuse.

A rule for any triangle linking all three sides and one angle.

Example: a² = b² + c² − 2bc·cosA.

The loss in value of an asset over time.

Example: A car losing value each year.

A function giving the gradient of a curve at any point; the result of differentiation.

Example: The derivative of x² is 2x.

A straight line through the centre of a circle, joining two points on it; twice the radius.

A special factorising pattern: a squared term minus another squared term.

Example: x² − 9 = (x + 3)(x − 3).

The process of finding the derivative — the rate of change or gradient of a function.

A reduction in the original price of an item.

Example: 20% off R500 saves R100.

The expression b² − 4ac, which reveals the nature of a quadratic's roots before solving.

Example: If b² − 4ac < 0 there are no real roots.

The set of all allowed input (x) values of a function.

A transformation that resizes a shape by a scale factor.

A mathematical statement that two expressions are equal, containing an equals sign.

Example: 4x − 7 = 9 is an equation.

A triangle with all three sides equal and all angles 60°.

To find an approximate answer, often by rounding.

A particular outcome or set of outcomes of an experiment.

Example: Rolling an even number.

The value of one country's currency in terms of another.

Example: R18 to 1 US dollar.

To multiply out brackets, writing an expression as a sum of terms.

Example: 2(x + 3) = 2x + 6.

The small raised number that tells you how many times to multiply the base by itself.

Example: In 2⁵, the exponent is 5.

The graph of a function where the variable is in the exponent, showing rapid growth or decay.

Example: y = 2ˣ.

A combination of numbers, variables and operations, with no equals sign.

Example: 4x − 7 is an expression.

A number that divides exactly into another number, leaving no remainder.

Example: The factors of 12 are 1, 2, 3, 4, 6 and 12.

To write an expression as a product of its factors — the reverse of expanding.

Example: x² + 3x = x(x + 3).

A rule or relationship written with symbols.

Example: Area of a circle: A = πr².

The number of times a value or category occurs in a data set.

A rule that assigns exactly one output value to each input value.

Example: f(x) = 2x + 1.

A sequence where each term is the previous one multiplied by a constant common ratio.

A measure of the steepness of a line: the change in y divided by the change in x.

Example: A gradient of 2 means y rises 2 for every 1 across.

The largest number that divides exactly into two or more numbers.

Example: The HCF of 12 and 18 is 6.

Buying an item by paying a deposit and then fixed instalments (with interest) until it is paid off.

A bar graph showing the frequency of grouped continuous data, with bars touching.

The two-branch curve of a function of the form y = a⁄x.

The longest side of a right-angled triangle, opposite the right angle.

An equation that is true for every value of the variable.

Example: sin²θ + cos²θ = 1.

Events where one happening does not affect the probability of the other.

A statement comparing two expressions using <, >, ≤ or ≥ instead of equals.

Example: 2x + 1 > 7.

The general rise in prices over time, which reduces the buying power of money.

A whole number, either positive, negative, or zero. Integers have no fractional or decimal part.

Example: −3, 0 and 17 are integers; ½ is not.

The difference between the upper and lower quartiles; the spread of the middle half of the data.

A function that reverses another, swapping inputs and outputs.

Example: The inverse of y = 2ˣ is y = log₂ x.

A number that cannot be written as a fraction of two integers; its decimal form never terminates or repeats.

Example: √2 and π are irrational.

A triangle with two equal sides and two equal base angles.

Terms with exactly the same variables raised to the same powers; only like terms can be added or subtracted.

Example: 3x and 5x are like terms; 3x and 3x² are not.

The power to which a base must be raised to produce a given number; the reverse of an exponent.

Example: log₂ 8 = 3 because 2³ = 8.

The smallest number that two or more numbers all divide into.

Example: The LCM of 4 and 6 is 12.

The average: add all the values and divide by how many there are.

The middle value when the data is arranged in order.

The value that appears most often in a data set.

The result of multiplying a number by an integer.

Example: Multiples of 4 are 4, 8, 12, 16, …

Events that cannot happen at the same time.

Example: A single coin toss being both heads and tails.

The counting numbers 1, 2, 3, … Some definitions include 0.

An angle greater than 90° but less than 180°.

Using calculus to find a maximum or minimum value, such as greatest area or least cost.

The point (0, 0) where the x-axis and y-axis cross.

A value that lies far away from the rest of the data.

The symmetric U-shaped curve of a quadratic function.

Example: The graph of y = x².

Lines in the same plane that never meet and stay the same distance apart.

A fraction expressed out of 100, shown with the % sign.

Example: 45% means 45⁄100 = 0.45.

The total distance around the outside of a 2D shape.

Two lines that meet at a right angle (90°).

A closed 2D shape with straight sides.

Example: Triangles, squares and pentagons are polygons.

An expression of a base raised to an exponent; also another word for the exponent itself.

Example: 3⁴ is 'three to the power four'.

A natural number greater than 1 with exactly two factors: 1 and itself.

Example: 2, 3, 5, 7, 11 are prime; 9 is not (3 × 3).

The original amount of money invested or borrowed, before any interest.

A measure of how likely an event is, from 0 (impossible) to 1 (certain).

Example: The probability of a coin landing heads is ½.

In a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides.

Example: a² + b² = c².

One of the four regions the Cartesian plane is divided into by its two axes.

An expression or equation where the highest power of the variable is 2.

Example: x² − 4x + 4 = 0.

A formula that solves any quadratic ax² + bx + c = 0 using its coefficients.

Example: x = (−b ± √(b² − 4ac)) ⁄ 2a.

A polygon with four sides.

Example: Squares, rectangles and parallelograms.

Values that split ordered data into four equal parts (lower quartile, median, upper quartile).

The distance from the centre of a circle to any point on it.

The set of all possible output (y) values of a function.

The difference between the highest and lowest values in a data set.

A comparison of two quantities measured in different units.

Example: 120 km in 2 hours = 60 km/h.

A comparison of two or more quantities of the same kind, showing their relative sizes.

Example: Mixing paint in a 2 : 3 ratio.

Any number that can be written as a fraction of two integers (with a non-zero denominator). Its decimal form either terminates or repeats.

Example: 0.75 = ¾ and 0.333… = ⅓ are rational.

The number you multiply by to get 1; found by 'flipping' a fraction.

Example: The reciprocal of ⅗ is 5⁄3.

A rule that rewrites the trig ratio of a large or negative angle in terms of an acute angle.

A transformation that flips a shape across a line to create a mirror image.

An angle greater than 180° but less than 360°.

A transformation that turns a shape around a fixed point.

Approximating a number to a given place value or number of decimals.

Example: 3.147 rounded to 2 decimals is 3.15.

The set of all possible outcomes of an experiment.

Example: For a die: {1, 2, 3, 4, 5, 6}.

Writing a number as a value between 1 and 10 multiplied by a power of 10, used for very large or very small numbers.

Example: 45 000 = 4.5 × 10⁴.

A compact way of writing the sum of a sequence using the Greek letter Σ.

The same shape but not necessarily the same size; corresponding angles equal and sides in proportion.

Interest calculated only on the original amount (the principal), the same each period.

Example: R1000 at 10% simple interest earns R100 every year.

To rewrite an expression in its shortest or simplest equivalent form.

Two or more equations solved together to find values that satisfy all of them at once.

Example: x + y = 5 and x − y = 1 give x = 3, y = 2.

In a right-angled triangle, the ratio of the opposite side to the hypotenuse.

Example: sinθ = opposite ⁄ hypotenuse.

A rule relating the sides of any triangle to the sines of their opposite angles.

Example: a ⁄ sinA = b ⁄ sinB.

To find the value(s) of the unknown that make an equation true.

The angles 0°, 30°, 45°, 60° and 90°, whose trig ratios have exact values worth memorising.

A measure of how spread out data values are around the mean.

To put a given number in place of a variable.

Replacing a variable with a given value or expression.

Example: If x = 4, then 3x = 12.

Two angles that add up to 180°.

An irrational root that cannot be simplified to a rational number, left in root form for exactness.

Example: √5 is a surd; √9 = 3 is not.

A straight line that touches a circle at exactly one point.

In a right-angled triangle, the ratio of the opposite side to the adjacent side.

Example: tanθ = opposite ⁄ adjacent.

A single number or variable, or numbers and variables multiplied together, separated by + or − signs.

Example: 3x² + 2x − 5 has three terms.

A mathematical statement that has been proven true using logical reasoning.

A transformation that slides a shape without rotating or resizing it.

An algebraic expression with three terms.

Example: x² + 5x + 6.

The lowest or highest point of a parabola, where the curve changes direction.

A letter that represents an unknown or changing number.

Example: In 2x + 5, x is the variable.

Value-Added Tax — a tax added to the price of most goods and services (15% in South Africa).

A diagram using overlapping circles to show how sets or events relate.

The equal angles formed opposite each other when two straight lines cross.

The amount of space a 3D object occupies, measured in cubic units.

A point where a graph crosses the x-axis, found by setting y = 0.

The point where a graph crosses the y-axis, found by setting x = 0.