Glossary

IGCSE Maths Glossary – All Key Terms

Q: How many all terms terms do I need to know for IGCSE?

This glossary covers 186 key all terms terms. Focus on understanding definitions and being able to use each term in context during exams.

Q: Are these terms for Core or Extended?

Terms are labelled as Core or Extended. Core students should focus on Core-labelled terms, while Extended students need to know all terms.

A comprehensive glossary of key terms and definitions for IGCSE Mathematics (0580). Use the alphabet links to jump to specific letters, or browse all terms below.

sine

Core

Ratio of opposite to hypotenuse in a right triangle

Example

$\sin 30° = 0.5$

cosine

Core

Ratio of adjacent to hypotenuse

Example

$\cos 60° = 0.5$

tangent

Core

Ratio of opposite to adjacent

Example

$\tan 45° = 1$

hypotenuse

Core

Longest side of right triangle, opposite the right angle

Example

In a 3-4-5 triangle, 5 is the hypotenuse

opposite

Core

Side across from the angle being used

Example

Opposite to angle A

adjacent

Core

Side next to the angle being used, not the hypotenuse

Example

Adjacent to angle A

bearing

Core

Direction measured clockwise from north as a three-figure number

Example

045° means north-east

sine rule

Extended

$\dfrac{a}{\sin A} = \dfrac{b}{\sin B} \text{ for any triangle}$

Example

Used when you have a side-angle pair

cosine rule

Extended

$a^2 = b^2 + c^2 - 2bc \cos A$

Example

Used with SAS or SSS

angle of elevation

Core

Angle measured upward from horizontal

Example

Looking up at a building

angle of depression

Core

Angle measured downward from horizontal

Example

Looking down from a cliff

included angle

Extended

Angle between two known sides

Example

$The C in Area = \tfrac{1}{2}ab\sin C$

Pythagoras theorem

Core

$a^2 + b^2 = c^2 \text{ for right triangles}$

Example

$3^2 + 4^2 = 5^2$

right angle

Core

An angle of exactly 90°

Example

Corner of a rectangle

three-figure bearing

Core

Bearing written with 3 digits

Example

North is 000°, East is 090°

variable

Core

Letter representing unknown value

Example

x in 3x + 5

coefficient

Core

Number multiplying a variable

Example

3 in 3x

constant

Core

Fixed number without a variable

Example

5 in 3x + 5

expression

Core

Combination of terms without an equals sign

Example

3x + 2y - 1

equation

Core

Statement with equals sign

Example

3x + 5 = 14

formula

Core

Equation showing relationship between variables

Example

$A = \pi r^2$

term

Core

Single number, variable, or product

Example

3x is one term

like terms

Core

Terms with same variable and power

Example

3x and 5x are like terms

factorise

Core

Write as a product of factors

Example

$x^2 + 5x + 6 = (x+2)(x+3)$

expand

Core

Multiply out brackets

Example

2(x+3) = 2x + 6

simplify

Core

Write in simplest form

Example

3x + 2x = 5x

substitute

Core

Replace variable with a value

Example

If x=3, then 2x+1=7

quadratic

Core

$\text{Expression with } x^2 \text{ as highest power}$

Example

$x^2 + 3x - 4$

linear

Core

Expression with x as highest power

Example

2x + 3

simultaneous equations

Extended

Two or more equations solved together

Example

x + y = 7 and x - y = 3

index

Core

Power or exponent

Example

$\text{In } x^3 \text{, 3 is the index}$

subject

Core

Variable on its own on one side

Example

In y = mx + c, y is the subject

algebraic fraction

Extended

Fraction with variables

Example

$\dfrac{x+1}{x-2}$

vector

Extended

Quantity with magnitude and direction

Example

Velocity is a vector

scalar

Core

Quantity with magnitude only

Example

Speed is a scalar

magnitude

Extended

Size or length of a vector

Example

$|\mathbf{v}| = \sqrt{x^2 + y^2}$

column vector

Core

Vector written as (x,y) column

Example

(3, -2)

position vector

Extended

Vector from origin to a point

Example

OA is position vector of A

resultant

Extended

Sum of two or more vectors

Example

a + b gives resultant

parallel vectors

Extended

Vectors in same or opposite direction

Example

a = kb means parallel

displacement

Core

Change in position as a vector

Example

From A to B = b - a

unit vector

Extended

Vector with magnitude 1

Example

Used for direction only

negative vector

Core

Vector in opposite direction

Example

-a reverses direction of a

midpoint vector

Extended

Average of two position vectors

Example

$M = \tfrac{1}{2}(\mathbf{a} + \mathbf{b})$

direction

Core

Way a vector points

Example

North-east, (1,1) direction

function

Extended

Rule that maps each input to exactly one output

Example

f(x) = 2x + 1

domain

Extended

Set of valid input values

Example

All real numbers except x=0

range

Extended

Set of possible output values

Example

$f(x) = x^2 \text{ has range } y \geq 0$

composite function

Extended

Function applied after another

Example

fg(x) = f(g(x))

inverse function

Extended

Reverses the original function

Example

$f^{-1}(x) \text{ undoes } f(x)$

mapping

Extended

How inputs relate to outputs

Example

x → 2x + 1

one-to-one

Extended

Each input gives unique output

Example

f(x) = 2x + 1 is one-to-one

many-to-one

Extended

Different inputs give same output

Example

$f(x) = x^2 \text{ maps } \pm 3 \text{ to } 9$

input

Extended

Value fed into a function

Example

x in f(x)

output

Extended

Value produced by a function

Example

f(3) = 7 means 7 is output

notation

Extended

$f(x) \text{ means function } f \text{ applied to } x$

Example

$f(x) = x^2$

self-inverse

Extended

Function that is its own inverse

Example

$f(x) = \dfrac{1}{x} \text{ is self-inverse}$

mean

Core

Sum of values divided by count

Example

$\dfrac{3+5+7}{3} = 5$

median

Core

Middle value when ordered

Example

In 2,5,8 median is 5

mode

Core

Most frequent value

Example

In 3,3,5,7 mode is 3

range

Core

Difference between highest and lowest

Example

Range of 2,5,9 is 7

frequency

Core

How many times a value occurs

Example

Score 5 appeared 8 times

cumulative frequency

Core

Running total of frequencies

Example

Add each frequency to previous total

probability

Core

Chance of event happening, 0 to 1

Example

P(heads) = 0.5

sample space

Core

All possible outcomes

Example

Dice: {1,2,3,4,5,6}

tree diagram

Core

Diagram showing sequential probabilities

Example

Multiply along branches

histogram

Extended

Bar chart where area represents frequency

Example

Height = frequency density

frequency density

Extended

Frequency divided by class width

Example

Used in histograms

pie chart

Core

Circle divided into sectors by proportion

Example

360° represents total

interquartile range

Core

Q3 minus Q1

Example

Middle 50% spread

quartile

Core

Values dividing data into quarters

Example

Q1, Q2 (median), Q3

correlation

Core

Relationship between two variables

Example

Positive, negative, or none

angle

Core

Amount of turn between two lines

Example

Measured in degrees

parallel

Core

Lines that never meet

Example

Same direction, equal distance apart

perpendicular

Core

Lines meeting at 90°

Example

Height perpendicular to base

polygon

Core

Closed shape with straight sides

Example

Triangle, square, pentagon

regular polygon

Core

All sides and angles equal

Example

Equilateral triangle, square

congruent

Core

Exactly the same shape and size

Example

SSS, SAS, ASA, RHS tests

similar

Core

Same shape but different size

Example

Corresponding angles equal

circle theorem

Extended

Rule about angles in circles

Example

$\text{Angle at centre} = 2 \times \text{angle at circumference}$

tangent line

Extended

Line touching circle at one point

Example

Perpendicular to radius at that point

chord

Core

Line segment with both ends on circle

Example

Diameter is longest chord

arc

Core

Part of circle circumference

Example

Major arc is the longer part

sector

Core

Region bounded by two radii and arc

Example

Like a pizza slice

segment

Extended

Region between chord and arc

Example

Minor and major segments

symmetry

Core

Shape looks same after transformation

Example

Line symmetry or rotational

bisector

Core

Line cutting something in half

Example

Perpendicular bisector of a line

integer

Core

Whole number positive or negative

Example

-3, 0, 7 are integers

prime

Core

Number with exactly 2 factors

Example

2, 3, 5, 7, 11...

factor

Core

Number that divides exactly

Example

Factors of 12: 1,2,3,4,6,12

multiple

Core

Product of a number and integer

Example

Multiples of 3: 3,6,9,12...

HCF

Core

Highest Common Factor

Example

HCF of 12 and 18 is 6

LCM

Core

Lowest Common Multiple

Example

LCM of 4 and 6 is 12

standard form

Core

$a \times 10^n \text{ where } 1 \leq a < 10$

Example

$3.5 \times 10^4 = 35\,000$

significant figures

Core

Digits that carry meaning

Example

3.456 to 2 s.f. = 3.5

decimal places

Core

Digits after decimal point

Example

3.456 to 2 d.p. = 3.46

upper bound

Extended

Highest possible value within rounding

Example

3.5 rounded to 1dp: UB = 3.55

lower bound

Extended

Lowest possible value within rounding

Example

3.5 rounded to 1dp: LB = 3.45

ratio

Core

Comparison of quantities

Example

2:3 means for every 2 of one, 3 of other

proportion

Core

Two ratios that are equal

Example

$\dfrac{2}{3} = \dfrac{4}{6}$

percentage

Core

Number out of 100

Example

$75\% = \dfrac{75}{100} = \dfrac{3}{4}$

reciprocal

Core

1 divided by the number

Example

$\text{Reciprocal of 5 is } \dfrac{1}{5}$

irrational

Extended

Cannot be written as exact fraction

Example

$\sqrt{2}, \pi are irrational$

gradient

Core

Steepness of a line, rise/run

Example

$m = \dfrac{y_2 - y_1}{x_2 - x_1}$

intercept

Core

Where line crosses an axis

Example

y-intercept is c in y=mx+c

midpoint

Core

Point halfway between two points

Example

$\left(\dfrac{x_1+x_2}{2},\, \dfrac{y_1+y_2}{2}\right)$

distance

Core

Length between two points

Example

$\sqrt{(\Delta x)^2 + (\Delta y)^2}$

parallel lines

Core

Lines with equal gradients

Example

y=2x+1 and y=2x-3

perpendicular lines

Extended

$\text{Lines with gradients multiplying to } {-1}$

Example

$m_1 \times m_2 = -1$

equation of line

Core

Algebraic rule for all points on line

Example

y = mx + c

origin

Core

Point (0,0)

Example

Where axes cross

axis

Core

Horizontal (x) or vertical (y) line

Example

x-axis and y-axis

coordinate

Core

Ordered pair (x,y) locating a point

Example

(3, -2) means x=3, y=-2

quadrant

Core

One of four regions of coordinate plane

Example

First quadrant: x>0 and y>0

tangent to curve

Extended

Line touching curve at one point

Example

$Gradient equals \dfrac{dy}{dx} at that point$

sequence

Core

Ordered list of numbers following a pattern

Example

2, 5, 8, 11, ...

term

Core

Individual number in a sequence

Example

The 3rd term is 8

nth term

Core

Formula giving any term from its position

Example

nth = 3n - 1

linear sequence

Core

Constant difference between terms

Example

2, 5, 8, 11 has difference 3

quadratic sequence

Extended

Second differences are constant

Example

1, 4, 9, 16 (second diff = 2)

geometric sequence

Extended

Constant ratio between terms

Example

2, 6, 18, 54 (ratio = 3)

common difference

Core

Constant added each time in linear sequence

Example

d = 3 in 2, 5, 8, 11

common ratio

Extended

Constant multiplied each time in geometric

Example

r = 3 in 2, 6, 18, 54

rule

Core

Description of how sequence works

Example

Add 3 each time

generate

Core

Produce terms from a rule

Example

nth = 2n gives 2, 4, 6, 8

position-to-term

Core

Rule converting position to value

Example

Position 4 → term 11

inequality

Core

Statement using < > ≤ ≥ symbols

Example

x > 3 means x is greater than 3

greater than

Core

Larger in value, symbol >

Example

5 > 3

less than

Core

Smaller in value, symbol <

Example

2 < 7

solution set

Core

All values satisfying the inequality

Example

{4, 5, 6, ...} for x > 3 integers

integer solution

Core

Whole number answers to inequality

Example

-2 < x ≤ 3 gives -1, 0, 1, 2, 3

number line

Core

Visual representation of inequality

Example

Open circle for < >, closed for ≤ ≥

region

Extended

Area on graph satisfying inequalities

Example

Shaded area on coordinate grid

boundary line

Extended

Line forming edge of region

Example

Solid for ≤ ≥, dashed for < >

strict inequality

Core

Does not include the boundary value

Example

x < 5 excludes 5

included inequality

Core

Includes the boundary value

Example

x ≤ 5 includes 5

transformation

Core

Change in position, size or orientation

Example

Reflection, rotation, translation, enlargement

reflection

Core

Mirror image across a line

Example

Reflected in y-axis

rotation

Core

Turning around a fixed point

Example

90° clockwise about origin

translation

Core

Sliding without turning or resizing

Example

Moved by vector (3, -2)

enlargement

Core

Scaling from a centre point

Example

Scale factor 2 from origin

scale factor

Core

Ratio of image to original size

Example

SF=2 means twice as big

centre of rotation

Core

Fixed point of rotation

Example

Rotate about (0,0)

line of reflection

Core

Mirror line

Example

y = x or x = 2

column vector

Core

Translation described as (x,y)

Example

(3,-2) means right 3 down 2

invariant point

Extended

Point unchanged by transformation

Example

Centre of rotation stays fixed

combined transformation

Extended

Two transformations applied in sequence

Example

Reflect then rotate

image

Core

Result after transformation

Example

A' is image of A

area

Core

Space inside a 2D shape

Example

$Measured in cm^2 or m^2$

perimeter

Core

Distance around a shape

Example

Sum of all side lengths

volume

Core

Space inside a 3D shape

Example

$Measured in cm^3 or m^3$

surface area

Core

Total area of all faces

Example

Sum of all face areas

circumference

Core

Distance around a circle

Example

$C = 2\pi r \text{ or } \pi d$

radius

Core

Distance from centre to edge of circle

Example

Half the diameter

diameter

Core

Distance across circle through centre

Example

Twice the radius

arc length

Core

Part of circumference

Example

$\dfrac{\theta}{360} \times 2\pi r$

sector area

Core

Area of pizza-slice shape

Example

$\dfrac{\theta}{360} \times \pi r^2$

cross-section

Core

Shape revealed by cutting through solid

Example

Cross-section of cylinder is circle

prism

Core

3D shape with uniform cross-section

Example

$V = \text{area of cross-section} \times \text{length}$

net

Core

2D pattern that folds into 3D shape

Example

Cube net has 6 squares

capacity

Core

Volume of liquid a container holds

Example

Often measured in litres

set

Core

Collection of distinct objects

Example

A = {1, 2, 3, 4}

element

Core

Object in a set

Example

3 ∈ A means 3 is in A

union

Core

All elements in either set

Example

A ∪ B

intersection

Core

Elements in both sets

Example

A ∩ B

complement

Core

Elements not in the set

Example

A' means not in A

universal set

Core

Set containing all elements under discussion

Example

ξ or U

empty set

Core

Set with no elements

Example

∅ or {}

subset

Core

Every element also in another set

Example

A ⊂ B

Venn diagram

Core

Overlapping circles showing set relationships

Example

Shows union and intersection visually

n of A

Core

Number of elements in set A

Example

n(A) = 4

curly brackets

Core

Used to list set elements

Example

{1, 2, 3}

finite set

Core

Set with countable elements

Example

{1, 2, 3} has 3 elements

infinite set

Core

Set with unlimited elements

Example

Set of all integers

derivative

Extended

Rate of change of a function

Example

$\dfrac{dy}{dx} \text{ of } x^2 \text{ is } 2x$

gradient of curve

Extended

Slope at a specific point

Example

$\dfrac{dy}{dx} \text{ evaluated at } x = a$

tangent

Extended

Line touching curve at one point

Example

Has same gradient as curve there

stationary point

Extended

Where gradient equals zero

Example

$\dfrac{dy}{dx} = 0$

maximum

Extended

Highest point locally

Example

$\dfrac{d^2y}{dx^2} < 0 \text{ at maximum}$

minimum

Extended

Lowest point locally

Example

$\dfrac{d^2y}{dx^2} > 0 \text{ at minimum}$

turning point

Extended

Where curve changes direction

Example

Maximum or minimum point

increasing function

Extended

Gradient is positive

Example

$\dfrac{dy}{dx} > 0$

decreasing function

Extended

Gradient is negative

Example

$\dfrac{dy}{dx} < 0$

second derivative

Extended

Derivative of the derivative

Example

$\dfrac{d^2y}{dx^2} \text{ tests nature of stationary point}$

rate of change

Extended

How quickly one quantity changes relative to another

Example

Speed is rate of change of distance

power rule

Extended

$\text{Differentiate } x^n \text{ to get } nx^{n-1}$

Example

$\dfrac{d}{dx}(x^3) = 3x^2$

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Frequently Asked Questions

How many all terms terms do I need to know for IGCSE?

This glossary covers 186 key all terms terms. Focus on understanding definitions and being able to use each term in context during exams.

Are these terms for Core or Extended?

Terms are labelled as Core or Extended. Core students should focus on Core-labelled terms, while Extended students need to know all terms.

Need Help with IGCSE Maths Concepts?

Book a free trial class with Teacher Rig for personalised concept explanations.

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