KS3 Maths Formulas*

Question 1

Area of a square

Answer 1

Area = side × side = s²

Question 2

Area of a rectangle

Answer 2

Area = length × width = l × w

Question 3

Area of a triangle

Answer 3

Area = ½ × base × height

Question 4

Area of a parallelogram

Answer 4

Area = base × height

Question 5

Area of a trapezium

Answer 5

Area = ½ × (a + b) × height

Question 6

Area of a circle

Answer 6

Area = πr²

Question 7

Perimeter of a rectangle

Answer 7

Perimeter = 2 × (length + width)

Question 8

Circumference of a circle

Answer 8

Circumference = 2πr or πd

Question 9

Volume of a cube

Answer 9

Volume = side³ = s³

Question 10

Volume of a cuboid

Answer 10

Volume = length × width × height

Question 11

Volume of a prism

Answer 11

Volume = area of cross-section × length

Question 12

Volume of a cylinder

Answer 12

Volume = πr²h

Question 13

Surface area of a cube

Answer 13

Surface Area = 6 × side²

Question 14

Surface area of a cuboid

Answer 14

Surface Area = 2(lw + lh + wh)

Question 15

Surface area of a cylinder

Answer 15

Surface Area = 2πrh + 2πr²

Question 16

Index Law 1

Answer 16

a^m × a^n = a^(m + n)

Question 17

Index Law 2

Answer 17

a^m ÷ a^n = a^(m - n)

Question 18

Index Law 3

Answer 18

(a^m)^n = a^(mn)

Question 19

Index Law 4

Answer 19

a⁰ = 1 (where a ≠ 0)

Question 20

Expanding brackets (single)

Answer 20

a(b + c) = ab + ac

Question 21

Expanding brackets (double)

Answer 21

(a + b)(c + d) = ac + ad + bc + bd

Question 22

Factorising (common factor)

Answer 22

ab + ac = a(b + c)

Question 23

Factorising (quadratic)

Answer 23

x² + bx + c = (x + m)(x + n), where m × n = c and m + n = b

Question 24

Solving equations

Answer 24

Use inverse operations and keep the equation balanced

Question 25

Mean

Answer 25

Mean = Total of values ÷ Number of values

Question 26

Median

Answer 26

Middle value when data is ordered

Question 27

Mode

Answer 27

Most frequently occurring value

Question 28

Range

Answer 28

Highest value − Lowest value

Question 29

Probability

Answer 29

Probability = Favourable outcomes ÷ Total outcomes

Question 30

Probability range

Answer 30

Between 0 (impossible) and 1 (certain)

Question 31

What is a ratio?

Answer 31

A comparison between two or more quantities

Question 32

What is a proportion?

Answer 32

An equation showing two ratios are equal

Question 33

What is a percentage?

Answer 33

A fraction out of 100

Question 34

Fraction to percentage

Answer 34

Multiply by 100

Question 35

Decimal to percentage

Answer 35

Multiply by 100

Question 36

Percentage to decimal

Answer 36

Divide by 100

Question 37

Sum of angles on a straight line

Answer 37

180°

Question 38

Sum of angles in a triangle

Answer 38

180°

Question 39

Sum of angles in a quadrilateral

Answer 39

360°

Question 40

Sum of angles in a full turn

Answer 40

360°

Question 41

Interior angle of a regular polygon

Answer 41

[(n − 2) × 180°] ÷ n

Question 42

Circle theorem - angle at centre

Answer 42

Twice the angle at the circumference

Question 43

Circle theorem - angle in semicircle

Answer 43

90°

Question 44

Circle theorem - opposite angles in cyclic quadrilateral

Answer 44

Sum to 180°

Question 45

BIDMAS / BODMAS

Answer 45

Brackets, Indices/Orders, Division, Multiplication, Addition, Subtraction

Question 46

Multiplying fractions

Answer 46

Multiply numerators and denominators

Question 47

Dividing fractions

Answer 47

Multiply by the reciprocal (second fraction flipped)

Question 48

Adding/subtracting fractions

Answer 48

Use a common denominator

Question 49

Non-calculator skills

Answer 49

Mental maths, long methods, estimating, simplifying

Question 50

Calculator skills

Answer 50

Using π, roots, solving equations, statistical functions

Question 51

Standard Form - Positive Power

Answer 51

3,500 = 3.5 × 10³

Question 52

Standard Form - Negative Power

Answer 52

0.006 = 6 × 10⁻³

Question 53

Convert from Standard to Normal Form

Answer 53

4.2 × 10² = 420

Question 54

Percentage Increase Formula

Answer 54

New = Original × (1 + percentage ÷ 100)

Question 55

Percentage Decrease Formula

Answer 55

New = Original × (1 − percentage ÷ 100)

Question 56

Multiplier for Percentage Increase

Answer 56

Multiplier = 1 + (percent ÷ 100)

Question 57

Multiplier for Percentage Decrease

Answer 57

Multiplier = 1 − (percent ÷ 100)

Question 58

Finding % Change from Multiplier (increase)

Answer 58

% Change = (Multiplier − 1) × 100

Question 59

Finding % Change from Multiplier (decrease)

Answer 59

% Change = (1 − Multiplier) × 100

Question 60

What if multiplier is less than 1?

Answer 60

It’s a percentage decrease. Subtract multiplier from 1, then × 100 to find the % decrease.

Question 61

What if multiplier is more than 1?

Answer 61

It’s a percentage increase. Subtract 1 from multiplier, then × 100 to find the % increase.