Maths formulas
The formulas to know for Year 9.
Area and perimeter
- Rectangle
- A = l × w
- Triangle
- A = ½ × b × h
- Parallelogram
- A = b × h
- Trapezium
- A = ½(a + b)h
- Circle: area
- A = πr²
- Circle: circumference
- C = πd = 2πr
Volume
- Cuboid
- V = l × w × h
- Prism
- V = area of cross-section × length
- Cylinder
- V = πr²h
- Units
- 1 litre = 1000 cm³1 m³ = 1 000 000 cm³
Pythagoras' theorem and trigonometry
- Pythagoras' theorem
- a² + b² = c²c is the hypotenuse, the longest side
- Sine (SOH)
- sin θ = oppositehypotenuse
- Cosine (CAH)
- cos θ = adjacenthypotenuse
- Tangent (TOA)
- tan θ = oppositeadjacent
Angles
- Angles on a straight line
- add up to 180°
- Angles around a point
- add up to 360°
- Angles in a triangle
- add up to 180°
- Angles in a quadrilateral
- add up to 360°
- Interior angles of an n-sided polygon
- sum = (n − 2) × 180°
- Exterior angles of any polygon
- add up to 360°
- Parallel lines
- alternate and corresponding angles are equalco-interior angles add up to 180°
Compound measures
- Speed
- speed = distancetime
- Density
- density = massvolume
- Pressure
- pressure = forcearea
Number
- Multiplying powers
- aᵐ × aⁿ = aᵐ⁺ⁿ
- Dividing powers
- aᵐ ÷ aⁿ = aᵐ⁻ⁿ
- Power of a power
- (aᵐ)ⁿ = aᵐⁿ
- Zero and negative powers
- a⁰ = 1, a⁻ⁿ = 1aⁿ
- Standard form
- A × 10ⁿ, where 1 ≤ A < 10
- Percentage change
- changeoriginal × 100
Graphs and probability
- Straight line
- y = mx + cm is the gradient, c is the y-intercept
- Gradient
- m = change in ychange in x
- Probability of not happening
- P(not A) = 1 − P(A)
- Expected frequency
- P(A) × number of trials
- Independent events
- P(A and B) = P(A) × P(B)
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