Maths formulas
Everything from Year 9, with the Year 10 formulas marked "New".
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)
SurdsNew
- Multiplying
- √a × √b = √(ab)
- Dividing
- √a ÷ √b = √ab
- Rationalising
- a√b = a√bb
- Conjugate pairs
- (a + √b)(a − √b) = a² − b
QuadraticsNew
- Quadratic formula
- x = −b ± √(b² − 4ac)2asolves ax² + bx + c = 0
- Completing the square
- x² + bx + c = (x + b2)² − (b2)² + c
- Difference of two squares
- x² − a² = (x + a)(x − a)
Growth and decayNew
- Compound interest
- A = P(1 + r100)ⁿ
- Depreciation
- A = P(1 − r100)ⁿP is the starting amount, r the % rate, n the number of years
Circles, spheres and conesNew
- Arc length
- θ360 × 2πr
- Sector area
- θ360 × πr²
- Sphere
- V = 43πr³, surface area = 4πr²
- Cone
- V = 13πr²h, curved surface = πrll is the slant height
- Pyramid
- V = 13 × base area × h
Similar shapesNew
- Lengths
- multiplied by k (the scale factor)
- Areas
- multiplied by k²
- Volumes
- multiplied by k³
- Congruent triangles
- SSS, SAS, ASA, RHS
Circle theoremsNew
- Angle at the centre
- twice the angle at the circumference
- Angle in a semicircle
- 90°
- Angles in the same segment
- are equal
- Cyclic quadrilateral
- opposite angles add up to 180°
- Tangent and radius
- meet at 90°
Vectors, statistics and probabilityNew
- Magnitude of a vector (x, y)
- √(x² + y²)
- Interquartile range
- upper quartile − lower quartile
- Mutually exclusive events
- P(A or B) = P(A) + P(B)
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