IGCSEMaths Formula Sheet.

Area of a trapezium

A = ½(a + b)h

where a and b are the parallel sides, h is the perpendicular height

Volume of a prism

V = area of cross-section × length

Volume of a cylinder

V = πr²h

where r is the radius, h is the height

Curved surface area of a cylinder

A = 2πrh

Area of a triangle

A = ½bh

Area of a circle & Circumference

A = πr²    C = 2πr

Curved surface area of a cone

A = πrl

where l is the slant height

Surface area of a sphere

A = 4πr²

Volume of a pyramid

V = ⅓Ah

where A is the base area

Volume of a cone

V = ⅓πr²h

Volume of a sphere

V = ⁴⁄₃πr³

The quadratic formula

x = (−b ± √(b² − 4ac)) ÷ 2a

for ax² + bx + c = 0 where a ≠ 0

Sine rule

a/sin A = b/sin B = c/sin C

Cosine rule

a² = b² + c² − 2bc cos A

Area of a triangle (using sine)

A = ½ab sin C

Sum of an arithmetic series

Sₙ = n/2 [2a + (n − 1)d]

where a is the first term, d is the common difference

Percentage change

% change = (change ÷ original) × 100

Reverse percentage

Original = New amount ÷ (1 ± r/100)

Compound interest / growth & decay

Total = P(1 ± r/100)ⁿ

P = principal, r = rate, n = number of periods; + for growth, − for decay

Simple interest

I = PRT ÷ 100

Equation of a straight line

y = mx + c

m = gradient, c = y-intercept

Gradient of a line

m = (y&sub2; − y&sub1;) ÷ (x&sub2; − x&sub1;)

Midpoint of two coordinates

M = ((x&sub1; + x&sub2;)/2, (y&sub1; + y&sub2;)/2)

Distance between two points

d = √[(x&sub2; − x&sub1;)² + (y&sub2; − y&sub1;)²]

Difference of two squares

a² − b² = (a + b)(a − b)

nth term of an arithmetic sequence

aₙ = a + (n − 1)d

Laws of indices

aᵐ × aⁿ = aᵐ⁺ⁿ    aᵐ ÷ aⁿ = aᵐ⁻ⁿ    (aᵐ)ⁿ = aᵐⁿ

a° = 1    a⁻ⁿ = 1/aⁿ    a½ = √a

Speed, distance, time

Speed = Distance ÷ Time

Density, mass, volume

Density = Mass ÷ Volume

Pressure, force, area

Pressure = Force ÷ Area

Direct & inverse proportion

Direct: y = kx    Inverse: y = k/x

Area of a parallelogram

A = base × height

Area of a sector

A = (θ/360) × πr²

Arc length

L = (θ/360) × 2πr

Interior angle sum of a polygon

Sum = (n − 2) × 180°

Exterior angle of a regular polygon

Ext. angle = 360° ÷ n

Pythagoras' theorem

a² + b² = c²

c is the hypotenuse (longest side, opposite the right angle)

SOHCAHTOA — right-angled triangle trigonometry

sin θ = O/H    cos θ = A/H    tan θ = O/A

Mean

Mean = sum of values ÷ number of values

Estimated mean (grouped data)

Mean = Σ(f × midpoint) ÷ Σf

Probability of an event

P(A) = favourable outcomes ÷ total outcomes

Complementary probability

P(not A) = 1 − P(A)

AND / OR rules

P(A and B) = P(A) × P(B)    P(A or B) = P(A) + P(B)

AND for independent events, OR for mutually exclusive events

Differentiation rule

If y = axⁿ then dy/dx = naxⁿ⁻¹

Turning points

At a turning point: dy/dx = 0

d²y/dx² > 0 → minimum    d²y/dx² < 0 → maximum

Magnitude of a vector

|v| = √(x² + y²)

for column vector (x, y)