Formulae

Mutual exclusivity

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

Independence

P(A) x P(B) = P(A and B)

Coding

Mean - includes addition/subtraction

Standard deviation - only multiplication/division

Small angle approximation for sinx

sinx ~ x

Small angle approximation for cosx

cosx ~ 1 - x²/2

Small angle approximation for tanx

tanx ~ x

sin(A+B)

sin(2A)

sinAcosB + cosAsinB

2sinAcosA

cos(A+B)

cos(2A)

cosAcosB - sinAsinB

cos²A - sin²A

1 - 2sin²A

2cos²A - 1

tan(A+B)

tan(2A)

(tanA + tanB)/(1 - tanAtanB)

(2tanA)/(1 - tan²A)

Identity involving tanx and secx

1 + tan²x = sec²x

Identity involving cosecx and cotx

1 + cot²x = cosec²x

Product rule

f’(x) = uv’ + vu’

Quotient rule

f’(x) = (vu’ - uv’)/v²

Integration by parts

∫uv’ = uv - ∫vu’

Arithmetic sequence

u_n= a +(n−1)d

Arithmetic series

s_n = n/2(2a + (n-1)d)

Geometric sequence

u_n = a*r^n-1

Geometric series

s_n = a(1-rⁿ)/1-r

Sum to infinity

s = a/1-r

(1 + ax)ⁿ

(1) + (n)(ax) + (1/2)(n)(n-1)(ax)² + (1/2)(1/3)(n)(n-1)(n-2)(ax)³ …

Suvat equations

v = u +at

s = ut + 1/2at²

s = vt - 1/2at²

v² = u² + 2as

s = 1/2(v+u)t

Derivative of tanx

sec²x

Derivative of secx

secxtanx

Derivative of cotx

-cosec²x

Derivative of cosecx

-cosecxcotx

Newton-Rhapson formula

x_n+1 = x_{n -} f(x_n)/f^’(x_n)

Trapezium rule

Area = h/2( y₀ + 2( y₁ + y₂ + y₃ …) + y_n )

F_max formula

F_max = μR

Z-score formula

Z = (x - μ)/σ

Moments

Moment = force x perpendicular distance

Median of discrete data

n/2

If result is a decimal, round up

If result is an integer, add 0.5

Median of continuous data

Grouped frequency table, cumulative frequency (remember to adjust UB and LB if rounded)

n/2

Linear interpolation