Formula Sheet

Area of an annulus:
A = π(R² – r²) Where R = radius of outer circle r = radius of inner circle

Area of an ellipse:
A = πab where a = length of semi-major axis b = length of semi-minor axis

Area of sector:
A = θ/360 (πr²) where θ = number of degrees in central angle

Arc length of a circle L = θ/360 x 2πr where θ = number of degrees in central angle

Simpson’s rule for area approximation A ≈ h/3(d_f + 4d_m + d_l)
where: h = distance between successive measurements, d_f = first measurement, d_m = middle measurement, d_l = last measurement

Surface Area of Sphere: A = 4πr²

Surface Area of Closed Cylinder: A = 2πrh + 2πr² where r = radius, h = perpendicular height

Volume of Cone: V = 1/3 π r²h where r = radius, h = perpendicular height

Volume of Cylinder: V = π r²h where r = radius, h = perpendicular height

Volume of Pyramid: V = 1/3 Ah where A = area of base, h = perpendicular height

Volume of sphere: V = 4/3 π r ³ where r = radius

The sine rule: a/sinA = b/sinB = c/sinC
Area of a triangle: A = ½ab sinC
The cosine rule: c² = a² + b² - 2ab cosC or
cosC = (a² + b² - c²)/2ab

Simple Interest: I = Prn
P = initial quantity, r = percentage interest rate per period, expressed as a decimal, n = number of periods

Compound interest: A = P(1 + r)ⁿ
A = final balance, P = initial quantity, n = number of compounding periods,
r = percentage interest rate per compounding period, expressed as a decimal

Future value (A) of an annuity: A = M[{(1+r)ⁿ-1}/r]
where M = contribution per period, paid at the end of the period.

Present value (A) of an annuity: A = M[{(1+r)ⁿ-1}/r(1+r)ⁿ]
or N = A/(1+r)ⁿ

Straight-line formula for depreciation: S = Vo – Dn
S = salvage value of asset after n periods, Vo = purchase price of asset
D = amount of depreciation apportioned per period, n = number of periods

Declining balance formula for depreciation: S = Vo(1 – r)ⁿ
S = salvage value of asset after n periods, r = percentage interest rate per period, expressed as a decimal.

Mean of a sample: x¯ = ∑x/n
x¯ = ∑fx/∑f
where x¯ = mean, x = individual score, n = number of scores, f = frequency

Formula for a z-score:z = x - ¯x /x where s = standard deviation

Gradient of a straight line: m = vertical change in position/horizontal change in position

Gradient-intercept form of a straight line: y = mx + b where m = gradient, b = y-intercept

Probability of an event: The probability of an event where outcomes are equally likely is given by:
P_event = number of favourable outcomes/total number of outcomes

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