The formulae below are used in GCSE, iGCSE and the N5 examinations. Check with your college / school or exam board which formulae must be learnt for the particular exams you are taking. The information shown below is a guide for GCSE ONLY.

GCSE: candidates must know or be able to derive these formulae:

Algebra:

{Higher} Quadratic formulae: `x = frac(-b +- sqrt(b^2 - 4ac))(2a)`

If `b^2 - 4ac` is negative, then there will be no real answers. The rest of the time there will be two answers, although the two answers may be the same.

Geometry:

Circumference of a circle: `C = 2pir text( or ) pid` (diameter is 2 x radius))

Area of a circle: `A = pir^2`

Area of a rectangle: `A = bh`

{Higher} Area of any triangle: `text(Area ) = frac(1)(2)bc sin C`

Area of a parallelogram: `A = bh` where `h` is the vertical height

Area of a triangle: `A = frac(1)(2)bh` where `h` is the vertical height

Area of a trapezium: `A = frac(a + b)(2)h` where `h` is the vertical height

Volume of a right prism: `V = Ah` where A is the cross-sectional area

Trigonometry:

Pythagoras's theorem: `a^2 + b^2 = c^2 text( where c is the hypotenuse)`

Sin: `sin x = frac(text(Opposite))(text(Hypotenuse))`

Cos: `cos x = frac(text(Adjacent))(text(Hypotenuse))`

Tan: `tan x = frac(text(opposite))(text(Adjacent))`

For Sin, Cos and Tan, the Opposite side is the side opposite the angle being calculated, and the Hypotenuse is the longest side.

{Higher} Sin rule: `frac(a)(sin A) = frac(b)(sin B) = frac(c)(sin C)`

{Higher} Cosine rule: `c^2 = a^2 + b^2 - 2bc cos C`

Ratio:

{Higher} Compound Interest: `A = P(1 + frac(r)(100))^(t)` where A is the calculated amount, P is the starting amount (Principal), r is the interest rate and t is the number of periods.

`text(speed) = frac(text(distance))(text(time))`

`text(density) = frac(text(mass))(text(volume))`

`text(pressure) = frac(text(force))(text(area))`

Probability:

{Higher} Probability Or: `P(A or B) = P(A) + P(B) - P(A-B)`

{Higher} Probability And: P(A and B) = P(A given B)P(B))

GCSE candidates will be given the following formulae and will be expected to know how to use those formulae:

Geometry:

Curved surface area of a cone: `A = pirl` where `l` is the sloping length

Surface area of a cone: `A = pirl + pir^2` where `r` is the radius of the base

Volume of a cone: `V = pir^2frac(h)(3)` where `h` is the vertical height

Surface area of a sphere: `A = 4pir^2`

Volume of a sphere: `V = frac(4)(3)pir^3`

Kinematics:

`v=u+at`

`s=ut + frac(1)(2)at^2`

`v^2 = u^2+2as`

where `u` is starting velocity, `v` is final velocity, `s` is displacement, `a` is acceleration and `t` is time.