Formulae

What is the formula for original amount (reverse percentage)?

new amount ÷ (1 ± %/100)

Quadratic inequality > 0

Roots are your critical values. Sketch a U-shaped parabola. Answer is OUTSIDE the roots. Use OR to combine: x < a or x > b

Quadratic inequality < 0

Roots are your critical values. Sketch a U-shaped parabola. Answer is INSIDE/BETWEEN the roots. Use AND to combine: a < x < b

What is the formula for percentage change?

(difference ÷ original) × 100

What is the formula for percentage score?

(score ÷ total available) × 100

What is the formula for the sum of interior angles of a polygon?

180(n - 2)

What is the relationship between interior and exterior angles?

interior + exterior = 180°

What is the formula for the exterior angle of a polygon?

360° ÷ n

What is the formula for the number of sides of a polygon?

360° ÷ exterior angle

What is the position of the median for an odd number of values?

(n + 1) ÷ 2

What is the position of the median for an even number of values?

n/2 and n/2 + 1

What is the formula for frequency density?

frequency ÷ class width

What is the formula for interquartile range?

UQ - LQ

What is the formula for speed?

speed = distance ÷ time

What is the formula for pressure?

pressure = force ÷ area

What is the formula for density?

density = mass ÷ volume

What is anything to the power of zero?

n⁰ = 1

How do you convert between cm and m?

÷ 100 to go cm → m, × 100 to go m → cm

How do you convert between cm² and m²?

÷ 10,000 to go cm² → m², × 10,000 to go m² → cm²

How do you convert between cm³ and m³?

÷ 1,000,000 to go cm³ → m³, × 1,000,000 to go m³ → cm³

What is the equation of a straight line?

y = mx + c

What is the formula for gradient?

difference in y ÷ difference in x

What is the formula for the midpoint of a line between two points?

((x₁ + x₂)/2, (y₁ + y₂)/2)

What is the equation of a circle?

x² + y² = r²

What is the area of a square or rectangle?

A = bh

What is the area of a triangle?

A = bh ÷ 2

What is the area of a parallelogram?

A = bh

What is the area of a trapezium?

A = ½(a + b)h

What is the circumference of a circle?

C = πd or C = 2πr

What is the area of a circle?

A = πr²

What is the surface area of a cylinder?

2πr² + πdh

What is the surface area of a sphere?

4πr²

What is the surface area of a cone?

πr² + πrl

What is the surface area of a frustum?

πr² + πR² + π(R + r)l

What is the volume of a cube or cuboid?

V = bhl

What is the volume of a triangular prism?

V = (bh ÷ 2)l

What is the volume of a cylinder?

V = πr²h

What is the volume of a pyramid?

V = ⅓ × base area × height

What is the volume of a cone?

V = ⅓πr²h

What is the volume of a sphere?

V = (4/3)πr³

What is the formula for arc length?

(θ ÷ 360) × πd

What is the formula for sector area?

(θ ÷ 360) × πr²

What is the formula for area of a segment?

area of sector - area of triangle

What is the formula for enlarged perimeter?

original perimeter × S.F.

What is the formula for enlarged area?

original area × (S.F.)²

What is the formula for enlarged volume?

original volume × (S.F.)³