Appreciation/depreciation (calculator)
Original amount x (percentage multiplier)
100 ± %
similarity length
Length scale factor = length of new shape/length of original shape
(LSF = new/original)
Similarity area
Area scale factor = (length scale factor)²
(ASF = (LSF)²)
Similarity volume
Volume scale factor = (length scale factor)³
(VSF = (LSF)³)
Gradient
m = y2-y1/x2-x1
Straight line (2)
y = mx+c
y-b = m(x-a)
arc length
AL = θ/360 πd
Sector area
SA = θ/360 πr²
Area of a triangle
A = 1/2bh
Area of a circle
A = πr²
Volume of a cylinder
V = πr²h
Discriminant
b²-4ac
Nature of roots(3)
b²-4ac > 0 “two real and distinct roots”
b2- 4ac = 0 “real and equal roots”
b2- 4ac < 0 “no real roots”
Pythagoras’ theorem
c² = a² + b²
Converse of Pythagoras’ theorem
By the Converse of Pythagoras’ Theorem, the triangle is right angled as c² = a² + b²
Right-angled triangle trigonometry (3)
SOH CAH TOA
sinx = opposite/hypotenuse
tanx = opposite/adjacent
cosx = adjacent/hypotenuse
Trig identity (2)
tanx = sinx/cosx
sinx² + cosx² = 1
Semi interquartile range
SIQR = (Q3-Q1)/2
Interquartile range
IQR = Q3-Q1
Quadratic equations
x=(-b±√(b²-4ac))/(2a)
magnitude of a vector
|a̲|= √(x² +y²)
(generally the same as a̲= (x,y)
multiplying with indices
aᵐ x aⁿ = aᵐ⁺ⁿ
dividing with indices
aᵐ ÷ aⁿ = aᵐ⁻ⁿ
“powers of powers”
(aᵐ)ⁿ = aᵐⁿ
(multiply the powers together)
