Formulae Flashcards
Percentage change
Percentage change = (difference / original) x 100
Compound interest
N = Ni (1 + r/100)^n
Nth term of a sequence
Un = a + (n-1)d
Sum of a sequence where the last term is known
Sn = n/2(a + L)
Sum of a sequence where the last term is unknown
Sn = n/2[a + (n-1)d]
Equation of a straight line (3 answers)
y = mx + c
ax + by + c = 0
y - y1 = m(x - x1)
Area of a circle
πr²
Circumference of a circle (2 answers)
πd
2πr
Frequency density
Frequency density = frequency / class width
Mean
Mean = sum of values / number of values
Range
Range = largest value - smallest value
Inter-quartile range
IQR = UQ - LQ
Direct proportion
y ∝ x
y = kx
Inverse proportion
y ∝ 1/x
y = k/x
Probability
P = number of specified item / total number of items
Pythagoras’ theorem
a² + b² = c²
Sine rule
sin A/a = sin B/b = sin C/c
Cosine rule
a² = b² + c² - 2bc cosA
Internal intersection in a circle
AP x PB = CP x PD
External intersection
AP x PB = CP x PD
Density
d = m/V
Average speed
v = s/t
Pressure
p = F/A
Quadratic formula
x = [-b ± √(b² - 4ac)]/2a
The discriminant
b² - 4ac
Volume of a sphere
V = 4/3(πr^3)
Surface area of a sphere
A = 4πr²
Volume of a cone
V = 1/3πr²h
Surface area of a cone
A = πrl + πr²
Volume of a cylinder
V = πr²h
Surface area of a cylinder
A = 2πr² + 2πrh
Area of a triangle
A = 1/2 ab sinC
Area of a trapezium
A = ((a+b)h)/2
Scale factor for area
SFlength ²
Scale factor for volume
SFlength^3
