Differentiation
dy/dx multiply by power then subtract 1 from power
Integration
add 1 to power then divide by new power
Line distance
√(x2 - x1) + (y2 - y1)
Line midpoint
(x1 + x2/2 , y1 + y2/2)
Line gradient
(y2 - y1 / x2 - x1)
completing the square
(x + a)² + b
half x term square and take away
Discriminant
b² - 4ac > 0 = 2
b² - 4ac = 0 = repeated
b² - 4ac < 0 = no solution
Transformations
y = f (x) +/- a = y coord changes
y = f (x +/- a) = x coord changes opposite to whatever it says
cosine rule
a² = b² + c² - 2bcCOSA
Sine rule
a/sinA = b/sinB
Area of a trapezium
1/2 (a + b)h
Area of a triangle
1/2abSINC
1/2(b x h)
(a + b)^n binomial expression
a^n + (nC1)a^n-1 b + (nC2)a^n-2 b²…
(1 + x)^n binomial expression
1 + nx + n(n-1)/2! (x)² + n(n-1)(n-2)/3! (x)^3…
area of a sector
1/2 r² ϑ
arc length
rϑ
cosecϑ =
1/sinϑ
secϑ =
1/cosϑ
cotϑ =
1/tanϑ
sin²ϑ + cos²ϑ =
1
1 + tan²ϑ =
sec²ϑ
1 + cot²ϑ
cosec²ϑ
sum of arthimetic series
a + (a + d) + (a +2d) + (a + 3d) AKA (a + n-1d)
sum to n terms
n / 2(2a + (n-1)d)
