Edexcel A Level Maths - Pure
∫1÷x - answer-ln|x| + c
∫cos²x - answer-½x + ¼sin2x + c
∫cos³x - answer-sinx - 1/3sin³x + c
∫cosec²x - answer--cotx + c
∫cosecx - answer--ln|cosecx + cotx| + c
∫cosecxcotx - answer--cosecx + c
∫cosx - answer-sinx + c
∫cotx - answer-ln|sinx| + c
∫eⁿ - answer-eⁿ + c
∫sec²x - answer-tanx + c
∫secx - answer-ln|secx + tanx| + c
∫secxtanx - answer-secx + c
∫sin²x - answer-½x - ¼sin2x + c
∫sin³x - answer--cosx + 1/3cos³x + c
∫sinx - answer--cosx + c
∫tanx - answer--ln|cosx| = ln|cosx|-¹ = ln|1÷cosx| = ln|secx| + c
1:1 relationship - answer-One value of x is associated with on value of y
e.g. x = y
1:Many relationship - answer-One value of x goes to many values of y
e.g. y =√x
A function f(x) is decreasing on the interval [a,b] if... - answer-f'(x) ≤ 0 for all values of x such
that a < x < b
A function f(x) is increasing on the interval [a,b] if... - answer-f'(x) ≥ 0 for all values of x such that
a<x<b
Angle between vector and axis for a vector a:
xi + yj + zk - answer-x axis : cosθ = (x ÷ |a|)
, y axis : cosθ = (y ÷ |a|)
z axis : cosθ = (z ÷ |a|)
Arithmetic nth Term - answer-uₙ = a + (n-1)d
Arithmetic Series - answer-Sₙ = n/2 (2a + (n-1)d)
Cartesian Equation - answer-Linking x and y together
Chain Rule
y = (f(x))ⁿ - answer-dy/dx = n(f(x))ⁿ-¹ × f'(x)
Cosine Rule - Know 2 sides, and the angle in between. You want the missing side. - answer-a²
= b² + c² - 2bcCosA
Cosine Rule - Know 3 sides. You want an angle. - answer-Cos A = (b² + c² - a²) ÷ 2bc
Differential of arccosx - answer--1 ÷ (√1-x²)
Differential of arcsinx - answer-1 ÷ (√1-x²)
Differential of arctanx - answer-1 ÷ (1+x²)
Differential of cosecx - answer--cosecxcotx
Differential of cosx - answer--sinx
Differential of cotx - answer--cosec²x
Differential of e^kx - answer-ke^kx
Differential of eⁿ - answer-eⁿ
Differential of lnx - answer-1/x
Differential of secx - answer-secxtanx
Differential of sinx - answer-cosx
Differential of tanx - answer-sec²x
Discriminant rules - answer-b² - 4ac > 0 = Two distinct real roots
b² - 4ac = 0 = One repeated root
b² - 4ac < 0 = No real roots
∫1÷x - answer-ln|x| + c
∫cos²x - answer-½x + ¼sin2x + c
∫cos³x - answer-sinx - 1/3sin³x + c
∫cosec²x - answer--cotx + c
∫cosecx - answer--ln|cosecx + cotx| + c
∫cosecxcotx - answer--cosecx + c
∫cosx - answer-sinx + c
∫cotx - answer-ln|sinx| + c
∫eⁿ - answer-eⁿ + c
∫sec²x - answer-tanx + c
∫secx - answer-ln|secx + tanx| + c
∫secxtanx - answer-secx + c
∫sin²x - answer-½x - ¼sin2x + c
∫sin³x - answer--cosx + 1/3cos³x + c
∫sinx - answer--cosx + c
∫tanx - answer--ln|cosx| = ln|cosx|-¹ = ln|1÷cosx| = ln|secx| + c
1:1 relationship - answer-One value of x is associated with on value of y
e.g. x = y
1:Many relationship - answer-One value of x goes to many values of y
e.g. y =√x
A function f(x) is decreasing on the interval [a,b] if... - answer-f'(x) ≤ 0 for all values of x such
that a < x < b
A function f(x) is increasing on the interval [a,b] if... - answer-f'(x) ≥ 0 for all values of x such that
a<x<b
Angle between vector and axis for a vector a:
xi + yj + zk - answer-x axis : cosθ = (x ÷ |a|)
, y axis : cosθ = (y ÷ |a|)
z axis : cosθ = (z ÷ |a|)
Arithmetic nth Term - answer-uₙ = a + (n-1)d
Arithmetic Series - answer-Sₙ = n/2 (2a + (n-1)d)
Cartesian Equation - answer-Linking x and y together
Chain Rule
y = (f(x))ⁿ - answer-dy/dx = n(f(x))ⁿ-¹ × f'(x)
Cosine Rule - Know 2 sides, and the angle in between. You want the missing side. - answer-a²
= b² + c² - 2bcCosA
Cosine Rule - Know 3 sides. You want an angle. - answer-Cos A = (b² + c² - a²) ÷ 2bc
Differential of arccosx - answer--1 ÷ (√1-x²)
Differential of arcsinx - answer-1 ÷ (√1-x²)
Differential of arctanx - answer-1 ÷ (1+x²)
Differential of cosecx - answer--cosecxcotx
Differential of cosx - answer--sinx
Differential of cotx - answer--cosec²x
Differential of e^kx - answer-ke^kx
Differential of eⁿ - answer-eⁿ
Differential of lnx - answer-1/x
Differential of secx - answer-secxtanx
Differential of sinx - answer-cosx
Differential of tanx - answer-sec²x
Discriminant rules - answer-b² - 4ac > 0 = Two distinct real roots
b² - 4ac = 0 = One repeated root
b² - 4ac < 0 = No real roots
