COMPLETE QUESTIONS AND ANSWERS
BUNDLED PREMIUM RESOURCE
●● How to find gradient when differentiating?.
Answer: Sub in x value given into dy/dx
●● The general binomial theorem.
Answer: (1+x)^n = 1 + nx + n(n-1)/2! (x)^2 + n(n-1)(n-2)/3! (x)^3...
●● Approx using binomial expansion.
Answer: 1. compare approx to formula
2. sub in to solve to find x e.g. 1 - x = 0.96
3. sub x back into equation to find approximation
●● Arithmetic Sequence: N'th term formula.
Answer: Un = a + (n-1)d
●● Geometric Sequence: N'th term formula.
Answer: Un = ar^n-1
, ●● Increasing functions.
Answer: f'(x) > 0
●● Decreasing functions.
Answer: f'(x) < 0
●● How to find stationary points & determine nature.
Answer: 1. differentiate
2. solve f'(x) = 0
3. put x coordinates back into f(x) to get y
4. plug in values bit to the left and right of stationary points into f'(x)
5. if signs of both derivatives are the same then you have a point of
inflection
6. if negative to left, positive to right = local min
7. if positive to left, negative to right = local max
●● Differentiate arcsin x.
Answer: 1/√1-x^2
●● Differentiate arccos x.
Answer: -1/√1-x^2