Practice · Edexcel 9MA0 · Pure 1 and 2

A-level Maths differentiation questions with worked answers

Six exam-style questions. Each part is marked on the scheme and shows the full working.

1 of 6

Edexcel 9MA0Papers 1 and 2 · Pure7.2 Differentiation

5 marksUnfamiliar problem

Calculator allowed

Spec and skills

Paper scope: Pure 1/2
Spec P7.2
Spec P2.4
Original practice question

The curve

C

has equation

y = a x^2 + \dfrac{b}{x}

x \ne 0

, where

a

and

b

are constants.

C

passes through

(1, 6)

and its gradient there is

3

(a)

Find the values of

a

and

b

(3 marks)

(b)

Find the gradient of

C

at the point where

x = -1

(2 marks)

Learn each method

Standard derivativesLesson in A-level Maths Pro
Tangents, normals, increasing and decreasingLesson in A-level Maths Pro
Stationary points and optimisationFree lesson
Product, quotient and chain rulesLesson in A-level Maths Pro

Questions people ask

What differentiation comes up in A-level Maths?

Year 1: powers of x, e^kx, ln x, sin and cos, tangents and normals, stationary points and optimisation. Year 2 adds the product, quotient and chain rules, implicit and parametric differentiation, and connected rates of change.

How do I find the nature of a stationary point?

Solve dy/dx = 0, then use the second derivative: positive gives a minimum, negative a maximum. If it is zero, check the gradient either side.

When do I need the chain rule?

When one function sits inside another, such as (3x + 1)^5 or e^(x^2). Differentiate the outside, keep the inside, then multiply by the derivative of the inside.

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