Differentiation | AQA GCSE Further Maths Topic Questions 2020

	Download	View
Medium

1

3 marks

$y = 2 x^{10} - \frac{3}{x^{2}}$

Work out $\frac{d y}{d x}$

[3]

How did you do?

Did this page help you?

2

3 marks

The curve $y = 2 x^{3} - 3 x^{2} - 12 x + 6$

has a maximum point at $L (- 1, 13)$

has a minimum point at $M (2, - 14)$

intersects the $y$ -axis at $N$ .

The curve crosses the $x$ -axis at three distinct points.

On the axes below, sketch the curve.

Label the points $L, M$ and $N$ on your sketch.

q8-paper1-spec2018-aqa-gcse-furthermaths

[3]

How did you do?

Did this page help you?

3

3 marks

$y = x (2 x^{4} - 7 x^{3})$

Work out an expression for the rate of change of $y$ with respect to $x$ .

[3]

How did you do?

Did this page help you?

4

1 mark

$y = 2 x (x^{2} - 5 x)$

Circle the expression for $\frac{d y}{d x}$

[1]

2 (2 x - 5)

6 x^{2} - 20

3 x^{2} - 10 x

6 x^{2} - 20 x

How did you do?

Did this page help you?

5

5 marks

A curve has the equation $y = x^{3} + a x^{2} - 7$ where a is a constant.

The gradient of the curve when $x = 4$ is twice the gradient of the curve when $x = - 1$

Work out the value of $a$ .
You must show your working.

[5]

How did you do?

Did this page help you?

6

1 mark

On the grid, sketch a graph for which

the rate of change of $y$ with respect to $x$ is always zero.

[1]

qp7a-2019-paper-2-aqa-gcse-further-maths

How did you do?

Did this page help you?

7

1 mark

On the grid, sketch a graph for which

the rate of change of $y$ with respect to $x$ is always a positive constant.

[1]

qp7b-2019-paper-2-aqa-gcse-further-maths

How did you do?

Did this page help you?

8

1 mark

Here is a sketch of a quadratic curve which has a maximum point at (–2, 5)

qp11-2019-paper-2-aqa-gcse-further-maths

What is the equation of the normal to the curve at the maximum point?

Circle your answer.

x = - 2

y = 5

x = 5

y = - 2

[1]

How did you do?

Did this page help you?

9

2 marks

$y = \frac{x^{6}}{2} + \frac{x^{4}}{4}$

Work out $\frac{d y}{d x}$

Simplify your answer.

[2]

How did you do?

Did this page help you?

10

4 marks

$y = \frac{2 x^{7} + 15 x^{2}}{3 x}$

Work out the value of $x$ when $\frac{d y}{d x} = 133$

[4]

How did you do?

Did this page help you?

11

4 marks

Work out the rate of change of $y$ with respect to $x$ at the point on the curve

$y = x^{2} (x^{2} - 9)$ where $x = - 2$

You must show your working.

[4]

How did you do?

Did this page help you?

12

3 marks

$y = x^{2} (x - 10)$

Work out $\frac{d y}{d x}$

[3]

How did you do?

Did this page help you?

13

3 marks

For the curve $y = f (x)$ ,

$\frac{d y}{d x} = \frac{3}{2} x - k x^{4} + k$ where $k$ is a constant.

When $x = - 2$ the gradient of the curve is 12

Work out the value of $k$ .

[3]

How did you do?

Did this page help you?

Differentiation (AQA GCSE Further Maths)

Topic Questions