Further Differentiation | Edexcel International A Level Maths: Pure 3 Topic Questions 2020

1a

2 marks

A curve has the equation $y = {5 e}^{- 2 x}$ .

Find an expression for $\frac{d y}{d x}$ .

How did you do?

1b

3 marks

(i)

Find the gradient of the tangent at the point where

x = 1

, giving your answer in the form

{- a e}^{- 2}

where a is a positive integer to be found.

(ii)

Hence show that the gradient of the normal to the curve at the point where

x = 1

is

\frac{1}{10} e^{2}

.

How did you do?

Did this page help you?

1

6 marks

A curve has the equation $y = e^{- 3 x} + \ln x, x > 0 .$

Show that the equation of the tangent to the curve at the point with x-coordinate 1 is

$y = (\frac{e^{3} - 3}{e^{3}}) x + \frac{4 - e^{3}}{e^{3}}$

How did you do?

Did this page help you?

1

4 marks

A curve has the equation $y = e^{- 3 x} + \ln x, x > 0 .$

Find the gradient of the normal to the curve at the point $(1, e^{- 3})$ , giving your answer correct to 3 decimal places.

How did you do?

Did this page help you?

1

4 marks

A curve has the equation $y = 3^{x} + 2^{- x}$ .

Show that the gradient of the normal to the curve at the point $(1, \frac{7}{2})$ is

$\frac{2}{\ln 2 - 6 \ln 3}$

How did you do?

Did this page help you?

Edexcel International A Level Maths: Pure 3