Di erentiation - Past Edexcel Exam Questions

Differentiation

Differentiation - Past Edexcel Exam Questions

1. Given

y = 3 x - 6x + 4,

(Question 2 - C1 May 2018) x>0

(a) (Integration Question)

(b)

i.

Find

dy dx

.

ii.

Hence find

the

value

of

x

such

that

dy dx

= 0.

[4]

2.

(Question 10 - C1 May 2018)

Figure 3 shows a sketch of part of the curve C with equation

y

=

1 2

x

+

27 x

-

12,

x>0

The point A lies on C and has coordinates

3,

-

3 2

.

(a) Show that the equation of the normal to C at the point A can be written as

10y = 4x - 27.

[5]



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(b) (Simultaneous Equations Question)

Differentiation

3.

(Question 2 - C1 May 2017)

Given

y

=

x

+

4 x

+

4,

x>0

find

the

value

of

dy dx

when

x

=

8,

writing

your

answer

in

the

form

a 2,

where

a

is

a

rational number.

[5]

4.

(Question 7 - C1 May 2017)

The curve C has equation y = f (x), x > 0, where

f

(x)

=

30

+

6

-5x2 x

.

Given that the point (4, -8) lies on C,

(a) find the equation of the tangent to C at P , giving your answer in the form

y = mx + c, where m and c are constants.

[4]

(b) (Integration Question)



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Differentiation

5.

(Question 10 - C1 May 2017)

This figure shows a sketch of part of the curve y = f (x), x R, where f (x) = (2x - 5)2(x + 3).

(a) (Transformations Question)

(b) Show that f (x) = 12x2 - 16x - 35.

[3]

Points A and B are distinct points that lie on the curve y = f (x).

The gradient of the curve at A is equal to the gradient of the curve at B.

Given that point A has x-coordinate 3,

(c) find the x-coordinate of point B.

[5]

6.

(Question 7 - C1 May 2016)

Given that

y

=

3x2

+

6x

1 3

+

2x3- 3x

7

,

x>0

find

dy dx

.

Give

each

term

in

your

answer

in

its

simplest

form.

[6]



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Differentiation

7.

(Question 11 - C1 May 2016)

The curve C has equation y = 2x3 + kx2 + 5x + 6, where k is a constant.

(a)

Find

dy dx

.

[2]

The point P , where x = -2, lies on C. The tangent to C at the point P is parallel to the line with equation 2y - 17x - 1 = 0. Find

(b) the value of k,

[4]

(c) the value of the y-coordinate of P ,

[2]

(d) the equation of the tangent to C at P , giving your answer in the form

ax + by + c = 0, where a, b and c are integers.

[2]

8.

(Question 3 - C1 May 2015)

Given

that

y

=

4x3

-

5 x2

,

x

=

0,

find

in

their

simplest

form

(a)

dy dx

[3]

(b) (Integration Question)

9. The curve C has equation

(Question 6 - C1 May 2015)

y = (x2 + 4)(x - 3) , 2x

x=0

(a)

Find

dy dx

in

its

simplest

form.

[5]

(b) Find an equation of the tangent to C at the point where x = -1.

Give your answer in the form ax + by + c = 0 where a, b and c are integers. [5]



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Differentiation

10.

(Question 10 - C1 May 2015)

A curve with equation y = f (x) passes through the point (4, 9).

Given that

f

(x)

=

3x 2

-

9 4x

+

2,

x>0

(a) (Integration Question)

Point P lies on the curve. The normal to the curve at P is parallel to the line 2y + x = 0.

(b) Find the x-coordinate of P .

[5]

11.

(Question 7 - C1 May 2014)

Differentiate with respect to x, giving each answer in its simplest form.

(a) (1 - 2x)2

[3]

(b)

x5+6x 2x2

[4]

12.

(Question 6 - C1 May 2015)

A curve with equation y = f (x) passes through the point (4, 25).

Given that

f

(x)

=

3 8

x2

-

10x-

1 2

+

1,

x>0

(a) (Integration Question)

(b) Find an equation of the normal to the curve at the point (4, 25).

Give your answer in the form ax + by + c = 0, where A, b and c are integers to be

found.

[5]



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