Integration - Past Edexcel Exam Questions

Integration

Integration - Past Edexcel Exam Questions

1. Given

y = 3 x - 6x + 4,

(a) find y dx, simplifying each term. (b) (Differentiation Question)

(Question 2 - C1 May 2018)

x>0 [3]

2. The curve C has equation y = f (x), where

(Question 9 - C1 May 2018)

f (x) = (x - 3)(3x + 5).

Given that the point P (1, 20) lies on C,

(a) find f (x), simplifying each term.

[5]

(b) Show that f (x) = (x - 3)2(x + A) where A is a constant to be found.

[3]

(c) (Curve Sketching Question)

3.

(Question 1 - C1 May 2017)

Find

2x5 - 1 - 5 dx 4x3

giving each term in its simplest form.

[4]

4.

(Question 7 - C1 May 2017)

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

6 - 5x2 f (x) = 30 + .

x

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



c StudyWell Publications Ltd. 2020

Integration

(a) (Differentiation Question)

(b) Find f (x), giving each term in its simplest form.

[5]

5.

(Question 1 - C1 May 2016)

Find

2x4

-

4

+3

dx

x

giving each term in its simplest form.

[4]

6.

(Question 3 - C1 May 2015)

Given

that

y

=

4x3

-

5 x2

,

x

=

0,

find

in

their

simplest

form

(a) (Differentiation Question)

(b) y dx.

[3]

7.

(Question 10 - C1 May 2015)

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

Given that

3x 9

f (x) =

- + 2,

2 4x

x>0

(a) find f (x), giving each term in its simplest form.

[5]

(b) (Differentiation Question)

8. Find

(Question 1 - C1 May 2014) 8x3 + 4 dx

giving each term in its simplest form.

[3]



c StudyWell Publications Ltd. 2020

Integration

9.

(Question 10 - C1 May 2014)

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

Given that

f

(x)

=

3 x2

-

10x-

1 2

+

1,

x>0

8

(a) find f (x), simplifying each term.

[5]

(b) (Differentiation Question)

10.

(Question 2 - C1 May 2013)

Find

10x4

-

4x

-

3

dx

x

giving each term in its simplest form.

[4]

11.

(Question 9 - C1 May 2013)

(a) Show that

(3 - x2)2

f (x) =

, x=0

x2

f (x) = 9x-2 + A + Bx2

where A and B are constants to be found.

[3]

(b) (Differentiation Question)

Given that the point (-3, 10) lies on the curve with equation y = f (x),

(c) find f (x).

[5]



c StudyWell Publications Ltd. 2020

Integration

12.

(Question 8 - C1 January 2013)

dy

=

-x3 +

4x - 5 ,

x=0

dx

2x3

Given that y = 7 at x = 1, find y in terms of x, giving each term in its simplest

form.

[6]

13.

(Question 1 - C1 May 2012)

Find

6x2 + 2 + 5 dx x2

giving each term in its simplest form.

[4]

14.

(Question 7 - C1 May 2012)

The point P (4, -1) lies on the curve C with equation y = f (x), x > 0, and

16

f (x) = x - + 3.

2

x

(a) (Differentiation Question)

(b) Find f (x).

[4]

15.

(Question 1 - C1 January 2012)

Given

that

y

=

x4

+

6x

1 2

,

find

in

their

simplest

form

(a) (Differentiation Question)

(b) y dx.

[3]



c StudyWell Publications Ltd. 2020

Integration

16.

(Question 7 - C1 January 2012)

A curve with equation y = f (x) passes through the point (2, 10). Given that

f (x) = 3x2 - 3x + 5,

find the value of f (1).

[5]

17.

(Question 2 - C1 May 2011)

Given

that

y

=

2x5

+

7

+

1 x3

,

x

=

0,

find,

in

their

simplest

form

(a) (Differentiation Question)

(b) y dx.

[4]

18.

(Question 6 - C1 May 2011)

5

Given that

6x+3x 2 x

can be written in the form 6xp + 3xq,

(a) write down the value of p and the value of q.

[2]

5

Given that

dy dx

=

6x+3x 2 x

and that y = 90 when x = 4,

(b) find y in terms of x, simplifying the coefficient of each term.

[5]

19. Find

(Question 2 - C1 January 2011)

12x5

-

3x2

+

1

4x 3

dx,

giving each term in its simplest form.

[5]



c StudyWell Publications Ltd. 2020

 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download