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7. (a) Show that can be written as (2)

Given that and that at x = 1,

(b) find y in terms of x.(6)

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23y =

2d (3 ) , 0,dy x xx x

− √= >

√

1 12 29 6 .x x− − +

2(3 )xx

− √√

14 *N23491C01424*

physicsandmathstutor.com June 2005

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12

8. The curve with equation y = f (x) passes through the point (1, 6). Given that

find f (x) and simplify your answer.(7)

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12

25 2f ( ) 3 , > 0,xx xx+

′ = +

*N20233A01220*

physicsandmathstutor.com January 2006

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2

1. Find , giving each term in its simplest form.(4)

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1226 2 d( )x x x−+ +∫

Q1

(Total 4 marks)

*N23557A0224*

physicsandmathstutor.com June 2006

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16

*H26107A01624*

9. The curve C with equation )(f xy = passes through the point (5, 65).

Given that ′ = − −f (x x x) ,6 10 122

(a) use integration to find )(f x . (4)

(b) Hence show that f ( ) ( )( )x x x x= + −2 3 4 . (2)

(c) In the space provided on page 17, sketch C, showing the coordinates of the points where C crosses the x-axis.

(3)

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physicsandmathstutor.com June 2007

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17

Turn over*H26107A01724*

Question 9 continued

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Q9

(Total 9 marks)

physicsandmathstutor.com June 2007

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*N25561A0224*

1. Find 3 4 72 5x x x+ −∫ d( ) .(4)

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___________________________________________________________________________ Q1

(Total 4 marks)

physicsandmathstutor.com January 2008

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2

*H29992A0228*

1. Find .(3)

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___________________________________________________________________________ Q1

(Total 3 marks)

∫ (2 + 5x2) dx

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*H29992A02628*

11. The gradient of a curve C is given by

(a) Show that = x2 + 6 + 9x–2.(2)

The point (3, 20) lies on C.

(b) Find an equation for the curve C in the form y = f(x).(6)

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ddyx

x

xx=

+( )≠

2 2

2

30, .

ddyx

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*H29992A02828*

Question 11 continued

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TOTAL FOR PAPER: 75 MARKS

END

Q11

(Total 8 marks)

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*n30081A0428*

2. Find , giving each term in its simplest form.(4)

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___________________________________________________________________________ Q2

(Total 4 marks)

12 8 +3 d5 3x x x( )−∫

physicsandmathstutor.com January 2009

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*n30081A0628*

4. A curve has equation y = f(x) and passes through the point (4, 22).

Given that

use integration to find f(x), giving each term in its simplest form.(5)

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f ( ) ,x x x3 3 7212– –′ =

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6

*N34854A0628*

4. ddyx

x x x= +−512 ,√

x > 0

Given that y = 35 at x = 4, find y in terms of x, giving each term in its simplest form. (7)

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physicsandmathstutor.com January 2010

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*H35383A0328* Turn over

2. Find

∫ (8 6 5) dx3 12x x –+

giving each term in its simplest form.(4)

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___________________________________________________________________________ Q2

(Total 4 marks)

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*H35402A0324* Turn over

2. Find

135 2(12 3 4 ) dx x x x− +∫

giving each term in its simplest form.(5)

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Q2

(Total 5 marks)

physicsandmathstutor.com January 2011

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*h35402A01224*

7. The curve with equation f ( )y x= passes through the point ( 1,0).−

Given that

2f ( ) 12 8 1x x x′ = − +

find f ( ).x(5)

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physicsandmathstutor.com January 2011

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*P38157A01228*

6. Given that 526 3x x

x+ can be written in the form 6 3 ,p qx x+

(a) write down the value of p and the value of q.(2)

Given that 52d 6 3 ,

dy x xx x

+= and that y = 90 when x = 4,

(b) find y in terms of x, simplifying the coefficient of each term.(5)

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2

*P40082A0228*

1. Given that y x x= +4126 , find in their simplest form

(a) ddyx

(3)

(b) y xd∫(3)

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physicsandmathstutor.com January 2012

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*P40082A01628*

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

′ = − +f ( )x x x3 3 52

find the value of f ( )1 . (5)

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physicsandmathstutor.com January 2012

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*P40684A0224*

1. Find 6 2 52

2xx

x+ +⎛⎝⎜

⎞⎠⎟∫ d

giving each term in its simplest form.(4)

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Q1

(Total 4 marks)

physicsandmathstutor.com June 2012

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*P41488A02032*

8. ddyx

x xx

x= − + − ≠33

4 52

0,

Given that y = 7 at x = 1, find y in terms of x, giving each term in its simplest form.(6)

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physicsandmathstutor.com January 2013

physicsandmathstutor.com June 2013 (R)

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3

*P41802A0328* Turn over

2. Find

∫ √10 4 34x x x− −⎛

⎝⎜⎞⎠⎟x

d

giving each term in its simplest form.(4)

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(Total 4 marks)

physicsandmathstutor.com June 2013

4 Edexcel AS/A level Mathematics Formulae List: Core Mathematics C1 – Issue 1 – September 2009

Core Mathematics C1

Mensuration

Surface area of sphere = 4π r 2

Area of curved surface of cone = π r × slant height

Arithmetic series

un = a + (n – 1)d

Sn = 21 n(a + l) =

21 n[2a + (n − 1)d]