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Mathematics A2 Level

Core 4 Revision Pack

Contents

CORE 3 FORMULA SHEET 2

CORE 4 FORMULA SHEET 3

JANUARY 2006 4

JUNE 2006 6

JANUARY 2007 9

JUNE 2007 12

JANUARY 2008 14

JUNE 2008 18

JANUARY 2009 22

MAY 2009 26

JAN 2010 30

JUN 2010 34

JAN 2011 38

JUN 2011 42

JAN 2012 46

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Core 3 Formula Sheet

Core Mathematics C3

Candidates sitting C3 may also require those formulae listed under Core Mathematics C1 and C2.

Logarithms and exponentials

xax a=lne

Trigonometric identities

BABABA sincoscossin)(sin =

BABABA sinsincoscos)(cos m=

))((tantan1

tantan)(tan 21 +

= kBABA

BABA

m

2cos

2sin2sinsin

BABABA

+=+

2sin

2cos2sinsin

BABABA

+=

2cos

2cos2coscos

BABABA

+=+

2

sin

2

sin2coscosBABA

BA +

=

Differentiation

f(x) f(x)

tan kx ksec2kx

secx secx tanx

cotx cosec2x

cosecx cosecxcotx

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Core 4 Formula Sheet

Integration (+constant)

f(x) xx d)f(

sec2kx

k

1tan kx

xtan xsecln

xcot xsinln

xcosec )tan(lncotcosecln21xxx =+

xsec )tan(lntansecln4

1

2

1 +=+ xxx

= x

x

uvuvx

x

vu d

d

dd

d

d

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January 2006Time: 1 hour 30 minutes

1. A curve Cis described by the equation 3x2

+ 4y2

2x+ 6xy 5 = 0.

Find an equation of the tangent to Cat the point (1, 2), giving your answer in the form

ax + by+ c= 0, where a, band care integers. (7)

2. (a) Given thaty= secx, complete the table with the values ofycorresponding tox=16

,

8

and

4

.

x 016

8

16

3

4

y 1 1.20269

(2)

(b) Use the trapezium rule, with all the values for y in the completed table, to obtain an estimate for

4

0

dsec

xx . Show all the steps of your working and give your answer to 4 decimal places. (3)

The exact value of

4

0

dsec

xx is ln (1 + 2).

(c) Calculate the % error in using the estimate you obtained in part (b). (2)

3. Using the substitution u2= 2x 1, or otherwise, find the exact value of

5

1

d

)12(

3x

x

x. (8)

4. Figure 1

Figure 1 shows the finite regionR, which is bounded by the curvey=xex, the linex= 1, the linex= 3 and thex-axis.

The regionRis rotated through 360 degrees about thex-axis. Use integration by parts to find an exact value for

the volumeof the solid generated. (8)

5. f(x) =2

2

)2)(31(

163

xx

x

++

=)31( x

A

+

)2( x

B

++

2)2( x

C

+, x