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Reference(s)

6664/01

Edexcel GCECore Mathematics C2

Advanced Subsidiary

Monday 22 May 2006 Mornin

!ime" 1 hour #0 minutes

Materials re$uired %or examination &tems included 'ith $uestion (a(ers

Mathematical Formulae (Green) Nil

Candidates may use any calculator E)CE*! those 'ith the %acility %or symbolic alebra+

di%%erentiation and/or interation, !hus candidates may -.! use calculators such as the

!exas &nstruments !& + !& 2+ Casio C) 0G+ 3e'lett *acard 3* 4G,

&nstructions to Candidates

Write the name of the examining body (Edexcel), your centre number, candidate number, the

unit title (Core Mathematics C), the !a!er reference ("""#), your surname, initials and

signature$

&n%ormation %or Candidates

% boo&let 'Mathematical Formulae and tatistical ables* is !ro+ided$Full mar&s may be obtained for ansers to %-- .uestions$

here are /0 .uestions in this .uestion !a!er$ he total mar& for this !a!er is 12$

Advice to Candidates

3ou must ensure that your ansers to !arts of .uestions are clearly labelled$

3ou must sho sufficient or&ing to ma&e your methods clear to the Examiner$ %nsersithout or&ing may gain no credit$

-2#55A his !ublication may only be re!roduced in accordance ith -ondon 4ualifications co!yright !olicy$500" -ondon 4ualifications -imited$

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1, Find the first 6 terms, in ascending !oers of x, of the binomial ex!ansion of ( 7 x)", gi+ing

each term in its sim!lest form$

47

2, 8se calculus to find the exact +alue of xx

x d

#

26

/

++$

57

#, (i) Write don the +alue of log"6"$

17

(ii) Ex!ress loga6 7 loga// as a single logarithm to base a$

#7

4, f(x) 9 x67 6x: ;x: "0$

(a) Find the remainder hen f(x) is di+ided by (x7 )$

27

(b) 8se the factor theorem to sho that (x7 6) is a factor of f(x)$

27

(c) Factorise f(x) com!letely$

47

5. (a) &etch the gra!h of y9 6x, x, shoing the coordinates of the !oint at hich the gra!h

meets theyium rule, ith all the +alues from your tables, to find an a!!roximation for the

+alue of

/

0

d6 xx

$

47

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N622=% 6

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6, (a) Gi+en that sin 9 2 cos , find the +alue of tan $

17

(b) ?ence, or otherise, find the +alues of in the inter+al0 @ 6"0for hich

sin 9 2 cos ,

gi+ing your ansers to / decimal !lace$

#7

, iure 1

he line y 9 6x: # is a tangent to the circle C, touching Cat the !oint A(, ), as shon inFigure /$

he !oint Qis the centre of C$

(a) Find an e.uation of the straight line throughPand Q$

#7

Gi+en that Qlies on the liney9 /,

(b) sho that thex

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, iure 2

Figure shos the crossontal and has length /$=" m$

he cur+eBCis an arc of a circle ith centreA, and CDis a straight line$

Gi+en that the si>e of BACis 0$"2 radians, find

(a) the length of the arcBC, in m, to decimal !laces,

27

(b) the area of the sectorBAC, in m, to decimal !laces,27

(c) the si>e of CAD, in radians, to decimal !laces,

27

(d) the area of the cross

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, % geometric series has first term aand common ratio r$ he second term of the series is # and the

sum to infinity of the series is 2$

(a) ho that 2r: 2r7 # 9 0$

47

(b) Find the to !ossible +alues of r$

27(c) Find the corres!onding to !ossible +alues of a$

27

(d) ho that the sum, Sn, of the first nterms of the series is gi+en by

Sn9 2(/ : rn)$

17

Gi+en that r ta&es the larger of its to !ossible +alues,

(e) find the smallest +alue of nfor hich Snexceeds #$

27

N622=% "

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10, iure #

Figure 6 shos a s&etch of !art of the cur+e ith e.uationy9 x6 : =x7 0x$ he cur+e has

stationary !ointsAandB$

(a) 8se calculus to find thex