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Paper Reference(s)

6664

Edexcel GCECore Mathematics C2

Advanced Subsidiary

Wednesday 19 anuary 2!!" Mornin#

$ime% 1 hour &! 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

al#ebra. di((erentiation and/or inte#ration0 $hus candidates may $ use

calculators such as the $exas )nstruments $) 39. $) 92. Casio C, 995!G.

e*lett -ac7ard - 43G0

)nstructions to Candidates

In the boxes on the answer book, write the name of the examining bo! ("excel), !our

centre number, caniate number, the unit title (#ore Mathematics #$), the paper reference

(%%%&), !our surname, other name an signature'

hen a calculator is use, the answer shoul be gien to an appropriate egree of accurac!'

)n(ormation (or Candidates

* booklet +Mathematical Formulae an tatistical -ables. is proie'

Full marks ma! be obtaine for answers to *// 0uestions'

-his paper has nine 0uestions'

-he total mark for this paper is 12'

Advice to Candidates

3ou must ensure that !our answers to parts of 0uestions are clearl! labelle'

3ou must show sufficient working to make !our methos clear to the "xaminer' *nswers

without working ma! gain no creit'

N$4&54*-his publication ma! onl! be reprouce in accorance with /onon 6ualifications /imite cop!right polic!'7$882 /onon 6ualifications /imite'

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10 Fin the first three terms, in ascening powers ofx, of the binomial expansion of (4 9 $x)2,

giing each term in its simplest form'

84

20 -he pointsAanBhae coorinates (2, :;) an (;4, ;;) respectiel!'

(a) Fin the coorinates of the mience sole, for 8 x? 4%8, the e0uation

2 cos$x= 4(; 9 sinx),

giing !our answers to ; ecimal place where appropriate'

8"

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"0 f(x) =x4: $x$9 ax9 b, where aan bare constants'

hen f(x) is iie b! (x: $), the remainer is ;'

hen f(x) is iie b! (x9 ;), the remainer is $@'

(a) Fin the alue of aan the alue of b'

86

(b) how that (x: 4) is a factor of f(x)'

82

60 -he secon an fourth terms of a geometric series are 1'$ an 2'@4$ respectiel!'

-he common ratio of the series is positie'

For this series, fin

(a) the common ratio,

82

(b) the first term,

82

(c) the sum of the first 28 terms, giing !our answer to 4 ecimal places,

82

(d) the ifference between the sum to infinit! an the sum of the first 28 terms, giing !our

answer to 4 ecimal places'

82

N$4&54* 4

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50 i#ure 1

Figure ; shows the triangleABC, withAB= @ cm,AC= ;; cm an BAC= 8'1 raians' -he

arcBD, whereDlies onAC, is an arc of a circle with centre Aan raius @ cm' -he regionR,

shown shae in Figure ;, is boune b! the straight linesBCan CDan the arcBD'

Fin

(a) the length of the arcBD,

82

(b) the perimeter ofR, giing !our answer to 4 significant figures,84

(c) the area ofR, giing !our answer to 4 significant figures'

8"

N$4&54* &

B

R@ cm

8'1 ra

;; cm

D

A

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30 i#ure 2

-he line with e0uationy= 4x9 $8 cuts the cure with e0uation y=x$9 %x9 ;8 at the points

AanB, as shown in Figure $'

(a) Ase algebra to fin the coorinates ofAan the coorinates ofB'

8"

-he shae region Sis boune b! the line an the cure, as shown in Figure $'

(b) Ase calculus to fin the exact area of S'

85

N$4&54* 2

y

y=x$9 %x9 ;8

y= 4x9 $8

O

A

B

S

x

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90 i#ure &

Figure 4 shows the plan of a stage in the shape of a rectangle Boine to a semicircle' -he

length of the rectangular part is $xmetres an the with is ymetres' -he iameter of the

semicircular part is $xmetres' -he perimeter of the stage is @8 m'

(a) how that the area,Am$, of the stage is gien b!

A= @8x:

+

$$

x$'

84

(b) Ase calculus to fin the alue ofxat whichAhas a stationar! alue'

84

(c) Proe that the alue ofx!ou foun in part (b) gies the maximum alue ofA'82

(d) #alculate, to the nearest m$, the maximum area of the stage'

82

$$A: ; -A-E;% 5" MA;