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Centre Number

Candidate Number

INFORMATION FOR CANDIDATES

TIME

1 hour 30 minutes.

INSTRUCTIONS TO CANDIDATES

Write your Centre Number and Candidate Number in the spaces provided at the top of this page.You must answer all eight questions in the spaces provided.Do not write outside the boxed area on each page or on blank pages.Complete in black ink only. Do not write with a gel pen.Questions which require drawing or sketching should be completed using an H.B. pencil.All working should be clearly shown in the spaces provided. Marks may be awarded for partially correct solutions. Answers without working may not gain full credit.Answers should be given to three significant figures unless otherwise stated.You are permitted to use a graphic or scientific calculator in this paper.

INFORMATION FOR CANDIDATES

The total mark for this paper is 75Figures in brackets printed down the right-hand side of pages indicate the marks awarded to each question or part question.A copy of the Mathematical Formulae and Tables booklet is provided.Throughout the paper the logarithmic notation used is 1n z where it is noted that 1n z ≡ loge z

ADVANCED SUBSIDIARY (AS)General Certificate of Education

2017

*AMC21*

*AMC21*

Mathematics

Assessment Unit C2assessingModule C2:AS Core Mathematics 2

[AMC21]FRIDAY 19 MAY, MORNING

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1 Find

∫ 6t2 + t12 + 9 – 3t–3 dt [5]

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2 (i) Use the trapezium rule with four ordinates to find an approximate value for

0.6

10x dx ∫0 [5]

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(ii) Briefly explain why in this case the trapezium rule gives a value greater than the exact value. [1]

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3 The line y = 8 crosses the curve y = 6x – x2 at the points A and B.

(i) Find the x coordinates of A and B. [2]

(ii) Hence find the area bounded by the line y = 8 and the curve y = 6x – x2 [7]

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4 (a) A girl invests £1 000 at 8% per annum compound interest added annually.

(i) Find the value of the investment at the end of n years. [1]

(ii) Hence find how many years it will be until the value of the investment exceeds £2 000 [3]

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(Questions continue overleaf)

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(b) (i) Show that the sum of the first n natural numbers is

Sn = n(n + 1)2 [4]

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(ii) Find the sum of the integers between 1 and 600 inclusive that are not divisible by 3 [6]

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5 Solve the equation

2tan2 θ + 8 = 7

sin θ

where 0° G H I J θ G H I J 180° [9]

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6 Use the binominal theorem to expand, in ascending powers of x,

(2 + x – x2)6

as far as the term in x3 [6]

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7 (i) Prove that

loga xn = n loga x [6]

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(ii) Find x given that

loga x = loga2 (x + 6) [6]

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8 Fig. 1 below shows a framework for part of a stained glass window. AB, BC and CA are tangents to the circle, centre O and radius r.

A

B

C

O

Fig. 1

AB = 20 cm AC = 16 cm BÂC = 90°

(i) Find the exact length of BC. [1]

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(ii) Hence show that r is 5.19 cm. [5]

(iii) Find, in radians, the angle ABC. [1]

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The framework is to be filled with glass of four different colours as shown in Fig. 2 below.

A

B

C

yellow

blue

red

green

Fig. 2

(iv) Find the area of the red glass. [7]

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THIS IS THE END OF THE QUESTION PAPER

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Permission to reproduce all copyright material has been applied for.In some cases, efforts to contact copyright holders may have been unsuccessful and CCEAwill be happy to rectify any omissions of acknowledgement in future if notified.

Examiner Number

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For Examiner’suse only

QuestionNumber Marks

1

2

3

4

5

6

7

8

TotalMarks

10386/10