C2 Past Paper Booklet - The Grange School Blogs

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1Jan 20122A4.2 radO12 cmBThe diagram shows a sector AOB of a circle with centre O and radius 12 cm. The reflex angle AOB is4.2 radians.(i) Find the perimeter of the sector. [3](ii) Find the area of the sector. [2]2yOxThe diagram shows the curve y = log 10(2x + 1).(i) Use the trapezium rule with 4 strips each of width 1.5 to find an approximation to the area of theregion bounded by the curve, the x-axis and the lines x = 4 and x = 10. Give your answer correct to3 significant figures. [4](ii) Explain why this approximation is an under-estimate. [1]3 One of the terms in the binomial expansion of (4 + ax) 6 is 160x 3 .(i) Find the value of a. [4](ii) Using this value of a, find the first two terms in the expansion of (4 + ax) 6 in ascending powers of x.[2]© OCR 20124722 Jan12
4Jan 2012N3A2.4 kmC40°2 kmBThe diagram shows two points A and B on a straight coastline, with A being 2.4 km due north of B.A stationary ship is at point C, on a bearing of 040° and at a distance of 2 km from B.(i) Find the distance AC, giving your answer correct to 3 significant figures. [2](ii) Find the bearing of C from A. [3](iii) Find the shortest distance from the ship to the coastline. [2]5 The cubic polynomial f(x) is defined by f(x) = 2x 3 + 3x 2 − 17x + 6.(i) Find the remainder when f(x) is divided by (x − 3). [2](ii) Given that f(2) = 0, express f(x) as the product of a linear factor and a quadratic factor. [4](iii) Determine the number of real roots of the equation f(x) = 0, giving a reason for your answer. [2]6 A sequence u 1, u 2, u 3, ... is defined by u n= 85 − 5n for n 1.(i) Write down the values of u 1, u 2and u 3. [2]20(ii) Find n. [3]Σn =1u(iii) Given that u 1, u 5and u pare, respectively, the first, second and third terms of a geometric progression,find the value of p. [4](iv) Find the sum to infinity of the geometric progression in part (iii). [2]© OCR 20124722 Jan12 Turn over
Page 1 and 2: The Grange SchoolMaths DepartmentCo
Page 3 and 4: June 200534In the diagram, ABCD is
Page 6 and 7: Jan 200635 In a geometric progressi
Page 8 and 9: June 200621 Find the binomial expan
Page 10 and 11: June 200649 (i) Sketch the curve y
Page 12 and 13: 3Jan 20076 (i) Find and simplify th
Page 14 and 15: June 200721 A geometric progression
Page 16 and 17: 1Jan 20082AO0.7 rad11 cmBThe diagra
Page 18 and 19: Jan 200849 (i)yO-180° 180°xFig. 1
Page 20 and 21: 5June 2008y3O2 14xThe diagram shows
Page 22 and 23: Jan 200921 Find(i) (x 3 + 8x − 5
Page 24 and 25: Jan 200947 In the binomial expansio
Page 26 and 27: 8June 20093ABOFig. 1Fig. 1 shows a
Page 28 and 29: Jan 201035yOxThe diagram shows part
Page 30 and 31: June 201021 The cubic polynomial f(
Page 32 and 33: Jan 201121 (i) Find and simplify th
Page 34 and 35: 9Jan 2011y4xThe diagram shows the c
Page 36 and 37: 4June 2011y331OxThe diagram shows t
Page 40: 4Jan 20127 (a) Find ∫ (x2 + 4)(x

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