C2 Past Paper Booklet - The Grange School Blogs

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Jan 200849 (i)yO–180° 180°xFig. 1Fig. 1 shows the curve y = 2sinx for values of x such that −180 ◦ ≤ x ≤ 180 ◦ . State the coordinatesof the maximum and minimum points on this part of the curve. [2](ii)ykO–180° 180°xFig. 2Fig. 2 shows the curve y = 2sinx and the line y = k. The smallest positive solution of the equation2sinx = k is denoted by α. State, in terms of α, and in the range −180 ◦ ≤ x ≤ 180 ◦ ,(a) another solution of the equation 2 sin x = k, [1](b) one solution of the equation 2 sin x =−k. [1](iii) Find the x-coordinates of the points where the curve y = 2sinx intersects the curve y = 2 − 3cos 2 x,for values of x such that −180 ◦ ≤ x ≤ 180 ◦ . [6]10 (i) Find the binomial expansion of (2x + 5) 4 , simplifying the terms. [4](ii) Hence show that (2x + 5) 4 −(2x − 5) 4 can be written as320x 3 + kx,wherethevalueoftheconstantk is to be stated. [2](iii) Verify that x = 2 is a root of the equation(2x + 5) 4 −(2x − 5) 4 = 3680x − 800,and find the other possible values of x. [6]Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonableeffort has been made by the publisher (OCR) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will bepleased to make amends at the earliest possible opportunity.OCR is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES),which is itself a department of the University of Cambridge.© OCR 2008 4722/01 Jan08
June 200821 Find and simplify the first three terms in the expansion of (2 − 3x) 6 in ascending powers of x. [4]2 A sequence u 1, u 2, u 3, ... isdefinedbyu 1= 3 and u n+1= 1 − 1 u nfor n ≥ 1.(i) Write down the values of u 2, u 3and u 4. [3](ii) Describe the behaviour of the sequence. [1]3AB48 cm 28cmThe diagram shows a sector AOB of a circle with centre O and radius 8 cm. The area of the sectoris 48 cm 2 .O(i) Find angle AOB,givingyouranswerinradians. [2](ii) Find the area of the segment bounded by the arc AB and the chord AB. [3]4 The cubic polynomial ax 3 − 4x 2 − 7ax + 12 is denoted by f(x).(i) Given that (x − 3) is a factor of f(x), find the value of the constant a. [3](ii) Using this value of a, find the remainder when f(x) is divided by (x + 2). [2]© OCR 2008 4722/01 Jun08
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 20 and 21: 5June 2008y3O2 14xThe diagram shows
Page 22 and 23: Jan 200921 Find(i) (x 3 + 8x − 5
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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 38 and 39: 1Jan 20122A4.2 radO12 cmBThe diagra
Page 40: 4Jan 20127 (a) Find ∫ (x2 + 4)(x

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