C2 Past Paper Booklet - The Grange School Blogs

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Jan 201121 (i) Find and simplify the first three terms, in ascending powers of x, in the binomial expansion of(1 + 2x) 7 . [3](ii) Hence find the coefficient of x 2 in the expansion of (2 − 5x)(1 + 2x) 7 . [3]2 A sequence S has terms u 1, u 2, u 3, . . . defined by u n= 3n + 2 for n ≥ 1.(i) Write down the values of u 1, u 2and u 3. [2](ii) State what type of sequence S is. [1](iii) Find200∑ u n. [3]n=1013yO3 5xThe diagram shows the curve y = √ x − 3.(i) Use the trapezium rule, with 4 strips each of width 0.5, to find an approximate value for the areaof the region bounded by the curve, the x-axis and the line x = 5. Give your answer correct to3 significant figures. [4](ii) State, with a reason, whether this approximation is an underestimate or an overestimate. [2]4 (a) Use logarithms to solve the equation 5 x−1 = 120, giving your answer correct to 3 significantfigures. [4](b) Solve the equation log 2x + 2 log 23 = log 2(x + 5). [4]5 In a geometric progression, the sum to infinity is four times the first term.(i) Show that the common ratio is 3 4 . [3](ii) Given that the third term is 9, find the first term. [3](iii) Find the sum of the first twenty terms. [2]© OCR 2011 4722 Jan11
Jan 20116 (a) Find x3 + 3x 1 2x3dx. [4](b)a(i) Find, in terms of a, the value of 6x −4 dx, where a is a constant greater than 2. [3]2∞(ii) Deduce the value of 6x −4 dx. [1]27 Solve each of the following equations for 0 ◦ ≤ x ≤ 180 ◦ .(i) 3 tan 2x = 1 [3](ii) 3 cos 2 x + 2 sin x − 3 = 0 [5]8AO rad5 cmBThe diagram shows a sector AOB of a circle with centre O and radius 5 cm. Angle AOB is θ radians.The area of triangle AOB is 8 cm 2 .(i) Given that the angle θ is obtuse, find θ. [3]The shaded segment in the diagram is bounded by the chord AB and the arc AB.(ii) Find the area of the segment, giving your answer correct to 3 significant figures. [3](iii) Find the perimeter of the segment, giving your answer correct to 3 significant figures. [4][Question 9 is printed overleaf.]© OCR 2011 4722 Jan11 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 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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