C2 Past Paper Booklet - The Grange School Blogs
C2 Past Paper Booklet - The Grange School Blogs C2 Past Paper Booklet - The Grange School Blogs
June 201021 The cubic polynomial f(x) is defined by f(x) = x 3 + ax 2 − ax − 14, where a is a constant.(i) Given that (x − 2) is a factor of f(x), find the value of a. [3](ii) Using this value of a, find the remainder when f(x) is divided by (x + 1). [2]2 (i) Use the trapezium rule, with 3 strips each of width 3, to estimate the area of the region boundedby the curve y = 3√ 7 + x, the x-axis, and the lines x = 1 and x = 10. Give your answer correct to3 significant figures. [4](ii) Explain how the trapezium rule could be used to obtain a more accurate estimate of the area.[1]3 (i) Find and simplify the first four terms in the binomial expansion of (1 + 1 2 x)10 in ascending powersof x. [4](ii) Hence find the coefficient of x 3 in the expansion of (3 + 4x + 2x 2 )(1 + 1 2 x)10 . [3]4 A sequence u 1, u 2, u 3, . . . is defined by u n= 5n + 1.(i) State the values of u 1, u 2and u 3. [1](ii) Evaluate40∑n=1u n. [3]Another sequence w 1, w 2, w 3, . . . is defined by w 1= 2 and w n+1= 5w n+ 1.(iii) Find the value of p such that u p= w 3. [3]5ED8 cm11cmAB65°CThe diagram shows two congruent triangles, BCD and BAE, where ABC is a straight line. Intriangle BCD, BD = 8 cm, CD = 11 cm and angle CBD = 65 ◦ . The points E and D are joined by anarc of a circle with centre B and radius 8 cm.(i) Find angle BCD. [2](ii) (a) Show that angle EBD is 0.873 radians, correct to 3 significant figures. [2](b)Hence find the area of the shaded segment bounded by the chord ED and the arc ED, givingyour answer correct to 3 significant figures. [4]© OCR 2010 4722 Jun10
June 201036 (a) Use integration to find the exact area of the region enclosed by the curve y = x 2 + 4x, the x-axisand the lines x = 3 and x = 5. [4](b) Find (2 − 6 √ y) dy. [3](c)Evaluate 1∞8dx. [4]3x7 (i) Show that sin2 x − cos 2 x1 − sin 2 x≡ tan 2 x − 1. [2](ii) Hence solve the equationsin 2 x − cos 2 x1 − sin 2 x= 5 − tan x,for 0 ◦ ≤ x ≤ 360 ◦ . [6]8 (a) Use logarithms to solve the equation 5 3w−1 = 4 250 , giving the value of w correct to 3 significantfigures. [5](b) Given that log x(5y + 1) − log x3 = 4, express y in terms of x. [4]9 A geometric progression has first term a and common ratio r, and the terms are all different. Thefirst, second and fourth terms of the geometric progression form the first three terms of an arithmeticprogression.(i) Show that r 3 − 2r + 1 = 0. [3](ii) Given that the geometric progression converges, find the exact value of r. [5](iii) Given also that the sum to infinity of this geometric progression is 3 + √ 5, find the value of theinteger a. [4]© OCR 2010 4722 Jun10
- 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 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
June 201021 <strong>The</strong> cubic polynomial f(x) is defined by f(x) = x 3 + ax 2 − ax − 14, where a is a constant.(i) Given that (x − 2) is a factor of f(x), find the value of a. [3](ii) Using this value of a, find the remainder when f(x) is divided by (x + 1). [2]2 (i) Use the trapezium rule, with 3 strips each of width 3, to estimate the area of the region boundedby the curve y = 3√ 7 + x, the x-axis, and the lines x = 1 and x = 10. Give your answer correct to3 significant figures. [4](ii) Explain how the trapezium rule could be used to obtain a more accurate estimate of the area.[1]3 (i) Find and simplify the first four terms in the binomial expansion of (1 + 1 2 x)10 in ascending powersof x. [4](ii) Hence find the coefficient of x 3 in the expansion of (3 + 4x + 2x 2 )(1 + 1 2 x)10 . [3]4 A sequence u 1, u 2, u 3, . . . is defined by u n= 5n + 1.(i) State the values of u 1, u 2and u 3. [1](ii) Evaluate40∑n=1u n. [3]Another sequence w 1, w 2, w 3, . . . is defined by w 1= 2 and w n+1= 5w n+ 1.(iii) Find the value of p such that u p= w 3. [3]5ED8 cm11cmAB65°C<strong>The</strong> diagram shows two congruent triangles, BCD and BAE, where ABC is a straight line. Intriangle BCD, BD = 8 cm, CD = 11 cm and angle CBD = 65 ◦ . <strong>The</strong> points E and D are joined by anarc of a circle with centre B and radius 8 cm.(i) Find angle BCD. [2](ii) (a) Show that angle EBD is 0.873 radians, correct to 3 significant figures. [2](b)Hence find the area of the shaded segment bounded by the chord ED and the arc ED, givingyour answer correct to 3 significant figures. [4]© OCR 2010 4722 Jun10
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