• Document: NAME: PAPER C. Date to be handed in: MARK (out of 100): Qu Practice Paper C: Time 2 hours. Questions to revise:
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NAME: PAPER C Date to be handed in: MARK (out of 100): Qu 1 2 3 4 5 6 7 8 9 10 11 12 13 Practice Paper C: Time 2 hours Questions to revise: 1 1. Prove, from first principles, that the derivative of 5x3 is 15x2. (Total 4 marks) ___________________________________________________________________________ 2. (a) Sketch the graph of y = 8x stating the coordinates of any points where the graph crosses the coordinate axes. (2) (b) (i) Describe fully the transformation which transforms the graph y = 8x to the graph y = 8x – 1. (1) (ii) Describe the transformation which transforms the graph y = 8x – 1 to the graph y = 8x – 1 + 5. (1) (Total 4 marks) ___________________________________________________________________________ 3. In  OAB, OA  a and OB  b . P divides OA in the ratio 3 : 2 and Q divides OB in the ratio 3 : 2. (a) Show that PQ is parallel to AB. (4) (b) Given that the length of AB is 10 cm, find the length of PQ. (1) (Total 5 marks) ___________________________________________________________________________ 4 4. g(x) = + 5, x  ℝ. x6 Sketch the graph y = g(x). Label any asymptotes and any points of intersection with the coordinate axes. (Total 5 marks) ___________________________________________________________________________ 2 5. f(x) = 2x3 – x2 – 13x – 6. Use the factor theorem and division to factorise f(x) completely. (Total 6 marks) ___________________________________________________________________________ 6. (a) Fully expand (p + q)5. (2) A fair four-sided die, numbered 1, 2, 3 and 4, is rolled 5 times. Let p represent the probability that the number 4 is rolled on a given roll and let q represent the probability that the number 4 is not rolled on a given roll. (b) Using the first three terms of the binomial expansion from part (a), or otherwise, find the probability that the number 4 is rolled at least 3 times. (5) (Total 7 marks) ___________________________________________________________________________ 7. In  ABC, AB  3i  6 j and AC  10i  2 j . (a) Find the size of  BAC, in degrees, to 1 decimal place. (5) (b) Find the exact value of the area of  ABC. (3) (Total 8 marks) ___________________________________________________________________________ 3 8. The points A and B have coordinates (3k − 4, −2) and (1, k + 1) respectively, where k is a constant. Given that the gradient of AB is − 3 , 2 (a) show that k = 3, (2) (b) find an equation of the line through A and B, (3) (c) find an equation of the perpendicular bisector of A and B. Leave your answer in the form ax + by + c = 0 where a, b and c are integers. (4) (Total 9 marks) ____________________________________________________

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