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Unformatted text preview: iving your answers correct to one decimal place. Working: Answer: (b) ………………………………………….. (Total 6 marks) 424 632. Let p = log10x, q = log10 y and r = log10z. x in terms of p, q and r. Write the expression log10 2 y z Working: Answer: ………………………………………….. (Total 6 marks) 633. In a triangle ABC, AB = 4 cm, AC = 3 cm and the area of the triangle is 4.5 cm2. Find the two possible values of the angle BAC. Working: Answer: ………………………………………….. (Total 6 marks) 425 634. Solve the equation 2cos2 x = sin 2x for 0 ≤ x ≤ π, giving your answers in terms of π. Working: Answer: ………………………………………….. (Total 6 marks) 635. A car starts by moving from a fixed point A. Its velocity, v m s–1 after t seconds is given by v = 4t + 5 – 5e–t. Let d be the displacement from A when t = 4. (a) Write down an integral which represents d. (b) Calculate the value of d. Working: Answers: (a) ………………………………………….. (b) ………………………………………….. (Total 6 marks) 426 636. The following table shows four series of numbers. One of these series is geometric, one of the series is arithmetic and the other two are neither geometric nor arithmetic. (a) Complete the table by stating the type of series that is shown. Series (i) (ii) Type of series 1 + 11 + 111 + 1111 + 11111… 1+ 3 9 27 + + … 4 16 64 (iii) (iv) (b) 0.9 + 0.875 + 0.85 + 0.825 + 0.8… 12345 ++++… 23456 The geometric series can be summed to infinity. Find this sum. Working: Answer: (b) ………………………………………….. (Total 6 marks) 427 637. The table below shows the marks gained in a test by a group of students. Mark 1 2 3 4 5 Number of students 5 10 p 6 2 The median is 3 and the mode is 2. Find the two possible values of p. Working: Answer: ………………………………………….. (Total 6 marks) 638. Two lines L1 and L2 have these vector equations. L1 : r = 2i + 3j + t(i– 3j) L2 : r = i + 2j + s(i – j) The angle between L1 and L2 is θ. Find the cosine of the angle θ. Working: Answer: ………………………………………….. (Total 6 marks) 428 639. The equation x2 – 2kx + 1 = 0 has two distinct real roots. Find the set of all possible values of k. Working: Answer: ………………………………………….. (Total 6 marks) 640. When the expression (2 + ax)10 is expanded, the coefficient of the term in x3 is 414 720. Find the value of a. Working: Answer: ………………………………………….. (Total 6 marks) 2 − 3 641. The points A and B have the position vectors and respectively. − 2 −1 (a) (i) Find the vector AB . (ii) Find AB . (4) 429 d The point D has position vector 23 (b) Find the vector AD in terms of d. (2) ˆ The angle BAD is 90°. (c) (i) Show that d = 7. (ii) Write down the position vector of the point D. (3) The quadrilateral ABCD is a rectangle. (d) Find the position vector of the point C. (4) (e) Find...
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This note was uploaded on 06/24/2013 for the course HISTORY exam taught by Professor Apple during the Fall '13 term at Berlin Brothersvalley Shs.

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