A the binary operation is defined on the set of real

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Unformatted text preview: P(1, p), where p > 0, lies on the curve 2x2y + 3y2 = 16. (a) Calculate the value of p. (b) Calculate the gradient of the tangent to the curve at P. Working: Answers: (a) ………………………………………….. (b) ………………………………………….. (Total 6 marks) 440 655. The line r = i + k + µ(i – j + 2k) and the plane 2x – y + z + 2 = 0 intersect at the point P. Find the coordinates of P. Working: Answer: ………………………………………….. (Total 6 marks) 656. Let f(x) = (a) k , x ≠ k, k > 0 x−k On the diagram below, sketch the graph of f. Label clearly any points of intersection with the axes, and any asymptotes. y k x 441 (b) On the diagram below, sketch the graph of 1 . Label clearly any points of intersection f with the axes. y k x Working: (Total 6 marks) 442 657. The function f is defined by f : x a x3. Find an expression for g(x) in terms of x in each of the following cases (a) ( f ° g ) ( x ) = x + 1; (b) ( g ° f ) ( x ) = x + 1. Working: Answers: (a) ………………………………………….. (b) ………………………………………….. (Total 6 marks) 658. (a) Find ∫ m 0 dx , giving your answer in terms of m. 2x + 3 443 (b) Given that ∫ m 0 dx = 1, calculate the value of m. 2x + 3 Working: Answers: (a) ………………………………………….. (b) ………………………………………….. (Total 6 marks) 659. The discrete random variable X has the following probability distribution. k , x = 1, 2, 3, 4 P(X = x) = x 0, otherwise 444 Calculate (a) the value of the constant k; (b) E(X). Working: Answers: (a) ………………………………………….. (b) ………………………………………….. (Total 6 marks) 660. Robert travels to work by train every weekday from Monday to Friday. The probability that he catches the 08.00 train on Monday is 0.66. The probability that he catches the 08.00 train on any other weekday is 0.75. A weekday is chosen at random. (a) Find the probability that he catches the train on that day. 445 (b) Given that he catches the 08.00 train on that day, find the probability that the chosen day is Monday. Working: Answers: (a) ………………………………………….. (b) ………………………………………….. (Total 6 marks) 661. Solve the inequality x+9 ≤2 x−9 Working: Answer: …………………………………………........ (Total 6 marks) 446 662. The function f is defined by f : x a 3x. Find the solution of the equation f″(x) = 2. Working: Answer: …………………………………………........ (Total 6 marks) 663. Find ∫ lnx dx . x Working: Answer: …………………………………………........ (Total 6 marks) 447 664. The following diagram shows an isosceles triangle ABC with AB = 10 cm and AC = BC. The vertex C is moving in a direction perpendicular to (AB) with speed 2 cm per second. C A B Calculate the rate of increase of the angle CAB at the moment...
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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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