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Unformatted text preview: ange of f ° g. Working: Answers: (a) ………………………………………….. (b) .................................................................. (Total 6 marks) 324 479. Consider the six numbers, 2, 3, 6, 9, a and b. The mean of the numbers is 6 and the variance is 10. Find the value of a and of b, if a < b. Working: Answers: ………………………………………….. ………………………………………….. (Total 6 marks) 480. Solve the inequality x2 – 4 + 3 < 0. x Working: Answers: ………………………………………….. ………………………………………….. (Total 6 marks) 325 481. Find an equation for the line of intersection of the following two planes. x + 2y – 3z = 2 2x + 3y – 5z = 3 Working: Answer: ………………………………………….. (Total 6 marks) 482. A particle moves in a straight line with velocity, in metres per second, at time t seconds, given by v(t) = 6t2 – 6t, t ≥ 0 Calculate the total distance travelled by the particle in the first two seconds of motion. Working: Answer: ………………………………………….. (Total 6 marks) 326 ˆ 483. Triangle ABC has AB = 8 cm, BC = 6 cm and BAC = 20°. Find the smallest possible area of ∆ABC. Working: Answer: ………………………………………….. (Total 6 marks) 484. Find ∫ (θ cos θ – θ )dθ. Working: Answer: ………………………………………….. (Total 6 marks) 327 485. Find the x-coordinate of the point of inflexion on the graph of y = xex, – 3 ≤ x ≤ 1. Working: Answer: ………………………………………….. (Total 6 marks) 486. The probability density function f(x), of a continuous random variable X is defined by 1 x(4 – x 2 ), 0 ≤ x ≤ 2 f ( x) = 4 0, otherwise. Calculate the median value of X. Working: Answer: ………………………………………….. (Total 6 marks) 328 487. Air is pumped into a spherical ball which expands at a rate of 8 cm3 per second (8 cm3 s–1). Find the exact rate of increase of the radius of the ball when the radius is 2 cm. Working: Answer: ………………………………………….. (Total 6 marks) 488. The point B(a, b) is on the curve f(x) = x2 such that B is the point which is closest to A(6, 0). Calculate the value of a. Working: Answer: ………………………………………….. (Total 6 marks) 329 489. Given two non-zero vectors a and b such that a + b = a – b, find the value of a ⋅ b. Working: Answer: ………………………………………….. (Total 6 marks) 490. The tangent to the curve y = f(x) at the point P(x, y) meets the x-axis at Q (x – 1, 0). The curve meets the y-axis at R(0, 2). Find the equation of the curve. Working: Answer: ………………………………………….. (Total 6 marks) 491. A sequence {un} is defined by u0 = 1, u1 = 2, un+1 = 3un – 2un–1 where n ∈ (a) + . Find u2,u3,u4. (3) 330 (b) (i) Express un in terms of n. (ii) Ve...
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