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Midterm

# Midterm 2 Nov 9th 2009.pdf

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Mathematics
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Mathematics 0110A/B
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Mathematics 0110A CODE 111 Friday, November 13, 2009 Test 2 Page 1 PART A - Multiple Choice (20 marks) Circle your answer in each question below and mark it on the (scantron) answer sheet. Code as you go. Extra time will NOT be given for coding answers at the end of the exam. Be advised that ONLY THE SCANTRON CARD WILL BE MARKED IN THIS SECTION, but only this question paper will be returned to you. 1 A1. Find f (2) where f(x) = 2 . mark x 1 1 A: −32 B: − C: 0 D: E: 1 2 2 √ 1 A2. Find f (1) where f(x) = x. mark A: − 1 B: − 1 C: 0 D: 1 E: 1 4 2 2 1 A3. Find f (0) where f(x) = (1 − x) . 4 mark A: −24 B: −12 C: −4 D: 12 E: 24 1 A4. Find f (x) where f(x) = (x + 1) 3 mark A: 6x(x + 1) 2 B: 12(x + 1) 2 2 2 C: 24x(x + 1) D: 6(x + 1)(5x + 1) E: 6(x + 1)(x + 4x + 1) 3 1 A5. The position of an object, in metres at any time t ≥ 0, is given by s(t) = t − 12t + 6. mark Find the acceleration at the instant the velocity is 0. A: −12 B: −6 C: 0 D: 6 E: 12 1 A6. Starting at t = 0, a particle moves along a line so that its position, in metres, after t mark seconds, is given by s(t) = t− 7t + 6. Find the velocity of the particle when its position is 14. A: 11 B: 9 C: 8 D: 7 E: 2 Mathematics 0110A CODE 111 Friday, November 13, 2009 Test 2 Page 2 dy 1 A7. Find where x − 5y = 4. mark dx x x 2x 2x A: − 5y B: 5y C: y D: − y E: none of A, B, C or D 1 A8. Find the slope of the tangent line to the curve x + 3y = 5 at the point (2,−1). mark 4 4 3 3 A: − 3 B: 3 C: − 4 D: 4 E: 0 1 A9. The top of a 5 metre ladder rests against a vertical wall. If the bottom of the ladder slides mark 1 away from the base of the wall at a rate 3fm/sec, how fast (in m/sec) is the top of the ladder sliding down the wall when it is 4 metres above the base of the wall? A: 3 B: 3 C: 1 D: 1 E: 1 4 5 3 4 5 1 A10. Which of the following is the equation of a vertical asymptote of f(x) =x ? mark x + 1 A: x = 1 B: y = −1 C: x = 2 D: x = −1 E: y = 2 2x 1 A11. Which of the following is the equation of a horizontal asymptote of f(x) = ? mark x + 1 A: x = 1 B: y = −1 C: x = 2 D: x = −1 E: y = 2 1 A12. Find the absolute minimum value of f(x) = x + 1 on the interval −1 ≤ x < 2. mark A: 5 B: 2 C: 1 D: 0 E: There is no absolute minimum value. 1 A13. Find the absolute maximum value of f(x) = x + 1 on the interval −1 ≤ x < 2. mark A: 5 B: 2 C: 1 D: 0 E: There is no absolute maximum value. 1 A14. Let y = f(x) be a function such that f (x) = 3(x−5)(4−x). Find all the critical numbers mark of f. A: 0,3,4,5 B: 3,4,5 C: 4,5 D: 0,4,5 E: f has no critical numbers Mathematics 0110A CODE 111 Friday, November 13, 2009 Test 2 Page 3 Use the following for questions A15 through A20.
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