Math_103_April_2009

Math_103_April_2009 - April 2009 Marks [24] 1. Mathematics...

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April 2009 Mathematics 103 Name Page 2 of 10 pages Marks [24] 1. Multiple Choice Questions: Select ONE correct answer (a, b, c, d, or e) for each question and write it in the table on the next page. You will not be graded for any work or answers outside those boxes. (Q1) Which of these integrals does the sum N X k =1 ± 3 N ² " ± - 2 + 3 k N ² 3 - 1 # approximate as N → ∞ ? (a) Z 3 0 x 3 dx (b) Z 1 - 2 ( x 3 - 1) dx (c) Z 3 0 ( x 3 - 2) dx (d) Z 1 - 2 x 3 dx (e) Z 1 0 ( x - 2) 3 dx (Q2) You are out Fshing. Every time you cast your line, the probability that you catch a Fsh is 1 / 4. What is the probability that you catch at least one Fsh within the Frst 2 attempts? (a) 1 / 16 (b) 7 / 16 (c) 1 / 2 (d) 9 / 16 (e) 15 / 16 (Q3) ±or which of these di²erential equations is y = 3 a steady state solution? (a) dy dt = 2 y - 6 (b) dy dt = y 2 + 9 (c) dy dt = 1 3 - y (d) dy dt = cos( πy ) (e) dy dt = 3 (Q4) A Math 103 class of 100 students took a test. The following graph shows how many students’ marks were in each of the intervals 1–10, 11–20, . . . , 91–100. 0 5 10 15 20 25 students 20 40 60 80 100 marks What was (approximately) the median? (a) 50 (b) 60 (c) 70 (d) 80 (e) 90 (Q5) A charged molecule moves in a changing electric Feld which results in an acceleration of a ( t ) = cos( t ) (in appropriate units). At time t = 0, the molecule is at rest at position x (0) = 1. What is the position x ( t ) when the molecule’s velocity reaches the value - 1 for the Frst time after time 0? (a) - 1 (b) 0 (c) 1 (d) 2 (e) The velocity never reaches - 1 Continued on page 3
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April 2009 Mathematics 103 Name Page 3 of 10 pages (Q6) Each mouse born with a certain genetic mutation has probability 0.7 of contracting a certain disease. Out of 10 mice born with the mutation, the probability that exactly 8 will contract the disease is (a) 45( . 7) 8 ( . 3)
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Math_103_April_2009 - April 2009 Marks [24] 1. Mathematics...

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