Test 1 (Fall 2007) - Mathematics - Ryerson University

Ryerson University
Department of Mathematics
Test One-V 1
October 4, 2007
MTH131
Modern Mathematics
NAME (print):
(Family)
(Given)
SIGNATURE:
SECTION NUMBER:
INSTRUCTORS: K. Lan (Sections 1-4) B. Tasic (Sections 5-8)
Instructions:
1. You have 1 hour for this test.
2. This test contains two parts: Part I is multiple-choice (Questions 1-6) and Part II is
full-answer (Questions 7-10)
3. This test has a total of 50 marks (4 marks as bonus)
4. Only answers to multiple-choice questions on the bubble sheet will be given credit
5. You are not allowed to use any AIDS including calculators, formula sheets and cell
phones.
6. Show all of your work in Part II. Only one solution for each question is allowed.
7. Pages 7 and 8 could be used for rough work.

MTH131
Test One
Page 1
October 4, 2007
Instructors use only
Marks
Part I Page 3 Page 4 Page 5 Page 6 Total
Before you start, please provide the following information:
Last Name (print): −−−−−−−−−−−−−−−−− Student No: −−−−−−−−−−−− Section No. −−−−
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MTH131
Test One
Page 2
October 4, 2007
Part I Multiple Choice
For each of the following clearly mark the box corresponding to the correct answer and enter
your answer of each question to the bubble sheet. Only answers to multiple-choice questions on
the bubble sheet will be given credit.
1. (4 marks) Which version of the test do you have (Hint: See the front page).
(a) V 1 (b) V 2 (c) V 3
a b c
2. (4 marks) cos 11π equals
6
a) 1 b) −1
√
3
c)
2 2
2
a b c d e
d) −√ 3
2
e) None of these.
3. (4 marks) The center and the radius of the circle given by the equation x 2 + y 2 +
2x − 4y + 1 = 0 are
a) center (−1, 2), radius r = 2 b) center (1, −2), radius r = 2
c) center (−1, −2), radius r = 1 d) center (1, 2), radius r = 1 e) None of these.
a b c d e
4. (4 marks) Solutions of the equation 2 x2 −5x = 1 64 are
a) x = 1 or x = 2. b) x = 1 or x = −2 c) x = 3 or x = 2
d) x = −3 or x = −2 e) None of these.
a b c d e
5. (4 marks) Let k be a positive integer. ( 3 −2k+3
3 4+k 3 −2k ) 3
equals
a) 1
3 k b)
1
3 k+1 c)
1
3 k−1 d) 3 k−1 (e) None of these
a b c d e
6. (4 marks) Let ⃗a =
⎛
⎜
⎝
x
x
−1
⎞
⎛
⎟
⎠ and ⃗ b = ⎜
⎝
x
−3
−2
⎞
⎟
⎠ . Find all x ∈ R such that ⃗a · ⃗b = 0.
a) x = 1 or x = 2. b) x = 1 or x = −2 c) x = −1 or x = 2
d) x = −1 or x = −2 (e) None of these
a b c d e
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MTH131
Part II Full Answer
Test One
Page 3
October 4, 2007
7. (7 marks) Solve the equation |2x − 4| = 6.
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MTH131
Test One
8. (8 marks) Determine if the vector ⃗a =
⎛
⎞
⃗a 1 = ⎝ 1 ⎠ and ⃗a 2 =
2
⎛
⎝ −2
1
⎞
⎠.
⎛
⎝ 7
−1
⎞
Page 4
October 4, 2007
⎠ is a linear combination of vectors
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MTH131
Test One
Page 5
October 4, 2007
9. (8 marks) Determine the equation of the line passing through (−1, −1) and parallel
to the line passing through (0, 1) and (3, 0).
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MTH131
Test One
Page 6
October 4, 2007
10. (7 marks) Let f(x) = x 2 − 1 and g(x) = 1 . Find (g ◦ f)(x) and its domain.
x−3
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MTH131
Rough work
Test One
Page 7
October 4, 2007
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MTH131
Rough work
Test One
Page 8
October 4, 2007