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Mathematics

MATA32H3

Raymond Grinnell

Fall

Description

***** Sorry - Solutions will not be posted *****
FINAL EXAMINATION
MATA32 - Calculus for Management I
Examiners: R. Grinnell E. Moore Date: December 10, 2008
P. Grover Duration: 3 hours
Provide the following information:
Surname (PRINT):
Given Name(s) (PRINT):
Student Number :
Signature:
Read these instructions:
1. This examination has 13 numbered pages. It is your responsibility to ensure that at the
beginning of the exam, all of these pages are included.
2. If you need extra space for any question, use the back of a page or the blank page at the end
of the exam. Clearly indicate the location of your continuing work. You may write in pencil,
pen, or other ink.
3. You may use one standard hand-held calculator. All other electronic devices, extra paper,
notes, and textbooks are forbidden at your workspace.
Print letters for the Multiple Choice Questions in these boxes:
1 2 3 4 5 6 7 8 9 10 11 12
Do not write anything in the boxes below.
A 1 2 3 4 5 6 7 8 9 TOTAL
48 9 6 11 10 11 12 13 15 15 150
1 The following may be helpful:
" n # " ¡n #
n rt (1 + r) ¡ 1 1 ¡ (1 + r)
S = P(1 + r) S = Pe S = R r A = R r
Part A: Multiple Choice Questions For each of the following, clearly print the
letter of the answer you think is most correct in the boxes on the ﬂrst page. Each right
answer earns 4 points and no answer/wrong answers earn 0 points. No justiﬂcation is required.
2 2 0
1. If w > 0 is a constant and f(x) = ln(wx + w x + w) then f (1) is equal to
(a) 2 + w (b) 1 (c) 1 ¡ w (d) none of (a) - (c)
0 p
2. If y = 3 x ¡ 1 and y(1) = 2 then y(0) is equal to
(a) 0 (b) 7=3 (c) 1 (d) ¡3=2 (e) none of (a) - (d)
2
3. The area of the region lying between y = x and y = ¡2 where 0 • x • 3 is
(a) 21 (b) 33 (c) 18 (d) 24 (e) none of (a) - (d)
2 Z 3x
2e + 1
4. ex dx equals
(a) 2e2x¡ e + C (b) e2x+ e ¡x+ C (c) ex + e + C (d) ex ¡ e¡x + C
5. The fewest whole number of months it takes a principal to increase by exactly 79% at 5:3%
APR interest compounding continuously is
(a) 133 (b) 132 (c) 131 (d) none of (a) - (c)
Z 1
6. The exact value of 3x dx is
0 3x + 1
p ln(27)
(a) ln(3) (b) ln( 3) (c) ln(2) (d) (d) none of (a) - (d)
2
3 7. If g(x) = 2x + 6x 2 then
(a) g has an in°ection point at x = ¡1 (b) g has a relative minimum at x = 2
(c) g has a relative maximum at x = 2 (d) both (a) and (b) are true
(e) both (a) and (c) are true
2x
8. If y = (3x + e) then y (0) equals
(a) 0 (b) 2ln(3 + e) (c) 2 (d) none of (a) - (c)
9. The premium on an insurance policy is $500 per quarter payable at the start of each quarter.
If the policy holder wishes to pay two year’s premiums in advance, how much (rounded up to
the nearest dollar) should be paid provided that interest is 6% compounding quarterly ?
(a) $3;743 (b) $3;800 (c) $3;300 (d) $3;662
4 10. If f(x) = 3e ¡3x then for all n ‚ 1, f (n(0) equals
(a) (¡1) 3n+1 (b) (¡1)n+1 3+1 (c) ¡(3 n+1) (d) none of (a) - (c)
Z 1
11. If h(x) dx = + 3 then h (x) equals
2 ¡ x
1 2 2 1
(a) 2 ¡ x (b) ¡ (2 ¡ x) 3 (c) (2 ¡ x) 3 (d) ¡ (2 ¡ x)2 (e) none of (a) - (d)
12. Exactly how many of the following four mathematical statements are always true:
(i) The deﬂnite integral represents area under a curve or beneath a curve.
(ii) The deﬂnite integral is a function obtained by taking the limit of a special sum.
Z
(iii) The deﬂnite integral of a function g(x) is a function G(x) such that G(x) dx = g(x)
Z b
(iv) f(x) dx is deﬂned to be F(b) ¡ F(a) where F is any antiderivative of f
a
(a) 4 (b) 3 (c) 2 (d) 1 (e) 0
(Be sure you have printed the letters for your answers in the boxes on the ﬂrst page)
5 Part B: Full-Solution Questions

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