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Mathematics

MATH 102

Martial Agueh

Winter

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UNIVERSITY OF VICTORIA
SAMPLE EXAMINATION
MATHEMATICS 102
THIS QUESTION PAPER HAS 5 PAGES PLUS COVER. Duration:3hus
Instructions:
• Fill in your name and student number in the spaces provided. Please print, and put your
family name ﬁrst.
• Sign the blue cover sheet at the back of the exam.
• The ONLY acceptable calculator is the SHARP EL-510R (B).
• No electronic devices other than your calculator are permitted.
• No paper material other than your test paper and bubble sheet are permitted.
There are 30 multiple choice questions worth 2 marks each, for a total of 60 marks, and 3 long-answer
questions worth a total of 12 marks.
Section A: Multiple Choice
• On the green computer sheet print and code your family name and student number.
• Use an HB or softer pencil to enter your answers.
• For questions requiring numerical answers choose the value closest to your unrounded an-
swer. If your unrounded answer is equidistant from two choices, choose the larger of the two
choices.
• Do your work in the space provided. For veriﬁcation purposes show all calculations. Unveriﬁed
answers may be disallowed. If extra space is needed use the backs of the pages.
Section B: Full Answer
• For each of these questions write your answers fully and clearly on the question paper. Marks
will be deducted for incomplete or poorly presented solutions.
• If you need to use the back of a page, make sure that this is clearly marked.
At the end of the examination put your green computer sheet inside your question paper and turn
it in to the correct box for your section, version and family name initial. Mathematics 102 Sample Examination Page 1
Section A: Multiple Choice
−2x +4 x
1. Evaluate lim .
x→2 x − 2
(A) −4B( −)C( −si(tose)−0((
(−2+ ▯x) 2 − 4
2. Evaluate lim .
▯x→0 ▯x
(A) −4B( −)C( −si(tose)−0((
60x2 +5 x
3. Let P (x)= 2 . Find x→∞ P (x).
3x +2
(A) 0 (B) 5 (C) 10 (D) 15 (E) 20 (F) 25 (G) 30 (H) 35 (I) 40 (J) does not exist
2 6
4. Find an equation of the tangent line to the curve y =( x 15) at the point where x =4 .
(A) y =8 x − 31 (B) y =6 x − 25 (C) y =48 x (D) 6y = x
2 5
(E) y =48 x − 191 (F) y =6 x − 23 (G) y = 12(x − 15) x (H) y =8 x − 33
(I) y =48 x + 193 (J) none of the above
x − x − 6
5. Let f (x)= 2 . Which of the following statements are true?
x − 4x +3
(i) f(x) has a removable discontinuity at x =3.
(ii) f(x) is not continuous at x =3.
(iii) f(x) has a removable discontinuity at x =1.
(A) None (B) (i) only (C) (ii) only (D) (iii) only
(E) (i) and (ii)(F) (ii) and (iii)(G) (i) and (iii)(H) All
6. Find the positivevalue ofx for which the graph of f (x)=2 x − 3x − 12x + 5 has a tangent
line that is horizontal.
(A) 1 (B) 2 (C) 3 (D) 4 (E) 5 (F) 6 (G) 7 (H) 8 (I) 9
(J) no such value exists
7. Given that the distance s(t)atyte t> 0ii y s(t)= tln(t) − t, ﬁnd the
acceleration s (t).
2 3
(A) ln(l4(t)) (1) ln(t)( /t (D) −1/t (E) 2/t
(F) −6/t (G) −ln(t)H( −ln(ln(t)) (I) −1/t (J) none of the above
.../ 2 Mathematics 102 Sample Examination Page 2
8. The proﬁt function for a particular company is P(x)= −0.01x + 2000x − 5000, where x is
the number of items produced and sold. Estimate the change in proﬁt corresponding to an
increase of sales of one item when x = 260.
(A) −38 (B) −28 (C) −18 2 (D4))GF((
9. Find the exact interval on which the graph of f (x)= x − 6x + 1 is concave down for every
x in the interval.
1 1 1 1
(A) −5

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