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Unformatted text preview: MATH 1M03: Test 1 — Version 1
Instructors: .Ievtic7 Lozinski, Wang, Wilson
Date: January 30, 2017  Group A
Duration: 75 min. Name: n; WWW/3‘ ID #: Instructions: This test paper contains 15 multiple choice questions printed on both sides of the page.
The questions are on pages 2 through 9. YOU ARE RESPONSIBLE FOR ENSURING
THAT YOUR COPY OF THE PAPER IS COMPLETE. BRING ANY DISCREAPAN—
CIES TO THE ATTENTION OF THE INVIGILATOR. Select the one correct answer to each question and ENTER THAT ANSWER INTO THE SCAN CARD PROVIDED USING AN HB PENCIL. Room for rough work has
been provided in this question booklet. You are required to submit this booklet along with your answer sheet. HOWEVER, N O MARKS WILL BE GIVEN FOR THE WORK
IN THIS BOOKLET. Only the answers on the scan card count for credit. Each ques
tion is worth 1 mark; the test is graded out of 15. There is no penalty for incorrect answers. Only the McMaster standard calculator, the Casio fX 991, is permitted. Computer Card Instructions: IT IS YOUR RESPONSIBILITY TO ENSURE THAT THE ANSWER SHEET
IS PROPERLY COMPLETED. YOUR TEST RESULTS DEPEND UPON
PROPER ATTENTION TO THESE INSTRUCTIONS. The scanner that will read the answer sheets senses areas by their non—reﬂection of light.
A heavy mark must be made, completely ﬁlling the circular bubble7 with an HB pen—
cil. Marks made with a pen or felt—tip marker will NOT be sensed. Erasures must be
thorough or the scanner may still sense a mark. Do NOT use correction ﬂuid. 0 Print your name, student number, course name7 and the date in the space provided
at the top of Side 1 (red side) of the form. Then the sheet MUST be signed in
the space marked SIGNATURE. a Mark your student number in the space provided on the sheet on Side 1 and ﬁll
the corresponding bubbles underneath. 0 Mark only ONE choice (A, B, C, D, E) for each question. 0 Begin answering questions using the ﬁrst set of bubbles, marked “1”. McMaster University Matth03 Winter 2017 Page 1 of 10 McMaster University MatthOB Winter 2017 Page 2 0f 10
3': 1. Expand 1n 1/324 (a)xln2—y1ne—zln4 Zyl , Ag; “/4757 (b) 21nm—31ny—41n2
(c) 21nm+3lny+4lnz : 2 )2” J glg) _ ”(A 2 (d) In 2:13 + 1n 3y +1n4z (e) 2111(256 — 3y — 42) 2. Find a: where 63 26
(a) 6 L
(b) 1/2 25,4 1/1, X2 x
(c) 3 3,3,...“ 3“— L/ Q “1" 3:3”
(d) 1/4 23 (g3 26’: 2 3 2142—1 2‘ Z > 3
:7 2¥*§:Y
j) ‘K 78/ McMaster University Math1M03 Winter 2017 Page 2 of 10 McMaster University MatthOB Winter 2017 Page 3 of 10 l
3. Which of the following is equal to 10g10 4 + 10g10 a — 31031001 + 1)? (a) Iogm (4a — gm +1)) (b)1n40+1na;1§1n(10a+10) J 1/3310 1/
10a 0 M 3
(c) 1% 3a + 1 i 3 , 4a
id) 10g10 ’3' 4a
a+l (e) 10810 3 4. Find a: Where 1n(3:c — 10) = 2 + a 2
(a)310~2—a :7 3y40 :8 (b) 2e+ea+10/3 2 q
(020/3 EY’QO 7"”5 (d) (€26“+10)/3
X ,(€1&Oi(O)/} (e) (1112 +1na+ 10)/3 McMaster University Matth03 Winter 2017 Page 3 of 10 McMaster University Matth03 Winter 2017 Page 4 of 10 5. When a camera ﬂash goes off, the batteries immediately begin to recharge the ﬂash’s
capacitor, which stores electric charge. The charge is Q(t) Where Q(t) = Q0(1 — 64/2) (the maximum charge capacity is Q0 and t is measured in seconds). How long does
it take to recharge the capacitor to 90% of its maximum capacity? a W W or 16 am (a) ~21n<01) M (b)—21n<0. 9) QM): Q0 (I \ C700 (C) e~0.1 “ é/‘L (d) 2 I ve —, Y ‘i 6/ (e) 60'9 ~ 2
ol 2 Q 6. Which of the following statements are true?
I) 7T‘/5 = 6/5”” II) If :17 > 07 then (11151:)6 = Glnzc.
III) Ifa > 0 and b > 0 then ln(a+b) = lna+lnb (9)104“) e (b
((9111 0:) a 9M writ # (MW m5; )II
)
d) IandII A f. /
(e)allofthem 017) [ma tij 3 M04) 2; A/oté) ”49265. <9 W 1 gala McMaster University Math1M03 Winter 2017 Page 4 of 10 McMaster University Math1M03 Winter 2017 Page 5 of 10 7. Find the ﬁrst derivative of the function f (:6) = V111; C Lam [oval 1 / >p/7 (a) m) = — 3L” 12(ﬂ 2:1: 1nl l  1 1 1X0?“ (y) jﬂ[i
(b) f/(x) ’ mm;
(c) f’(m) — —ﬁin§; : /, J,” T/L. g: i) aja q
(d) f’(w) — 296;; 2 Mt) C V)
(e) f’(w) = 3 5 1 X «I 8. What is the slope of the tangent line to the function f (as) = ln(me“”2) at the point
(1, —1)? (
(c) 8 q
(d) 26 2 : e~v (l‘QXZ) : /_ 2%;
(e) 111(2) 7" ”>7
I,
t/[q : :39 / ~/ McMaster University Matth03 Winter 2017 Page 5 of 10 McMaster University Math1M03 Winter 2017 Page 6 of 10 9. Consider the graph of the function y = f (as) If the ﬁrst derivative of y is given by
y’ = ln(ar2 —— 6x + 10), Where does the graph of y have a point of inﬂection? (a)m=6 97m“; 0'; I/VPQUPIAlu/w WM J”; O (b) 3:20
(C) 9:: 2 31/; ”I L [ﬂaw/0)
(d) as=~1 M
(6) 23:3 : “L5 (erc>
\(1'024/0
SEMI? 717m dﬁwwmalar ca» NW €20.05}, 0 ) C ’O
{1‘9 Dab {Joint 01E mlmgjr ,3 UZUA “9 NOW lK’XIC'j 10. Public health records indicate that 16 weeks after the outbreak of inﬂuenza 80
Q“) _ 4 + 76e12t Where Q(t) is the number of people (in thousands) that had caught the disease. For
What values of t is Q(t) decreasing? (a) t>00n1y &/ 3 0f 80 (b) t>1n4 only it , 5%.”?
(c) t < 1114 only ((1) t > 2 only I __ 80 (e) it is never decreasing I / 000 (2/9) IS Vie/UM OeQCfcaSp’c
McMaster University Math1M03 Winter 2017 Page 6 of 10 McMaster University MatthOS Winter 2017 Page 7 of 10 11. Which of the following is o_ne of the antiderivatives of the function f given by f(as) = mun/i? (b) 2%;2a9/24—x/?m+2 y
(c) §(2m+7)3/2+5 : (QLL 4, Ex + <—
(d) 33+)?“ 3/1
(QEJQ—‘M/ﬂ :gng/7+ tY‘LC 3
[,0le C L3 0/3 WEIMI‘J CWS’LEM(
3Q _,, want/gm 12. Find the function f (x) satisfying the differential equation df 2 1
8225—? 95>” whose graph pass through the given point (1, ~1).
2 l
(a)§1nx+—g;§—3 “Ff j i ”i? ”205
(b) 111m2+216~~2 V y ,[
(0)1n$2+;1§~—2 : Qﬂmy ? X 4C“
(d) i2 + l — 3 ”I
”3 ”3 / + f C,
(e) lnm + 111(272) — 1 / 2 Mi :2 4
} _ _~
QMCQ £{¢\:~l 1% tytc”!
@ ' C:JZ
McMaster University MatthOB Winter 2017 Page 7 of 10 CM): ZLY +JQ~Z fins/‘4‘} 27/ X McMaster University Math1M03 Winter 2017 Page 8 of 10 13. An amount P is invested and earns a continuously compounding rate.
After 3 years, the investment is worth $10,000.
After 5 years, the investment is worth $12,100. What was P? 3 3r _
(a) $10,000 (§) PC  [0,000 EN '7 Owe I .
(b)$6,850 (Pg F:12,[00 47 ﬁve“
(a) $10,0006—3/121 '
(d) $10,000e03 '95:: $4 6% : @539 _: LU
(e) $10,000(1 ~1n1.21) pear page zoo
r_ [I Talon Siaxre {034’ C ’ * Br «Br (I
(‘40: 105 S 10,000 "P: IO,Q’)OG r lo,ooo (73) 14. An investment earns an annually compounding rate of r for 5 years (that is, com—
pounded once per year). At the end of the 5 years, the resulting amount then earns
a new rate of 27" per year, which is then compounded twice a year for two more
years. If, at the end of this 7 year process, the investment has exactly doubled in
value, what is 7"? 7 y ’2. 5/ _
(a)(1+2/7)1/7—1 :0 (”ﬂ (”2%) /2 __?_._. _ , (4 
(b)(1+1/2)2 L)+f\> (Hr) ’ 2
(C) 21/9“ 1 7 : ’2
(d) (low/7 ( ”A [/7
(e) (10g2)/5—1 [W p Z McMaster University Math1M03 Winter 2017 Page 8 of 10 McMaster University Math1M03 Winter 2017 Page 9 of 10 15. Find an antiderivative of the function f given by f(x) = (x3 — 2x2) (1 — 5) CE ( )
w m: (mew) (b) —a; —21n(a:)—2:c2
4 Z
’2 , 3440K
(0) ~§$3——21n(m)+m2 j X FQK _ b k
(d) —§x4—%x3—2x2 Z /) y1'2¥~ 3')“;
3 4 7 3 2
(e) ~11: 3:1: 2:I: : //><3 ’21; "315/ #C
2 2 ‘2’ END OF TEST QUESTIONS McMaster University Math1MO3 Winter 2017 Page 9 of 10 ...
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 Math, 1M03

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