Test 1 Version 1 Answer.pdf - MATH 1M03 Test 1 — Version...

Info icon This preview shows pages 1–9. Sign up to view the full content.

View Full Document Right Arrow Icon
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
Image of page 3

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 4
Image of page 5

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 6
Image of page 7

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 8
Image of page 9
This is the end of the preview. Sign up to access the rest of the document.

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 + 76e-1-2t 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 :g-ng/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—3/1-21 ' (d) $10,000e-03 '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 ...
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern