Math 1M03 Sample Test #1 (Version X)

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1 Math M0 Sample Test # (Version X) Name: (Last Name) (First Name) Student Number: This test consists of 0 multiple choice questions worth mark each (no part marks), and question worth mark (no part marks) on proper computer card filling. All questions must be answered on the COMPUTER CARD with an HB PENCIL. Marks will not be deducted for wrong answers (i.e., there is no penalty for guessing). You are responsible for ensuring that your copy of the test is complete. Bring any discrepancy to the attention of the invigilator. Only the McMaster standard calculator Casio f-99 is allowed.. Find the value of a if (. / ) / = a Find all real values of that satisfy the following equation. 0 ( ) =, -0-6,., -6 -, 0 -, 6 Find the values of C and a so that the curve C=, a= C=, a= y=c C=, a= contains the points (,) and (a,6). C=, a= C=, a=. Suppose that $000 is invested at an annual rate of 7%. Compute the balance after years if the interest is compounded quarterly. $6. $676.7 $69. $6.0 $60.. How much money should be invested at 6% to obtain $0000 in years if interest is compounded continuously? $.9 $0.7 $. $09.96 $06.70

2 6. Use the laws of logarithms to epand and simplify the following epression ln( + ) ( ) ln ln +ln ( +) ln ( ) ln (+) ln ln ( ) 7. ln ln +ln Solve the following equation for. 7 e9 = e ln 7. ln 7 9 ln 9 ln 9 7 Solve the following equation for ln ln( ln 9 )=ln 9. Suppose that you invest $000 at an annual interest rate of % compounded continuously. How long will it take (in years) for your money to triple? A hot drink is taken outside on a cold winter day when the air temperature is -0 C. According to a principle of physics called Newton's Law of Cooling, the temperature T (in degrees Celsius) of the drink t minutes after being taken outside is given by T (t )= 0+ Ae kt,where A and k are constants. Suppose that the temperature of the drink is 9 C when it is taken outside, and that 0 minutes later the drink is 6 C. When (i.e., after how many minutes) will the temperature reach 0 C?

3 . Find f ' (t) if f (t)= ( t +)e t (t +). Find e t e t t + t (t+)e t e t (t+) tet (t +) e t (t +) f ' () if f ()=ln (7 ) Find the second derivative of h()=( +)e ( + +)e. ( + +)e e ( )e Find the largest interval(s) on which is increasing. (, ),(, ) (, ) (, ),(, ) (, ) Find the equation of the line that is tangent to the graph of the function f ()=ln ( +) at the point (0, ln ). 6. ( +) e Let f ()=e. y= +ln y= +ln y= +ln y= +ln Find the smallest value (i.e., absolute minimum) of the function f ()= ln y= +ln (, )

4 on the interval. e 7. Evaluate the following integral, e 0 ( +)0 d 0 ( +)+C ( +) +C ( +) +C 0( +)9 +C. ( + ) +C Evaluate the following integral. ( + ) d ( )+C + ln +C ( + ln )+C + ln +C 9. +C Suppose that the slope at each point (,y) on the curve f ' ( )= y=f () is given by ln and that the function passes through the point (,). Find f(). (ln ) + (ln ) + ln + ln (ln )+ 0. Solve the following initial value problem where y= when + dy = d =. ln ln ln e ln +

5 . Correctly fill out the bubbles corresponding to your student number and the version number of your test in the correct places on the computer card. (Use the below computer card for this sample test.)

6 Answers for Sample Test #. b. d. a. c. e 6. b 7. c. e 9. b 0. e. a. c. b. e. e 6. c 7. a. b 9. b 0. c. NOTE: On the sample tests, a version number is not given. On the actual tests, it will say "Version X" at the top, where X is the version number that you will have to fill in on the computer card. The sample answer above assumes that the test says "Version " at the top. On the actual test you will have to fill in the bubble corresponding to the version number of YOUR test (which may or may not be Version ). The sample below also assumes that your student number is 6. On the actual test, you will have to fill in the bubbles corresponding to YOUR student number (not 6). Please also check the website for instructions.

Math 1M03 (Version 1) Sample Exam

Math 1M03 (Version 1) Sample Exam Name: (Last Name) (First Name) Student Number: Day Class Duration: 3 Hours Maximum Mark: 40 McMaster University Sample Final Examination This examination paper consists