Math 101: Exam 2 Review Sheet

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1 Math 101: Exam 2 Review Sheet Exam Date, Time, Locations & Coverage Exam 2 will be given on Friday, November 20, from 8:00-8:50 a.m. You should arrive by 7:50 a.m. Use the following table to determine your correct exam location: Exam Room Instructors Sections Main Auditorium Falco, Odintsova, Wadke, Yang 1, 2, 3, 4, 12, 15, 18, 22, 23, 24, 26 PISB 120 Rickert 13, 14, 21 CAT 061 Gilman, Grinshpan 7, 10, 25 Stratton 113 Onderdonk, Wong 11, 19 Randell 121 Coppola, Patel 16, 20 Korman 249 Extra Time Accommodations Bring your AVL for the proctor. Math Resource Center The exam will cover the following topics: Chapter 10.3: Polynomial and Rational Functions Chapter 10.4: Exponential Functions Chapter 10.5: Logarithmic Functions Chapter 5.1: Simple and Compound Interest Chapter 5.2: Future Value of an Annuity Chapter 5.3: Present Value of an Annuity; Amortization The exam is closed book and closed notes. You may use a scientific calculator. No other calculators will be permitted. See the calculator policy on the course syllabus. You may not use scrap paper for the exam. All work should be written on the exam paper. A formula sheet containing financial math formulas will be provided on the exam. It is also on the last page of this review sheet as a reference. 1

2 Reminders & Advice Review the lecture notes, MyMathLab (MML) assignments, practice problems on the syllabus, quizzes, and the appropriate chapter contents from the textbook. Make sure that you get a good night s sleep before the test day. DON T CRAM OR PULL AN ALL-NIGHTER! If you miss the exam because you overslept, missed your train, etc. you will earn a 0 on the exam, and you will not be entitled to a makeup exam. See the makeup exam policy on the course syllabus. Arrive early to the exam location. If you arrive late then you get less time, not more time. Know where your exam location is. Visit the room a day or two before the exam so that you are not looking for it the morning of the exam. Bring a watch. Cell phones should be turned off and packed away before the exam begins. Bring your student ID card. It is recommended that you use a pencil instead of a pen, and to bring more than one with you. Cross out or erase any work that you do not want graded. As soon as you receive your exam, write your name and section number on the front page. Exams without names or section numbers will result in a loss of 5 points. Quickly skim through all of the problems on the exam before doing any one problem. Then do the problems that you think are easiest first. Pace yourself. Know when you should stop working on a problem and move on to another one. If you have the time, you should check your answers. (Just be sure to manage your time - see previous bullet point). It doesn t pay to leave 20 minutes early without checking your answers. A lot of silly mistakes can be avoided by going through your work again. 2

3 Practice Problems 1. Section 10.3 Exercises # For the following rational functions find: the domain, any holes, the vertical and horizontal asymptotes (if any), and the x and y intercepts (if any). Then graph the functions. a. b. c. 3. Solve each equation. a. 2 b c. 2 1 d. 1 e The projected Hispanic population (in millions) can be modeled by the exponential function , where t is the number of years since 2000 and is the projected Hispanic population. a. Find the projected Hispanic population for b. When will the population be double that of 2020? 5. Suppose the quantity (in grams) of a radioactive substance present at time t is given by , where t is measured in months. a. How much will be present in 6 months? b. How long will it take to reduce the substance to 8 grams? 6. Suppose that a population of bacteria in a petri dish is given by 2530., where t is the time in hours. a. What is the initial population of bacteria? b. When will the population reach 10,000?

4 7. Solve each equation. a b c. 5 d. log 64 6 e. log f. log 9 log 4 3 g. log2 log4 1 h. ln Simplify the following: a. log log10 b. ln ln 9. If log 2 and log 3, express the following in terms of x and y. a. log b. log 64 c. log Use the properties of logs to write as a sum, difference, or product of simpler logs: a. log b. log c. ln 11. Find the domain. a. ln2 7 b. log 82 c.

5 12. Amorie deposits $1,200 into an account earning 4.675% compounded weekly. a. What will her account balance be in 14 weeks? b. How long will it take for her account balance to grow to $5,000? 13. Ashley lends $500 to a friend for 8 months. What simple interest rate should she charge if she wants to be paid back a total of $535? 14. Geoff Jordan wants to have $32,000 in 5 years in order to purchase a car. a. How much should he deposit today, in an account earning 6.4% compounded quarterly, to have the required amount in 5 years? b. How much interest will be earned? c. If he can deposit only $16,000 now, how short of $32,000 will he be in 5 years? d. Suppose that he can deposit $16,000 now in an account that pays interest continuously. What interest rate would be needed to accumulate the entire $32,000 in 5 years? e. Suppose that instead of making one deposit, he wishes to make deposits at the end of each quarter into an account earning 6.4% compounded quarterly. How much should his quarterly deposit be so that he will have the entire $32,000 in 5 years? 15. Tami bought a television with money borrowed from the bank at 9% interest compounded semiannually. What effective interest rate did she pay? 16. The Fisher family bought a house for $191,000. They paid $40,000 down and took out a 15-year mortgage for the balance at 5.25% interest compounded monthly. a. What is their monthly payment? b. After paying the loan off over 15 years, how much interest did the Fisher family pay? 17. An accountant loans $28,000 to a small business. The loan is charged 6.5% simple interest which results in a total interest charge of $1,365. Find the length of the loan. 18. If $4,000 is deposited at the end of each quarter for 7 years into a bank account that earns 5% interest compounded quarterly, how much money is in the account at the end of 7 years? 19. Find the interest earned on $10,000 invested for 5 years at 4% interest compounded continuously. 20. How long will it take to double your money if you earn 5% compounded continuously? 21. After making a down payment of $15,000 for a house, a couple paid $1, per month for 30 years with interest charged at a rate of 6% compounded monthly on the unpaid balance. a. What was the original cost of the house? b. How much of the total house payments went towards interest?

6 Answers 1. Section 10.3: 7) D 8) C 9) E 10) B 11) I 12) F 13) G 14) H 15) A 2. a. Domain =, 3 3,, no holes, vertical asymptote: 3, horizontal asymptote: 1, x intercept at 4, y intercept at b. Domain =, 4 4,, no holes, vertical asymptote: 4, horizontal asymptote: 0, no x intercept, y intercept at 1 c. Domain =, 4 4,, hole at 4, no vertical or horizontal asymptotes, x intercept at 1, y intercept at 1

7 3. (a) x = 5 (b) y = 6 (c) x = 1, x = 1 (d) x = 0 (e) x = (a) 57, 265, 326 (b) In the year (a) grams (b) 10 months 6. (a) 2530 (b) 5.73 hours 7. (a) p = (b) x = (c) x = (d) k = 2 (e) x = 119 (f) x = 23 7 (g) p = 1 (h) x = (a) 3 log x (b) ln x 3 9. (a) 4x 2y 3 (b) 6x + 4 (c) 4x + 3y 10. (a) 1 log 3 4 log x 2 (b) 2 + log 4 y 2 log 4 z (c) 3 2 ln x ln y 11. (a) x > 7 2 (b) x < 4 (c) All real numbers 3

8 12. (a) $ (b) years % 14. (a) $23, (b) $ (c) $10, short (d) 13.86% (e) $ % 16. (a) $ (b) $67, years (or 9 months) 18. $133, $ years 21. (a) $276, (b) $303,

9 Potentially Useful Formulas: 1) 2) 1 or or 3) 1 or 1 4) 5a) 1 1 5b) 1 6) or 7) or 8) or 9) or

Page Points Score Total: 100

Page Points Score Total: 100 Math 1130 Spring 2019 Sample Midterm 2b 2/28/19 Name (Print): Username.#: Lecturer: Rec. Instructor: Rec. Time: This exam contains 10 pages (including this cover page) and 9 problems. Check to see if any