Download Math 120 Midterm Two Study Guide - Spring 2009 - Prof. Denise J. Hum and more Exams Algebra in PDF only on Docsity!
Spring2009 Math 120
Study Guide for Midterm Two
The midterm is 85 minutes long and will be given on Wednesday, April 1, 2009 at the beginning of class. Please arrive early so that we can start on time. The test will cover 10.4 โ 10.6, 11.2, and all of chapter 12. To study for this test, go through your homework, previous quizzes, class handouts, and class examples. The test is closed book and closed notes. You will need your calculator for the test. Please seek help in the Math Lab and Learning Center early and frequently.
Be familiar with the instructions specified in the textbook exercises and class handouts. The wording on the test will be similar. It is important to not just know how to do a problem, but to understand what exactly the problem is asking you to do.
Any use of other electronic devices such as cell phones and mp3 players will result in a 0 on the exam.
1. Perform the indicated operation. Simplify if possible.
a) 2 3 3 ๐^4 โ 3 ๐ 381 ๐ b) 48 4 5 ๐ฅ โ^
2 43 10 ๐ฅ
c) ( 3 ๐ฅ โ 2 )^2
2. A wire is to be attached to support a telephone pole. Because of surrounding buildings, sidewalks, and roadways, the wire must be anchored exactly 15 feet from the base of the pole. Telephone company workers
have only 30 feet of cable, and 2 feet of that must be used to attach the cable to the pole and to the stake on the ground. How high from the base of the pole can the wire be attached?
a) In your own words, what is the problem asking you to do? b) Draw a picture of the problem and point to what exactly you are trying to find. c) Translate the problem into math. d) Solve the problem. e) Answer the question in a complete sentence.
3. Solve. a) 8 ๐ฅ^2 โ 2 ๐ฅ = (^7) b) 1 3 ๐ฅ
6 =^0
c) 5 ๐ฅ^2 โ 3 = 14 ๐ฅ
4. Circle the following functions are one to one.
f = {( 6, 0), ( 0, 1), ( - 2, 2), ( - 4, 0)}
f = {( 4, 7), ( - 7, - 4), ( 6, 2), ( - 6, - 2)}
5. Find the inverse of each function.
f ( x )๏ฝ 3 x ๏ซ 1
x
f x
f ( x )๏ฝ 5 x ๏ซ 2
6. If ๐(๐) = ๐๐ + ๐, show that ๐โ๐^ ๐ = ๐ฑ+๐ ๐
Spring2009 Math 120
7. Find the equation for each table. a) x 0 1 2 3 ๐(๐ฅ) 4 2 1 0.
b) x 0 1 2 3 ๐(๐ฅ) 5 7 9 11
8. Write the following expressions in equivalent exponential or logarithmic form. (Fill in the blanks). Exponential form
53 = 125
Logarithmic Form
_______________________________
_______________________________ ln 3 = x
9. Write the expressions as sums or differences of multiples of logarithms.
log 7 9 ๐ฅ 2 ๐ฆ
log 6 5 ๐ฆ ๐ง^2 logb 3 ๐ฆ
10. Solve each equation for x. Give an exact solution and a four-decimal place approximation.
3 2x + 1^ = 6 log 4 10 - log 4 x = 2 ln 3 + ln (x โ 1) = 0
11. Use log rules and/or your calculator to find the four decimal approximations of the following logs.
a) log 5 2 3
b) ln 104.
12. The compound interest formula is A = ๐ท ๐ + ๐ ๐
๐๐ where n represents the number of times interest is
compounded each year, P is the initial deposit, r is the annual interest rate, t is the number of years, and A is the amount accrued. a) Clearly define your variables. b) How long will it take a $1000 investment to earn $150 in interest if it is invested in an account that pays 9% interest compounded quarterly? c) If you deposit $500 into an account that pays 6% interest compounded monthly, how much money will you have in 7 years? Write your answer in a complete sentence.
13. Retail revenue from shopping on the internet is currently growing at a rate of 56% per year. In 2000, a total of $42.1 billion in revenue was collected through internet retail sales. Answer the following questions using ๐ = ๐๐. ๐(๐. ๐๐)๐^ where ๐ is internet revenue in billions of dollars and ๐ is the number of years after 2000. Round answers to the nearest tenth of a billion dollars. Write your answers in complete sentences.
a) Clearly define your variables. b) According to the model, what were the retail revenues from internet shopping in 2001? c) What will the internet shopping revenues be in 2010? d) When will the internet shopping revenues be $100 billion?
