Math 103: Quiz One Name:____________________ Location: Al Jaber Instructor: Alfredo Bonilla 1. Find the value: (− ) (6 )− 2 3 + 1 3 + 3 − 8 3 2. Find the value: [− (5 ) (4 )]8 − 3 2 − 7 − 5 − 2 3. Perform the indicated operations, reduce to lowest terms, and write the answer as a mixed

number if possible: 7 )÷2( 21 − 33

161

4. Perform the indicated operations and simplify the answer if possible: 6 √48 + 3√27 − 5√75

5. Use the distributive property to simplify: ( )√6 √2 − √6 6. Perform the indicated operation and reduce if possible:

a. − )512 − (

215

b. ÷(− )–25

14 710

7. Perform the indicated operations and reduce to lowest terms:

÷2517

−453 5

1 − 21

8. Perform the indicated operation by first expressing both numbers in Scientific notation. Write

the answer in scientific notation: 9. First use the properties of exponents to simplify each expression and then evaluate if

possible. a. ∙336 −3 b. − 50 c. 29

27

10. a. Find the prime factorization of 48 and 180.

b. Use the prime factorization to find the greatest common divisor (also called greatest common factor) of 48 and 180.

c. Use the prime factorization to find the least common multiple of 48 and 180.

Math 103: Quiz Two Name:____________________ Location: Al Jaber Instructor: Alfredo Bonilla 1. Evaluate for x xy4 2 − 3 − y2 − , y −x = 2 = 3 2. Simplify the algebraic expression: [3(2x ) 4x )]6 − 2 − 5 − ( − 7 3. The sum of two numbers is thirty. Using z to represent the smaller number (and no other

variables), translate "the sum of twice the larger number and negative ten" into an algebraic expression and simplify.

4. Solve: x 7 − 36 − 1 = 8 5. Solve the proportion: 10

x−3 = 52

6. Solve for r: S = P + Prt 7. The bus fare in a city is $1.50. People who use the bus have the option to purchase a monthly

discount pass for $30. With the discount pass the bus costs $0.25. How many times must somebody use the pass in a month so that the cost without the discount pass is the same as the cost with the discount pass? (For full credit you must solve an appropriate equation and write your answer with the correct units.)

8. The cost of a new car can be estimated by the formula where x is− .4x 50x , 00C = 2 2 + 9 + 8 5

the number of years after 1990. a. Use the formula to estimate the cost of a new car in 2005.

b. If the actual cost of a new car in 2005 was $21,750, does the formula underestimate or overestimate the actual price? By how much?

9. If the average salary for a first year doctor was $2950 in 1926 and that average salary increased $470 every year, in what year was the average salary for a first year doctor $27,390? (For full credit you must solve an appropriate proportion and write your answer with the correct units.)

10. In a wildlife preserve 45 elk are captured, tagged, and then released. Later 132 elk are

captured and 11 are found to have tags. Estimate the number of elk in the preserve. (For full credit you must solve an appropriate proportion and write your answer with the correct units.)

11. Solve: (2x ) (3x 4) x 75 − 5 − 2 − 1 = 6 − 1

Math 103: Quiz Three Name:____________________ Location: Al Jaber Instructor: Alfredo Bonilla 1. Multiply: 7x )(2x )( − 2 + 3 2. Multiply: x (4x x 0x )5 4 4 − 2 3 − 1 2 3. Given the function , find the following:(x)f = 2x2 − 5

a. (− )f 2

b. (0)f

c. (1)f

4. Which of the following graphs are graphs of functions:

5. Factor: x 1x2 + 4 − 2 6. Solve: x x4 2 + 3 − 2 = 0

7. Solve the inequality and graph the solution: x 67 + x < 4 + 1

8. In a course that has four equally weighted tests a student makes grades of 96, 80, and 97 on the first three tests. If the student needs to have an average of at least a 90 on the four tests to get an A, what must the student get on the fourth test in order to get an A for the course? (For full credit you must solve an appropriate inequality and state the answer correctly.)

9. Use graph paper to graph −y = 3

1 + 1

Math 103: Quiz Four Name:____________________ Location: Al Jaber Instructor: Alfredo Bonilla 1. Two yogurts and three salads contain 930 calories. Four yogurts and two salads contain 940

calories. Find the number of calories contained in the yogurt and the number of calories contained in the salad.

2. Solve the system of equations using the addition method:

4x – 5y = 22 3x + 2y = 5

3. Solve the system of equations using the substitution method:

3x – y = 5 x + 3y = –5

4. Find the slope of the line containing the points and − , )( 1 2 2,− )( 4 5. A company that makes coffee machines believes that its profit in dollars, P, can be modeled

by the formula , where t is the number of coffee makers(t) − .4x 00x 5, 00P = 0 2 + 8 − 2 0 produced and sold. What is the maximum profit that the company can expect?

6. Given the quadratic function xy = x2 + 4 + 3 a. Determine whether the parabola opens upwards or downwards. b. Find the vertex. c. Find the x­intercepts. d. Find the y­intercept. e. Graph the function on graph paper

7. Answer the following:

a. Write logarithmic form.127 = 3

−3 b. Write in exponential form.100, 005 = log10 0

8. The number of people living in Europe can be modeled using the function . The function represents the number of people living in Europe in millions(x) 40∙2f = 5 0.013x and x is the number of years after 2000. a. According to this model what will the population in Europe be in the year 2018? b. Does the model over estimate or under estimate the actual population in Europe in the year 2018 if the actual population turns out to be 695 million? By how much?

Graph the following on graph paper: 9. xy = log2 10. x = − 2

11. (x)f = 3x−2

Math 103: Quiz Five Name:____________________ Location: Al Jaber Instructor: Alfredo Bonilla 1. A principal of $2100 is borrowed over 9 months. The future value is $2210. Determine the

loan’s simple interest rate to the nearest tenth of a percent. 2. A salesman receives a large Christmas bonus for meeting the company’s goals:

a. How much of the Christmas bonus must be put aside now in order to have $10,000 in 7 years if the interest is compounded quarterly at 4.5%?

b. If the salesman puts aside $7000 at 4.2% compounded continuously, how much money will he have in 10 years?

3. Answer all three questions:

a. 42 is 12% of what number?

b. 90.2 is what percent of 220?

c. A car dealer’s sales went from 12,300 cars in 2006 to 9,800 cars sold in 2009. What is the percent decrease in the car dealer’s sales to the nearest tenth of a percent?

4. A worker decides to put aside $650 each month in a retirement account that pays 5.5%

compounded monthly.

a. How much will he have accumulated after 35 years? b. Find the interest.

5. The price of a home is $250,000. The bank requires a 10% down payment for a 20 year mortgage at 3.9%.

a. Find the monthly payment.

b. Find the total cost of the interest.

Math 103: Quiz Six Name:____________________ Location: Al Jaber Instructor: Alfredo Bonilla 1. The set of 8 equally likely outcomes for flipping a fair coin three times are

HHH, HHT, HTH, HTT, THH, THT, TTH, TTT

HHT means a head (H) on the first toss, a head (H) on the second toss, and a tail (T) on the third toss. Find the probability of flipping the following when the coin is flipped three times:

a. Exactly two tails.

b. At least one head. 2. If the probability of winning $10,000 in a lottery is , what is the probability of not1

50,000 winning $10,000 in the lottery?

For questions 3, 4, 5, 6, and 7 amateur athletes were classified according to nutrition and injury rate. The results are in the chart.

Injury Rate

Low Average High Poor 2 7 14

Nutrition Good 16 5 6 3. If one athlete is randomly selected, what is the probability that the athlete has a high injury

rate? 4. If one athlete is randomly selected, what is the probability that the athlete has good nutrition

and an average injury rate? 5. If one athlete is randomly selected, what is the probability that the athlete has a low or

average injury rate? 6. If one athlete is randomly selected, what is the probability that the athlete that has good

nutrition or an average injury rate?

7. If one athlete is randomly selected, what is the probability that the athlete has good nutrition

given that the athlete has a low injury rate? 8. How many results are there for first, second, and third, in a race of eight sprinters? 9. How many ways can a committee of 3 teachers and 4 students be formed from a group of 8

teachers and 16 students? 10. How many possible license plates are there that have three letters followed by five digits? For 11, 12, 13, 14, and 15, consider a jar that contains the following. Each token has an equal probability of being chosen and the four problems are unrelated.

four green tokens numbered 1, 2, 3, and 4 three red tokens numbered 1, 2,and 3 three orange tokens numbered 1, 2, and 3

11. One token is drawn from the jar. What is the probability of drawing a number 2 token or a

number 3 token? 12. One token is drawn from the jar. What is the probability of drawing a number 2 token or a

token that is orange? 13. Two tokens are drawn in succession. What is the probability of drawing two number 3

tokens? 14. A token is drawn, replaced, and then a second token is drawn. What is the probability of

drawing two green tokens? 15. If one token is drawn, what is the probability of drawing a number 2 token given that the

token is green?

UMUC Math 103

Final Exam – Practice You have two and a half hours to complete this exam. The examination has 20 questions. This is a closed book, closed notes examination. You may use a calculator on the examination. A formula sheet and a statistical table are available from your instructor should you not have

your copy with you. 1. Solve:

2. A 30­year­old worker plans to retire at age 65. He believes that $500,000 is needed to retire

comfortably. How much should be deposited now at 3.5% compounded monthly to meet the $500,000 retirement goal?

3. A muffin recipe calls for 3/4 cups sugar for 3 dozen muffins. How much sugar will you

use to make 8 dozen? 4. Weights of the Pacific yellowfin tuna follow a normal distribution with mean 68 pounds

and standard deviation 12 pounds. a. What percent of the tuna have a weight of more than 89 pounds? b. What percent of the tuna have a weight of between 53 and 74 pounds?

5. The function C(x) = .76x + 171.4 models the cholesterol level of a person, as a function of his age x, in years. a) Compute C(20) b) Interpret the answer.

6) Given the equation of a line

a) Find the x­intercept. b) Find the y­intercept. c) Find the slope. d) Graph the line.

7) A car can be rented from Continental Rental for $80 per week plus 25 cents for each mile driven. How many miles can you travel if you can spend at most $400 for the week?

8) You are taking a multiple choice test that has 5 questions. Each of the questions has three answer choices, with one correct answer per question. If you select one of these three choices for each question and leave nothing blank, in how many ways can you answer the questions?

9) A farmer wants to find out about the relationship between the amount of rain in March

and crop yield in June.

March Rainfall in inches x

3

7

2

6

5

Crop yield in bushels per acre y

5

12

4

10

6

a) Set up a scatter diagram for the data. b) Does there appear to be a positive linear correlation, negative linear correlation, or

no linear correlation?

10) Solve: 11) A baseball franchise is owned by three people. The first owns 5/12 of the franchise. The

seconds owns 1/3. What fraction of the franchise is owned by the third person?

12) Given the function a) Find the vertex. b) Find the x­intercepts. c) Find the y­intercept. d) Graph the function

13) A class is collecting data on eye color and gender. They organize the data they collected

into the table below. Numbers in the table represent the number of students from the class that belong to each of the categories.

Brown Blue Green Male 22 18 10 Female 18 20 12

Find the probability that a randomly selected student from this class a) Does not have brown eyes. b) Has brown eyes or blue eyes. c) Is female or has green eyes. d) Is male, given the student has blue eyes. e) Is female and has green eyes.

14) The population P of bass in a lake is predicted by the function where t is time in months since the lake was initially stocked. Evaluate P(12) and explain what this means.

15) At age 25 you decide to put aside $80 each month into a retirement annuity that pays

2.5% compounded monthly. a) How much will you have saved after 40 years? b) Find the interest.

16) The price of a home is $180,000. The bank requires a 20% down payment for a 15­year mortgage at 4%. a) Find the monthly payment. b) Find the total interest paid.

17) Two McDonald's Quarter Pounders and three Burger King Whoppers with cheese contain

520 milligrams of cholesterol. Three Quarter Pounders and one Whopper with cheese contain 353 milligrams of cholesterol. Determine the cholesterol content in each item.

18) There are 22 cars in the parking lot. Robert wants to find some statistical data concerning these cars and finds out how old these cars are. The results can be read from the following frequency polygon.

a) Find the modal car age b) Find the median car age c) Find the mean age of the cars d) Find the standard deviation of the ages of the cars

19) The names of 10 men and 7 women are entered in a sweepstakes drawing. Two names are drawn at random in succession. What is the probability that a) the first name is a man’s and the second is a woman’s? b) both names are women’s?

20) The function can be used to model the number of cell phone subscribers in the Unites States from 2000 through 2007, where f(x) represents the number of cell phone subscribers in millions, x years after 2000. Evaluate and interpret f(4).

21) Solve: 22) If $10,500 is borrowed and $12,000 must be paid back after three years, what is the

simple interest rate? 23) A telephone manufacturer believes that the profit in dollars, P, the company makes is

related to the number of telephones produced and sold, x, by the function

. According to the function, what is the maximum profit that the manufacturer can expect?

24) From a class of 20 students:

a) How many ways are there to select 5 students to work on a committee? b) How many ways are there to select a president, vice president, and treasurer?

25) Consider the lifetime of 8 television sets: 7, 9, 5, 7, 8, 7, 12, 10 a) Find the mode b) Find the median c) Find the mean d) Find the standard deviation

Answers to Math 103 Practice Final Exams

1. x=5/2 2. $147,140.97 3. 2 cups sugar 4. 0.0401 or 4.01% ; 0.5859 or 58.59% 5. 186.6; at age 20, cholesterol level is 186.6 6. (2,0); (0,­4); m=2; graph 7. 1280 miles

8. ways 9. scatter plot, positive linear correlation

10. 11. 1/4 12. (­1,­4); (­3,0) & (1, 0); (0,­3); graph 13. 3/5; 39/50; 3/5; 9/19; 3/25

14. 743.54; population of bass in lake after 12 months is ~ 744 15. $65,873.50; $27,473.50 16. $1,065.15; $47,727 17. 77 mg chol in quarter pounder & 122 mg chol in whopper 18. mode = 3 ; med = 3 ; mean = 2.68 ; st. dev. = 1.2 19. 35/136 ~ 0.26; 21/136 ~ 0.154 20. 180.17; 180.17 million cell phone subscribers in 2004

21. 22. r = 4.76% 23. $2,380,000

24. ; 25. 7 years ; 7.5 years ; 8.125 years ; 2.17 years