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MATH 107 COLLEGE ALGEBRA FULL COURSE LATEST-

UMUC

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MATH 107 College Algebra Full Course Latest-UMUC

MATH107

College Algebra Entire Course

MATH 107 Week 1 Participation Latest-UMUC

For this week, consider these exercises:

Section 0.2 (p. 36): 4, 12, 19, 22, 23, 30, 34

Section 0.3 (p. 47): 8, 9, 18, 28a, 28b, 32, 33, 34, 41, 43, 46

Section 0.4 (p. 58): 9, 14, 17, 19, 20, 21, 22, 23

Section 0.5 (p. 68): 3, 5, 6, 7, 10, 13, 28, 29, 30

Section 0.6 (p. 81): 11, 25, 33, 34, 37, 39, 40

Section 0.8 (p. 108): 2, 3, 5, 6, 9, 10, 11, 12

Section 0.9 (p. 124): 8, 10, 30, 31

MATH 107 Week 2 Participation Latest-UMUC

For this week, consider these exercises:

Section 1.1 (p. 15): 23, 24, 25, 26, 27, 37(b), 38

Section 1.2 (p. 29): 41, 42, 43, 45, 46, 47, 48, 4

* Use some additional/different points than the solutions.

Section 1.3 (p. 49): 35, 39, 41, 47, 49, 50, 51, 52, 53

Section 1.4 (p. 63): 11-16, 19-26, 30-36, 40, 48, 53, 64, 67, 70, 72, 74

Section 1.5 (p. 84): 1, 5, 9, 13, 17, 21, 25, 47, 49

MATH 107 Week 3 Participation Latest-UMUC

Section 1.6 (p. 107): 2, 5, 8, 9, 11, 13, 15, 17, 19, 27, 30, 31, 32, 36, 39

* Use some additional/different points than the solutions for problems 2, 5, 8, 9, 11, 13, 15, 17, 19.

Section 1.7 (p. 140): 9, 12, 14, 15, 30-36, 42, 44, 67-71.

* Use some additional/different points than the solutions for problems 9, 12, 14, 15, 30-36, 42, 44.

Section 2.1 (p. 163): 1, 3, 5, 7, 11, 13, 15, 17, 21, 23, 25, 30, 32, 33, 35, 37, 39, 41, 54, 56, 60, 61, 66, 67

* Use some additional/different points than the solutions for problems 21, 23, 25.

Section 2.2 (p. 183): 22-26

* Use some additional/different points than the solutions.

Section 2.5 (p. 230): 2, 3, 4

MATH 107 Week 4 Participation Latest-UMUC

Section 0.7 (Ch. 0, p. 95): (1-27) odd

Section 0.10 (Ch. 0, p. 132): 1, 3, 5, 7, 27-36

Section 2.3 (p. 200): 1-6, 10, 11, 15, 19, 20, 21, 22, 23, 25

* Use some additional/different points than the solutions for problems 1-6.

Section 2.4 (p. 220): 18, 19, 20, 23, 24, 25, 33, 34, 36

Section 2.5 (p. 232): 6(b)

MATH 107 Week 5 Participation Latest-UMUC

Section 3.1 (p. 246): 11, 13, 15, 16, 21, 22, 23, 27, 29, 30, 33, 34

* Use some additional/different points than the solutions for problems 11, 13, 15, 16, 21, 22, 23.

Section 4.1 (p. 314): 1-12 (show asymptotes and holes in graphs), 19, 21, 23

Section 4.2 (p. 333): 1-12 (hand-drawn graphs), 17, 18, 19 (include table of points), 21

Section 0.8 (Ch. 0, p. 108): 19, 20, 21, 22, 23, 34, 36

Section 4.3 (p. 353): 8, 11, 12, 21, 23, 25, 27, 30, 40, 41

MATH 107 Week 6 Participation Latest-UMUC

Section 5.1 (p. 369): (1-24)odd

Section 5.2 (p. 394): 1, 4, 7, 10, 15, 17, 25, 26, 28

Section 0.9 (Ch. 0, p. 124): 17, 18, 19, 20, 21, 22

Section 5.3 (p. 407): 22, 23, 27, 38, 39, 42

Section 6.1 (p. 429): (10–41)odd, 45-49, 58, 60, 62, 64, 66, 75, 76, 77

* Use some additional/different points than the solutions for problems 58, 60, 62, 64, 66.

Section 6.5 (p. 487): 36, 39, 40, 41

MATH 107 Week 7 Participation Latest-UMUC

Section 6.2 (p. 445): (5-29)odd, 34, 37, 38, 42

Section 6.3 (p. 456): 5, 6, 10, 11, 12, (13-33)odd, 34, 35

Section 6.4 (p. 466): 1, 3, 5, 7, 9, 11, 13, 15, 17, 25, 38, 39, 40, 41

Section 6.5 (p. 482): 7, 8, 9, 14, 18, 19, 20, 21, 23, 25, 26, 28, 31, 37, 39

MATH 107 Week 8 Participation Latest-UMUC

This is the last graded discussion. The due date is March 3 (with NO extra days with penalty) but, if

possible, post your response by Wednesday of this week so that your classmates will be able to benefit

from your post.

When reviewing for an exam, it is a good idea to take some time to consider what types of questions will

be on the exam. (What should I study?) The answer to this question will guide you as you study for the

exam.

This discussion is your opportunity to share with your classmates what you have determined will be a

sample final exam question.

Post a question that you think will be reflective of one of the final exam questions and then give a detailed

solution to the question. Follow the discussion rubric as you write out the solution. This should not be a

problem from the text – make up one of your own.

Take some to review the sample questions/solutions of your classmates. If you see a post that is helpful

to you – let your classmate know.

Hopefully, this discussion will contain lots of different types of problems that will give you an additional

review for the final exam.

After the exam, you might want to check back and see if your type of problem was included on the final

exam. If yes, then it would be reasonable to conclude that you are indeed quite brilliant…heh, heh, heh

Here is where you will post your extra credit problem. This problem is optional. You can earn up to 10

extra credit points for your participation problems by posting a problem from one of the previous

discussion problem sets that has not already been posted.

Label the problem as extra credit.

Just to clarify, the Week 8 discussion post will be a problem that you make up and the Extra Credit

problem will be from the previous 7 weeks discussion problems.

MATH 107 Week 5 Linear project Latest-UMUC

Curve-fitting Project – Linear Model

(Due at the end of Week 5)

Instructions

For this assignment, collect data exhibiting a relatively linear trend, find the line of best fit, plot the data

and the line, interpret the slope, and use the linear equation to make a prediction. Also, find r2 (coefficient

of determination) and r (correlation coefficient). Discuss your findings. Your topic may be that is related to

sports, your work, a hobby, or something you find interesting. If you choose, you may use the suggestions

described below.

A Linear Model Example and Technology Tips are provided in separate documents.

Tasks for Linear Regression Model (LR)

(LR-1) Describe your topic, provide your data, and cite your source. Collect at least 8 data points. Label

appropriately. (Highly recommended: Post this information in the Linear Model Project discussion as well

as in your completed project. Include a brief informative description in the title of your posting. Each

student must use different data.)

The idea with the discussion posting is two-fold: (1) To share your interesting project idea with your

classmates, and (2) To give me a chance to give you a brief thumbs-up or thumbs-down about your

proposed topic and data. Sometimes students get off on the wrong foot or misunderstand the intent of the

project, and your posting provides an opportunity for some feedback. Remark: Students may choose

similar topics, but must have different data sets. For example, several students may be interested in a

particular Olympic sport, and that is fine, but they must collect different data, perhaps from different

events or different gender.

(LR-2) Plot the points (x, y) to obtain a scatterplot. Use an appropriate scale on the horizontal and vertical

axes and be sure to label carefully. Visually judge whether the data points exhibit a relatively linear trend.

(If so, proceed. If not, try a different topic or data set.)

(LR-3) Find the line of best fit (regression line) and graph it on the scatterplot. State the equation of the

line.

(LR-4) State the slope of the line of best fit. Carefully interpret the meaning of the slope in a sentence or

two.

(LR-5) Find and state the value of r2, the coefficient of determination, and r, the correlation coefficient.

Discuss your findings in a few sentences. Is r positive or negative? Why? Is a line a good curve to fit to

this data? Why or why not? Is the linear relationship very strong, moderately strong, weak, or

nonexistent?

(LR-6) Choose a value of interest and use the line of best fit to make an estimate or prediction. Show

calculation work.

(LR-7) Write a brief narrative of a paragraph or two. Summarize your findings and be sure to mention any

aspect of the linear model project (topic, data, scatterplot, line, r, or estimate, etc.) that you found

particularly important or interesting.

You may submit all of your project in one document or a combination of documents, which may consist of

word processing documents or spreadsheets or scanned handwritten work, provided it is clearly labeled

where each task can be found. Be sure to include your name. Projects are graded on the basis of

completeness, correctness, ease in locating all of the checklist items, and strength of the narrative

portions.

MATH 107 Final Exam Latest-UMUC

College Algebra

MATH 107 spring, 2017, V.1.7

This is an open-book exam. You may refer to your text and other course materials as you work on the

exam, and you may use a calculator. You must complete the exam individually.

Neither collaboration nor consultation with others is allowed.

Record your answers and work on the separate answer sheet provided.

There are 30 problems.

Problems #1–12 are Multiple Choice.

Problems #13–21 are Short Answer. (Work not required to be shown)

Problems #22–30 are Short Answer with work required to be shown.

MULTIPLE CHOICE

1. Determine the domain and range of the piecewise function. 1. ______

4

2

-4-2 2 4

-2 -4

1. Domain [– 2, 4]; Range [– 3, 1]

2. Domain [– 2, 2.5]; Range [–3, 0]

3. Domain [–2, ?); Range [–3,?)

4. Domain [– 3, 1]; Range [– 2, 4]

5. Solve: ? 7 ? 4x ? x ? 3 2. _____

6. ?8, ?2

7. ?2

8. ?1/2

9. No solution

10. Determine the interval(s) on which the function is increasing. 3. ______

11. (– 0.5, 3)

12. (1, 5)

14. (–2, 2)

15. Determine whether the graph of y ? 3 x is symmetric with respect to the origin,

the x-axis, or the y-axis. 4. ______

1. not symmetric with respect to the x-axis, not symmetric with respect to the y-axis, and not

symmetric with respect to the origin

2. symmetric with respect to the x-axis only

3. symmetric with respect to the y-axis only

4. symmetric with respect to the origin only

5. Solve, and express the answer in interval notation: | 8 – 6x | ? 2. 5. ______

6. [1, 5/3]

7. [1, ?)

8. (–?, 1] ? [5/3, ?)

9. (–?, 5/3] ? [1, ?)

10. Which of the following represents the graph of 7x ? 4y = 28 ? 6. ______

11. B. C. D.

Page 3 of 11

7. Write a slope-intercept equation for a line parallel to the line x – 2y = 6 which passes through the

point (10, – 4). 7. ______

8. y ? 1 x ? 4

2

1. y ? ?2 x ? 4

2. y ? ? 1 x ? 1

2

1. y ? 1 x ? 9

2

8. Which of the following best describes the graph? 8. ______

9. It is the graph of a function and it is one-to-one.

10. It is the graph of a function but not one-to-one.

11. It is the graph of an absolute value relation.

12. It is not the graph of a function.

13. Express as an equivalent expression: 5 log y + log 1 – log (x – 7) 9. ______

log(5 y)

log( x ? 7)

5 y ? 1 B. log x ? 7

1. x ? 7

2. log ?5 y ? 6 ? x ?log

3. Which of the functions corresponds to the graph? 10. _____

4. f ? x ? ? ?e x

5. f ? x ? ? e? x ? 1

6. f ? x ? ? e x ? 2

7. f ? x ? ? e? x ?1

Page 5 of 11

11. Suppose that a function f has exactly one x-intercept.

Which of the following statements MUST be true? 11. ______

1. f is a linear function.

2. f (x) ? 0 for all x in the domain of f.

3. The equation f (x) = 0 has exactly one real-number solution.

4. f is an invertible function.

5. The graph of y = f (x) is shown at the left and the graph of y = g(x) is shown at the right. (No

formulas are given.) What is the relationship between g(x) and f (x)?

6. ______

4 4

2

-4 -2 2 4 -4 -2 2 4

-2 -2

-4 -4

y = f (x) y = g(x)

1. g(x) = f (x – 2) – 1

2. g(x) = f (x + 2) + 2

3. g(x) = f (x + 2) – 1

4. g(x) = f (x + 1) – 2

Page 6 of 11

SHORT ANSWER:

13. Multiply and simplify: (3 + 4i) 2.

Write the answer in the form a + bi, where a and b are real numbers.

14. Solve, and write the answer in interval notation: x ? 6 ? 0 .

Answer: ________ x ? 2

15. A can of soda at 81? F. is placed in a refrigerator that maintains a constant temperature of 38? F.

The temperature T of the soda t minutes after it is placed in the refrigerator is given by

T(t) = 38 + 43e – 0.058 t

Find the temperature of the soda 20 minutes after it is placed in the refrigerator. (Round to the nearest

tenth of a degree.)

Answer: ________ 1

16. Find the value of the logarithm: log8 .

Answer: ________ 64

17. Solve: 36 x ? 1 ? 9 .

Answer: ________

18. Suppose $2,700 is invested in an account at an annual interest rate of 8.8% compounded

continuously. How long (to the nearest tenth of a year) will it take the investment to double in

size?

Answer: _______

19. Let f (x) = x2 ? 8x + 9.

(a) Find the vertex. Answer: ________

(b) State the range of the function. Answer: ________

(c) On what interval is the function decreasing?

Answer: ________

Page 7 of 11

20. Consider the polynomial P(x), shown in both standard form and factored form.

P ( x ) ? 1 x 4 ? 3 x 3 ? 3 x 2 ? 13 x ? 3 ? 1 ( x ? 2)( x ? 1)( x ? 3)( x ? 4)

(a) Which sketch illustrates the end behavior of the polynomial function?

1. B. C. D.

vvv

vvv vvvv vvv

Answer: ________

(b) State the zeros of the function.

Answer: ________________

(c) State the y-intercept.

Answer: ________________

(d) State which graph below is the graph of P(x).

Answer: ________

GRAPH A GRAPH B

GRAPH C GRAPH D

Page 8 of 11

21. Let f ( x) ? 3×2 ? 3 .

x 2 ? 4

(a) State the domain.

Answer: _________________

(b) State the horizontal asymptote.

Answer: _________________

(c) State the vertical asymptote(s).

Answer: _________________

(d) Which of the following represents the graph of f ( x) ? 3×2 ? 3

x 2 ? 4

GRAPH A. GRAPH B.

GRAPH C. GRAPH D.

Page 9 of 11

SHORT ANSWER, with work required to be shown, as indicated.

22. Let f (x) = x + 5 and g ( x) ?? 8 ? x .

f

(a) Find (?1) . Show work.

g

(b) Find the domain of the quotient function f . Explain.

23. Points (7, 5) and (–1, 3) are endpoints of the diameter of a circle.

(a) What is the length of the diameter? Give the exact answer, simplified as much as possible. Show

work.

(b) What is the center point C of the circle?

(c) Given the point C you found in part (b), state the point symmetric to C about the x-axis.

24. Find the equation for a line which passes through the points (–2, 9) and (2, 5) . Write the equation

in slope-intercept form. Show work.

25. A salesperson earns a base salary of $1,960 per month and a commission of 6.8% on the

amount of sales. If the salesperson has a paycheck of $5,591.20 for one month, what was the

amount of sales for the month? Show work.

26. Let f (x) = 4×2 + 9 and g(x) = x – 5.

(a) Find the composite function ( f o g )( x) and simplify. Show work.

(b) Find ? f o g ? (3) . Show work.

27. Find the exact solutions and simplify as much as possible: 5×2 ? 3 = 10x. Show work.

28. Given the function f ( x) ? 3 ? 1 x , find a formula for the inverse function. Show work. 7

Page 10 of 11

29. The fuel efficiency F for a particular car is given by

F(x) = –0.018 x2 + 1.548 x + 5.8

where x is the speed of the car in miles per hour (mph) and F(x) is the corresponding fuel efficiency in

miles per gallon (mpg).

(a) What is the fuel efficiency if the car’s speed is 60 mph?

(b) What speed will yield the maximum fuel efficiency? Show work.

30. Solve: x ? 11 ? 56 ? 0 . Show work.

x2 ? 16

x ? 4

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