Name: ________________________________ Teacher:____________ Per:______

Semester

Exam Review

2014

Fall Semester Exam Review: Chapter 1

I. Evaluate then state the sets of numbers to which each belongs.

1. 3 8 9 2 4 2. 12 77 111

3 9

II. Solve each of the literal equations for the indicated variable and state any

restrictions.

3. ay + by = c, for y 4. 21V r h

3, for h

5.

c d

a2

, for c 6. a(x d) 2ad b(c x) bc,for x

III. Solve each of the following inequalities. Write your answer in interval notation.

7. x 4 and x 10 8. x 7 and x 4

9. x 5 or x 3 10. 3 2x or x - 4 2

IV. Solve each of the following by writing an inequality.

11. Mike earns $8.50 an hour plus 5% commission on the price of each item that he sells.

Mike can work 80 hours this month, and would like to make at least $1200. What must his total

sales be for the month if he wants to reach his goal?

12. Robert wants to buy lunch for his coworkers. He plans to buy each person a “Bubba Joe’s

Lunch Special” which cost $6.50. There is a $4 delivery charge, and he has to $60 to spend.

How many coworkers can he provide lunch for?

V. Solve each absolute value equation.

13. 5 3y 6 60 14. r 12 2 4 15. 2 5x 1 2x 10

VI. Solve each absolute value inequality. Write your answer in interval notation.

16. x 2 8 17. 2 x 6 7 5 18. 2x 5 x 5 19. 3x 5 2x 7

VII. Write an equation, then solve.

20. The sides of a triangle are in the ratio 3:4:5. What is the length of each side if the

perimeter of the triangle is 72 cm.

21. Find consecutive odd integers that the sum of the second and third is 48. What are the

three numbers?

Fall Semester Exam Review: Chapter 2

I. Functions

1. For the graph shown to the right:

a. Make a mapping of the following relation.

b. Is the relation a function? yes or no

II. Function Notation

Given 2f(x) x 2x 5 g(x) x 5 h(x) 3x 21

Find:

2. f(-2) 3. f(0) + g(3) 4. h( 7)

g(2)

5. g(x + 4) 6. h (x - 1) 7. f(1) + g(2) – h(7)

III. Writing Equations of Lines

8. Find the slope of the line that passes through 1 2,

2 5

, 3 3

,4 2

.

Write the equation of the line from the information given.

9. m =1

2, goes through (-2,6) in standard form.

10. goes through (-3,-1) and (5,7) in standard form

11. parallel to 2x + 3y = 12 and contains (-5,4) in slope intercept form

12. perpendicular to 2x – 5y = 12 and contains (2,4) in point slope form

13. x-intercept of 6 and y-intercept of -5 written in standard form

IV. Graphing Equations of Lines

14. 2x 3y 15 15. x = 5 16. y = -2

-10-9-8-7-6-5-4-3-2-1 1 2 3 4 5 6 7 8 910

-10-9-8-7-6-5-4-3-2-1

123456789

10

-10-9-8-7-6-5-4-3-2-1 1 2 3 4 5 6 7 8 910

-10-9-8-7-6-5-4-3-2-1

123456789

10

-10-9-8-7-6-5-4-3-2-1 1 2 3 4 5 6 7 8 910

-10-9-8-7-6-5-4-3-2-1

123456789

10

-10-9-8-7-6-5-4-3-2-1 1 2 3 4 5 6 7 8 910

-10-9-8-7-6-5-4-3-2-1

123456789

10

-10-9-8-7-6-5-4-3-2-1 1 2 3 4 5 6 7 8 910

-10-9-8-7-6-5-4-3-2-1

123456789

10

-10-9-8-7-6-5-4-3-2-1 1 2 3 4 5 6 7 8 910

-10-9-8-7-6-5-4-3-2-1

123456789

10

V. General Transformations

17-21 Explain in words what transformations have occurred from the parent function: ( )y k x

17. 1

( )5

y k x 18. ( 1) 9y k x 19. 2 ( 6)y k x

20. 2 ( 8) 3y k x 21. 1

( 2) 43

y k x

VI. Transformations

22-27 Graph the following using transformations. Then state the domain and range.

22. 2y 2 3(x 4) 23. 1

y 4x 3

24. y 2 x 1 3

D= ____________ D= ____________ D= ____________

R=_____________ R=_____________ R=_____________

25. 1

y x 2 13

26. 31y (x 1)

2 27. y 2 3 x 5

D= ____________ D= ____________ D= ____________

R=_____________ R=_____________ R=_____________

28-32 State the domain and range.

28. y 2 x 5 1 29. y x 3 1 30. 2y 2 3(x 5)

31. 31y (x 5) 9

2 32.

1y 7

x 2

Fall Semester Exam Review: Chapter 3

Solve each system equations by graphing.

1. 4x 3y 6

2x 3y 12

2. y 3x 2

x 2y 6

Solve each system equations using substitution:

3. 2x 4y 6

x y 3

4.

6x 2y 2

y 2x 3

Solve each system of equations using elimination.

5.

4x 6y 26

2x 3y 13 6.

5x 7y 2

3x 4y

Set up a system for each of the following then solve.

7. A store sells cashews for $5.00 per pound and peanuts for $1.50 per pound. The manager decides to

sell a 20-pound bag mixture for $47.50. How many pounds of each will be in the mixture?

8. A Broadway theater has 500 seats left to sell divided into orchestra and balcony seats. Orchestra

seats sell for $50, and balcony seats sell for $25. If they sell all the seats their sell will total revenue

will be $18,000. How many of each ticket will they have to sell?

Given the following system of equations, find the value of x, y, and z.

9.

2x y 5

3y z 0

x 4z 14

10.

x y z 1

2x 3y z 3

x 2y 4z 4

Graph each system of constraints. Find all vertices. Then find the Max/Min as indicated.

11.

x y 8

y 5

x 0

Minimum for P = 3x + 2y

12. Set up a system of constraints and an objective function. DO NOT SOLVE.

A fish market buys tuna for $0.50 per pound and spends $1.50 per pound to clean and package it. Salmon

costs $2.00 per pound to buy and $2.00 per pound to clean and package. The market makes $2.50 per

pound profit on tuna and $2.80 per pound profit for salmon. The market can spend only $106 per day to

buy fish and $134 per day to clean it. How much of each type of fish should the market buy to maximize

profit?

Objective Function: ________________________________

Constraints:

13. Set up and solve.

Kay grows tomatoes and beans. It costs $1 to grow a bushel of tomatoes, and it costs $3 to grow a

bushel of beans. It takes 1 square yard of land to grow a bushel tomatoes and it takes 6 square yards

of land to grow a bushel of green beans. Kay’s budget is $15, and she has 24 square yards of land

available. If she makes $1 profit on each bushel of tomatoes and $4 profit on each bushel of beans,

how many bushels of each should she grow in order to maximize profits?

Objective Function ________________________

Constraints:

Fall Semester Exam Review: Chapter 4

I. Perform the indicated operation if possible, otherwise write undefined. Box your

answers.

3 6 0A

1 3 9

2 1B

4 0

1 2

C0 3

4 2

D 1 1

0 3

1. 1

3B + 3C 2. A + C 3. 2B + 3C 4. AD 5. BC

II. Refer to the matrices A-D above, Identify each matrix element.

6. a23 7. b22 8. c11 9. d31

III. Refer to the matrices A-D above, state the dimensions of each matrix.

10. A=__________ B=__________ C=__________ D=__________

11. Is it possible to multiply the following?

BA?__________ CB?___________ CD?__________ DC?___________ DA? ___________

IV. Solve for the missing matrix. Box your answers.

12.

1 3 2 3X

0 3 6 4 13.

3 4 0 22X

4 5 0 28

14. Show that B is the Multiplicative Inverse of A.

2 3A

1 2

2 3B

1 2

15. 2x y 5

x 4y 7

16.

2 3 1

5 2 8

9 5

x y z

x y z

x y z

VIII. Write a system of equations & show the matrices used to find the solution (Set-Up Only).

17. A coin bank holds nickels, dimes, and quarters. There are 45 coins in the bank and the value

of the coins is $4.75. If there are 5 more nickels than quarters, find the number of each type

of coin in the bank.

18. John invested $6500 in 3 different mutual funds for one year. He earned a total of $560 in

simple interest on the three investments. The first fund paid 5% interest, the second fund paid

8% interest, and the third interest fund paid 10% interest. If the sum of the first two

investments was $500 less than the amount of the third investment, find the amount he

invested at each rate.

Fall Semester Final Exam Review Chapter 7 Radicals

Simplify. Show all of your work on your own paper.

1.

10

7

3

3 2.

7 8

2 5

7a b

35a b 3. 2

2 2

5ab

15a b

4. 63 (x 12) 5. 12z 4x 6. 3 8 2 956a b c

7. 32 250 8. 10149a 9. 2 4 633xy 16x y

10. 4 12 2 3 11. 6

2

32x

8x 12.

5

6

15 2a

12a

13. 6 8

2

24x y

2xy 14.

10 6

4 2

300x y

5x y 15. 5 27 2 12

16. 3 332 2 108 17. (5 3 2)(4 6) 18. (5 15)(7 10)

19. 2(2 3 3)

Solve the following radical equations. Check your solution(s).

20. d 3 4 21. 11x 3 2x 22. x 7 5 x

23. 3a 2 12 5

Rational Exponents

Write each of the following in radical form.

24. 1

5x 25. 9

7x 26. .1 4x 27. 1

3 2 9m

Write each of the following in exponential form.

28. 4 y 29. 7 4x 30. 16 31. 6 3 2 4a b c

Evaluate.

32. 1

416 33. 3

3

34. 2

38

Solve each equation for x.

35. 1

32 2x 4 36.

2

32 x 2 50 37.

3

4x 5 6 14

Fall Semester Exam Review: Ch. 5 Factoring

Factor each of the following polynomials completely. If the polynomial is not factorable,

write prime.

1. 2 24a 19ab 5b 2. 2 25a 15ab 200b

3. 12 464 x y 4. 2 21 9x y

16 4

5. 3 964x 125y 6. 2 4x 10x 25 y

7. 4 2 2 4a 29a b 100b 8. 4ax 14ay 10bx 35by

9. 4 481x y 10. 2 28x 24xy 18y

11. 3 627x 8y 12. 10 5x 16x 80

13. 22x 98 14. 2 22xy 3y 18x 27

15. 4 2x 13x 36

2y x 5

3

Answers to Fall Semester Review:

Chapter 1

1. 11 2. -9 3. c

y ;a b 0a b

4. 2

3Vh ;r 0

r 5. c = 2a – d; none

6. ad

xa b

; a b 0,a b 7. [-4,10 ) 8. ∅ (no intersection)

9. (-∞,∞) all real numbers 10. 3

, U 6,2

11. 8.50(80) + 0.05x ≥ 1200; $10,400

12. 6.50x 4 60 ; 8 co-workers 13. y = 2 or y = -6 14. No solution

15. No solution 16. No solution 17. , 18. ,0 U 10,

19. 2

,125

20. 18 cm, 24cm, 30cm 21. #21, 23, 25

______________________________________________________________________

Chapter 2

1. a. b. yes

2. -5 3. -7 4. 14 5. x - 1 6. 3x - 24

7. -11

8.38

25 9. x - 2y = -14 10. x - y = -2

11. 2 2

3 3y x 12.

54 ( 2)

2y x 13. 5x - 6y = 30

14. 2x 3y 15 15. x 5 16. y 2

17. Compress by a factor of 1/5 18. 1 unit left, 9 units down

19. Reflect over x-axis, Stretch by a factor of 2, 6 units to the right

20. Stretch by a factor of 2, 8 units right, 3 units down.

21. Reflect over x-axis, compress by a factor of 1/3, 2 units right, 4 units down.

22. D : ( , )

R : 2,

23.

D : ( , 3)U( 3, )

R : ( ,4)U(4, )

24.

D : 1,

R : 3,

25.

D : ( , )

R : 1,

26. D : ( , )

R : ( , )

27.

D : ( , )

R : ,2

28. D: [5, ) 29. D: (- , ) 30. D: (- , ) 31. D: (- , ) 32. D: (- ,-2)U(-2, )

R: (- ,1] R: [1, ) R: (- ,-2] R: (- , ) R: (- ,-7)U(-7, )

Chapter 3

1. (3,-2) 2. (-2,-4) 3. (1,-2)

4. 2 11

,5 5

5. Infinitely many solutions 6. (-8,-6) 7. 15 lbs peanuts, 5 lbs cashews

8. 220 orchestra, 280 balcony 9. (2, -1, 3) 10. (1, 0, -2)

11. min. value 16 @ (0, 8) 12. Objective function

2.5 2.8P x y

Constraints: (x = tuna, y = salmon) .50 2.00 106

1.50 2 134

0

0

x y

x y

x

y

13. Max profit $18 @ (6,3) 6 bushels of tomatoes, and 3 bushels of beans.

Chapter 4

1.

7 17

3 34

93

2. Undefined 3. 1 4

8 9

4. 18 0

7 28

5.

2 1

4 8

6. -9 7. 0 8. -1 9. 0 10. A= 2x3 B= 2x2 C= 2x2 D= 3x2

11. BA? yes CB? yes CD? no DC? yes DA? yes

12.

3 0

6 1 13.

0 2

0 4 14. B*A =

1 0

0 1

(identity matrix) 15. x = 3, y = 1

16. x = 4, y = -10, z=1 17.

1 1 1 n 45

.05 .10 .25 d 4.75

1 0 1 q 5

18.

1 1 1 x 6500

.05 .08 .1 y 560

1 1 1 z 500

______________________________________________________________________

Chapter 7 Radicals

1. 27 2. 5 3a b

5 3.

2 2

1

9a b 4. 2(x 12) 5. 6z 2x

6. 32 3 2 22a c 7a b 7. 310 2 8. 507a a 9. 32 46x y 2x

10. 48 11. 22x 12. 5 6a

2a 13. 2 32x y 3x 14. 3 22x y 15

15. 19 3 16. 34 4 17. 20 5 6 12 2 6 3

18. 35 5 10 7 15 5 6 19. 31 12 3 20. d 49 21. x 3

22. x 9 23. No solution 24. 5 x 25. 7 2x x 26. 5 2x x 27. 3 2m

28. 1

4y 29. 4

7x 30. 2 31.

21

32

1

3

a c

b

32. 2 33. 1

27 34. 4

35. x 4 36. x 127, 123 37. x 11

Chapter 5: Factoring

1. (4a b)(a 5b) 2. 5(a 8b)(a 5b) 3. 6 2 6 2(8 x y )(8 x y )

4. 1 3 1 3

x y x y4 2 4 2

5. 3 2 3 6(4x 5y )(16x 20xy 25y )

6. 2 2(x 5 y )(x 5 y ) 7. (a 5b)(a 5b)(a 2b)(a 2b) 8. (2x 7y)(2a 5b)

9. 2 2(9x y )(9x y)(9x y) 10. 22(2x 3y) 11. 2 2 2 4(3x 2y )(9x 6xy 4y )

12. 5 5(x 20)(x 4) 13. 2(x 7)(x 7) 14. (2x 3)(y 3)(y 3)

15. (x 3)(x 3)(x 2)(x 2)