7/27/2019 Math 0312 Final Review FA12

1/8

Math 0312 Final Review

Martin-Gay, 6e

1. Solve: 4 2 3 7 6 7z z a. 47 b. 23 c. 23 d. 27

2. Solve: 1 4 10 9 6 22 3

xx

a. 5, b. , 3 c. d. ,

3. Solve: 31 5 4 16c

a. 4,7 b. 4,7 c. 7, 4 d. 7, 4

4. Solve: 9 3 6b

a. b. 0 c. 0,18 d. 18, 0

5. Solve: 4 5 12 20x

a. 3, 7 b. 7, 3 c. 5 d.

6. Solve: 2 9h

a. 7,11 b. 7,11 c. 7,14 d.

7. Solve: 3 2x

a. , b. c. 5, 1 d. , 5 1,

8. Solve: 2 4 8ab b for b

a.4

2 1a b. 2 4a c.

1

2ad.

2

1a

7/27/2019 Math 0312 Final Review FA12

2/8

9. Solve: 26 2x x

a.3 1

,2 2

b.1

, 23

c.2 1

,3 2

d. 3, 2

10. Solve: 236 84 49 0x x

a.7

6 b.

6

7c.

7 7,

6 6 d.

7

6

11. Solve: 1 2 4x x

a. 2, 3 b. 3, 2 c. 3, 6 d. 2, 3

12. Solve: 22 10 5x x

a.5 15

2

b.

5 15

4

c.

10 15

2

d.

5 35

2

13. Solve: 2 6 25 0x x

a. 3 4i b. 3 8i c. 3 4i d. 3 8i

14. Factor completely: 215 26 8y y

a. Prime b. 15 4 2y y c. 3 4 5 2y y d. 3 4 5 2y y

15. Factor completely: 3 23 3 36x x x

a. Prime b. 23 9 4x x x c. 3 3 4x x x d. 3 3 4x x x

16. Factor: 32 16x

a. 22 2 4x x x b. 22 4 2x x c. 3

2 2x

d. 22 2 2 4x x x

17. Given 2( ) 3f x x x , find ( 6)f u .

a. 26 11 24u u b. 2 11 18u u c. 2 9 18u u d. 26 9 24u u

7/27/2019 Math 0312 Final Review FA12

3/8

18. Solve forx :5 11

2 4 0

x y

x y

a. 1 b. 3 c. 2 d. 4

19. Solve fory :

42 3

24 6

x y

x y

a. 0 b. 12 c. d. 3

, 122

x y y x

20. Solve forz:

3 2 7

2 12

3 10

x y z

x y z

x y z

a. 4 b. 16 c. 3 d. 7

21. Write the equation of the line through 5, 6 and 10, 21 . Write the equation in

standard form.

a. 3 9x y b. 3 9x y c. 3 9x y d. 3 9x y

22. Rationalize the denominator:3

2 4

a.3 2 12

14

b.

3 2 12

14

c.

3 2 12

14

d.

3 2 12

14

23. Perform the indicated operation and simplify if possible:2 2

2 2

8 16 4

11 28 2 63

x x x x

x x x x

a.9x

x

b. 9x c.

2

9

7

x

x x

d.

2 11 28

x

x x

24. Find the midpoint of the line segment whose endpoints are 3, 7 and 9, 3 .

a. 6, 5 b. 12,10 c. 6, 4 d. 5, 6

7/27/2019 Math 0312 Final Review FA12

4/8

25. Use the distance formula to find the distance between the pair of points:

5, 5 and 7, 1 .

a. 2 b. 12 3 c. 12 d. 2 5

26. Perform the indicated operation and simplify if possible: 2 24 2 3 2

5 4 5 4

x x

x x x x

a. 7 4x b. 4x c.1

1x d.

1

5x

27. Perform the indicated operation and simplify if possible:2 2 2

2

9 3 6

3 3

a ab a b

a b a ab

a. 3 a b b. 3 a b c. a b d.a b

a b

28. Solve:7 1 1

8 8

x

x x x

a. 1 b. 8,1 c. 8,1 d. 8, 1

29. Solve: 2 1 8x x

a. 5 b. 13, 5 c. 6 d. 13

30. Solve: 3 2 9 2 5x

a. 6 b. 0 c. 9 d. 3

31. Perform the indicated operation and simplify if possible: 5 6 125 2 45

a. 35 5 b. 8 5 c. 35 5 d. 7 5

7/27/2019 Math 0312 Final Review FA12

5/8

32. Simplify:

22 3

4

2x y

z

a.6 8

44

y z

xb.

6 8

4

4y z

x

c.

9 16

4

4y z

x

d.

9 16

44

y z

x

33. Simplify: 3125

8

a.5

2b. 5 3 c.

5 10

4d. 2 5

34. Simplify: 15 135

a. 9 5 b. 45 c. 27 15 d. 75

35. Simplify: 125

a. 5 5 b. 25 5 c. 5 5i d. 5 5i

36. Perform the indicated operation and write in standard form:3 3

3

i

i

a.48 24

5 5i b.

3 3

2 16i c.

3 3

32 16i d.

3 6

5 5i

37. Perform the indicated operation and write in standard form: 4 20 5i i

a. 4i b. 104i c. 40 104i d. 40 104i

38. Multiply and simplify:

22 3 4 20x x x

a. 3 23 10 12 40x x x b. 3 23 22 52 40x x x

c. 3 23 10 12 40x x x d. 3 23 2 28 40x x x

39. Solve: 2

11 25x

a. 6,16 b. 16, 6 c. 11 5i d. 11 5i

7/27/2019 Math 0312 Final Review FA12

6/8

40. Solve: 2 7 12x x

a. 3, b. 4, 3 c. , 4 d. , 4 3,

41. What must be added to both sides of the equation 2 6 0x x in order to solve by

completing the square?

a. 9 b. 3 c. 6 d. 5

42. A boat travels 6 kilometers upstream in the same amount of time it moves 18 kilometers

downstream. If the rate of the current is 6 kilometers per hour, find the rate of the boat in

still water.

a. 6 km/hr b. 9 km/hr c. 3 km/hr d. 12 km/hr

43. If the perimeter of a rectangle is 224 cm and the width is four more than three times the

length, then what is the width of the rectangle?

a. 20 cm b. 76 cm c. 27 cm d. 85 cm

44. How many gallons of 20% acid should be mixed with eight gallons of 45% acid in order to

obtain a mixture of 30% acid?

a. 153

gallons b. 16.5 gallons c. 12 gallons d. 20 gallons

45. Find the length of the shorter leg of a right triangle if the longer leg is 24 meters and the

hypotenuse is 6 more than twice the shorter leg.

a. 9 m b. 18 m c. 10m d. 17 m

46. The function 2( ) 2 32h t t t gives the height of a baseball hit straight up with an initial

velocity of 32 feet per second. What will the height of the baseball be after 2.5 seconds?

a. 75.5feet b. 67.5feet c. 75 feet d. 675feet

47. Kathy can paint a house in 15 hours. With Janes help it takes only 6 hours. How long

would it take Jane by herself?

a. 4.5 hours b. 9 hours c. 15 hours d. 10 hours

7/27/2019 Math 0312 Final Review FA12

7/8

48. Find ( 2)f for 2( ) 5 4 1f x x x

a. 13 b. 27 c. 15 d. 29

49. Graph 2 3 9x y

a. b. c. d.

50. Graph 3 2x y

a. b. c. d.

7/27/2019 Math 0312 Final Review FA12

8/8

KEY

1. a 26. c

2. d 27. b

3. a 28. a

4. d 29. d5. d 30. c

6. a 31. c

7. d 32. a

8. a 33. a

9. c 34. b

10. a 35. d

11. a 36. d

12. a 37. b13. c 38. c

14. d 39. d

15. c 40. d

16. d 41. a

17. c 42. d

18. c 43. d

19. d 44. c

20. a 45. c21. c 46. b

22. b 47. d

23. a 48. d

24. a 49. c

25. d 50. a