ELEMENTARY ALGEBRA PRACTICE FINAL EXAM

(Revised 10/2016)

1. Simplify:

2. Evaluate: for x = 4, y = 32, and z = 1.

3. Simplify:

4. The number of employees increased from 134 to 189. Find the percent increase to the nearest

tenth of a percent.

5. Macy’s advertised a 20%-off sale. If a pair of boots originally sold for $119, find the decrease

in price and the sale price.

6. 242 is what percent of 550?

7 – 12. Solve.

7. 8. 9.

10. 11. 12.

13. Solve for A in

14. In an election between two candidates, 660 votes were cast. If the winner received 170 more votes

than the loser, how many votes did the loser receive?

15. When a number is increased by 25, the result is 23. Find the number.

16. The directions for a certain bug spray concentrate is to mix 3 ounces of concentrate with 2 gallons of water.

How many ounces of concentrate are needed to mix with 5 gallons of water?

17 – 19. Solve. Express solutions in interval notation.

17. 18. 19.

20. The length of a rectangle is 3 feet more than twice the width. Find the width if the perimeter is 30 ft.

21. Find two consecutive odd integers whose sum is 168.

22. Graph using the slope and y-intercept.

23 - 26. Graph

23. 24. 25. 26.

27. What are the - and y-intercepts of the line: ?

28. Give the slope of the line that contains and .

29. What is the slope and y-intercept of the line ?

30. Determine the slope of the line graphed below.

31. Find the slope-intercept form of the equation of the line that passes through the points and .

32. Write the standard form of the equation of the line with slope 0 passing through (– 4 , – 1)

33. Find the slope-intercept form of the equation of the line that passes through the points (3, – 4) and

parallel to the line

34. Which ordered pair(s) are solutions of the equation ?

A. (4, – 4) B. (– 4, 4) C. (3, – 4) D. (– 4,3)

35. If find and write as an ordered pair.

36. Solve the system of linear equations by graphing

37. Solve the system of linear equations by substitution

38. Solve the system of linear equations by addition

39. Solve the system of linear equations.

40. The Forrest Theater can seat a total of 360 people. They take in $15,150 when every seat is sold. If

orchestra section tickets cost $45 and balcony tickets cost $35, find the number of seats in the orchestra

section and the number of seats in the balcony.

41 - 52. Simplify.

41. 42. 43.

44. 45. 46.

47. 48. 49.

50. 51.

52.

53 – 55. Multiply.

53. 54. 55.

56 – 62. Factor Completely.

56. 57. 58.

59. 60. 61.

62.

63 – 66. Solve.

63. 64. 65.

66.

67. The length of a rectangle is 3 feet less than twice the width. If the area is 65 ft², find the dimensions.

68. Divide:

69. Write in standard notation.

70. Write in scientific notation: 6,900,000

71. A woman walked to a lake at the rate of 3 mph and returned via a different path at the rate of 4 mph. If the

return trip took one hour less time, and the round-trip distance was 10 miles, how long did the round-trip

take to complete?

72. A trail mix worth $3.50 per pound is to be made by combining 20 pounds of peanuts worth $3 per pound

with raisins worth $5 per pound. How many pounds of raisins should be used?

73. The hypotenuse of a right triangle is two feet more than the shorter leg. If the longer leg is 4 feet, find the length of the shorter leg.

74. Find the dimensions of a right triangle where the second leg is 1 meter less than double the first leg, and the hypotenuse is 1 meter more than double the length of the first leg.

75. Simplify the following

a. b. c. d.

SOLUTIONS

1. 17 2. 1 3.

4. 41.0% 5. $23.80 decrease, 6. 44%

$95.20 sale price

7. 8. 9. No solution

10. 11. 12. All real numbers

13. 14. 245 votes 15. – 2

16. 7.5 ounces 17. 18.

19. 20. 4 ft 21. 83, 85

22. 23. 24.

25. 26.

27. , (0, 3) 28. Undefined 29. ,

30. 3 31. 32.

33. 34. C 35. ,

36. 37. 38.

39. Infinite solutions 40. 255 orchestra tickets 41. 1

105 balcony tickets

42. 43. 44. 25

45. 46. 47.

48. 49. 50.

51. 52. 53.

54. 55. 56.

57. 58. 59.

60. 61. 62.

63. 64. 65.

66. 67. ft by 10 ft 68.

69. 0.0000245 70. 71. 3 hours

72. pounds 73. 3 feet

74. Leg: 8 meters leg: 15 meters hypotenuse: 17 meters

75.