2. This is a sample test for the prealgebra–level algebra–ready placement test at the Harbor College The solution and a link to the topic review are provided for each question. The review–links of all the topics may be accessed here.here This is an interactive PowerPoint file. For the best viewing, download it and run it in the viewing–mode.

3. A B C D Question 1. Answer for Question 1: 28 42 The reduced form ofis 6 7 3 4 4 7 2 3

4. Solution to Q1 28 42 The correct answer is 2/3. To reduce a fraction, we divide the numerator and the denominator by their greatest common factor (i.e. the largest number that can go into both numbers) which is 14. =

5. Link to reviewNext Question Solution to Q1 28 42 The correct answer is 2/3. To reduce a fraction, we divide the numerator and the denominator by their greatest common factor (i.e. the largest number that can go into both numbers) which is 14. = ÷14 28 42 ÷14 = 2 3

6. Correct! Next Question A B C D Question 1. 28 42 The reduced form of 6 7 3 4 4 7 2 3 is

7. A B C D Question 2. Answer for Question 2: 5 6 1 4 = 4 2 5 12 7 13 24

8. Link to review Next Question Solution to Q2 5 6 1 4 = Convert into fractions with LCD = 12 12 (5 x 2 – 1 x 3) = 7 12 The correct answer is. 7 12

9. Correct! Next Question A B C D Question 2. 5 6 1 4 = 4 2 5 12 7 13 24

10. A B C D Question 3. Answer for Question 3: 27 14 18 7 =÷ 3 4 9 4 9 8 3 8

11. Solution to Q3 27 14 18 7 = ÷ 27 1418 7 x The answer is. 3 4 reciprocate and multiply

12. Link to reviewNext Question Solution to Q3 27 14 18 7 = ÷ 27 1418 7 x 3 22 = 3 4 The answer is. 3 4 reciprocate and multiply 1

13. Correct! Question 3. 27 14 18 7 =÷ Next Question A B C D 3 4 9 4 9 8 3 8

14. A B C D Question 4. Answer for Question 4: 4 2 3 1 4 3 = 3 4 2 1 4 1 1 4 1 3

15. Next Question Solution to Q4 3 1 4 3 =3 – 1 4 3 =2 4 3 1 4 1 = The answer is. 1 4 1 Link to review

16. Correct! Next Question A B C D Question 4. 4 2 3 1 4 3 = 3 4 2 1 4 1 1 4 1 3

17. A B C D Answer for Question 5:, 4 3, 9 8 3 2 4 3 9 8 4 3 9 8 3 2 9 8 9 8 4 3 < < < < 3 2 4 3 3 2 3 2 < < < < Question 5. Arrange from the smallest to the largest.

18. Solution to Q5, 4 3 3 2 We cross multiply to compare the fractions. The answer is B: So 98 3 2, similarly we have that 4 3 9 8 < 3 2 < 4 3 < 4 3 9 8 <. ← larger

19. Solution to Q5, 4 3 3 2 We cross multiply to compare the fractions. The answer is B: So 98 3 2, similarly we have that 4 3 9 8 < 3 2 < 4 3 < 4 3 9 8 <. ← larger 4 3 = Or multiply by the LCD = 36 36 x 9 8 = 3 2 = Link to reviewNext Question 9412 27 32 24 the largestthe middlethe smallest

20. Question 5. Arrange from the smallest to the largest. Correct! Next Question A B C D, 4 3, 9 8 3 2 4 3 9 8 4 3 9 8 3 2 9 8 9 8 4 3 3 2 4 3 3 2 3 2 < < < < < < < <

21. Question 6. A bag has 48 pieces of candies. Joe ate 7/8 of the whole bag. How many pieces of candies did Joe eat? D B C A 42 36 40 30 Answer for Question 6:

22. Link to reviewNext Question Solution to Q6 48 x = 42 8 7 6 The answer is 42.

23. Question 6. A bag has 48 pieces of candies. Joe ate 7/8 of the whole bag. How many pieces of candies did Joe eat? Correct! Next Question 42 36 40 30 D B C A

24. 6 4 0 –4 A D C B Question 7. –3 – (–5) – (–2) = Answer for Question 7:

25. Link to review Next Question Solution to Q7 The answer is 4. –3 – (–5) – (–2) = –3 + 5 + 2 = 4

26. 6 4 0 –4 Correct! Next Question Question 7. –3 – (–5) – (–2) = A D C B

27. 3939 3737 3535 3434 A B D C Question 8. Answer for Question 8:3 = 3 2 x 3 6

28. Solution to Q8 3 = 3 2 x 3 6 3 3838 2+6=8 The answer is 3 5.

29. Link to reviewNext Question Solution to Q8. 3 = 3 2 x 3 6 3 3838 =3535 2+6=88–3=5 The answer is 3 5.

30. 3939 3737 3535 3434 Correct! Next Question Question 8. 3 = 3 2 x 3 6 A B D C

31. 2 4 6 8 A B C D Question 9. 24 ÷ 6 x 2 Answer for Question 9:

32. Link to reviewNext Question Solution to Q9 The answer is 8. 24 ÷ 6 X 2 = 4 x 2 = 8

33. Correct! Next Question 2 4 6 8 A B C D Question 9. 24 ÷ 6 x 2

34. 15 –9 6 0 D B C A Question 10. 6 – 3(–3) = Answer for Question 10:

35. Link to reviewNext Question Solution to Q10 The answer is 8. 6 – 3(–3) = 6 + 9 = 15

36. Correct! Next Question Question 10. 6 – 3(–3) = 15 –9 6 0 D B C A

37. A D C B Question 11. 2.3 – 0.45 + 0.08 = Answer for Question 11: 1.93 1.83 1.73 2.03

38. Link to reviewNext Question Solution to Q11 The answer is 1.93. 2.3 – 0.45 + 0.08 = 1.85 + 0.08 = 1.93

39. Correct! Next Question Question 11. 2.3 – 0.45 + 0.08 = 1.93 1.83 1.73 2.03 A D C B

40. A B C D Question 12. 1.2 2 x 0.5 = Answer for Question 12: 0.36 0.6 0.24 0.72

41. Link to reviewNext Question Solution to Q12 The answer is 0.72. 1.2 2 x 0.5 = 1.44 x 0.5 = 0.72

42. Correct! Next Question Question 12. 1.2 2 x 0.25 = A B C D 0.36 0.6 0.24 0.72

43. D B C A Question 13. 0.108 ÷ 1.8 = Answer for Question 13: 0.6 0.06 0.006 0.0006

44. Link to reviewNext Question Solution to Q13 The answer is 0.6. 0.108 ÷ 1.8 = 1.08 ÷ 18 = 0.6

45. Correct! Next Question A B C D Question 13. 0.108 ÷ 1.8 = 0.6 0.06 0.006 0.0006

46. A B D Question 14. Answer for Question 14: –0.5 –0.8 –0.7 4 3 – 1.35 = C –0.6

47. Link to reviewNext Question Solution to Q14 The answer is –0.6. 4 3 – 1.35 = 0.75 – 1.35 = –0.6

48. Correct! Next Question A B D Question 14. –0.5 –0.8 –0.7 4 3 – 1.35 = C –0.6

49. A B D Question 15. 2.3 X 10 3 = Answer for Question 15: C 0.00023 0.023 230 2300

50. Link to reviewNext Question Solution to Q15 The answer is 230. 2.3 X 10 3 = 2.3 x 1,000 = 2300

51. Correct! Next Question A B D Question 15. 2.3 X 10 3 = C 0.00023 0.023 230 2300

52. C B D Question 16. How many grams of pure alcohol are there in 300 grams of cough syrup that is 5% alcohol? Answer for Question 16: A 1.5 g 150 g 15 g 0.15 g

53. Solution to Q16 The answer is 15 grams. 5% of 300 is 100 5 x 300

54. Link to reviewNext Question Solution to Q16 The answer is 15 grams. 5% of 300 is 100 5 x 300 = 15 3

55. Correct! Next Question Question 16. How many grams of pure alcohol are there in 300 grams of cough syrup that is 5% alcohol? C B D A 1.5 g 150 g 15 g 0.15 g

56. A B D Question 17. Which of the following percentages is the closest to 2/7. Answer for Question 17: C 30% 20% 10% 40%

57. Solution to Q17 The answer is C: 30% 7 2 = 0.28… Link to reviewNext Question

58. Correct! Next Question A B D Question 17. Which of the following percentages is the closest to 2/7. C 30% 20% 10% 40%

59. A C D Question 18. Arrange the numbers 60%, 2/3, 0.61 from the smallest to the largest. Answer for Question 18: B 60%, 2/3, 0.61 60%, 0.61, 2/3, 2/3, 0.61, 60%, 0.61, 60%, 2/3,

60. Solution to Q18 The answer is B: Link to reviewNext Question 60%, 0.61, 2/3, 60% = 0.60 2/3 ≈ 0.66

61. Correct! Next Question A C D Question 18. Arrange the numbers 60%, 2/3, 0.61 from the smallest to the largest. B 60%, 2/3, 0.61 60%, 0.61, 2/3, 2/3, 0.61, 60%, 0.61, 60%, 2/3,

62. B C D Question 19. Joe got a raise from $15/hr to $18/hr. What is the % increase in Joe’s hourly wages? Answer for Question 19: A 3%, 18%, 15%, 20%,

63. Solution to Q19 The answer is A: Link to reviewNext Question 20% From $15 Joe got a of raise of 3$. so the % increase is 3/15 = 20%.

64. Correct! Next Question B C D Question 19. Joe got a raise from $15/hr to $18/hr. What is the % increase in Joe’s hourly wages? A 3%, 18%, 15%, 20%,

65. B C A Question 20. Let x = 4, then 6 – 5x is Answer for Question 20: D –14 –4 14 4

66. Solution to Q20 The answer is A: Link to reviewNext Question –14 Set x = 4 in 6 – 5x, we get 6 – 5(4) = 6 – 20 = –14

67. Correct! Next Question B C A Question 20. Let x = 4, then 6 – 5x is D –14 –4 14 4

68. B C A Question 21. If x = 3, y = 6, then xy – x – y is Answer for Question 21: D 9 0 6 –3

69. Solution to Q21 The answer is 9. Link to reviewNext Question Set x = 3, y = 6 in xy – x – y we have 3(6) – 3 – 6 = 9

70. Correct! Next Question B C A Question 21. If x = 3, y = 6, then xy – x – y is D 9 0 6 –3

71. B D A Question 22. If 3x – 2 = 16, then x is Answer for Question 22: C 12 8 6 4

72. Solution to Q22 The answer is x = 6. Link to reviewNext Question 3x – 2 = 16 add 2 to both sides 3x = 18 divide both sides by 3 x = 6

73. Correct! Next Question B D A Question 22. If 3x – 2 = 16, then x is C 12 8 6 4

74. B D C Question 23. If b = 2, and a – 2b = 10 then a = Answer for Question 23: A 14 8 –12 6

75. Solution to Q23 The answer is a = 14. Link to reviewNext Question If b = 2, the a – 2(2) = 10 so a = 14.

76. Correct! Next Question B D C Question 23. If b = 2, and a – 2b = 10 then a = A 14 8 –12 6

77. A D C Question 24. A medium bag of chocolates has 24 pieces and a small bag has 6 pieces. We bought 2 medium bags and 4 small bags. How many pieces of chocolates we have in total? Answer for Question 24: B 80 72 96 60

78. Solution to Q24 The answer is 72. Link to reviewNext Question We have 2 x 24 + 4 x 6 = 72.

79. Correct! Next Question A D C Question 24. A medium bag of chocolates has 24 pieces and a small bag has 6 pieces. We bought 2 medium bags and 4 small bags. How many pieces of chocolates we have in total? B 80 72 96 60

80. A D B Question 25. From experience, it’s sunny every 5 out of 7 days at Sunny Hills. In a period of 140 days, how many sunny days are expected? Answer for Question 25: C 60 80 100 120

81. Solution to Q25 The answer is 100. Link to reviewNext Question We have that 7 5 140 x = 700 = 7x or 100 = x

82. Correct! Next Question A D B Question 25. From experience, it’s sunny every 5 out of 7 days at Sunny Hills. In a period of 140 days, how many sunny days are expected? C 60 80 100 120

83. D C B Question 26. A bag of chocolates cost $24 and a bag of peanuts cost $6. We bought 2 bags of chocolates and 6 bags of peanuts. What is the difference between the cost for chocolates and the cost for the peanuts? Answer for Question 26: A $12 $10 $8 $6

84. Solution to Q26 The answer is $12. Link to reviewNext Question The chocolates cost 2 x 24 = $48, the peanuts cost 6 x 6 = $36, so the difference is 48 – 36 = $12.

85. Correct! D C B Question 26. A bag of chocolates cost $24 and a bag of peanuts cost $6. We bought 2 bags of chocolates and 6 bags of peanuts. What is the difference between the cost for chocolates and the cost for the peanuts? A $12 $10 $8 $6Next Question

86. A C B Question 27. A triangle has sides with lengths of Answer for Question 27: D ft,1½ ft and 2 ft, what’s its perimeter? 1 2 3 ft4 5 6 5 1 6 5 5 6 4 1 6

87. Solution to Q27 The answer is 5 1/6 ft. Link to reviewNext Question The perimeter is + 1 2 3 1 1 2 + 2 = 1 + 1 + 2 + 2/3 + 1/2 = 4 + 1 1 6 = 5 1 6

88. Correct! Next Question A B Question 27. A triangle has sides with lengths of ft,1½ ft and 2 ft, what’s its perimeter? 1 2 3 ft4 5 6 5 1 6 5 5 6 4 1 6 C D

89. A D B Question 28. The perimeter of a square is 16 ft, what is the area? Answer for Question 28: C 256 ft 2 144 ft 2 16 ft 2 12 ft 2

90. Solution to Q28 The answer 16 ft 2. Link to reviewNext Question The perimeter is 16 ft so the square is 4 ft x 4 ft with area 4 x 4 = 16 ft 2

91. Correct! Next Question A D B Question 28. The perimeter of a square is 16 ft, what is the area? C 256 ft 2 144 ft 2 16 ft 2 12 ft 2

92. A B Question 29. Which of the following is the closest to the circumference of a circle with a 8–ft radius? Answer for Question 29: 20 ft 30 ft 40 ft 50 ft C D

93. Solution to Q29 The answer D: 50 ft. Link to reviewNext Question The circumference of circle is 2 π r where π ≈ 3.14, if r = 8 then the circumference is 16 π ≈ 16 x 3.1 ≈ 50.

94. Correct! Next Question A B 20 ft 30 ft 40 ft 50 ft C D Question 29. Which of the following is the closest to the circumference of a circle with a 8–ft radius?

95. A D Question 30. Which of the following pictures represents A, B and C on the real line most accurately if A = 3, B = 9 and C = 12? Answer for Question 30: C B 0 0 0 0

96. Solution to Q30 The answer is B. Link to reviewNext Question 0 6129 3

97. Correct! Next Question A D Question 30. Which of the following pictures represents A, B and C on the real line most accurately if A = 3, B = 9 and C = 12? C B 0 0 0 0

98. A D Question 31. The vertices of a rectangle are (1, 1), (6, 1), (1, 8), and (6, 8). What is the perimeter of this rectangle? Answer for Question 31: C B 20 24 30 36

99. Solution to Q31 The answer is 24. Link to reviewNext Question We have the following 5 x 7 rectangle: (1, 1)(6, 1) (6, 8)(1, 8) So the perimeter is 5 + 5 + 7 + 7 = 24 5 7

100. Correct! Next Question 0 A D Question 31. The vertices of a rectangle are (1, 1), (6, 1), (1, 8), and (6, 8). What is the perimeter of this rectangle? C B 20 24 30 36

101. A D Question 32. The vertices of a rectangle are (–1, –1), (4, –1), (–1, 3), and (4, 3). What is the area of this rectangle? Answer for Question 32: B C 36 24 20 10

102. Solution to Q32 The answer is 20. Link to reviewNext Question We have the following 5 x 4 rectangle: (–1, 1)(4, 1) (4, 3)(–1, 3) So the area is 5 x 4 = 20 5 4

103. Correct! Next Question A D Question 32. The vertices of a rectangle are (–1, –1), (4, –1), (–1, 3), and (4, 3). What is the area of this rectangle? B C 36 34 20 10

104. A D Question 33. The following are the temperatures recorded from 1 pm to 5 pm, what is the largest difference in the temperature during this time period given this data? Answer for Question 33: B C 20 o 15 o 10 o 5o5o 1 pm2 pm3 pm (1, 16 o ) (2, 10 o ) (4, 20 o ) (3, 17 o ) (5, 11 o ) 4 pm5 pm

105. Solution to Q33 The answer is 10 0. Link to reviewNext Question The highest temperature is 20 o and the lowest is 10 o so the largest difference is 20 – 10 = 10 o

106. Correct! A D Question 33. The following are the temperatures recorded from 1 pm to 5 pm, what is the largest difference in the temperature during this time period given this data? B C 20 o 15 o 10 o 5o5o 1 pm2 pm3 pm (1, 16 o ) (2, 10 o ) (4, 20 o ) (3, 17 o ) (5, 11 o ) 4 pm5 pm Next Question

107. C D Question 34. Given the following right triangle, what is the length of A? Answer for Question 34: B A 8 ft 8 ½ ft 9 ft 9 ½ ft 10 ft 6 ft A

108. Solution to Q34 The answer is 8 ft. Link to reviewNext Question By Pythagorean Theorem that A 2 + 6 2 = 10 2 A 2 + 36 = 100 A 2 = 64 A = 8

109. Next Question C D Question 34. Given the following right triangle, what is the length of A? B A 8 ft 8 ½ ft 9 ft 9 ½ ft 10 ft 6 ft A Correct!

110. A D Question 35. Which of the following value is closest to √20? Answer for Question 35: B C 7.5 6.5 4.5 3.5

111. Solution to Q35 The answer is 4.5 ft. Link to review √16 < √20 < √25 4 < √20 < 5 So √20 ≈ 4.5

112. Correct! A D Question 35. Which of the following value is closest to √20? B C 7.5 6.5 4.5 3.5