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This is a sample test for the elementary algebra diagnostic test at the Harbor College.

This is a sample test for the elementary algebra diagnostic test at the Harbor College. This is an interactive PowerPoint file. F or the best viewing, download it and run it in the viewing–mode. T he solution and a link to the review of the topics are provided for each question.

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This is a sample test for the elementary algebra diagnostic test at the Harbor College.

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  1. This is a sample test for the elementary algebra diagnostic test at the Harbor College. This is an interactive PowerPoint file. For the best viewing, download it and run it in the viewing–mode. The solution and a link to the review of the topics are provided for each question. The review–links of all the topics may be accessed at here http://www.lahc.edu/math/algebra/ele-alg-place-review.html

  2. Question 1. A bag contained 48 pieces of candies. Joe took 2/3 of the bag, Mary took 3/4 of what was left, and Chuck got the rest. How many pieces of candies did Chuck get? 8 A 6 B 4 C 3 D Answer for Question 1:

  3. Solution to Q1 The correct answer is 4. The statement “(fraction or %) of an amount” is translated to the multiplication operation.

  4. Solution to Q1 The correct answer is 4. The statement “(fraction or %) of an amount” is translated to the multiplication operation. Joe took ¾ of the bag so ¼ of the bag was left, 1 12 i.e. (48) = 12 pieces were left. 4

  5. Solution to Q1 The correct answer is 4. The statement “(fraction or %) of an amount” is translated to the multiplication operation. Joe took ¾ of the bag so ¼ of the bag was left, 1 12 i.e. (48) = 12 pieces were left. 4 Mary took 2/3 so Chuck got 1/3 of 12, 1 4 i.e. (12) = 4 pieces. 3 Link to review Next Question

  6. Question 1. A bag contained 48 pieces of candies. Joe took 2/3 of the bag, Mary took 3/4 of what was left, and Chuck got the rest. How many pieces of candies did Chuck get? 8 A 6 B 4 Correct! C 3 D Next Question

  7. 2 1 Question 2. 1 3 = 3 3 1 –1 A 3 2 –1 B 3 1 –2 C 3 2 –2 D 3 Answer for Question 2:

  8. Solution to Q2 2 –1 The correct answer is . 3 1 2 3 1 3 3 2 1 1 3 = 3 3

  9. Solution to Q2 2 –1 The correct answer is . 3 1 2 3 1 3 3 2 1 1 3 = 3 3 2 1 = 2 3 3 2 1 = 3 2 2 1 Link to review hence 1 3 = –1 3 3 3 Next Question

  10. 2 1 Question 2. 1 3 = 3 3 1 –1 A 3 2 –1 Correct! B 3 1 –2 C 3 2 –2 D 3 Next Question

  11. Question 3. After Joe got a 8% raise he earns $1,350 per week. How much was his weekly wage before the raise? A $1,250 B $1,225 C $1,200 D $1,175 Answer for Question 3:

  12. Solution to Q3 The answer is $1,250. Suppose Joe’s wage was x before the raise, then a raise of 8% is 0.08x.

  13. Solution to Q3 The answer is $1,250. Suppose Joe’s wage was x before the raise, then a raise of 8% is 0.08x. Hence his new wage is x + 0.08x or 1.08x, which is $1,350.

  14. Solution to Q3 The answer is $1,250. Suppose Joe’s wage was x before the raise, then a raise of 8% is 0.08x. Hence his new wage is x + 0.08x or 1.08x, which is $1,350. Therefore 1.08x = 1350 so that 1350 x = = 1250. 1.08 Link to review Next Question

  15. Question 3. After Joe got a 8% raise he earns $1,350 per week. How much was his weekly wage before the raise? Correct! A $1,250 B $1,225 C $1,200 D $1,175 Next Question

  16. Question 4. 4,000 x (7.5 x 10–9) x (8 x 103) = 240. A 24 B 2.4 C D 0.24 Answer for Question 4:

  17. Solution to Q4 The answer is 0.24. 4,000 x (7.5 x 10–9) x (8 x 103) = 4 x 103 x (7.5 x 10–9) x (8 x 103)

  18. Solution to Q4 The answer is 0.24. 4,000 x (7.5 x 10–9) x (8 x 103) = 4 x 103 x (7.5 x 10–9) x (8 x 103) = 4 x 7.5 x 8 x 103 x 10–9 x 103 Next Question

  19. Solution to Q4 The answer is 0.24. 4,000 x (7.5 x 10–9) x (8 x 103) = 4 x 103 x (7.5 x 10–9) x (8 x 103) = 4 x 7.5 x 8 x 103 x 10–9 x 103 = 240 x 10-3 = 0.24 Link to review Next Question

  20. Question 4. 4,000 x (7.5 x 10–9) x (8 x 103) = 240. A 24 B 2.4 C D 0.24 Correct! Next Question

  21. Question 5. Given the right triangle as shown with c = 12, a = 5, which is the closest approximated value of x? A 12 11 B 10 C 9 D Answer for Question 5:

  22. Solution to Q5 The answer is 11. By the Pythagorean Theorem it must be that x2 + 52 = 122

  23. Solution to Q5 Solution to Q5 The answer is 11. By the Pythagorean Theorem it must be that x2 + 52 = 122 x2 + 25 = 144 x2 = 119 or that x = √119 ≈ 11 Link to review Next Question

  24. Question 5. Given the right triangle as shown with c = 12, a = 5, which is the closest approximated value of x? A 12 11 Correct! B 10 C 9 D Next Question

  25. Question 6. Which of the following percentages is closest to 2/7? 30% A 25% B C 20% 15% D Answer for Question 6:

  26. Solution to Q6 The answer is 30%. 2/7 = 0.285.. ≈ 30% Link to review Next Question

  27. Question 6. Which of the following percentages is closest to 2/7? 30% A Correct! 25% B C 20% 15% D Next Question

  28. Question 7. 4.5 x 0.2 – (3.5 – 2 x 0.85) = 7.2 A B –0.9 C 10 D –4.8 Answer for Question 7:

  29. Solution to Q7 The answer is 7.2. 4.5 x 0.2 – (3.5 – 2 x 0.85) = 0.9 – (3.5 – 1.7)

  30. Solution to Q7 The answer is 7.2. 4.5 x 0.2 – (3.5 – 2 x 0.85) = 0.9 – (3.5 – 1.7) = 0.9 – 1.8 = –0.9 Link to review Next Question

  31. Question 7. 4.5 x 0.2 – (3.5 – 2 x 0.85) = 7.2 A B –0.9 Correct! C 10 D –4.8 Next Question

  32. is approximately Question 8. 13 A B 11 C 9 D 7 Answer for Question 8:

  33. Solution to Q8 The answer is 9. is approximately 3(4) = 12, is approximately 3 Next Question

  34. Solution to Q8 The answer is 9. is approximately 3(4) = 12, is approximately 3 so that ≈ 12 – 3 = 9. Link to review

  35. is approximately Question 8. 13 A B 11 Correct! C 9 D 7 Next Question

  36. Question 9. If x = 3, and that xy – x – y = –4, what is y? 3/2 A –3/2 B 1/2 C –1/2 D Answer for Question 9:

  37. Solution to Q9 The answer is -1/2. If x = 3, then xy– x – y = –4 is 3y – 3 – y = –4.

  38. Solution to Q9 The answer is -1/2. If x = 3, then xy– x – y = –4 is 3y – 3 – y = –4 so that 2y = –1 or y = –1/2 Link to review Next Question

  39. Question 9. If x = 3, and that xy – x – y = –4, what is y? 3/2 A –3/2 B 1/2 C –1/2 Correct! D Next Question

  40. Question 10. If x = –3, then –x2 – 2x + 3 is 0 A 6 B 12 C 18 D Answer for Question 10:

  41. Solution to Q10 The answer is 8. If x = –3, then –x2 – 2x + 3 is –(–3)2– 2(–3)+ 3 = –9 + 6 + 3 = 0 Link to review Next Question

  42. Question 10. If x = –3, then –x2 – 2x + 3 is Correct! 0 A 6 B 12 C 18 D Next Question

  43. Question 11. If a = –2, b = –1, c = 3, then b2 – 4ac is 23 A 25 B C –25 –23 D Answer for Question 11:

  44. Solution to Q11 The answer is 25. If a = –2, b = –1, c = 3, then (–1)2– 4(–2)(3) = 1 + 24 = 25 Link to review Next Question

  45. Question 11. If a = –2, b = –1, c = 3, then b2 – 4ac is 23 A 25 Correct! B C –25 –23 D Next Question

  46. Question 12. If a – bx = c, then x = A B C D Answer for Question 12:

  47. Solution to Q12 The answer is . If a – bx = c then a – c = bx so = x Link to review Next Question

  48. Question 12. If a – bx = c, then x = A B C Correct! D Next Question

  49. Question 13. –2(3A – 4B) – 5(–7A + 6B) = 29A – 22B A –41A – 22B B 29A – 38B C –41A – 38B D Answer for Question 13:

  50. Solution to Q13 The answer is 29A –22B. –2(3A – 4B) – 5(–7A + 6B) = –6A + 8B + 35A – 30B = 29A – 22B Link to review Next Question

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