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Algebra Practice Test

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Updated on Aug 24, 2011

If you have completed all 20 lessons in this book, then you are ready to take the test to measure your progress. The test has 50 multiple-choice questions covering the topics you studied in this book.While the format of the test is similar to that of the introductory test (Introductory Algebra Practice Test), the questions are different.

Take as much time as you need to complete the test.When you are finished, check your answers with the answer key at the end of the section. Once you know your score on the test, compare the results with your score on the introductory test. If you scored better on this test than you did on the introductory test, congratulations! You have profited from your hard work.At this point, you should look at the questions you missed, if any. Do you know why you missed the question, or do you need to go back and review the concept?

If your score on the test doesn't show as much improvement as you had hoped, take a second look at the questions you missed. Did you miss a question because of an error you made? If you can figure out why you missed the problem, then you understand the concept and just need to concentrate more on accuracy when taking a test. If you missed a question because you did not know how to work the problem, go back and spend more time working that type of problem. Take the time to understand basic algebra thoroughly.You need a solid foundation in basic algebra if you plan to use this information or progress to a higher level of algebra.

  1. Simplify the expression: 18 + 3 – 11 +4

    a.–36

    b. –36

    c. 1

    d. 0

  2. Simplify the expression: –4 · –2 · –6 · 3

    a. –144

    b. 144

    c. –9

    d. 9

  3. Simplify the expression: –5(x + 3y) + 4(x + 2y)

    a. x + 7y

    b. x – 7y

    c. x– 7y

    d. x + 7y

4. Solve the equation: x – 13.6 = 16.4
  a. x = –30
  b. x = 30
  c. x = 2.8
  d. x = –2.8
5. Solve the equation: 4x + 5 = –2x + 17
  a. x = 11
  b. x = –2
  c. x = –11
  d. x = 2
6. At what rate will $6,000 earn $2,484 interest in 3 years? (I = prt)
  a. 13.8%
  b. 13.9%
  c. 0.13%
  d. 0.138%
7. Solve the equation: –2(x + 3) = 8 – 3(x + 6)
  a. –1
  b. –2
  c. –3
  d. –4
8. Find the slope of the line defined by the equation: y = –3x + 5
  a. 5
  b. Posttest
  c. –3
  d. 2
9. Find the values of x and y:
  y = –2x
  3x + 4y = 10
  a. (4,–2)
  b. (–2,4)
  c. (–4,2)
  d. (2,–4)
10. Simplify the expression: 4√108
  a. 24√3
  b. 24
  c. 432
  d. 4√108
11. Simplify the expression: [(r 4 s 2)3]2
  a. r9s7
  b. r24s12
  c. r14s12
  d. r12s24
12. Factor: 38r4s2t+ 19rst
  a. 19r4s2t(2 + rst)
  b. 19(2rst + 1)
  c. 19rst(2r3s + 1)
  d. 19rst(2r2s)
13. Factor: x2 + 4x – 32
  a. (x – 8)(x – 4)
  b. (x + 4)(x – 8)
  c. (x + 4)(x + 8)
  d. (x + 8)(x – 4)
14. Solve using the quadratic equation:
  x2 + 4x – 5 = 0
  a. 1
  b. 5
  c. 1, –5
  d. –1,–5
15. Find two values for x:
  x2 + 5x – 14
  a. –7,2
  b. 7,–2
  c. –7,–2
  d. 7,2
16. Solve the equation:
  a. 100
  b. –100
  c. 4
  d. –4
17. Solve the equation:4d = 6d – 10
  a. 1
  b. –5
  c. –1
  d. 5
18. Solve the equation: 6c – 4 = 2c + 16
  a.
  b. 3
  c. 5
  d. –3
19. Convert 50° Fahrenheit into degrees Celsius using the formula 
  a. 45° C
  b. 2° C
  c. 10° C
  d. 122° C
20. What amount of money would you have to invest to earn $3,000 in 10 years if the interest rate is 5%? Use the formula I = prt.
  a. $1,500
  b. $60,000
  c. $600
  d. $6,000
21. What is the slope in the equation y = –3x + 5?
  a.
  b.–3
  c. 5
  d. 3
22. Transform the equation 6x + 3y = 15 into slope-intercept form.
  a. 3y = 6x + 15
  b. 3y = –6x + 15
  c. y = –2x + 5
  d. y = –2x+ 5
23. Choose the equation that fits the graph. Posttest
  a. y = 2x + 3
  b. 3x + y = 2
  c. y = – 2x + 3
  d. –3x + y = 2
24. Solve the inequality: 5x – 5 < 20.
       a. x < 5
       b. x > 5
       c. x > 3
       d. x < 3
25. Solve the inequality: –4x – 8 >12
       a. x < –5
       b. x < 5
       c. x > –1
       d. x > –5
26. Match the graph with the inequality: x > 4

Posttest

27. Match the inequality with the graph.

Posttest

  a. y ≤ 2x + 3
  b. y < 2x + 3
  c. y > 2x + 3
  d. y ≥ 2x + 3
28. Determine the number of solutions the system of equations has by looking at the graph.

Posttestx

  a. 1
  b. 0
  c. infinite
  d. none of the above
29. Determine the number of solutions for the system of equations using the slope and y-intercept:
  y = 3x + 2
  3x +y = 2
  a. 1
  b. 0
  c. infinite
  d. none of the above
30. Select the graph for the system of inequalities:
  y ≥ 2
  y ≤2x + 1

Posttest

31. Solve the system of equations algebraically:
  x + 3y = 11
  x – 5y = –3
  a. (17,4)
  b. (1,4)
  c. (1,4)
  d. (–23,–4)
32. Solve the system of equations algebraically:
  5x + 2y = 10
  2xy = –5
  a. (–5,0)
  b. (5,0)
  c. (0,5)
  d. (0,–5)
33. Simplify: 3x2y(2x3y2)
  a. 6x6y2
  b. 6x5y2
  c. 6x5y3
  d. 6x6y3
34. Simplify: 4(3x3)2
  a. 12x5
  b. 144x6
  c. 12x6
  d. 36x6
35. Multiply the polynomials: 8xy(2x – 3y + 10x2y)
  a. 72x2y2
  b. 16x2y – 24xy2 + 80x3y2
  c. 26x2y – 3y
  d. 96x2y – 24xy2
36. Multiply the binomials: (5x – 2)(4x + 7)
  a. 20x2 – 14
  b. 20x2+ 20x – 14
  c. 20x2 + 43x – 14
  d. 20x2 + 27x – 14
37. Factor the polynomial: 3ab2 + 6a3b2 – 15a2b4
  a. 3ab2(2a2 – 5ab2)
  b. 3ab(b + 2a2b – 5ab3)
  c. 3ab2(1 + 2a2 – 5ab2)
  d. 3ab2(1 + 2ab – 5ab2)
38. Factor the polynomial: 64w2 – 49
  a. (8w – 7)(8w – 7)
  b. (8w + 7)(8w + 7)
  c. (8w – 7)(8w + 7)
  d. (8w – 7)2
39. Factor the polynomial: x2 + x – 12
  a. (x + 2)(x – 6)
  b. (x – 4)(x + 3)
  c. (x – 4)(x – 3)
  d. (x + 4)(x – 3)
40. Factor the polynomial: 2x2 + 9x – 5
  a. (2x – 1)(x + 5)
  b. (2x + 5)(x – 1)
  c. (2x + 1)(x – 5)
  d. (2x + 5)(x + 1)
41. Solve the equation: 3x2 – 75 = 0
  a. 0, 5
  b. 5, 5
  c. 5, –5
  d. –5, –5
42. Solve the equation: 2x2 – x = 3
  a. –1,
  b. , 1
  c. 3, –
  d. –3,
43. Simplify: 3√x – 2√x + 3√y
  a. 5√xy
  b. x – 3√ y
  c. x + 3√ y
  d. 5√x + 3√ y
44. Simplify: 3√2 · 6√x
  a. 36x
  b. 36√x
  c. 18√2x
  d. 9√2x
45. Simplify: 2√20 – 5√45
  a. –15
  b. –11√5
  c. 19√5
  d. –3√–25
46. Simplify:
  a. x
  b. 3x
  c. 15x
  d. 5x
47. Solve the equation: 2√x – 1 = 15
  a. 7
  b. 8
  c. 49
  d. 64
48. Solve the equation: 2√x – 3 + 4 = 8
  a. 4
  b. 7
  c. 39
  d. 67
49. Use the quadratic formula to solve:
  3x2 – 7x + 2 = 0
  a. , 2
  b. , –2
  c. , –2
  d. , 2
50. Use the quadratic formula to solve:
  4x2 + 7x + 1 = 0
  a.
  b.
  c.
  d.

Answers

  1. d 
  2. a 
  3. c 
  4. b 
  5. d 
  6. a 
  7. d 
  8. c
  9. b 
  10. a 
  11. b
  12. c
  13. d
  14. c
  15. a
  16. a
  17. d
  18. c
  19. c
  20. d
  21. b
  22. c
  23. c
  24. a
  25. a
  26. c
  27. d
  28. c
  29. a
  30. b
  31. d
  32. c
  33. c
  34. d
  35. b
  36. d
  37. c
  38. c
  39. d
  40. a
  41. c
  42. a
  43. c
  44. c
  45. b
  46. c
  47. d
  48. b
  49. a
  50. d
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