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Algebra 2 Practice Test: printable

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Algebra 2 Practice Test

Name: ______________________   Date: __________   Score: ____ / 40

40 questions. Calculator allowed. Show your working. steplyclass.com/algebra-2/practice-test/

  1. 1

    Solve h(x) = 10 − x, h(4)

    Answer: ____________________

  2. 2

    Is x = y2 a function
    1. A) Yes
    2. B) No

  3. 3

    f(x) = x2 + 2, find x when f(x) = 27

    Answer: ____________________

  4. 4

    f(x) = x2 + 1, g(x) = x + 1, find (fg)(3)
    1. A) 52
    2. B) 10
    3. C) 9
    4. D) 4

  5. 5

    Find the average rate of change of f(x) = x3 from x = 0 to x = 2.

    Answer: ____________________

  6. 6

    Solve f(x) = 7 − 2x, inverse

    Answer: ____________________

  7. 7

    Find the inverse of f(x) = x3 − 2.

    Answer: ____________________

  8. 8

    Divide (3x2 − 10x + 3) ÷ (x − 3)

    Answer: ____________________

  9. 9

    −10, −6, −2, 2, ..., find the 25th term

    Answer: ____________________

  10. 10

    Arithmetic sequence a_4 = 20, a_8 = 36, find the nth term

    Answer: ____________________

  11. 11

    Find the sum from i = 1 to 5 of (2i + 1).

    Answer: ____________________

  12. 12

    Find the sum 20 + 10 + 5 + 52 + ...

    Answer: ____________________

  13. 13

    Expand (x − 1)3

    Answer: ____________________

  14. 14

    Calculate log_2(18)

    Answer: ____________________

  15. 15

    Solve ln(2x) = 1

    Answer: ____________________

  16. 16

    Solve log_2(x + 6) − log_2(x) = 2
    1. A) x = 3
    2. B) x = 2
    3. C) x = 4
    4. D) x = 6

  17. 17

    $1500 is invested at 4% interest compounded daily. How much is in the account after 2 years?

    Answer: ____________________

  18. 18

    $2000 grows by 3% a year. How many years until it is $2600?

    Answer: ____________________

  19. 19

    A loan of $8,000 at 9% for 3 years is paid monthly. Find the monthly payment.
    1. A) $222.222222
    2. B) PMT = $254.40
    3. C) PMT = $0.0912
    4. D) PMT = $9

  20. 20

    Find the domain of f(x) = √(x + 4).

    Answer: ____________________

  21. 21

    Write −x2 − 6x + 4 in vertex form

    Answer: ____________________

  22. 22

    y = (x + 3)(x − 1): which form shows where it crosses the x axis

    Answer: ____________________

  23. 23

    Simplify x2 − x − 6x2 − 9

    Answer: ____________________

  24. 24

    Simplify 4 − 121 + 34

    Answer: ____________________

  25. 25

    Simplify 3/(x(x + 1)) × (x + 1)/6

    Answer: ____________________

  26. 26

    Solve 2x − 1x + 1 >= 0

    Answer: ____________________

  27. 27

    Solve √(5 − x) = 3

    Answer: ____________________

  28. 28

    Simplify (4 − i) − (2 + 3i)

    Answer: ____________________

  29. 29

    Solve x6 − 26x3 − 27 = 0

    Answer: ____________________

  30. 30

    Solve x2 >= 3x

    Answer: ____________________

  31. 31

    Calculate [1, 0; 0, 1] × [7, 2; −3, 5]

    Answer: ____________________

  32. 32

    Det [3, −2; −4, 1]

    Answer: ____________________

  33. 33

    Solve 3x + y = 5, x + y = 3 using the inverse matrix

    Answer: ____________________

  34. 34

    Solve 3x + y = 1, 2x + 2y + z = −1, 3x + 2y + z = 0 by Cramer's rule

    Answer: ____________________

  35. 35

    Solve 3x + y = 13, x + y = 7 with a matrix

    Answer: ____________________

  36. 36

    Solve x2 + y2 = 25 and y = 2x − 5

    Answer: ____________________

  37. 37

    f(x) = 2x if x < 0, x + 5 if x >= 0, find f(3)

    Answer: ____________________

  38. 38

    Zeros of f(x) = (x − 3)(x + 1)2

    Answer: ____________________

  39. 39

    Asymptotes of f(x) = 3x2 + 2x − 1x + 2

    Answer: ____________________

  40. 40

    Find all zeros of f(x) = x3 − 4x2 + x + 6
    1. A) x = −1
    2. B) x = −1 or x = 2 or x = 3
    3. C) x = 1 or x = −2 or x = −3
    4. D) x = 1 or x = 2 or x = 3

Answer key

  1. h(4) = 6
  2. B No
  3. x = 5 or x = −5
  4. A 52
  5. 4
  6. (7 − x)/2
  7. ∛(x + 2)
  8. 3x − 1
  9. a_25 = 86
  10. a_n = 4n + 4
  11. 35
  12. S = 40
  13. x3 − 3x2 + 3x − 1
  14. log_2(18) = −3
  15. x ≈ 1.359
  16. B x = 2
  17. A ≈ $1624.92
  18. t ≈ 8.88
  19. B PMT = $254.40
  20. x ≥ −4
  21. −(x + 3)2 + 13
  22. points = (−3, 0) and (1, 0)
  23. x + 2x + 3
  24. 2
  25. 12x
  26. x < −1 or x ≥ 12
  27. x = −4
  28. 2 − 4i
  29. x = −1, 3
  30. x ≤ 0 or x ≥ 3
  31. (7, 2, −3, 5)
  32. D = −5
  33. (x, y) = (1, 2)
  34. (x, y, z) = (1, −2, 1)
  35. (x, y) = (3, 4)
  36. (0, −5) and (4, 3)
  37. f(3) = 8
  38. 3 crosses, −1 touches
  39. y = 3x − 4, x = −2
  40. B x = −1 or x = 2 or x = 3

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