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Calculus Practice Test: printable

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Calculus Practice Test

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

  1. 1

    Find the limit of x2 − 4x − 2 as x -> 2 using a table.
    1. A) 4.1
    2. B) 3.99
    3. C) 4
    4. D) 3.9

  2. 2

    Find the limit of x2 + 3x − 10x + 5 as x -> −5 using a table.

    Answer: ____________________

  3. 3

    Find lim x->3 (x2 + 2x − 1)

    Answer: ____________________

  4. 4

    Find the limit as x -> −2 of x2 + 5x + 6x2 − 4.

    Answer: ____________________

  5. 5

    Find lim x->4 √x − 2x − 4
    1. A) 14
    2. B) 1
    3. C) −14
    4. D) 0

  6. 6

    Find lim x->6 (x − 6)/(2 − √(x − 2))

    Answer: ____________________

  7. 7

    Solve f(x) = x + 1 for x < 2, 5 − x for x >= 2, limit as x -> 2

    Answer: ____________________

  8. 8

    Solve f(x) = x2 + 2x for x < 1, 5 − 2x for x >= 1, limit as x -> 1

    Answer: ____________________

  9. 9

    Find the limit as x -> infinity of 3x2 + 1x2 − 4.
    1. A) −3
    2. B) −14
    3. C) 3

  10. 10

    Find the limit as x -> infinity of 9x2 − 43x2 + 2x.

    Answer: ____________________

  11. 11

    Is f(x) = x2 − 3 continuous at x = 2
    1. A) 1
    2. B) −2
    3. C) 2

  12. 12

    Solve f(x) = x2 + 2x for x < 1, x + 2 for x >= 1, continuous at x = 1

    Answer: ____________________

  13. 13

    Find the derivative of x2 from the definition.

    Answer: ____________________

  14. 14

    Find the derivative of 4x2 − 8x + 1 from the definition.

    Answer: ____________________

  15. 15

    Find the derivative of x5.

    Answer: ____________________

  16. 16

    Find the derivative of 2√x + 3x.

    Answer: ____________________

  17. 17

    Find the derivative of (x2 + 1)(3x − 2).
    1. A) 9x2 + 4x + 3
    2. B) 6x
    3. C) 9x2 − 4x + 3

  18. 18

    Find the derivative of (5 − x)(x2 + 2).

    Answer: ____________________

  19. 19

    Find the derivative of (3x + 1)4.

    Answer: ____________________

  20. 20

    Find the derivative of 2/(x2 + 4).

    Answer: ____________________

  21. 21

    Find the derivative of ex + x2.

    Answer: ____________________

  22. 22

    Find the derivative of ln(2x + 5).

    Answer: ____________________

  23. 23

    x2 + y2 = 25, find dy/dx

    Answer: ____________________

  24. 24

    Xy + y2 = 12, find dy/dx

    Answer: ____________________

  25. 25

    A 10 ft ladder leans against a wall. The bottom slides away at 2 ft/s. How fast is the top sliding down when the bottom is 6 ft from the wall?
    1. A) 64 ft/s
    2. B) 0 ft/s
    3. C) 1.5 ft/s
    4. D) −1.5 ft/s

  26. 26

    A 20 m ladder leans against a wall. The bottom slides away at 1 m/s. How fast is the top sliding down when the bottom is 16 m from the wall?

    Answer: ____________________

  27. 27

    Tangent line to y = x2 at x = 1

    Answer: ____________________

  28. 28

    Tangent line to y = x2 + 3x − 1 at x = −1

    Answer: ____________________

  29. 29

    Turning points of f(x) = x3
    1. A) Yes
    2. B) No

  30. 30

    Two numbers add up to 14. Find the largest product.
    1. A) 0
    2. B) 14
    3. C) 7
    4. D) 49

  31. 31

    Integrate ∫ 3x2 dx

    Answer: ____________________

  32. 32

    Integrate ∫ (2x5 − x2) dx

    Answer: ____________________

  33. 33

    Evaluate ∫ from 1 to 3 of (2x + 1) dx

    Answer: ____________________

  34. 34

    Find the area between y = −x2 + 4x and the x-axis.

    Answer: ____________________

  35. 35

    Integrate ∫ 2x(x2 + 1)3 dx

    Answer: ____________________

  36. 36

    Integrate ∫ from 1 to 2 of 3x2(x3 − 1)2 dx

    Answer: ____________________

  37. 37

    Estimate the area under y = x2 from x = 0 to x = 3 with 3 left rectangles
    1. A) 4 square units
    2. B) 5 square units
    3. C) 1 square units
    4. D) 0 square units

  38. 38

    Estimate the area under y = 2x2 from x = 0 to x = 2 with 4 left rectangles

    Answer: ____________________

  39. 39

    Find the area between y = x2 − 4x and the x-axis.
    1. A) area = 323 square units
    2. B) area = 0 square units
    3. C) area = 4 square units
    4. D) area = −323 square units

  40. 40

    Find the area between y = x2 − 5x + 4 and the x-axis from x = 1 to x = 3.

    Answer: ____________________

Answer key

  1. C 4
  2. −7
  3. 14
  4. −14
  5. A 14
  6. −4
  7. 3
  8. 3
  9. C 3
  10. 3
  11. C 2
  12. 1
  13. 2x
  14. 8x − 8
  15. 5x4
  16. 1/√x + 3
  17. C 9x2 − 4x + 3
  18. −3x2 + 10x − 2
  19. 12(3x + 1)3
  20. −4x/((x2 + 4)2)
  21. ex + 2x
  22. 2/(2x + 5)
  23. −xy
  24. −y/(x + 2y)
  25. D −1.5 ft/s
  26. −1.33 ms
  27. 2(x − 1)
  28. (x + 1)
  29. B No
  30. D 49
  31. x3 + C
  32. x63 − x33 + C
  33. 10
  34. area = 323 square units
  35. ((x2 + 1)4)/4 + C
  36. 3433
  37. B 5 square units
  38. 3.5 square units
  39. A area = 323 square units
  40. area = 103 square units

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