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Precalculus Practice Test: printable

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Precalculus Practice Test

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36 questions. Calculator allowed. Show your working. steplyclass.com/precalculus/practice-test/

  1. 1

    Vector from (1, 2) to (4, 6)

    Answer: ____________________

  2. 2

    Vector from (โˆ’2, 1) to (2, โˆ’2)

    Answer: ____________________

  3. 3

    Vector from (0, โˆ’2) to (5, 0)

    Answer: ____________________

  4. 4

    u = <3, โˆ’2>, v = <โˆ’1, 4>, find u + v

    Answer: ____________________

  5. 5

    u = <4, 1>, v = <1, 3>, find u โˆ’ v

    Answer: ____________________

  6. 6

    u = <โˆ’1, 2>, v = <2, 1>, find 3u + v

    Answer: ____________________

  7. 7

    OA = a, OB = b, find AB

    Answer: ____________________

  8. 8

    OA = a, OB = b, M is the midpoint of AB, find BM

    Answer: ____________________

  9. 9

    OA = a, OB = b, P divides AB in the ratio 2 : 1, find BP

    Answer: ____________________

  10. 10

    Magnitude and direction of <3, 3>

    Answer: ____________________

  11. 11

    Unit vector of <0, โˆ’5>

    Answer: ____________________

  12. 12

    Unit vector of <8, 15>

    Answer: ____________________

  13. 13

    Calculate <3, 4> โ€ข <2, 1>

    Answer: ____________________

  14. 14

    Dot product of <6, 2> and <โˆ’1, 3>

    Answer: ____________________

  15. 15

    Angle between <6, 8> and <3, 4>

    Answer: ____________________

  16. 16

    Graph x2 = 8y
    1. A) โˆ’2
    2. B) 4
    3. C) 2
    4. D) 8

  17. 17

    Graph y2 = โˆ’8x
    1. A) โˆ’2
    2. B) 12
    3. C) โˆ’8
    4. D) 2

  18. 18

    Graph (y + 2)2 = โˆ’4(x โˆ’ 1)

    Answer: ____________________

  19. 19

    Graph x225 + y29 = 1

    Answer: ____________________

  20. 20

    Graph x24 + y29 = 1

    Answer: ____________________

  21. 21

    Graph (x + 1)2/4 + (y + 3)2/9 = 1

    Answer: ____________________

  22. 22

    Graph x216 โˆ’ y29 = 1

    Answer: ____________________

  23. 23

    Graph 9x2 โˆ’ 4y2 = 36

    Answer: ____________________

  24. 24

    Graph (x โˆ’ 3)2/4 โˆ’ y24 = 1

    Answer: ____________________

  25. 25

    Which conic is 4x2 + 9y2 = 36

    Answer: ____________________

  26. 26

    Which conic is x2 + y2 โˆ’ 6x โˆ’ 7 = 0
    1. A) 9
    2. B) โˆ’16
    3. C) 7
    4. D) 16

  27. 27

    Which conic is 4x2 โˆ’ 9y2 + 8x + 36y โˆ’ 68 = 0

    Answer: ____________________

  28. 28

    Polar (4, 60ยฐ) to rectangular

    Answer: ____________________

  29. 29

    Convert (4, 7ฯ€/4) to rectangular

    Answer: ____________________

  30. 30

    Convert r = โˆ’2 sin ฮธ to rectangular

    Answer: ____________________

  31. 31

    Write 2(cos 60ยฐ + i sin 60ยฐ) in rectangular form

    Answer: ____________________

  32. 32

    Simplify (โˆš3 + i)6
    1. A) 64
    2. B) โˆ’64
    3. C) 30
    4. D) 2

  33. 33

    Simplify (โˆ’โˆš3 + i)3

    Answer: ____________________

  34. 34

    Graph x = t + 1, y = 2t

    Answer: ____________________

  35. 35

    Graph x = t, y = t2 โˆ’ 3

    Answer: ____________________

  36. 36

    Graph x = 5 cos t, y = 3 sin t

    Answer: ____________________

Answer key

  1. v = (3, 4)
  2. v = (4, โˆ’3)
  3. v = (5, 2)
  4. (2, 2)
  5. (3, โˆ’2)
  6. (โˆ’1, 7)
  7. AB = b โˆ’ a
  8. BM = 12a โˆ’ 12b
  9. BP = 13a โˆ’ 13b
  10. 3โˆš2 and ฮธ = 45ยฐ
  11. u = (0, โˆ’1)
  12. u = (817, 1517)
  13. 10
  14. 0
  15. 0ยฐ
  16. A โˆ’2
  17. D 2
  18. 2
  19. vertices = (โˆ’5, 0) and (5, 0)
  20. vertices = (0, โˆ’3) and (0, 3)
  21. vertices = (โˆ’1, โˆ’6) and (โˆ’1, 0)
  22. vertices = (โˆ’4, 0) and (4, 0)
  23. vertices = (โˆ’2, 0) and (2, 0)
  24. vertices = (1, 0) and (5, 0)
  25. 1
  26. D 16
  27. 1
  28. (x, y) = (2, 2โˆš3)
  29. (x, y) = (2โˆš2, โˆ’2โˆš2)
  30. 1
  31. 1 + โˆš3 i
  32. B โˆ’64
  33. 8i
  34. y = 2x โˆ’ 2
  35. y = x2 โˆ’ 3
  36. 1

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