Name: ________________________ Class: ___________________ Date: __________ ID: A

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PreCalculus: Chapter 9 Test Review

Short Answer

1. Plot the point given in polar coordinates.

2. Plot the point given in polar coordinates.

3. Plot the point given in polar coordinates.

(-4, -225°)

4. The polar coordinates of a point are given. Find

the rectangular coordinates of the point.

5. The polar coordinates of a point are given. Find

the rectangular coordinates of the point.

(-3, -135°)

6. The rectangular coordinates of a point are

given. Find polar coordinates for the point.

(0, -4)

7. The letters x and y represent rectangular

coordinates. Write the equation using polar

coordinates (r, θ).

x2 = 3y

Name: ________________________ ID: A

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8. The letters x and y represent rectangular

coordinates. Write the equation using polar

coordinates (r, θ).

2xy = 1

9. The letters r and θ represent polar coordinates.

Write the equation using rectangular

coordinates (x, y).

r = 1 + 2 sin θ

10. The letters r and θ represent polar coordinates.

Write the equation using rectangular

coordinates (x, y).

r = 10 sin θ

11. The letters r and θ represent polar coordinates.

Write the equation using rectangular

coordinates (x, y).

r = 2(sin θ - cos θ)

12. Transform the polar equation to an equation in

rectangular coordinates. Then identify and

graph the equation.

r = 2 sin θ

13. Plot the complex number in the complex plane.

2 + 5i

14. Plot the complex number in the complex plane.

-8 + i

15. Write the complex number in polar form.

Express the argument in degrees, rounded to the

nearest tenth, if necessary.

- i

16. Write the complex number in polar form.

Express the argument in degrees, rounded to the

nearest tenth, if necessary.

-5

Name: ________________________ ID: A

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17. Write the complex number in rectangular form.

8

18. Write the complex number in rectangular form.

4(cos 300° + i sin 300°)

19. Find zw or as specified. Leave your answer

in polar form.

z = 10(cos 30° + i sin 30°)

w = 5(cos 10° + i sin 10°)

Find zw.

20. Find zw or as specified. Leave your answer

in polar form.

z = 5(cos 35° + i sin 35°)

w = 2(cos 40° + i sin 40°)

Find zw.

21. Find zw or as specified. Leave your answer

in polar form.

z = 6

w = 12

Find zw.

22. Find zw or as specified. Leave your answer

in polar form.

z =

w =

Find .

23. Find zw or as specified. Leave your answer

in polar form.

z = 1 + i

w = - i

Find zw.

24. Find zw or as specified. Leave your answer

in polar form.

z = 1 - i

w = 1 - i

Find .

25. Write the expression in the standard form a +

bi.

3

26. Write the expression in the standard form a +

bi.

4

27. Write the expression in the standard form a +

bi.

(- + i)6

28. Find all the complex roots. Leave your answers

in polar form with the argument in degrees.

The complex fourth roots of -16

29. Find all the complex roots. Leave your answers

in polar form with the argument in degrees.

The complex fifth roots of -2i

Name: ________________________ ID: A

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30. Use the vectors in the figure below to graph the

following vector.

u + z

31. Use the vectors in the figure below to graph the

following vector.

v - w

Name: ________________________ ID: A

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32. Use the vectors in the figure below to graph the

following vector.

2u - z - w

33. Use the figure below. Determine whether the

given statement is true or false.

A + H = F

34. Use the figure below. Determine whether the

given statement is true or false.

A + B + C + D + E = 0

35. The vector v has initial point P and terminal

point Q. Write v in the form ai + bj; that is, find

its position vector.

P = (3, 3); Q = (-2, -5)

36. Find the indicated quantity.

Find u - v given u = -2i - 2j and v = 7i + 7j.

37. Find the indicated quantity.

If v = 3i - 5j and w = -7i + 4j, find 3v - 4w.

38. Find the indicated quantity.

If v = -i - j, find .

39. Find the quantity if v = 5i - 7j and w = 3i + 2j.

+

40. Find the quantity if v = 5i - 7j and w = 3i + 2j.

41. Find the unit vector having the same direction

as v.

v = -3j

42. Find the unit vector having the same direction

as v.

v = -4i - 3j

ID: A

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PreCalculus: Chapter 9 Test Review

Answer Section

SHORT ANSWER

1. ANS:

PTS: 1

2. ANS:

PTS: 1

ID: A

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3. ANS:

PTS: 1

4. ANS:

PTS: 1

5. ANS:

PTS: 1

6. ANS:

PTS: 1

7. ANS:

r cos2 θ = 3 sin θ

PTS: 1

8. ANS:

r2 sin 2θ = 1

PTS: 1

9. ANS:

x2 + y2 = + 2y

PTS: 1

ID: A

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10. ANS:

x2 + y2 = 10y

PTS: 1

11. ANS:

x2 + y2 = 2y - 2x

PTS: 1

12. ANS:

x2 + (y - 1)2 = 1; circle, radius 1, center at (0, 1) in rectangular coordinates

PTS: 1

13. ANS:

PTS: 1

ID: A

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14. ANS:

PTS: 1

15. ANS:

2(cos 330° + i sin 330°)

PTS: 1

16. ANS:

5(cos 180° + i sin 180°)

PTS: 1

17. ANS:

4 + 4i

PTS: 1

18. ANS:

2 - 2 i

PTS: 1

19. ANS:

50(cos 40° + i sin 40°)

PTS: 1

20. ANS:

10(cos 75° + i sin 75°)

PTS: 1

21. ANS:

72

PTS: 1

ID: A

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22. ANS:

PTS: 1

23. ANS:

2 (cos 15° + i sin 15°)

PTS: 1

24. ANS:

(cos 15° + i sin 15°)

PTS: 1

25. ANS:

4 + 4 i

PTS: 1

26. ANS:

-4

PTS: 1

27. ANS:

-64

PTS: 1

28. ANS:

2(cos 45° + i sin 45°), 2(cos 135° + i sin 135°), 2(cos 225° + i sin 225°), 16(cos 315° + i sin 315°)

PTS: 1

29. ANS:

(cos 54° + i sin 54°), (cos 126° + i sin 126°), (cos 198° + i sin 198°), (cos 270° + i sin 270°),

PTS: 1

ID: A

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30. ANS:

PTS: 1

31. ANS:

PTS: 1

32. ANS:

PTS: 1

33. ANS:

True

PTS: 1

ID: A

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34. ANS:

True

PTS: 1

35. ANS:

v = -5i - 8j

PTS: 1

36. ANS:

-9i - 9j

PTS: 1

37. ANS:

37i - 31j

PTS: 1

38. ANS:

PTS: 1

39. ANS:

+

PTS: 1

40. ANS:

PTS: 1

41. ANS:

u = -j

PTS: 1

42. ANS:

u = - i - j

PTS: 1