Math1112 : Review for Final Exam
This is not a practice test. You should review your old tests as well as using this review for extra practice.
Convert to polar coordinates. Express the answer in radians, using the smallest possible positive angle.
1) (2, -2 3)
5
5
11
11
A) 2,
B) 4,
C) 2,
D) 4,
3
3
6
6
1)
Convert to rectangular coordinates.
2) 12, -
2)
4
A) (-6 2, -6 2)
B) (6 2, -6 2)
C) (-6 2, 6 2)
D) (6 2, 6 2)
Convert to a polar equation.
3) x2 + y2 - 4x = 0
3)
A) r cos2 = 4 sin
C) r sin2 = 4 cos
B) r = 4 sin
D) r = 4 cos
Convert to a rectangular equation.
4) r = 5
A) x + y = 25
5) r = cos
A) (x + y)2 = x
B) x + y = 5
C) x2 - y2 = 25
D) x2 + y2 = 25
B) (x + y)2 = y
C) x2 + y2 = x
D) x2 + y2 = y
Match the figure with one of the given equations.
6)
A) r = 3sin 2
4)
5)
6)
B) r = 2sin 3
C) r = 2cos 3
D) r = 3cos 2
Convert to polar coordinates. Express the answer in radians, using the smallest possible positive angle.
7) (-2, -2 3)
4
4
7
7
A) 2,
B) 4,
C) 4,
D) 2,
3
3
6
6
Multiply or divide and leave the answer in trigonometric notation.
8) 5(cos 33° + i sin 33°) · 2(cos 7° + i sin 7°)
A) 10(cos 26° + i sin 26°)
B) 7(cos 231° + i sin 231°)
C) 7(cos 40° + i sin 40°)
D) 10(cos 40° + i sin 40°)
1
7)
8)
Express the complex number in trigonometric form.
9) - 5 3 - 5i Express your answer in radians.
4
4
+ i sin
A) 10 cos
3
3
C) 5 3 cos
13
6
+ i sin
9)
4
4
+ i sin
B) 5 3 cos
3
3
13
6
D) 10 cos
7
7
+ i sin
6
6
Provide an appropriate response.
10) State the range of the inverse tangent function.
A) [-1, 1]
B)
2
,-
10)
2
C) (- , )
D) -
C)
7
D)
4
Find the exact value in radians.
11) tan-1 (-1)
5
A)
4
B)
4
4
,
2 2
11)
12) sin-1 (0.5)
A)
12)
B) -
3
C)
3
D) -
6
6
13) sec-1 (-1)
A)
A)
B)
2
14) sin-1 -
13)
C)
D) 0
3
2
3
14)
B)
7
6
C) -
List the quadrants in which the function has the given sign.
15) tangent is positive
A) II, IV
B) I, II
3
C) I, III
Find the exact circular function value.
16) cos 2
1
A)
B) 1
2
D)
D) I, IV
15)
16)
C) 0
Find the focus and directrix of the parabola.
17) y2 = 20x
A) F: (5, 5); D: x = 5
C) F: (5, 0); D: x = -5
B) F: (5, 0); D: x = 5
D) F: (0, 5); D: y = -5
2
D) -1
17)
Find an equation of a parabola satisfying the given conditions.
18) Focus at (-5, 0), directrix x = 5
1 2
1 2
y
x
A) x = B) 20y = x2
C) y = 20
20
Find the vertex, the focus, and the directrix of the parabola.
19) (x + 3)2 = 20(y + 2)
A) V: (-2, -3); F: (-2, 2); D: y = -8
C) V: (-3, -2); F: (-3, -7); D: x = 3
18)
D) y2 = 20x
B) V: (-3, -2); F: (-3, 3); D: y = -7
D) V: (3, 2); F: (3, 7); D: y = -3
Find the vertices and the foci of the given ellipse.
x2 y2
+
=1
20)
36
4
20)
A) V: (0, -6), (0, 6);
F: (0, - 4 2), (0, 4 2)
B) V: (0, -4), (0, 4);
F: (0, -2) and (0, 2)
C) V: (-36, 0), (36, 0)
F: (-6, 0) and (6, 0)
D) V: (-6, 0), (6, 0);
F:(- 4 2, 0), (4 2, 0)
Find the center and the radius of the circle.
21) x2 + y2 - 6x + 6y = -2
A) (3, -3); r = 4
19)
B) (3, -2); r = 4
C) (6, -3); r = 4
3
D) (3, -3); r = 6
21)