Math 128 Practice Final (Questions on new material.) KEY
Number of Questions:
Expect the final to be 25-30 questions long, 1/3 on this material and 2/3 on old material.
Question 1
What is the polar equation for the polar function graphed below?
1.
r
= cos(2
t
)
2.
r
= cos(3
t
)
3.
r
= 1+cos(
t
) This one
4.
r
= 1-cos(
t
)
5.
r
= cos(
t
)
Question 2
Mark all of the points (r,
) below that lie on the graph of the polar equation r = 2 + sin
1.
(2,0) This one
2.
(5/2,
/6) This one
3.
(5/2,
/3)
4.
(3,0)
5.
(3,
/2 This one)
Question 3
Match the complex number to its value
1. (-6 +
i
) (-6 -
i
)
a
a. 37
2. (24 + 12
i
) + (12 - 24
i
)
b
b. 36 - 12
i
3. (6 +
i
)
2
c
c. 35 + 12
i
4. (2 + 74
i
)/(1 +
i
)
d
d. 38 + 36
i
5. (36 - 6
i
) - (1 + 6
i
)
e
e. 35 - 12
i
Question 4
What is the polar form for the conjugate
of the complex number
?
1.
2.
3.
4.
This one
Question 5
What is DeMoivre's theorem about?
1.
Converting complex numbers from Cartesian to polar form
2.
Calculating sums and differences of complex numbers
3.
Calculating powers of complex numbers This one.
4.
Solving quadratic equations with real or complex roots
Question 6
The magnitude of a vector
v
, denoted ||
v
||, corresponds to what property of a complex number
z
?
1.
The real part of
z
2.
The imaginary part of
z
3.
The argument of
z
4.
The absolute value of
z
This one
5.
The reciprocal of
z
Question 7
Calculate a unit vector in the direction of the vector 3
i
- 4
j
Answer: 0.6 i - 0.8 j
Question 8
Use this picture to match the vector combinations
A + C
-->
B -D
B - D + E - H
-->
A+G 0
F + D
-->
C C
F + E - K
-->
0 A+G
K
-->
-D B
Question 9
Calculate the dot product of
v
= 4
i
+
j
and
w
= 2
i
-
j
Answer: 7
Question 10
Use the dot product to find the angle between the vectors
v
= 4
i
+ 3
j
and
w
= -5
i
+ 12
j
. Answer to the nearest degree.
Answer: 76