Name ________________________________________
Practice Final
1) What is the polar form of the complex number !2 + 2i 3
a) 6cis120
!
b) 4cis150
!
c) 2 3cis120
!
d) 4cis120
!
2) What is the rectangular form of the complex number 2cis135 º?
a) -2
b) i 2
c) ! 2 + i 2
d) !2 + 2i
3) What is the product of the complex numbers 2cis12º and 4cis9º?
a) 6cis21º
b) 6cis108º
c) 8cis21º
d) 8cis108º
4) Which of these is equivalent to (2cis60º)4?
a) !8 ! 8i 3
b) !4 ! 4i 3
c) 8i
d) 16 ! 16i
5) 2 ! 2i is a fourth root of which of the following?
a) –8
b) 8i
c) -64
d) 32
6) Which of these is a cube root of 27cis210º?
a) 3cis140º
b) 9cis70º
c) 3cis190º
d) 9cis270º
!
Given vectors u = (!5,2) and v = (!2,!1) answer questions 7-9.
7) What is | v ! u | ?
a) 4
b) 3 2
c) 2 3
d) 18
c) (7, -3)
d) (-4, 7)
8) What is 2u – 3v?
a) (-16, 1)
b) (-6, -1)
9) Let w = u ! 3v . If you draw w with its tail at the origin and treat it as the terminal ray
of an angle in standard position, approximately what is that angle?
a) 15º
b) 75º
c) 105º
d) 345º
10) A child fires a toy rocket. The rocket lifts off straight into the air with a speed of 36
mph. But, the wind is blowing the helicopter directly sideways at 15 mph. Ignoring
other forces like gravity, what is the resultant speed of the toy?
a) 13 mph
b) 24 mph
c) 30 mph
d) 39 mph
11) A plane is flying at 400 mph due west and encounters a headwind of 280 mph
blowing northeast. Which of these is closest to the component form of the plane's
resultant velocity?
a) (-200, -140)
b) (-480, 200)
c) (-200, 200)
d) (140, -200)
12) What is the length of the major axis of 9x2 + 4y2 = 36?
a) 2
b) 3
c) 4
13) Which of these points is a focus of
a) (!2 5,0)
x2 y2
!
= 1?
16 4
b) (2, 2 5)
14) Which of these is the directrix of x =
a) x = !2
b) x = !
1
2
d) 6
c) (!4,0)
d) (20,0)
y2
! 1?
2
c) x = !
3
2
d) x =
1
2
15) How many solutions are there for the system of equations x + y = 25 and
2
2
y = x2 + 5 ?
a) 0
b) 1
c) 2
16) How many solutions are there for the system of equations
d) 4
x2
+ y 2 = 1 and
8
y2
x +
= 1?
8
2
a) 0
b) 1
c) 2
d) 4
The next two questions refer to this hyperbola (assume each tick mark represents an
increment of one).
17) Which of these might be the equation for the hyperbola above?
a)
y2 x2
!
=1
3
2
y2 x2
!
=1
b)
4
9
y2 x2
!
=1
c)
9
4
x2 42
!
=1
d)
9
4
18) What are the asymptotes for the hyperbola?
a) y = ±
2
x
3
b) y = ±
3
x
2
c) y = ±
9
x
4
d) x = ±
4 16x±
y
9
19) Which of these is the solution to | 2x ! 3 | " 5 ?
a) !1 " x " 4
b) x ! 4
20) What is the solution to (x
x ! "2
a)
21)
a)
b)
b)
!2 " x " 3
x = !2 or x " 3
c)
d)
x = !2 or x = 3
d)
x < !1 or x > 1
x+1
<0
2
x !1
!1 < x < 1
log 12 =
Solve
a) x = 1
24)
c)
x < 1, x ! "1
a) log 3 + log 4
23)
d) x ! "4 or x # "1
+ 2)2 (x ! 3) " 0 ?
Which of the following is the solution to
x > !1
22)
c) x ! "1 or x # 4
Solve
a) x = -1
b) 3 log 4
12
c) ln(e )
d) log 3 • log 4
c) x = 4
d) x = 7
c) x = 0
d) No solution
23x!1 = 32 .
b) x = 2
ln x = !1.
b) x = 1/e
25)
What is the total value after 6 years of an initial investment of $2250 that earns 7%
annual interest compounded quarterly?
a) $3376.64
b) $3412.00
c) $3424.41
d) $3472.16
26)
A single cell amoeba doubles every 4 days. About how long will it take one
amoeba to produce a population of 1000?
a) 10 days
b) 20 days
c) 30 days
d) 40 days
27) An investment gives 5.75% annual interest compounded continuously. What is the
effective annual yield?
a) 5.75%
28)
d) 105.9%
c) 3
d)
x+1
x!" x 3 # 1
b) 1
!
x2 " 1
lim
x!"1 x 2 " 3x " 4
a) 0
30)
c) 6.03%
lim
a) 0
29)
b) 5.92%
b)
f(x) =
a) x = - 3
2
5
3x ! 3
x 2 + 2x ! 3
b) x = -1
c)
!
d) Does not exist
has a hole at...
c) x = 1
d) There are no holes
At a large family picnic you have a contest to see who can eat the most pieces of
grandma’s pie. The following numbers show how many pieces various family members
ate.
1
5
4
2
6
2
3
4
2
1
0
3
31) What is the mean number of pieces consumed?
a) 2
b)
2.33
c) 2.5
d) 2.75
32) What is the median number of pieces consumed?
a) 2
b) 2.25
c) 2.5
d) 3
33) What is the mode for the number of pieces consumed?
a) 1
b) 2
c) 2.5
d) data is multimodal
34) What is the standard deviation for the number of pieces consumed?
a) 1.67
b) 1.85
c) 2.8
d) 33.66
35) What is the interquartile range for the number of pieces consumed?
a) 1.5
b) 2
c) 2.5
d) 3
36)
If the calorie contents of robin eggs are normally distributed with a mean of 25
and a standard deviation of 1.2, then 73% of all robin eggs will have a calorie content
roughly greater than...
a) 22.5
b) 23.5
c) 24.5
d) 25.5