Dear Student,
1) These problems should be completed over the summer and ready to turn in on the
FIRST day of school. (They will not be accepted late!)
2) This assignment will be graded on completion as well as accuracy.
3) It will be counted as your first TEST grade. You MUST show your work in the
space provided. Please put all your answers in the space provided. These problems
are reflective of the knowledge that is prerequisite to the course you will take next
year.
ANSWERS SHOULD BE IN SIMPLEST
FORM!! PLEASE SHOW ALL WORK!!!
Have a Great Summer time!!!!
CSP MATH TEAM
Name:____________________________
____
____
1. The day before the parade, the school band’s starting point was changed. The band director called three band
members. Each of these band members called 4 other band members. Then all of these band members called
three members. How many band members, including the band director, are notified of the new starting point?
a. 40 band members
c. 36 band members
b. 51 band members
d. 28 band members
2. What is the perimeter of the fifth square in this pattern?
Area = 16
____
Area = 64
Area = 144
a. 60 units
b. 80 units
c. 400 units
d. 256 units
3. Aaron, Bob, Charles, and Daniel live in Tulsa, Portland, Miami, and Michigan. Bob is the brother of the man
who lives in Portland. Daniel is not Bob’s brother and does not live in Michigan. Either Aaron or Charles
lives in Tulsa. Aaron is an only child. Which person lives in which city?
a. Aaron, Miami; Bob, Michigan; Charles, Tulsa; Daniel, Portland
b. Aaron, Tulsa; Bob, Michigan; Charles, Portland; Daniel, Miami
c. Aaron, Portland; Bob, Miami; Charles, Michigan; Daniel, Tulsa
d. Aaron, Tulsa; Bob, Portland; Charles, Miami; Daniel, Michigan
Simplify.
____
____
____
____
4. –2 + (–3)
a. 1
5.
a. –20
b. 5
c. –1
d. –5
b. –5
c. 5
d. 20
a. 512
b. 4,096
c. 16
d.
a.
b. –22.5
c. –3.6
d.
b. 1
c.
d.
6.
7.
Divide.
____
8.
a.
____
4
3
9. Solve bx + cy = d for x.
3
4
1
3
a.
b.
____ 10. Evaluate
a. 3,817.04
for r = 9 and h = 15.
b. 1,215
c.
d.
c. 6,361.73
d. 424.12
Find the area.
____ 11.
7.7 cm
4.4 cm
Not drawn to scale
b.
c.
a.
____ 12. Find the volume of the cone to the nearest hundredth.
d.
7m
4m
Not drawn to scale
a.
b.
c.
____ 13. A sphere has radius 5 cm. Find the volume to the nearest hundredth.
a. 130.9 cm3
b. 104.72 cm3
c. 314.16 cm3
____ 14. Find the slope of the line.
d.
d. 523.6 cm3
y
8
6
4
2
–8
–6
–4
–2
2
4
6
8
x
–2
–4
–6
–8
a.
b.
1
−
1
c. −3
d. 3
c. 19.4 ft
d. 15.6 ft
3
3
____ 15. Find the value of c. Round to the nearest tenth.
c
19 ft
15 ft
Not drawn to scale
a. 586 ft
b. 24.2 ft
Solve the equation.
____ 16.
a. 8
b. –8
c. –40
d. 40
a. 5
b. 13
c. 6
d. 14
a. –0.5
b. –2
c. 0.5
d. 2
____ 17.
____ 18.
____ 19.
a.
x = 2 or x = −1
1
c. x = 2 or x = −2
3
b. x = 2 or x = −4
d.
a. 14, 4
b. –4, –14
c. 14, –14
d. –4, 4
1
x = −1 or x = −2
3
____ 20.
____ 21. Solve and graph
a.
.
c.
y
–4
y
4
4
2
2
–2
2
4
–4
x
–2
–2
–2
–4
–4
2
4
x
2
4
x
d.
b.
y
–4
4
4
2
2
–2
____ 22. Solve
a. –9 < d < 5
–10 –8
y
–6
2
4
____ 23. Graph
–6
–2
–2
–2
–4
–4
. Graph the solutions.
c. –8 < d < 5
–4
–2
0
2
4
6
8
10
b. –8 > d > 4
–10 –8
–4
x
–10 –8
–6
–4
–2
0
2
4
6
8
10
–10 –8
–6
–4
–2
0
2
4
6
8
10
d.
–4
–2
.
0
2
4
6
8
10
a.
c.
y
y
8
8
6
6
4
4
2
2
–8 –6 –4 –2
–2
2
4
6
8
–8 –6 –4 –2
–2
x
–4
–4
–6
–6
–8
–8
b.
d.
y
8
6
6
4
4
2
2
2
4
6
8
–8 –6 –4 –2
–2
x
4
6
8
x
2
4
6
8
x
y
8
–8 –6 –4 –2
–2
2
–4
–4
–6
–6
–8
–8
Simplify the expression.
____ 24.
a.
b.
c.
d.
a.
b.
c.
d.
a.
b.
c.
d.
____ 25.
____ 26.
____ 27.
a. 36
b. –36
c. –36i
d. 36i
Find the product or quotient. Write the answer in scientific notation and in standard form. Round to
the appropriate number of significant digits.
____ 28.
a.
b.
; 0.0000026703
; 0.1059
c.
d.
; 0.26703
; 0.645
____ 29. Find the distance between (3, 4) and (4, –6). If necessary, round to the nearest tenth.
a. 10 units
b. 101 units
c. 7.3 units
d. 53 units
____ 30. The city commission wants to construct a new street that connects Main Street and North Boulevard as shown
in the diagram. The construction cost has been estimated at $174 per linear foot. Estimate the cost for
constructing the street.
str
ee
t
North Blvd.
ne
w
5 mi
Main St.
W
4 mi
S
a. $5,115,216
b. $469,054
c. $5,882,678
d. $588,268
Write the number in scientific notation.
____ 31. 0.0000234
a.
c.
b.
d.
____ 32. Graph the parametric equations x(t) = –2t and y(t) = –t – 1.
y
c.
a.
–5
–4
–3
–2
y
5
5
4
4
3
3
2
2
1
1
–1
–1
1
2
3
4
5
x
–5
–4
–3
–2
–1
–1
–2
–2
–3
–3
–4
–4
–5
–5
1
2
3
4
5
x
b.
d.
y
–5
–4
–3
–2
y
5
5
4
4
3
3
2
2
1
1
–1
–1
1
2
3
4
5
–5
x
–4
–3
–2
–1
–1
–2
–2
–3
–3
–4
–4
–5
–5
____ 33. Graph y ≤ 2x2 + 2x – 4.
a.
–4
–3
–2
2
3
4
5
x
1
2
3
4
5
x
1
2
3
4
5
x
c.
y
–5
1
y
5
5
4
4
3
3
2
2
1
1
–1
–1
1
2
3
4
5
–5
x
–4
–3
–2
–1
–1
–2
–2
–3
–3
–4
–4
–5
–5
b.
d.
y
–5
–4
–3
–2
y
5
5
4
4
3
3
2
2
1
1
–1
–1
1
2
3
4
5
x
–5
–4
–3
–2
–1
–1
–2
–2
–3
–3
–4
–4
–5
–5
To which sets of numbers does the number belong?
____ 34. –17
a. integers, rational numbers, real numbers
b. whole numbers, integers, rational numbers, real numbers
c. whole numbers, integers, real numbers
d. rational numbers, real numbers
____ 35. The formula
relates the speed S in miles per hour a car was traveling to the length d in feet that
the car skidded when brakes were applied. The variable f is the coefficient of friction, which varies depending
on the road surface and the condition of the tires. Which sets of numbers contain the value of S for f = 0.8 and
d = 51?
a. integers, rational numbers, real numbers
b. irrational numbers, real numbers
c. whole numbers, integers, rational numbers, real numbers
d. natural numbers, whole numbers, integers, rational numbers, real numbers
Insert <, >, or = to make the sentence true.
____ 36. 20.28
a. <
b. =
c. >
a. <
b. >
c. =
____ 37.
Find the opposite and the reciprocal of the number.
____ 38. 500
a.
b.
c.
–500,
d.
–500,
500,
500,
Name the property of real numbers illustrated by the equation.
____ 39.
a.
b.
c.
d.
Associative Property of Multiplication
Commutative Property of Addition
Commutative Property of Multiplication
Closure Property
Evaluate the expression for the given value of the variable(s).
____ 40.
;
,
a. –55
b. 55
c. 5
d. –5
b. 17
c. –11
d. 21
b. –1
c. 11
d. –17
; x = –3
b. 62
c. 32
d. 30
____ 41.
;b=2
a. 19
____ 42.
; x = –3
a. 3
____ 43.
a. –76
Simplify by combining like terms.
____ 44.
a.
b.
c.
d.
Solve the equation or formula for the indicated variable.
____ 45.
, for t
b.
a.
c.
d.
____ 46. Michael has $12,500 to invest. He invests part in an account which earns 4.2% annual interest and the rest in
an account which earns 6.2% annual interest. He earns $669.50 in interest at the end of the year. How much
was invested at each rate?
a. $5,000 at 4.2%, $7,500 at 6.2%
c. $7,500 at 4.2%, $5,000 at 6.2%
b. $7,225 at 4.2%, $5,275 at 6.2%
d. $5,275 at 4.2%, $7,225 at 6.2%
Solve the inequality. Graph the solution set.
____ 47. –4k + 5 ≤ 21
a. k ≥ –4
–8 –6 –4 –2
b.
k ≥ −6
c. k ≤ –4
0
2
4
6
8
–8 –6 –4 –2
d.
1
2
–8 –6 –4 –2
0
2
4
6
8
0
2
4
6
8
0
2
4
6
8
0
2
4
6
8
–8 –6 –4 –2
0
2
4
6
8
–20 –15 –10 –5
0
5
10 15 20
k ≤ −6
1
2
–8 –6 –4 –2
____ 48.
2(4y – 5) < –10
a. y > 0
–8 –6 –4 –2
b.
y<−
c. y < 0
0
2
4
6
8
–8 –6 –4 –2
d.
5
8
–8 –6 –4 –2
0
2
4
6
8
y>−
5
8
Solve the inequality. Graph the solution.
____ 49.
a.
c.
–40 –30 –20 –10 0
b.
10 20 30 40
d.
–20 –15 –10 –5
0
5
10 15 20
–20 –15 –10 –5
0
5
10 15 20
____ 50.
a. –18 > x > 8
–20 –15 –10 –5
c. –36 < x < 16
0
5
10 15 20
b. –18 < x < 8
–20 –15 –10 –5
–40 –30 –20 –10 0
10 20 30 40
–20 –15 –10 –5
5
d.
0
5
10 15 20
0
10 15 20
____ 51. A biologist has determined that a particular osprey has a 70% chance of catching a fish on any given day.
Carry out a simulation of twenty trials using the random number table below to find the probability that the
osprey will actually catch a fish on all of the next three days. Explain your method.
945
106
832
793
025
746
180
726
354
981
250
864
793
105
871
496
236
012
835
947
a. Using the digits 0–7 to represent a caught fish, the probability of catching a fish on each of
the next three days is 70%.
b. Using the digits 0–7 to represent a caught fish, the probability of catching a fish on each of
the next three days is 65%.
c. Using the digits 0–6 to represent a caught fish, the probability of catching a fish on each of
the next three days is 35%.
d. Using the digits 0–7 to represent a caught fish, the probability of catching a fish on each of
the next three days is 7%.
____ 52. This is a spinner used in a board game. What is the probability that the spinner will land on a multiple of 3
and 4?
a.
b.
c.
d.
____ 53. If a dart hits the target at random, what is the probability that it will land in the shaded region?
12 in.
3 in.
Drawing not to scale
a.
b.
1
1
c.
π
1
d. 16π
4
16
16
____ 54. Write the ordered pairs for the relation. Find the domain and range.
y
4
2
–4
–2
O
2
4
x
–2
–4
a.
b.
c.
d.
{(–2, 5), (–1, 2), (0, 1), (1, 2), (2, 5)}; domain: {–2, –1, 0, 1, 2}; range: {1, 2, 5}
{(5, –2), (2, –1), (1, 0), (2, 1), (5, 2)}; domain: {–2, –1, 0, 1, 2}; range: {1, 2, 5}
{(–2, 5), (–1, 2), (0, 1), (1, 2), (2, 5)}; domain: {1, 2, 5}; range: {–2, –1, 0, 1, 2}
{(5, –2), (2, –1), (1, 0), (2, 1), (5, 2)}; domain: {1, 2, 5}; range: {–2, –1, 0, 1, 2}
Find the slope of the line.
____ 55.
a.
−
1
2
b.
1
2
Find an equation for the line:
____ 56. through (–4, 6) and parallel to y = −3x + 4.
c. –4
d. none of these
a. y = −3x − 6
b. y = 3x + 18
c.
d.
1
22
y= x+
3
3
1
14
y=− x+
3
3
____ 57. A leaky valve on the water meter overcharges the residents for one gallon of water in every
months. The
overcharged amount w varies directly with time t.
a. Find the equation that models this direct variation.
b. How many months it will take for the residents to be overcharged for 8 gallons of water?
a.
c.
; 20 months
b.
d.
; 20 months
;
months
;
months
Find the value of y for a given value of x, if y varies directly with x.
____ 58. If y = 4.8 when x = 2.4, what is y when x = 2.05?
a. 4.1
b. 1.03
c. –1.03
____ 59. Write the equation for the translation of
.
d. –4.1
y
6
4
2
–6
–4
–2 O
–2
2
4
6
x
–4
–6
a.
b.
c.
d.
____ 60. Compare the graphs of the pair of functions. Describe how the graph of the second function relates to the
graph of the first function.
a.
b.
c.
d.
The second function is the graph of
The second function is the graph of
The second function is the graph of
The second function is the graph of
____ 61. Write an equation for the horizontal translation of
moved to the right 3 units.
moved up 3 units.
moved to the left 3 units.
moved down 3 units.
.
y
8
4
–8
–4
O
4
8
x
–4
–8
a.
b.
c.
d.
____ 62. Write the equation that is the translation of
left 1 unit and up 2 units.
a.
c.
d.
b.
____ 63. An electronics store makes a profit of $20 for every portable DVD player sold and $45 for every DVD
recorder sold. The manager’s target is to make at least $180 a day on sales of the portable DVD players and
DVD recorders. Write and graph an inequality that represents the number of both kinds of DVD players that
can be sold to reach or beat the sales target. Let p represent the number of portable DVD players and r
represent the number of DVD recorders.
c. 45p + 20r ≥ 180
a. 20p + 45r ≥ 180
r
r
6
6
4
4
2
2
0
2
b. 45p + 20r ≥ 180
4
6
p
0
2
d. 20p + 45r ≥ 180
4
6
p
r
r
6
6
4
4
2
2
0
2
4
6
0
p
2
4
6
p
Graph the absolute value inequality.
____ 64. y < |x + 2| – 2
a.
–6
c.
y
–3
6
6
3
3
O
3
6
–3
O
–3
–6
–6
d.
y
–3
–6
x
–3
b.
–6
y
6
3
3
3
6
x
–6
–3
O
–3
–3
–6
–6
Write an inequality for the graph.
6
x
3
6
x
y
6
O
3
____ 65.
y
6
3
–6
O
–3
3
6
x
–3
–6
a. y ≤ |x + 3| – 1
b. y ≤ |x – 3| + 1
c. y ≤ |x – 3| – 1
d. y ≥ |x – 3| – 1
Solve the system by graphing.
____ 66.
a.
c.
y
–4
(–1, 3)
–2
y
4
4
2
2
O
2
4
–4
x
–2
O
–2
–2
–4
–4
(1, 3)
2
4
x
b.
d.
y
–4
–2
y
4
4
2
2
O
2
4
–4
x
–2
O
–2
–2
–4
–4
(3, –1)
2
4
(3, 1)
Without graphing, classify each system as independent, dependent, or inconsistent.
____ 67.
a. dependent
b. inconsistent
c. independent
Solve the system by the method of substitution.
____ 68.
a. (2, 1, –1)
b. (2, –1, 1)
c. (–2, 1, 1)
d. (2, 1, 1)
Use the elimination method to solve the system.
____ 69.
a. (3, 5)
b. (5, 3)
c. (–3, –5)
____ 70.
a. infinite solutions
b. (–5, 2)
c. (5, –2)
d. no solutions
a. (5, –6)
b. no solutions
c. (–5, 6)
d. infinite solutions
____ 71.
d. (–5, –3)
x
____ 72.
a. (1, –3, 1)
b. (1, 3, 1)
c. (–1, 3, 1)
d. (1, 3, –1)
Solve the system of inequalities by graphing.
____ 73.
a.
–6
–4
4
4
2
2
–2 O
–2
2
4
6
–4
–6
x
–4
–2 O
–2
–4
–4
–6
–6
d.
y
–6
y
6
b.
____ 74.
c.
y
6
6
4
4
2
2
2
4
6
x
4
6
x
2
4
6
x
y
6
–2 O
–2
2
–6
–4
–2 O
–2
–4
–4
–6
–6
a.
c.
y
–4
–2
4
4
2
2
O
2
4
–2
O
–2
–4
–4
d.
y
–2
–4
x
–2
b.
–4
y
4
2
2
2
4
–4
x
4
x
2
4
x
2
4
x
y
4
O
2
–2
O
–2
–2
–4
–4
____ 75.
a.
c.
y
–4
–2
y
4
4
2
2
O
2
4
x
–4
–2
O
–2
–2
–4
–4
b.
d.
y
–4
–2
y
4
4
2
2
O
2
4
–4
x
–2
O
–2
–2
–4
–4
2
4
x
____ 76. Your computer supply store sells two types of inkjet printers. The first, type A, costs $137 and you make a
$50 profit on each one. The second, type B, costs $100 and you make a $40 profit on each one. You can order
no more than 100 printers this month, and you need to make at least $4400 profit on them. If you must order
at least one of each type of printer, how many of each type of printer should you order if you want to
minimize your cost?
a. 40 of type A
c. 60 of type A
60 of type B
40 of type B
b. 30 of type A
d. 70 of type A
70 of type B
30 of type B
____ 77. A factory can produce two products, x and y, with a profit approximated by P = 12x + 23y – 900. The
production of y can exceed x by no more than 200 units. Moreover, production levels are limited by the
formula
What production levels yield maximum profit?
a. x = 0
b. x = 1000
c. x = 0
d. x = 200
y=0
y=0
y = 200
y = 400
Solve the system using either method of substitution or elimination.
____ 78.
a. no solution
b. (2, –5, –2)
c. (–2, –5, 2)
Find the sum or difference.
____ 79.
a.
c.
b.
d.
d. (2, 5, 2)
Use matrices A, B, and C. Find the sum or difference if you can.
____ 80. B + A
a.
c. not possible
b.
d.
a. not possible
c.
b.
d.
a.
c.
b.
d. none of these
____ 81.
____ 82.
Find the values of the variables.
____ 83.
a. x = 2, y = 4
b. x = –1, y = 3
c. x = 4, y = 2
d. x = 3, y = –1
a. t = –8, y = 4
b. t = 6, y = –8
c. t = –2, y = 6
d. t = –8, y = 6
____ 84.
Solve the matrix equation.
____ 85.
a.
c.
b.
d.
a.
c.
b.
d.
a.
c.
b.
d.
____ 86.
____ 87.
____ 88. A(0, 0), B(–1, 3), and C(2, 1); a rotation of 180º
y
4
–1
2
–4
–2
O A
–2
–4
C
2
4
x
a.
4
–1
B'
2
–4
–2
b.
B'–2
4
–1
O A
2
4 x
–4
–2
–4
–4
d.
y
4
–1
2
4 x
–4
–2
–4
–4
C
2
B'
Find the coordinates of the image after a reflection in the given line.
____ 89.
-axis
a.
c.
b.
d.
Determine whether the matrix has an inverse. If an inverse exists, find it.
____ 90.
a.
c. does not exist
b.
d.
4 x
y
–2C' O A
–2
B'
C'
2
C
2
C
O A
–2
–2
O A
y
2
C
C'
4
–1
C'
2
–4
c.
y
4 x
Assign each letter and a blank space to a number as shown by the alphabet table below:
0=_
1=A
2=B
3=C
4=D
5=E
6=F
7=G
8=H
9=I
10 = J
11 = K
12 = L
13 = M
14 = N
15 = O
16 = P
17 = Q
18 = R
19 = S
20 = T
21 = U
22 = V
23 = W
24 = X
25 = Y
26 = Z
____ 91. The matrix
was used to encode to
. Find
to decode the matrix.
a. IN BROAD DAYLIGHT
b. RUN LIKE THE WIND
c. GRIND TO A HALT
d. LEAPS AND BOUNDS
____ 92. Use an augmented matrix to solve the system
b. no solution
a.
.
c.
d.
Use Cramer’s Rule to solve the system.
____ 93.
.
a. (3, 5, 4)
b. (3, –5, –4)
c. (–2, –25, 10)
d. (–3, –5, –4)
Solve the system.
____ 94.
a. (19, 14, –2, –7)
b. (3, –4, –3, 0)
c. (3, 4, –3, 0)
d. (–3, 4, 3, –1)
____ 95.
a.
b.
c. no solution
d.
and use it
____ 96. A gem store sells beads made of amber and quartz. For 4 amber beads and 4 quartz beads, the cost is $46.00.
For 1 amber bead and 3 quartz beads, the cost is $14.50. Find the price of each type of bead.
a. amber $10.00, quartz $1.50
c. amber $10.25, quartz $1.75
b. amber $9.75, quartz $1.25
d. amber $1.50, quartz $10.00
Identify the vertex and the axis of symmetry of the parabola. Identify points corresponding to P and Q.
y
____ 97.
8
4
P
–8
–4
O
4
8
x
Q
–4
–8
a. (–3, 1), x = –3;
P'(–2, 0), Q'(–5, –3)
b. (1, –3), x = 1;
P'(–2, 0), Q'(–5, –3)
c. (–3, 1), x = –3;
P'(–4, 0), Q'(–1, –3)
d. (1, –3), x = 1;
P'(–4, 0), Q'(–1, –3)
Find a quadratic model for the set of values.
____ 98. (–2, 8), (0, –4), (4, 68)
a.
b.
c.
d.
____ 99. A manufacturer determines that the number of drills it can sell is given by the formula
, where p is the price of the drills in dollars.
a. At what price will the manufacturer sell the maximum number of drills?
b. What is the maximum number of drills that can be sold?
a. $60; 285 drills
c. $31; 2,418 drills
b. $30; 2,415 drills
d. $90; 8,385 drills
____ 100. Dalco Manufacturing estimates that its weekly profit, P, in hundreds of dollars, can be approximated by the
formula
, where x is the number of units produced per week, in thousands.
a. How many units should the company produce per week to earn the maximum profit?
b. Find the maximum weekly profit.
a. 1,000 units; $1300
c. 1,000 units; $600
b. 3,000 units; $100
d. 2,000 units; $1100
____ 101. Use vertex form to write the equation of the parabola.
y
8
6
4
2
–8 –6 –4 –2 O
–2
2
4
6
8
x
–4
–6
–8
a.
b.
c.
d.
Write the equation of the parabola in vertex form.
____ 102. vertex (0, 3), point (–4, –45)
a.
b.
c.
d.
Factor the expression.
____ 103.
a.
b.
c.
d.
____ 104.
a.
b.
____ 105. Solve by factoring.
=0
a.
b. –8, 4
1
8, −
2
____ 106. Find the additive inverse of
.
a.
b.
c.
d. no solution
c. –8, 1
d.
1, −
1
2
c.
d.
____ 107. Find the first three output values of the fractal-generating function
input value.
a.
, 536828 + 336604i
b.
, 536828 + 336604i
c.
d.
, 536828 + 336604i
Solve the quadratic equation by completing the square.
. Use z = 0 as the first
____ 108.
a.
c.
7
−
6
b.
−
____ 109.
____ 110.
____ 111.
____ 112.
____ 113.
7
6
d.
7
7
3
3
5
3
Classify –3x – 2x by degree and by number of terms.
a. quintic binomial
c. quintic trinomial
b. quartic binomial
d. quartic trinomial
Classify –7x5 – 6x4 + 4x3 by degree and by number of terms.
a. quartic trinomial
c. cubic binomial
b. quintic trinomial
d. quadratic binomial
Zach wrote the formula w(w – 1)(5w + 4) for the volume of a rectangular prism he is designing, with width w,
which is always has a positive value greater than 1. Find the product and then classify this polynomial by
degree and by number of terms.
a.
; quintic trinomial
b.
; quadratic monomial
c.
; cubic trinomial
d.
; quartic trinomial
Write 4x2(–2x2 + 5x3) in standard form. Then classify it by degree and number of terms.
a. 2x + 9x4; quintic binomial
c. 2x5 – 8x4; quintic trinomial
5
4
b. 20x – 8x ; quintic binomial
d. 20x5 – 10x4; quartic binomial
The table shows the number of hybrid cottonwood trees planted in tree farms in Oregon since 1995. Find a
cubic function to model the data and use it to estimate the number of cottonwoods planted in 2006.
Years since 1995
1
3
5
7
9
Trees planted (in thousands)
1.3
18.3
70.5
177.1
357.3
a.
; 630.3 thousand trees
b.
; 630.3 thousand trees
c.
; 618.1 thousand trees
d.
; 618.1 thousand trees
____ 114. Miguel is designing shipping boxes that are rectangular prisms. One shape of box with height h in feet, has a
volume defined by the function
. Graph the function. What is the maximum volume
for the domain
? Round to the nearest cubic foot.
a. 10 ft3
b. 107 ft3
c. 105 ft3
d. 110 ft3
____ 115. Find the zeros of
. Then graph the equation.
a. 3, 2, –3
c. 3, 2
y
–6
–4
y
6
6
4
4
2
2
–2
2
4
6
x
–6
–4
–2
–2
–2
–4
–4
–6
–6
b. 0, –3, –2
4
6
x
2
4
6
x
d. 0, 3, 2
y
–6
2
–4
y
6
6
4
4
2
2
–2
2
4
6
x
–6
–4
–2
–2
–2
–4
–4
–6
–6
____ 116. Find the zeros of
and state the multiplicity.
a. 2, multiplicity –3; 5, multiplicity 6
b. –3, multiplicity 2; 6, multiplicity 5
c. –3, multiplicity 2; 5, multiplicity 6
d. 2, multiplicity –3; 6, multiplicity 5
____ 117.
a. 3
b. –3
c. –3, 3
d. no solution
____ 118. The dimensions in inches of a shipping box at We Ship 4 You can be expressed as width x, length x + 5, and
height 3x – 1. The volume is about 7.6 ft3. Find the dimensions of the box in inches. Round to the nearest
inch.
a. 15 in. by 20 in. by 44 in.
c. 15 in. by 20 in. by 45 in.
b. 12 in. by 17 in. by 35 in.
d. 12 in. by 17 in. by 36 in.
____ 119. Find the rational roots of
.
a. 2, 6
b. –6, –2
c. –2, 6
d. –6, 2
Find the roots of the polynomial equation.
____ 120.
a. –3 ± 5i, –4
b. 3 ± 5i, –4
c. –3 ± i, 4
d. 3 ± i, 4
____ 121. For the equation
, find the number of complex roots and the possible number of real
roots.
a. 4 complex roots; 0, 2 or 4 real roots
b. 4 complex roots; 1 or 3 real roots
c. 3 complex roots; 1 or 3 real roots
d. 3 complex roots; 0, 2 or 4 real roots
For the equation, find the number of complex roots, the possible number of real roots, and the possible
rational roots.
____ 122.
a.
b.
c.
d.
6 complex roots; 2, 4, or 6 real roots; possible rational roots:
6 complex roots; 2, 4, or 6 real roots; possible rational roots:
6 complex roots; 0, 2, 4, or 6 real roots; possible rational roots:
6 complex roots; 0, 2, 4, or 6 real roots; possible rational roots:
____ 123. In how many ways can 3 singers be selected from 5 who came to an audition?
a. 1
b. 10
c. 5
d. 60
Find the real-number root.
____ 124.
a.
b.
c.
d.
Multiply and simplify if possible.
____ 125.
a.
b.
c.
d.
Divide and simplify.
____ 126.
a.
b.
c.
Divide and simplify. Assume that all variables are positive.
____ 127.
d.
a.
b.
c.
d.
Rationalize the denominator of the expression. Assume that all variables are positive.
____ 128.
a.
c.
b.
d. none of these
a.
c.
b.
d.
____ 129.
Add if possible.
____ 130.
a.
b.
c.
d. not possible to simplify
____ 131. A rope is
units long. The rope is cut into two pieces, so that the lengths of the pieces are in the ratio 2 :
3. What is the length of the longer piece expressed in simplest radical form?
a.
c.
units
units
b.
d.
units
units
____ 132. Write the radical expression
a.
in exponential form.
b.
c.
d.
Solve. Check for extraneous solutions.
____ 133.
a.
−
b. −1
2
c.
3
1 and −
2
d. 1
3
____ 134.
a.
b.
7
6
____ 135. Let
2
c.
−
3
and
1
4
. Find f(x) – g(x).
d.
6
7
a. 2x – 5
b. 2x + 5
____ 136. Let
c. 4x – 1
and
. Find
d. 2x – 1
and its domain.
a. 3x + 2; all real numbers except x = 4
b. –9x + 6; all real numbers except x = 4
c. –3x + 2; all real numbers except x = –4
d. 9x – 6; all real numbers except x = –4
____ 137. Let
and
. Find
.
a. 23
b. –53
c. –9
d. 3
____ 138. Graph the relation and its inverse. Use open circles to graph the points of the inverse.
x
0
4
9
10
y
3
2
7
–1
a.
c.
y
–8
8
8
4
4
–4
4
8
–8
x
–4
–4
–4
–8
–8
b.
d.
y
–8
y
8
4
4
4
8
x
–8
–4
–4
–4
–8
–8
____ 139. For the function
a.
, find
;
. Determine whether
is not a function.
b.
;
is not a function.
8
x
4
8
x
y
8
–4
4
is a function.
c.
;
is a function.
d.
;
is a function.
____ 140. Police can estimate the speed of a vehicle before the brakes are applied using the formula
,
where s is the speed in miles per hour and d is the length of the vehicle’s skid marks. What was the
approximate speed of a vehicle that left a skid mark measuring 100 feet?
a. about 29 miles per hour
c. about 48 miles per hour
b. about 10 miles per hour
d. about 43 miles per hour
Graph the function.
____ 141.
a.
c.
y
–8
8
8
4
4
–4
4
8
–4
–4
–8
–8
d.
y
____ 142. xy + 16 = 0
–8
x
–4
b.
–8
y
8
4
4
4
8
x
8
x
4
8
x
y
8
–4
4
–8
–4
–4
–4
–8
–8
a.
10
c.
y
10
5
–10
5
–5
5
10 x
–10
–5
–5
–5
–10
–10
b.
10
d.
y
10
5
–10
–5
10 x
–10
–5
–5
–5
–10
–10
10 x
5
10 x
y
to make it easy to graph using a translation. Describe the graph.
.
translated 4 units left and 4 units down.
It is the graph of
b.
. It is the graph of
c.
.
translated 4 units left and 4 units down.
translated 4 units right and 4 units down.
It is the graph of
d.
5
5
5
____ 143. Rewrite
a.
y
.
It is the graph of
translated 4 units right and 4 units down.
____ 144. Write an exponential function
for a graph that includes (1, 15) and (0, 6).
a.
c.
b.
d.
____ 145. For an annual rate of change of –31%, find the corresponding growth or decay factor.
a. 0.31
b. 0.69
c. 1.31
d. 1.69
____ 146. Use a graphing calculator. Use the graph of
to evaluate
to four decimal places.
a. 5.4739
b. 4.6211
c. 2.7183
d. 0.1827
Evaluate the logarithm.
____ 147. log 0.01
a. –10
b. –2
____ 148. Write the equation
c. 2
d. 10
in exponential form.
a.
b.
c.
d.
Graph the logarithmic equation.
____ 149.
a.
c.
y
y
5
4
3
2
1
5
4
3
2
1
–5 –4 –3 –2 –1
–1
–2
–3
–4
–5
b.
1 2 3 4 5
–10 –8 –6 –4 –2
–1
–2
–3
–4
–5
x
d.
y
y
5
4
3
2
1
–5 –4 –3 –2 –1
–1
–2
–3
–4
–5
2 4 6 8 10 x
5
4
3
2
1
1 2 3 4 5
x
–5 –4 –3 –2 –1
–1
–2
–3
–4
–5
1 2 3 4 5
State the property or properties of logarithms used to rewrite the expression.
____ 150.
a. Commutative Property
b. Product Property
c. Quotient Property
d. Power Property
a. Quotient Property
b. Product Property
c. Difference Property
d. Power Property
____ 151.
x
Write the expression as a single logarithm.
____ 152.
a.
b.
c.
d.
Expand the logarithmic expression.
____ 153.
a.
c.
b.
d.
____ 154. Solve
. Round to the nearest ten-thousandth.
a. 0.6616
b. 2.6466
c. 1.7509
d. 1.9091
____ 155. Use the Change of Base Formula to solve
. Round to the nearest ten-thousandth.
a. 7.6133
b. 9.3658
c. 3.2459
d. 12.9837
____ 156. Solve
.
a. –1.8847
b. –0.1069
c. 0.3375
d. 1.0378
____ 157. Solve
. Round to the nearest ten-thousandth.
a. 10.7722
b. 5
c. 2.7826
d. 0.6309
____ 158. The generation time G for a particular bacteria is the time it takes for the population to double. The bacteria
, where t is the time period of the population
increase in population is shown by the formula
increase, a is the number of bacteria at the beginning of the time period, and P is the number of bacteria at the
end of the time period. If the generation time for the bacteria is 6 hours, how long will it take 8 of these
bacteria to multiply into a colony of 7681 bacteria? Round to the nearest hour.
a. 177 hours
b. 76 hours
c. 4 hours
d. 85 hours
Is the relationship between the variables in the table a direct variation, an inverse variation, or neither?
If it is a direct or inverse variation, write a function to model it.
____ 159.
a.
b.
x
–5
–1
4
7
y
16
8
–2
–8
direct variation; y = −
inverse variation;
c. neither
16
5
x
____ 160. Suppose that x and y vary inversely and that
when x = 3. Write a function that models the inverse
variation and find y when x = 10.
a.
c.
1
1
;
;
20
6
b.
d.
1
1
;
;
20
54
____ 161. The values (9.4, 11) and (11, y) are from an inverse variation. Find the missing value and round to the nearest
hundredth.
a. 9.4
b. 9.4
c. 103.4
d. 1137.4
____ 162. Suppose that y varies directly with x and inversely with z y = 25 when x = 35, and z = 7. Write the equation
that models the relationship. Then find y when x = 12 and z = 4.
c.
a.
5
7
3
b.
21
3
d.
15
____ 163. Suppose that y varies jointly with w and x and inversely with z and y = 360 when w = 8, x = 25 and z = 5.
Write the equation that models the relationship. Then find y when w = 4, x = 4 and z = 3.
c.
a.
80
48
3
b.
d.
27
15
16
Describe the combined variation that is modeled by the formula or equation.
____ 164.
a.
b.
c.
d.
a varies directly as F and inversely as m.
a varies directly as m and inversely as F.
a varies directly as F and m.
y varies inversely as F and m.
Find any points of discontinuity for the rational function.
____ 165.
a. x = 6, x = 2, x = 8
b. x = 9, x = 7
c. x = –9, x = –7
d. x = –6, x = –2, x = –8
a. x = 1, x = 7
b. x = 8
c. x = 1, x = –7
d. x = –1, x = 7
____ 166.
____ 167. Describe the vertical asymptote(s) and hole(s) for the graph of
.
a.
b.
c.
d.
asymptote: x = –4 and hole: x = 2
asymptotes: x = –4 and x = 2
asymptote: x = –5 and hole: x = –4
asymptote: x = 4 and hole: x = –2
Multiply or divide. State any restrictions on the variables.
____ 168.
a.
c.
b.
d.
____ 169. A group of college students are volunteering for Help the Homeless during their spring break. They are
putting the finishing touches on a house they built. Working alone, Irina can paint a certain room in 7 hours.
Paulo can paint the same room in 6 hours. Write an equation that can be used to find how long it will take
them working together to paint the room. How many hours will it take them to paint the room? If necessary,
round your answer to the nearest hundredth.
c.
a.
; 13 hours
; 6.5 hours
b.
; 3.23 hours
d.
____ 170. The sum of the reciprocals of two consecutive even integers is
; 6.5 hours
11
60
. Write an equation that can be used to find
the two integers. Find the two integers.
a.
c.
11
11
= ; 8 and 10
= ; 10 and 12
60
60
b.
d.
11
11
= ; 10 and 12
= ; 8 and 10
60
60
____ 171. Linda has 7 quarts of juice. The juice is a mixture that is 10% pineapple juice and 90% orange juice. How
much pineapple juice should she add to get a mixture that is 60% pineapple juice? Round your answer to the
nearest tenth of a quart.
a. 8.8 qt
b. 1.8 qt
c. 3.9 qt
d. 4.2 qt
Graph the equation. Describe the graph and its lines of symmetry.
____ 172.
a.
c.
y
y
8
8
6
6
4
4
2
2
–8 –6 –4 –2
–2
2
4
6
8
–8 –6 –4 –2
–2
x
–4
–4
–6
–6
–8
–8
The graph is an ellipse. The center is at the
origin. It has two lines of symmetry, the xaxis and the y-axis.
b.
8
6
6
4
4
2
2
2
4
6
8
x
–8 –6 –4 –2
–2
–4
–4
–6
–6
–8
–8
The graph is an ellipse. The center is at the
origin. It has two lines of symmetry, the xaxis and the y-axis.
4
6
8
x
y
8
–8 –6 –4 –2
–2
2
he graph is a circle. The center is at the
origin. Every line through the origin is a
line of symmetry.
d.
y
T
T
2
4
6
8
x
he graph is a circle. The center is at the
origin. Every line through the origin is a
line of symmetry.
Identify the center and intercepts of the conic section. Then find the domain and range.
____ 173.
y
8
6
4
2
–8 –6 –4 –2
–2
2
4
6
8
x
–4
–6
–8
a. The center of the ellipse is (0, 0). The x-intercepts are (0, 5) and (0, –5). The y-intercepts
are (–3, 0) and (3, 0). The domain is {x | –3 ≤ x ≤ 3}. The range is {y | –5 ≤ y ≤ 5}.
b. The center of the ellipse is (0, 0). The x-intercepts are (–3, 0) and (3, 0). The y-intercepts
are (0, 5) and (0, –5). The domain is {x | –3 ≤ x ≤ 3}. The range is {y | –5 ≤ y ≤ 5}.
c. The center of the ellipse is (0, 0). The x-intercepts are (0, 5) and (0, –5). The y-intercepts
are (–3, 0) and (3, 0). The domain is {x | –5 ≤ y ≤ 5}. The range is {y | –3 ≤ x ≤ 3}.
d. The center of the ellipse is (0, 0). The x-intercepts are (–3, 0) and (3, 0). The y-intercepts
are (0, 5) and (0, –5). The domain is {x | –5 ≤ y ≤ 5}. The range is {y | –3 ≤ x ≤ 3}.
____ 174.
y
8
6
4
2
–8 –6 –4 –2
–2
2
4
6
8
x
–4
–6
–8
a. The center of the circle is (6, 6). The x-intercepts are (6, 0) and (–6, 0). The y-intercepts
are (0, 6) and (0, –6). The domain is {y | 6 ≤ y ≤ –6}. The range is {x | 6 ≤ x ≤ –6}.
b. The center of the circle is (6, 6). The x-intercepts are (6, 0) and (–6, 0). The y-intercepts
are (0, 6) and (0, –6). The domain is {x | –6 ≤ x ≤ 6}. The range is {y | –6 ≤ y ≤ 6}.
c. The center of the circle is (0, 0). The x-intercepts are (6, 0) and (–6, 0). The y-intercepts
are (0, 6) and (0, –6). The domain is {x | –6 ≤ x ≤ 6}. The range is {y | –6 ≤ y ≤ 6}.
d. The center of the circle is (0, 0). The x-intercepts are (6, 0) and (–6, 0). The y-intercepts
are (0, 6) and (0, –6). The domain is {y | 6 ≤ y ≤ –6}. The range is {x | 6 ≤ x ≤ –6}.
____ 175. Identify the focus and the directrix of the graph of
a. focus (0, –3), directrix at y = –3
.
c. focus (0, –3), directrix at y = 3
b. focus (–3, 0), directrix at y = –3
d. focus (–3, 0), directrix at y = 3
____ 176. Identify the vertex, focus, and directrix of the graph of
.
a. vertex (2, 5), focus (2, 7), directrix at y = 3
b. vertex (2, –5), focus (0, 7), directrix at y = –2
c. vertex (–2, –5), focus (0, 2), directrix at y = 2
d. vertex (–2, 5), focus (2, –2), directrix at y = 3
____ 177. Write an equation in standard form for the circle.
y
4
2
–4
–2
2
4
x
–2
–4
a.
c.
b.
d.
____ 178. Graph
.
a.
c.
y
y
8
–8
8
8
–8
x
–8
8
–8
x
b.
d.
y
y
8
–8
8
8
–8
x
–8
8
x
–8
____ 179. An elliptical track has a major axis that is 80 yards long and a minor axis that is 72 yards long. Find an
equation for the track if its center is (0, 0) and the major axis is the x-axis.
a.
c.
b.
d.
Write an equation of an ellipse in standard form with the center at the origin and with the given
characteristics.
____ 180.
a vertex at (–5, 0) and a co–vertex at (0, 4)
a.
c.
b.
d.
____ 181. height of 12 units and width of 19 units
a.
b.
____ 182. Write an equation for the graph.
c.
d.
y
4
2
–4
–2
2
4
x
–2
–4
a.
c.
b.
d.
____ 183. Find the foci of the graph
a. (
. Draw the graph.
c. (0, 3)
41 , 0)
y
y
–12
b. ( 3, 0)
–8
12
12
8
8
4
4
–4
4
8
12 x
–12
–8
–4
4
–4
–4
–8
–8
–12
–12
d. (0,
41 )
8
12 x
y
–12
–8
y
12
12
8
8
4
4
–4
4
8
12 x
–12
–8
–4
4
–4
–4
–8
–8
–12
–12
8
12 x
____ 184. Find an equation that models the path of a satellite if its path is a hyperbola, a = 55,000 km, and c = 81,000
km. Assume that the center of the hyperbola is the origin and the transverse axis is horizontal.
a.
b.
c.
d.
Identify the conic section. If it is a parabola, give the vertex. If it is a circle, give the center and radius.
If it is an ellipse or a hyperbola, give the center and foci.
____ 185.
a. parabola; vertex (–5, 3)
c. parabola; vertex (5, 4)
b. parabola; vertex (5, –3)
d. parabola; vertex (4, 3)
____ 186. Find the center and radius of the circle with equation
a. center (–1, 1); radius 4
c. center (–1, 1); radius 2
b. center (1, –1); radius 4
d. center (1, –1); radius 2
.
____ 187. Write an explicit formula for the sequence , , ,
.
a.
c.
b.
d.
,
, .... Then find
____ 188. The table shows the predicted growth of a particular bacteria after various numbers of hours. Write an explicit
formula for the sequence of the number of bacteria.
Hours (n)
Number of
Bacteria
1
2
3
4
5
19
38
57
76
95
a.
c.
b.
d.
Is the sequence arithmetic? If so, identify the common difference.
____ 189. 13, 20, 27, 34, ...
a. yes, 7
b. yes, –7
c. yes, 13
____ 190. Find the missing term of the arithmetic sequence 22,
d. no
, 34,...
a. 46
b. 16
c. 28
d. 40
____ 191. A grocery clerk sets up a display of 12-pack cartons of cola. There are 15 cartons at the base of the triangle
and one at the top. How many cartons of cola are needed for the complete display?
a. 180 cartons
b. 30 cartons
c. 120 cartons
d. 15 cartons
Write the explicit formula for the sequence. Then find the fifth term in the sequence.
____ 192.
a.
b.
; 243
; –243
c.
d.
; 243
; –729
Find the missing term of the geometric sequence.
____ 193. 1250,
, 50, ...
a. 1200
b. 650
c. 250
d. 125
____ 194. A rope is swinging in such a way that the length of the arc is decreasing geometrically. If the first arc is 18
feet long and the third arc is 8 feet long, what is the length of the second arc?
a. 12 feet
b. 10 feet
c. 5 feet
d. 72 feet
Use the finite sequence. Write the related series. Then evaluate the series.
____ 195. 26, 29, 32, 35, 38, 41, 44
a. 26 + 29 + 32 + 35 + 38 + 41 + 44 = 219
b. 26 + 29 + 32 + 35 + 38 + 41 + 44 = 245
c. 26 – 29 – 32 – 35 – 38 – 41 – 44 = –193
d. 26 + 29 + 32 + 35 + 38 + 41 + 44 = 201
____ 196. The sequence –5, 0, 5, 10, ..., 65 has 15 terms. Evaluate the related series.
a. 900
b. 455
c. 450
d. 445
____ 197. Use summation notation to write the series 49 + 54 + 59 + ... for 14 terms.
a.
c.
b.
d.
____ 198. For the series
a. 7 terms
____ 199. For the series
, find the number of terms in the series.
b. 16 terms
c. 8 terms
d. 9 terms
, find the first and the last term.
a. 5, 8
b. –3, 1
____ 200. Evaluate the series 1000 + 500 + 250 + ... to
a. 968.75
b. 1062.5
c. 5, 9
.
c. 1937.5
d. 4, 20
d. 12,500
Evaluate the infinite geometric series. Round to the nearest hundredth if necessary.
____ 201.
a. 16
b. 2
c. 16
d. 8
____ 202. The area under this curve has been subdivided into rectangles. Use the rectangles to approximate the area
under the curve.
a. 10 square units
c. 48 square units
b. 12 square units
d. 55 square units
____ 203. The dartboard has 8 sections of equal area. The letters represent the colors red (R), yellow (Y), blue (B), and
green (G). Use a table to show the probability distribution for a dart that hits the board at a random location.
Y
G
G
G
Y
Y
B
R
a.
c.
b.
d.
____ 204. Show the probability distribution described by
for x = 1, 2, 3, and 4. Include the cumulative
probability.
a.
c.
b.
d.
Find the mean, median, and mode of the data set. Round to the nearest tenth.
____ 205. 15, 13, 9, 9, 7, 1, 11, 10, 13, 1, 13
a. mean = 9.3,
b. mean = 8.5,
median = 8, mode
median = 10,
=13
mode = 13
c. mean = 9.3,
median = 10,
mode = 13
d. mean = 8.5,
median = 10,
mode = 8
Make a box-and-whisker plot of the data.
____ 206. 24, 18, 29, 21, 16, 23, 13, 11
a.
10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
b.
10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
c.
10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
d.
10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Find the values of the 30th and 90th percentiles of the data.
____ 207. 129, 113, 200, 100, 105, 132, 100, 176, 146, 152
a. 30th percentile = 105;
c.
90th percentile = 200
b. 30th percentile = 113;
d.
90th percentile = 200
30th percentile = 105;
90th percentile = 176
30th percentile = 113;
90th percentile = 176
Find the outlier in the set of data.
____ 208. 17, 13, 16, 18, 38, 14, 21, 24
a. 38
b. 14
c. 16
d. 17
Find the range and interquartile range of the data. Round to the nearest tenth.
____ 209. 44, 45, 38, 8, 40, 35, 10, 55, 23, 36
a. range = 37; interquartile range = 21
b. range = 47; interquartile range = 14
c. range = 37; interquartile range = 14
d. range = 47; interquartile range = 21
____ 210. Another measure of variation is variance, which equals . Find the variance and standard deviation of the
data set. Round to the nearest tenth.
7, 8, 4, 10, 6, 10
a. variance = 4.6;
c. variance = 1.5;
standard deviation = 2.3
standard deviation = 2.3
b. variance = 1.5;
d. variance = 4.6;
standard deviation = 2.1
standard deviation = 2.1
____ 211. A survey of 480 high school students found that 37% had a pet. Find the margin of error. Round to the nearest
percent. Use the margin of error to find an interval that is likely to contain the true population proportion.
a. margin of error =
;
c. margin of error =
;
interval, 37% to 42%
interval, 30% to 44%
b. margin of error =
;
d. margin of error =
;
interval, 32% to 42%
interval, 37% to 44%
____ 212. The numbers of cookies in a shipment of bags are normally distributed, with a mean of 64 and a standard
deviation of 4. What percent of bags of cookies will contain between 60 and 68 cookies?
a. 50%
b. 13.5%
c. 68%
d. 34%
____ 213. A grocery store will only accept yellow onions that are at least 3 in. in diameter. A grower has a crop of
onions with diameters that are normally distributed, with a mean diameter of 3.25 in. and a standard deviation
of 0.25 in. What percent of the onions will be accepted by the grocery store?
a. 34%
b. 97.5%
c. 84%
d. 50%
Sketch the angle in standard position.
____ 214. –150º
a.
c.
y
ο
–150
b.
y
ο
–150
x
d.
y
ο
–150
x
x
y
ο
–150
x
____ 215. Find the measure of an angle between 0º and 360º coterminal with an angle of –110º in standard position.
a. 250º
b. 20º
c. 110º
d. 70º
____ 216. Find the exact value of cos 300º and sin 300º.
a.
c.
b.
d.
____ 217. For an angle in standard position measuring 92º, find the values of cos and sin . Round your answers to the
nearest hundredth.
a. 0.03, –1.00
b. 0.03, 1.00
c. –0.03, –1.00
d. –0.03, 1.00
Write the measure in degrees.
____ 218. –
radians
a.
º
b.
c. –315º
º
d. –5.5º
____ 219. A Ferris wheel has a radius of 80 feet. Two particular cars are located such that the central angle between
them is 165º. To the nearest tenth, what is the measure of the intercepted arc between those two cars on the
Ferris wheel?
a. 27.8 feet
b. 13,200.0 feet
c. 502.7 feet
d. 230.4 feet
____ 220. Find the amplitude of the sine curve shown below.
y
4
2
O
π
2π
3π
θ
–2
–4
a. 2π
b. 8
c. 2
d. 4
____ 221. A particular sound wave can be graphed using the function
. Find the amplitude and period of the
function.
c. amplitude = 2π, period = 3
a. amplitude = 3, period = 2π
b.
d.
1
1
amplitude = π, period = –3
amplitude = –3, period =
2
2
____ 222. Use a graphing calculator to graph the function
on the interval
and
.
Evaluate the function at
. Round to the nearest tenth.
a. –171.4, 329.7, 32.2
c. 171.4, –329.7, –32.2
b. –329.7, 100.7, –69.3
d. –2.7, 0.8, –0.6
____ 223. Use a graphing calculator to solve the equation
answers to the nearest hundredth.
a. 1.21, 4.35
b. 3.64
in the interval from
c. 1.21, 2.26, 3.31, 4.35, 5.40
d. 0.404, 1,452.5, 3.55, 4.59, 5.64
Graph the function in the interval from 0 to 2π.
____ 224.
1
y = 4 cos θ
2
. Round your
a.
c.
y
y
4
4
2
2
2π
π
O
O
θ
–2
–2
–4
–4
b.
d.
y
4
2
2
2π
π
O
θ
2π
θ
π
2π
θ
y
4
O
π
–2
–2
–4
–4
____ 225.
a.
c.
y
y
4
4
2
2
O
O
π
2π
π
θ
–2
–2
–4
–4
2π
θ
b.
d.
y
y
4
4
2
2
O
O
2π
π
π
θ
–2
–2
–4
–4
____ 226. Suppose
. Find
a. 120
b.
2π
θ
.
c.
d.
____ 227. Find the exact value of csc 135º. If the expression is undefined, write undefined.
a. 0
b. undefined
c.
d.
____ 228. Find the exact value of sec (–270º). If the expression is undefined, write undefined.
a. undefined
b. 1
c. 0
d. –1
____ 229. Evaluate
to the nearest hundredth. The angle is given in radians.
a. –0.58
b. 0
____ 230. Find the amplitude of the periodic function.
c. 1.73
d. –1.73
c. 7
d. 1.75
y
4
2
–4
–2
2
4
x
–2
–4
a. 3.5
b. 3
Use the graph of the inverse of y = cos θ. Find the radian measure(s) of the angle with the given cosine.
θ
–1
1
____ 231. 0
a.
x
c.
b.
____ 232. 1
a.
d. No such angle exists.
b.
d. No such angle exists.
c.
Use a unit circle and 30°-60°-90° triangles to find the degree measures of the angle.
____ 233. angles whose tangent is
a. 120° + n ⋅ 180°
b. 120° + n ⋅ 360°
c. 60° + n ⋅ 180°
d. 30° + n ⋅ 360°
Use a calculator and inverse functions to find the radian measures of the given angle. Round your
answer to the nearest hundredth.
____ 234. angles whose sine is 0.48
a. 1.07 + 2πn and –1.07 + 2πn
b. 0.50 + 2πn and –3.64 + 2πn
Solve the equation for 0 ≤
c. –0.46 + 2πn and 2.68 + 2πn
d. 0.50 + 2πn and –0.50 + 2πn
< 2π. Write your answer as a multiple of π, if possible.
____ 235.
____ 236.
a.
c.
b.
d.
a.
c.
b.
d.
____ 237.
a.
b.
c.
d.
a.
b.
c.
d.
____ 238.
____ 239. The equation
models the height h in centimeters after t seconds of a set of keys attached to the
end of a spring that has been stretched and then released. When will the set of keys first be 3 inches above the
resting position?
a. 1.6 seconds
b. 1 second
c. 3.3 seconds
d. 2 seconds
____ 240. In ∆XYZ, ∠Y is a right angle and
. Find sin Z in fraction and in decimal form. Round to the nearest
hundredth, if necessary.
Z
5
4
X
Y
a.
b.
____ 241. In
,
is a right angle. Find
c.
d.
to the nearest tenth of a degree.
B
x
64.6
A
24
60
C
a. 20.4
b. 68.2
c. 42.9
____ 242. Find the area of the triangle. Round your answer to the nearest tenth.
d. 21.8
B
4 m
49 °
A
C
4 m
a. 9.2 m2
b. 6.0 m2
c. 8 m2
d. 12.1 m2
____ 243. In
, j = 9 in., k = 5 in., and
= 43°. Find
.
a. 28°
b. 59°
c. 32°
d. 75°
____ 244. On a baseball field, the pitcher’s mound is 60.5 feet from home plate. During practice, a batter hits a ball 216
feet deep. The path of the ball makes a 34° angle with the line connecting the pitcher and the catcher, to the
right of the pitcher’s mound. An outfielder catches the ball and throws it to the pitcher. How far does the
outfielder throw the ball?
?
216 ft
60.5 ft 34
°
a. 207.4 ft
b. 224.3 ft
Find the exact value of the expression.
____ 245. sin 165°
c. 169.3 ft
d. 198.7 ft
a.
b.
c.
d.
Rewrite the expression as a trigonometric function of a single angle measure.
____ 246.
a.
b.
c.
d.
a.
b.
c.
d.
____ 247.
Use a half-angle identity to find the exact value of the expression.
____ 248.
sin 105°
a.
b.
c.
d.
____ 249. cos 67.5°
a.
b.
c.
d.
____ 250. Given
a.
and
, find the exact value of
b.
c.
.
d.