# Bonus Quiz Review

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```					                                              Quiz Review - Intermediate (Bonus points)

Simplify by combining like terms.                                                   10r3 (r-5)-2
15)
1) 9z - 3z 2 + 3z                                                             13(r-2 )-4

2) 9p2 + 9p3 - 2p2 - 5p3                                   Simplify using posivtive exponents only.
2x3 y-3 -5
16)
3) -9x2 + 9x3 + 6x - x2 + 8x - x3                                     x-3y4

Solve.                                                                              6a 2 b-5 0
17)
4) 6x - (5x - 1) = 2                                                      3a -4b6

5) -6x + 2(-3x - 3) = -10 - 8x                             Graph the inequality.
18) x > 1
1    1
6)     a - = -5
4    4

1   3                                                          19) x ≤ 0
7)     p- p=2
4   8

Solve for the specified letter.
8) I = Prt, for r
Solve and graph the inequality.
20) f - 4 < -12
1
9) V =     Bh, for B
3

y- x
10) w =        , for x                                               21) 7x + 2 > 51
z

Solve the problem.
11) If Gloria received a 6 percent raise and is now
making \$23,320 a year, what was her salary                               n
22)      <2
before the raise?                                                        -3

12) In a local election, 32,900 people voted. This
was a decrease of 11% over the last election.
How many people voted in the last election?
Round to the nearest whole person if                                     2     6
23) -     x≤-
necessary.                                                               3     7

Simplify using posivtive exponents only.
13) (2r2 s)2 (2r3 s-4)5
Solve.
14) (6x-3 y-5 )(4xy-3 )                                              24) -4(5x + 11) < -24x - 24

25) 12x - 18 > 3(3x - 1)

1
Quiz Review - Intermediate (continued)

Find the intercepts for the equation.                                      30) 3y - 21x = -18
26) -2x + y = 0                                                                                y
10

Graph the equation.
27) y = 3x - 4                                                                              5

y
10
-10    -5               5   10   x

5                                                                   -5

-10
-10       -5             5   10     x

-5
Graph.
-10                                           31) 7x = 28
y
10

3
28) y =     x
5                                                                                5

y
10
-10    -5               5   10   x

5                                                                   -5

-10
-10       -5             5   10     x

-5
32) y = 3
y
-10
10

29) 2x - y = 4                                                                             5

y
10
-10    -5               5   10   x

5                                                                   -5

-10
-10       -5             5   10     x

-5

-10

2
Quiz Review - Intermediate (continued)

Find the x- and y-intercepts for the equation. Then graph                38)
the equation.                                                                                      y
33) -6x - 24y = 24                                                                    10
y
10                                                                   5

5
-10     -5             5    10   x

x                                              -5
-10    -5             5    10

-5                                                                 -10

-10
Find an equation of the line containing the given pair of
points.
Find the slope and the y-intercept of the line.                          39) (-5, 7) and (8, -3)
34) 5x + 8y = 49
Write the equation of the line, with the given properties.
Find the slope of the line containing the two given points.               40) Through (-6, -1) and (4, -2)
35) (9, 3) and (7, 7)
Tell whether the lines are "parallel", "perpendicular", or
Find equation for the line with the indicated slope and            "neither."
y-intercept.                                                             41) y + 10 = -4x
4                 40                                        6y = 36x - 5
36) Slope - ; y-intercept 0,
7                  7
Find an equation of the line meeting the specified
Find the equation for the graph.                                   conditions.
37)                                                                               3
42) Through 0,     and parallel to 5x - 7y = 8
8
y
10
43) Containing the point (-7, -9), perpendicular to
5                                                  3x - 2y = -39

44) Containing the point (-3, 9), perpendicular to
-10    -5             5    10     x                             -4x - 9y = 93

-5
45) Containing the point (-1, 9), perpendicular to
-8x + 5y = -37
-10

3
Quiz Review - Intermediate (continued)

Graph on a plane.                                                       49) 5x + y ≤ 2
46) x ≥ 3                                                                                      y
y                                                              10
10

5
5

-10       -5             5   10   x
-10     -5             5   10     x
-5
-5

-10
-10

50) 2x + 5y ≥ -10
47) y < -5                                                                                    y
y                                                              10
10

5
5

-10       -5             5   10   x
-10     -5             5   10     x
-5
-5

-10
-10

Determine whether the graph is the graph of a function.
48) y ≥ 2x                                                        51)
y                                                                    y
10                                                                   10

5                                                                    5

-10     -5             5   10     x                                -10       -5             5   10   x

-5                                                                   -5

-10                                                                  -10

4
Quiz Review - Intermediate (continued)

52)                                                               For the function represented in the graph, determine the
y                                  domain or range, as requested.
10                                                  57) Find the domain.
20   y
5
15

10
-10     -5                  5   10     x                                               5

-5                                                                                                            x
-5 -4 -3 -2 -1          1   2   3       4       5
-5

-10                                                                   -10

-15

-20
53)
y
58) Find the range.
5    y

4
3
x                                                      2
1

-5 -4 -3 -2 -1            1   2       3       4       5x
-1
-2
-3

54)                                                                                           -4
-5
y
10
59) Find the domain.
5                                                                       5    y

4
3
-10     -5                  5   10     x
2

-5                                                                      1

-5 -4 -3 -2 -1            1   2       3       4       5x
-1
-10
-2
-3

Find the domain of f(x).                                                                            -4
55) f(x) = 9x + 6                                                                            -5

-9
56) f(x) =
x+2

5
Quiz Review - Intermediate (continued)

60) Find the domain.                                                                      For the functions f(x) and g(x), determine the domain of
y                                                     (f/g)(x) (the quotient of f and g).
4                                                                      69) f(x) = 11x2 , g(x) = 5x - 2
3
2                                                              The graph of a function f is provided. Determine the
1                                                              requested function value.
70) f(-1)
-5 -4 -3 -2 -1                     1       2       3       4   5x
-1                                                                                                          y
-2                                                                                             6
-3
4
-4
2

-6   -4   -2                2       4   6    x
61) Find the range.
-2
y
6
5                                                                                                  -4
4
-6
3
2
1

-4 -3 -2 -1-1                1       2       3       4   5     x
-2                                                                            71) f(2)
-3                                                                                                           y
-4
6
-5
-6                                                                                                      4

2
Find the function value.
62) Find f(2) when f(x) = -x + 5.                                                                          -6   -4   -2                2       4   6    x
-2

63) Find f(-1) when f(x) = -4x - 7.                                                                                       -4

-6

64) Find f(2) when f(x) = x2 - 3x + 7.

For the pair of functions, find the indicated sum,
72) f(1)
difference, product, or quotient.
65) Find (f + g)(4) when f(x) = x - 1 and g(x) = x                                                                        5    y

- 4.                                                                                                                  4
3
2
66) Find (f - g)(-3) when f(x) = 2x2 + 6 and g(x) =
1
x - 1.
-5 -4 -3 -2 -1                1       2   3   4   5x
-1
67) f(x) = x2 + 1, g(x) = 6x - 3
-2
Find (f · g)(x).
-3
-4
68) f(x) = 8x2 - 7x, g(x) = x2 - 3x - 28                                                                                  -5
Find (f/g)(x).

6
Quiz Review - Intermediate (continued)

A function of x is depicted in the graph. Find any input                                77) In 1820 the population of a midwest city was
values that produce the indicated output.                                                   16,000. By 1850 it had grown to 18,000. If it
73) f(x) = -1                                                                         continues to grow at the same rate, what will
4
the nearest whole number.
3
2                                                       78) In 1985, John invested \$15,000 in the stock
1                                                           market. By 1991 his investment had grown to \$
19,600. If the market continues to grow at the
-5 -4 -3 -2 -1               1       2   3   4   5x                             same rate, how much will be in his account in
-1
-2
-3
-4
79) The average value , V, of a certain type of car is
a linear function of the year, x. The average
-5
value was \$15,900 in 1993 and depreciated to
\$5940 in 1996. Let x = 0 represent 1993. Write
74) f(x) = 2                                                                         the value, V, as function of the year, x.
y
6                                                       80) An investment is worth \$3276 in 1994. By 1999
4                                                           it has grown to \$5011. Let V be the value of the
investment in the year x, where x = 0
2                                                           represents 1994. Write a linear function that
models the value of the investment in the year
-6     -4   -2                2       4   6     x
x.
-2

-4                                                      81) A vendor has learned that, by pricing hot dogs
-6                                                          at \$1.25, sales will reach 130 hot dogs per day.
Raising the price to \$1.75 will cause the sales to
fall to 110 hot dogs per day. The number of
hot dogs, N, is a linear function of the price, x.
75) f(x) = 3
Write a linear function that models the number
5    y                                                      of hot dogs sold per day when the price is x
4                                                           dollars each.
3
2                                                       82) In 1995, the average annual salary for
1                                                           elementary school teachers was \$24,269. In
2000, the average annual salary for elementary
-5 -4 -3 -2 -1               1       2   3   4   5x
-1                                                                school teachers was \$28,148. Let S be the
-2                                                          average annual salary in the year x, where x =
-3                                                          0 represents the year 1995.
-4                                                          a) Write a linear function that models the
-5                                                          average annual salary for elementary school
teachers in terms of year x.
b) Use this function to determine the average
Solve the problem.
annual salary for elementary school teachers in
76) The total sales made by a salesperson was
1999.
\$25,000 after 3 months and \$68,000 after 23
months. Predict the total sales after 32 months.

7
Quiz Review - Intermediate (continued)

83) In 1995 the United States recovered 25% of its                         90) 2 ≤ 3t - 4 ≤ 17
municipal wastes through recycling, up from
17% in 1990. Let P represent the percentage                                 -8 -7 -6 -5 -4 -3 -2 -1 0     1   2   3   4   5   6   7   8
recycled and t the number of years since 1990.
Find a linear function P(t) that fits this data.
Use this function to predict the percentage                      Graph the solution set.
recycled in 2007.                                                     91) x ≤ 2 and x ≥ -2

84) Persons taking a 30-hour review course to                                    -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
prepare for a standardized exam average a
score of 620 on that exam. Persons taking a
Solve the inequality and graph the solution set.
70-hour review course average a score of 799.
92) 9x + 10 ≥ 28 and 9x + 10 ≤ 64
Find a linear function, S(t), which fits this data,
and which expresses score as a function of
time. Use this function to predict an average                               -8 -7 -6 -5 -4 -3 -2 -1 0     1   2   3   4   5   6   7   8

score for persons taking a 47-hour review
course. Round your answer to the tenths place.                         93) 5 < 3x + 5 and 8x + 4 < 36

85) A gas station sells 4820 gallons of regular                                 -8 -7 -6 -5 -4 -3 -2 -1 0     1   2   3   4   5   6   7   8
unleaded gasoline in a day when they charge
\$1.35 per gallon, whereas they sell 3865 gallons
on a day that they charge \$1.40 per gallon.                            94) 6x + 4 ≥ -32 and 6x + 4 ≤ -8
Find a linear function that expresses gallons
sold as a function of price. Use this function to                           -8 -7 -6 -5 -4 -3 -2 -1 0     1   2   3   4   5   6   7   8
predict the number of gallons sold at a price of
\$1.19 per gallon.
95) -21 ≤ 7x - 7 and 8x - 4 < 12

Graph the solution set.
86) 3 ≤ x < 7                                                                    -7 -6 -5 -4 -3 -2 -1 0   1   2    3   4   5   6   7

96) -10 < 6x + 2 and 6x - 9 < 3

Solve the inequality and graph the solution set.                                      -8 -7 -6 -5 -4 -3 -2 -1 0     1   2   3   4   5   6   7   8

87) 20 < 5x ≤ 30
Graph the solution set.
-8 -7 -6 -5 -4 -3 -2 -1 0   1   2   3   4   5   6   7   8            97) x < 5 or x < 7

88) -10 ≤ -2c + 4 < 0                                                            -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9

-8 -7 -6 -5 -4 -3 -2 -1 0   1   2   3   4   5   6   7   8
98) x ≥ -4 or x < 1

89) 8 ≤ 3t + 2 ≤ 23
-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9

-8 -7 -6 -5 -4 -3 -2 -1 0   1   2   3   4   5   6   7   8

8
Quiz Review - Intermediate (continued)

Solve the inequality and graph the solution set.                      113) The distance D that a spring is stretched by a
99) -3x + 1 ≥ 7 or 4x + 3 ≥ -13                                     hanging object varies directly as the weight W
of the object. If a 24-kg object stretches a spring
-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
62 cm, find the distance the spring is stretched
when the weight is 30-kg.

100) 6x - 4 < 2x or -4x ≤ -12
114) The number G of gears a machine can make
varies directly as the time T it operates. If it can
-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7                            make 5126 gears in 10 hours, how many gears
can it make in 20 hours?
Solve the equation.
101) x = 9                                                       115) According to Ohm's law, the electric current I,
in amperes, in a circuit varies directly as the
voltage V. When 14 volts are applied, the
102) r - 6 = 8
current is 4 amperes. What is the current when
20 volts are applied?
103) k - 6 = 6
116) The monthly payment p on a mortgage varies
104) b + 4 + 5 = 14                                                   directly with the amount borrowed b. Suppose
that you decide to borrow \$120,000 using a
30-year mortgage. You are told that your
105) b - 8 + 6 = 10
monthly payment is \$713.42. Assume that you
have decided to buy a more expensive home
106) 6m + 3 = 9                                                       that requires you to borrow \$180,000. What
107) 5m + 4 = 7
Find an equation of variation in which y varies inversely
as x and the following is true.
108) 8m + 5 + 5 = 11
117) y = 30, when x = 3

109) 6m + 2 + 6 = 10
118) y = 0.5, when x = 24

Find an equation of variation if the following conditions
Solve.
exist.
119) The current I in an electrical conductor varies
110) Suppose m varies directly as p and m = 20
inversely as the resistance R of the conductor.
when p = 5 .
The current is 7 amperes when the resistance is
796 ohms. What is the current when the
111) y varies directly as x, and y = 13 when x = 10                   resistance is 517 ohms?

Solve.                                                                120) The pitch P of a musical tone varies inversely
112) The weight W of an object on the Moon varies                     as its wavelength W. One tone has a pitch of
directly as the weight E on earth. A person                      246 vibrations per second and a wavelength of
who weighs 113 lb on earth weighs 22.6 lb on                     7.9 ft. Find the wavelength of another tone that
the Moon. How much would a 128-lb person                         has a pitch of 297 vibrations per second.
weigh on the Moon?

9
Quiz Review - Intermediate (continued)

121) The current I in an electrical conductor varies          Determine the solution to the system of linear equations
inversely as the resistance R of the conductor.          graphically. If the system has an infinite number of
The current is 2 amperes when the resistance is          solutions or no solution, state this.
619 ohms. What is the current when the                         130) x + 8y = 8
resistance is 521 ohms? Round to the nearest                        3x - 7y = -7
tenth of an ampere if necessary.                                                             y
8

6
122) The number of miles per gallon of gasoline
that a car averages varies inversely as the                                             4
average speed the car travels. A car gets 13
2
miles per gallon at 58 mph. How many miles
per gallon will it get at 67 mph?
-8   -6   -4   -2            2   4   6   8 x
-2
123) The amount of tread left on a tire varies
-4
inversely as the number of miles the tire has
traveled. A tire that has traveled 76,000 mi has                                        -6
5
16
on a tire that has traveled 83,000 mi?
131) 3x + y = 0
124) The weight that a horizontal beam can support                      4x + 5y = 22
varies inversely as the length of the beam.                                                  y
8
Suppose that a 10-m beam can support 540 kg.
6
How many kilograms can a 1-m beam
support?                                                                                4

2
125) The volume V of a gas varies inversely as the
pressure P on it. The volume of a gas is                            -8   -6   -4   -2            2   4   6   8 x
220 cm3 under a pressure of 19 kg/cm2 . What                                            -2
will be its volume under a pressure of 38 kg/                                           -4
cm2 ?
-6

Determine whether the ordered pair is a solution of the                                           -8
system of equations.
126) (3, 1);    9x + y = 28
132) y - 6x = 3
3x - 2y = 7
6y = 36x + 18
y
127) (4, -4); 2x - y = 12                                                                    8

x+ y= 1                                                                       6

4
128) (-2, -5); y = 2x + 8
5x - y = -5                                                                      2

-8   -6   -4   -2            2   4   6   8 x
129) (-1, -1); x - y = 0
-2
y = 3x + 2
-4

-6

-8

10
Quiz Review - Intermediate (continued)

133) 2x + y = 0                                                    Solve the system using elimination. If the system has an
5x + 5y = 0                                                   infinite number of solutions or no solution, state this.
y                                       140) x - 3y = 10
8
-2x - 3y = -11
6

4                                           141) x + 9y = 3
2x + 9y = -3
2

-8   -6    -4   -2            2   4   6   8 x
142) x + 3y = 21
-2                                              -7x + 3y = -3

-4
143) 7x + 5y = 10
-6                                               -2x + 2y = 4
-8
144) 4x + 9y = 12
-2x - 2y = -6
134) x = -y
y+ x=6
Solve using any appropriate method. If the system has an
y
8                                      infinite number of solutions, or no solution, state this.
6
145) x + 4y = 0
x - 4y = 40
4

2                                           146) 4x - 8y = -36
5x + 5y = 75
-8   -6    -4   -2            2   4   6   8 x
-2
147) 7x + 5y = 6
-4                                               7x + 5y = 12
-6
148) 4x + 8y = 24
-8
9x + 6y = 6

Solve the system using substitution. If the system has an                    149) y = 5x + 22
infinite number of solutions or no solution, state this.                          5x + 8y = -49
135) x + 5y = 5
3x - 2y = -2                                                      150) x - 5y = 4
x = 6 + 5y
136) 5x - 2y = -1
x + 4y = 35                                                  Solve the problem.
151) The sum of two numbers is 38, and their
137) 4y + x = -3                                                             difference is 18. What are the numbers?
x = 2y + 5
152) The sum of two numbers is 76. The second
138) 3x - 1 = y                                                              number is three times as large as the first
y - 3x = 2                                                              number. What are the numbers?

139) x + 7y = -2                                                        153) Two angles are supplementary. One angle is
3x + y = 34                                                             264° less than three times the other. Find the
measures of the angles.

11
Quiz Review - Intermediate (continued)

154) Two angles are complementary. The sum of                   163) Ellen wishes to mix candy worth \$1.80 per
the first angle plus twice the second angle is                  pound with candy worth \$2.40 per pound to
159°. Find the measures of the angles.                          form 48 pounds of a mixture worth \$2.00 per
pound. How many pounds of the more
155) The three angles in a triangle always add up to                 expensive candy should she use?
180°. If one angle in a triangle is 69° and the
second is 2 times the third, what are the three            164) How many liters of a 50%-alcohol solution
angles?                                                         must be mixed with 30 liters of a solution that
is 90% alcohol to get a solution that is 60%
156) The perimeter of a rectangular room is 174 feet.                alcohol?
Find the length and width of the room if the
length is 9 feet longer than twice the width.              165) Anne and Nancy use a metal alloy that is
21.4% copper to make jewelry. How many
157) The perimeter of a rectangle is 36 cm. The                      ounces of an alloy that is 16% copper must be
length is 8 cm longer than the width. Find the                  mixed with an alloy that is 25% copper to form
dimensions.                                                     105 ounces of the desired alloy?

158) Ron and Kathy are ticket sellers for their class           166) A merchant has coffee worth \$4 a pound that
play. Ron sells student tickets for \$2.00 each,                 she wishes to mix with 9 pounds of coffee
and Kathy sells adult tickets for \$4.50 each. If                worth \$9 a pound to get a mixture that can be
their total revenue for 364 tickets is \$1175.50,                sold for \$7 a pound. How many pounds of the
then how many tickets did Ron sell?                             \$4 coffee should be used?

159) Don runs a charity fruit sale, selling boxes of            167) Mardi received an inheritance of \$50,000. She
oranges for \$11 and boxes of grapefruit for \$10.                invested part at 8% and deposited the
If he sold a total of 762 boxes and took in \$8125               remainder in tax-free bonds at 7%. Her total
in all, then how many boxes of oranges did he                   annual income from the investments was
sell?                                                           \$3900. Find the amount invested at 8%.

160) There were 460 people at a play. The                       168) Andy has 29 coins made up of quarters and
admission price was \$3.00 for adults and \$1.00                  half-dollars, and their total value is \$12.25.
for children. The admission receipts were \$960.                 How many quarters does he have?
How many adults and children attended?
169) A sum of money amounting to \$4.55 consists of
161) 37,000 people attended a ballgame at a                          dimes and quarters. If there are 23 coins in all,
stadium that offers two kinds of seats: general                 how many are quarters?
admission and reserved. The day's receipts
were \$271,000. How many people paid \$13.00
for reserved seats, and how many paid \$6.00

162) Tim and Judy mix two kinds of feed for
pedigreed dogs. They wish to make 54 pounds
of feed worth \$0.28 per pound by mixing one
kind worth \$0.24 per pound with another
worth \$0.42 per pound. How many pounds of
the cheaper kind should they use in the mix?

12
Quiz Review - Intermediate (continued)

Graph the system of linear inequalities.                                               173) x - 2y ≤ 2 and x + y ≤ 0
170) 2x + y ≤ 4 and x - 1 > 0
y
6
y                                                                        5
4
4
3                                                                             3
2
2
1
1
-6 -5 -4 -3 -2 -1
-1       1 2 3 4 5 6 x
-4   -3   -2   -1            1   2   3   4     x                                                  -2
-1                                                                            -3
-2                                                                            -4
-5
-3
-6
-4

174) x + 2y ≥ 2 and x - y ≤ 0
171) 2x + y ≤ 4 and y - 1 < 0
y
6
y                                                                        5
4
4
3                                                                             3
2                                                                             2
1
1
-6 -5 -4 -3 -2 -1
-1       1 2 3 4 5 6 x
-4   -3   -2   -1            1   2   3   4     x                                                  -2
-1
-3
-2                                                                            -4
-5
-3
-6
-4

175) x > 2 and y ≤ -2
172) x + 2y ≤ 2 and x + y ≥ 0
y
6
y
5
4
4
3                                                                             3
2                                                                             2
1
1
-6 -5 -4 -3 -2 -1
-1       1 2 3 4 5 6 x
-4   -3   -2   -1            1   2   3   4     x                                                  -2
-1
-3
-2                                                                            -4
-5
-3
-6
-4

176) (8a3 + 6a 2 ) + (9a 3 + 6a2 )

177) (-8 + 5x5 + 9x7 + 4x6 ) + (6x6 + 8x5 + 4 + 9x7 )

13
Quiz Review - Intermediate (continued)

178) (2x8 - 8x5 + 3x2 + 4) + (8x7 + 5x5 - 4x)                              9m 6 n - 18m 5 n 3 + 6m 4 n 5
196)
3m 3 n
Subtract.
179) (-17a 5 + 13a 2) - (-2a5 - 11a2 )                         Divide.
197) (x2 + 4 x - 32 ) ÷ (x + 8 )
180) (6n 5 + 16n 4 - 17) - (10n 4 + 9n 5 + 4)
198) ( 9 m 2 + 11 m - 14 ) ÷ (m + 2 )
181) (-3n + 2n 5 + 6n 4 ) - (15n 4 + 4n 5 + 7n)
p2 + 2p - 32
199)
182) (-4x7 + 5x9 + 3 - 7x8 ) - (-9 - 4x8 + 7x9 - 9x7 )                        p+7

183) (-6x6 + 2x8 + 3 - 9x7 ) - (-9 - 5x7 + 5x8 + 8x6 )                     x2 + 13x + 33
200)
x+9

Multiply.
184) 4x(9x - 12)                                               Factor out the greatest common factor.
201) 18m 9 + 30m 6 + 15m 4

185) 3x7 (10x4 - 9)
202) 160m 9 + 80m 7 - 32m 5

186) -9x7 (-12x7 + 7x5 )
Factor out the common binomial.
203) s(s - 9) + 3(s - 9)
187) (2x - 5)(x + 4)

204) 4x(5x + 6) + 3(5x + 6)
188) (4x + 12)(4x - 12)

Factor by grouping.
189) (x + 3)(x2 - x + 8)                                            205) p2 + 8p + 6p + 48

190) (x - 5)(7x2 + x + 8)                                           206) 6x2 - 15x + 4x - 10

191) (x2 - x - 9)(x - 1)                                       Factor.
207) t2 + 8t + 15
192) (n + 6)2
208) a 2 - 13a + 40
193) (w - 5)2
209) x2 - x - 6
194) (3m + 8)2
210) 77 - 18y + y2
Divide and Simplify.
4x10 + 8x6                                                     211) x2 - 10x + 25
195)
2x2

212) a 2 - 17a + 70

14
Quiz Review - Intermediate (continued)

213) x2 - x - 72                                      233) 72 - 2a 2

214) 22 - 13y + y2                                    234) 48x2 - 147

215) x2 - 18x + 81                                    235) 81x3 - 16x

216) x2 + 2xy - 8y2                                   236) y5- 625y

217) 40 - 13y + y2                                    237) x3 - 5x2 - 25x + 125

218) a 2 + 12ab + 11b2                                238) x4 + 2x2 + 4x3 + 8x

219) x2 + 4xy - 12y2                                  239) y3 + wy2 - 25y - 25w

220) 7x2 - 21xy - 28y2                           Solve using the zero product rule.
240) (x - 4)(x + 2) = 0

221) 2x3 + 2x2 y - 12xy2
241) x(6x + 36) = 0

222) 6x2 - 7xt - 3t2
Solve by factoring and using the zero product rule.
242) a 2 - 9a + 14 = 0
223) 6x2 - 5xy - 6y2

243) b2 + 15b = 0
224) 2x2 + 6xy - 20y2

244) x2 - x = 6
225) 42x2 + 35xy - 42y2
Solve the problem.
226) 64p3 - 1                                         245) A number is 56 less than its square. Find all
such numbers.

227) 8a3 - 125b3
246) The product of two consecutive integers is 89
more than their sum. Find the integers.
228) 27s3 + 1
247) One leg of a right triangle is 2 cm shorter than
the other leg. The length of the hypotenuse is
229) 343c3 + 125
10 cm. Find the length of the shorter leg.

230) -64 + t2                                         248) A 15-ft ladder is leaning against a building. If
the bottom of the ladder is 9 ft from the base of
231) 25x2 - 36                                             the building, how high does the ladder reach?

232) x2y2 - 100

15
Quiz Review - Intermediate (continued)

249) A rectangular garden is three times as long as                             8v2                5v + 5
262)                       ·
it is wide. If the area of the garden is 1452 ft2 ,                   5v2 + 20v + 15           2v
find the length and width of the garden.

2x + 2 4x2 + 16x + 16
250) The height of a triangle is 5 cm more than the                 263)         ·
x+2        x2 - 1
length of the base. If the area of the triangle is
75 cm2 , find the height and length of the base.
k2 + 12k + 35   k2 + 8k
264)                 ·
Simplify.                                                                       k2 + 13k + 40 k2 + 3k - 28

a2 - 25
251)                                                                       x2 + 2x - 15 9x3 - 25x
a 2 + 7a + 10                                                265)               ·
3x3 - 5x2    5x - 15

4x + 4
252)                                                                       2x2 - 50   7x - 7
12x2 + 20x + 8                                               266)            ·
8x 2 - 8 14x + 70

y2 + 14y + 45
253)                                                                       5a - 15 6a2 + 7a + 1
y2 + 17y + 72                                                267)          ·
9 - a2    30a + 5

t3 + 8
254)                                                            Divide and simplify.
t3 - 2t2 + 4t
8p - 8 9p - 9
268)       ÷
p      3p2
4t - 16
255)
4-t
4x2 - 25 2x + 5
269)           ÷
x2 - 9   x-3
7k - 14
256)
12 - 6k
x2 - 4   x-2
270)           ÷
2s2 - 10t2                                                          16x2 - 9 3 - 4x
257)
10t2 - 2s2
z2 + 5 z + 6      z2 + 2 z
271)                 ÷
Multiply and simplify.                                                          z 2 + 7 z + 12 z 2 - 4 z - 32
7x2 24y6
258)      ·
3y2    x3                                                               x2 - 25              5x - 25
272)                   ÷
x2 - 18x + 81       x 2 - 6x - 27
y2 - 49 y + 5
259)          ·
8y - 56 y + 7                                                       y3 - 2y y2 - 7y - 30
273)          ÷
y2 - 4   y2 - 8y - 20
x-7           x2 - 3x - 28
260)              ·
(x + 4)2         (x - 7)2                                           a 2 + 13a + 42 a 2 + 12a + 36
274)                  ÷
a 2 - 14a + 49   a2 + 5a - 14
z 2 - 2z + 1 z + 10
261)               ·
z 2 - 100   z-1

16
Quiz Review - Intermediate (continued)

x3 + 64   x2 - 16                                         289)
3
-
9
275)           ÷                                                        14x 10x2
x3 - 64 x2 + 4x + 16

Add or subtract and simplify.                                                 7   1
290)      +
3      2                                                           x+6 x
276)      +
12x 12x
4    5
291)     +
5 + 6t 5t - 2                                                      r   r- 7
277)       -
4t     4t
10       10
292)          -
3a + 16 2a + 3                                                     x + 10   x - 10
278)        -
a+1     a+1
5x   2
293)       +
3m   -12                                                           x+4 x-4
279)    +
m-4 m-4
6            5
294)                +
m 2 - 8m          12                                             (x + 4)2         x+4
280)                +
m-2            m-2
20x      x
295)           -
2x + 5       x+4                                              x2 - 100 x - 10
281)               -
x 2 + 5x + 4 x2 + 5x + 4
6       8
296)        +
x2 - 7x       6x - 30                                        x- 1   1 -x
282)                 +
x 2 + 10x + 25 x2 + 10x + 25
6    4
297)        -
1 - y y- 1
3x + 24     x + 16
283)               -
x 2 + 2x - 8 x2 + 2x - 8
1        4
298)          +
6x - 7   7 - 6x
10    7
284)      +
x    5x
8        7
299)          -
8x - 3   3 - 8x
5        2
285)        -
z2       z
4x     10
300)           -
x 2 - 49 7 - x
7   2
286) -       -
30 5x
Simplify.
1
z + 14 z - 7                                                       1+
287)       -                                                                     5
8z    5z                                                  301)
1
1+
10
3    9
288)      +
10x 14x2

17
Quiz Review - Intermediate (continued)

1                                     4   7
4+                                           -
3                                     x x2
302)                                       310)
2                                      5        4
2-                                               -
27                                    x3        x

1                                                    4
-2                                        2x +
a                                                    x
303)                                       311)
1                                           1            1
-5                                                 +
a
3x2           6

8
x+                                         1   9
x                                       -
304)                                              x2 y2
x                              312)
x+                                         7y - 21x
8

4             5
5-y                                              -
5                                         6x3           12x
305)                                       313)
1 1                                        2   2
-                                           +
5 y                                        2x 6x3

6 x                                        x   7
-                                           -
x 6                                        2y 4y3
306)                                       314)
1 1                                         7   x
-                                            -
6 x                                        4y3 2y

x 2                                          7     4
-                                              -
6 x                                        a 2b4 a 3 b
307)                                       315)
2 1                                          6    4
+                                              +
x 3                                          3 b ab2
a

1 1
-                                          5              9
9 a                                              +
308)                                              xy2           x 2y
9-a                                 316)
9                                           9   5
+
x 2y xy2

x2 - y2
y                                            9
8-
309)                                                   a3
x-y                                317)
y3                                            8
9+
a4

18
Quiz Review - Intermediate (continued)

6                                 Solve. Check for invalid solutions.
9+
x2y                                          5
326) -
4
=
x
318)                                                      4 11 22
6+x
xy3
6   9   1
327)     -   =
5 10 x
x+4
x3
319)                                                            36
3    8                                        328) x +      = -12
-                                                     x
x 3 x2
x 6
329)    - =0
x   x                                               6 x
+
x+1 x-1
320)
6   4                                               4       3
-                                          330)     = 5 +
x+4 x-4                                              x       x

x   7                                               34      1
+                                          331)      =5 -
x-4 x+2                                              x       x
321)
2   x
-
x+2 x-4                                                  4
332) m -     =3
m

7   1
+                                               7 3
x 2-4 x-2                                     333)     + =1
322)                                                        6t t
5           7
+
x2 - 4       x+2
14   1    1
334)      +   =-
7x 2x     14
a   6
-
a+9 a-8
323)                                                        a   a   1
a   1                                        335)     -   =
-                                                 7 12 7
a+9 a-8

x   x
336)     -   = 8
1 1                                                 2   7
-
x y
324)
1    1                                               x-7    10
-                                          337)       =
x 3 y3                                               x-9   x-9

x-8 2
x- 1                                          338)      =
x2                                                x+1 3
325)
x- 1
x3                                                 5   6
339)      =
x+8 x-4

19
Quiz Review - Intermediate (continued)

5    t+2                                                      1 1 1
340)       =                                                   354)    + =  for f
t- 3 t-3                                                       p q f

x-3     x+3                                        Solve.
341)       -1=
7       6                                              355) Frank can type a report in 4 hours and James
takes 5 hours. How long will it take the two of
them typing together?
2   4
342)      =
x+5 x
356) Martha can rake the leaves in her yard in 4
hours. Her younger brother can do the job in 6
x+3       6                                                 hours. How long will it take them to do the job
343)          =
x + 10   x + 10                                              if they work together?

2   x                                                  357) A painter can finish painting a house in 5
344)      =
x-2 x-2                                                      hours. Her assistant takes 7 hours to finish the
same job. How long would it take for them to
complete the job if they were working
x-5   10
345)       =                                                        together?
x-3 3-x

358) One maid can clean the house three times
1       4                                                     faster than another. Working together they can
346)      +        =3
x- 4   2x - 8                                                  clean the entire house in 3 hours. How long
would it take the faster maid cleaning alone?
x     7    x2 + 49
347)        -     =
x + 7 x - 7 x2 - 49                                     359) A baker can decorate the day's cookie supply
four times as fast as his new assistant. If they
decorate all the cookies working together in 16
9   4       8                                               minutes, how long would it take for each of
348)      -    =
y+4 y-4   y2 - 16                                            them to decorate the cookies working
individually?
y+ 1     y     y- 3
349)        -       =
y + 6 y2 - 36 y - 6                                     360) An experienced accountant can balance the
books twice as fast as a new accountant.
Working together it takes the accountants 10
x     4    x2 + 16                                         hours. How long would it take the experienced
350)        -     =
x + 4 x - 4 x2 - 16                                          accountant working alone?

Solve the formula for the indicated variable.                       361) Jeff takes 5 hr longer to build a fence than it
A                                                        takes Bill. When they work together, it takes
351) P =           for r                                            them 6 hours. How long would it take Bill to
1 + rt
do the job alone?

2A
352) h =       for b                                           362) Amy can clean the house in 7 hours. When she
B+b
works together with Tom, the job takes 4
hours. How long would it take Tom, working
1 1                                                          by himself, to clean the house?
353)    + = c for b
a b

20
Quiz Review - Intermediate (continued)

363) Glenn and Paula want to dig an irrigation                     371) A boat goes 640 miles downstream in the same
channel for their garden. Together it takes                        time it can go 560 miles upstream. The speed
them 1.7 hours to dig an appropriately sized                       of the current is 7 miles per hour. Find the
irrigation channel. If Paula can dig the channel                   speed of the boat in still water.
by herself in 2.8 hours, how long would it take
Glenn to dig the channel by himself? (Round                   372) A boat moves 6 kilometers upstream in the
your answer to the nearest tenth of an hour, if                    same amount of time it moves 20 kilometers
necessary.)                                                        downstream. If the rate of the current is 5
kilometers per hour (kph), find the rate of the
Solve.                                                                       boat in still water.
364) A boat moves 28 km/h in still water. It travels
80 km upstream and 80 km downstream in a                      373) A plane flies 400 miles with the wind and 350
total time of 7 hours. What is the speed of the                    miles against the wind in the same length of
current?                                                           time. If the speed of the wind is 22 mph, what
is the speed of the plane in still air?
365) A man rode a bicycle for 12 miles and then
hiked an additional 8 miles. The total time for               374) A boat can go 136 mph in still water. It takes as
the trip was 5 hours. If his rate when he was                      long to go 720 miles upstream as it does to go
riding a bicycle was 10 miles per hour faster                      downstream 810 miles. How fast is the
than his rate walking, what was each rate?                         current?

366) From a point on a river, two boats are driven                 375) Jim can run 5 miles per hour on level ground
in opposite directions, one at 10 miles per hour                   on a still day. One windy day, he runs 13 miles
and the other at 13 miles per hour. In how                         with the wind, and in the same amount of time
many hours will they be 115 miles apart?                           runs 7 miles against the wind. What is the rate
of the wind?
367) From a point on a river, two boats are driven
in opposite directions, one at 6 miles per hour          Find all square roots of the number.
and the other at 5 miles per hour. In how many                376) 100
hours will they be 22 miles apart?

377) 1444
368) A loaded moving truck is traveling 30 mph
faster than a freight train. In the time it takes
the train to travel 60 miles, the truck travels          Simplify.
120 miles. Find the speed of the truck.                      378)      121

369) Fred bicycles 4 km/h slower than Samantha. In                          256
the time it takes Fred to bicycle 56 km,                      379)
361
Samantha travels 72 km. How fast does Fred
bicycle?
380) -    484
370) The speed of a stream is 6 mph. If a boat
travels 64 miles downstream in the same time             Evaluate the radical function at the indicated value.
that it takes to travel 32 miles upstream, what               381) f(x) = 2x - 5
is the speed of the boat in still water?                           f(7)

382) f(x) = - 2x - 2
f(3)

21
Quiz Review - Intermediate (continued)

Find the indicated function value. and simplify.                                                  3
398) For f(x) =           x + 1, find f(-28).
383) For g(x) = (x + 1)2 , find g(7).

5
3                                                     399) For f(x) =           x + 2, find f(-1026).
384) f(x) =           x + 4 , find f(121)

Simplify.                                                                                         3
400) For f(x) =           2x - 1, find f(-171).
3
385)       64
Rewrite the expression using radical notation and, if
possible, simplify.
3
386)       -125                                                        401) x1/3

4                                                           402) 161/2
387) -         81
403) (mn)1/4

3         8
388)       -
125                                                    404) (x8y8 )1/3

3                                                           405) 167/4
389) -         -125x3

406) 644/3
4 81
390)
625                                                           407) (9y4 )3/2

391)       z8                                                     Rewrite using exponential notation.
3
408) 17
392)       (2t)2
409)    x9
3
393)       x6                                                                            2
5
410)       5x3y
4
394)       16a 4                                                                         3
5
411)       3x4y
395)       (b + 4)2
Rewrite with positive exponents.
412) x-4/5
396)       4x2 + 8x + 4

1
Find the indicated function value. and simplify.                            413)
7p-6/7
397) For g(x) = (x + 1)2 , find g(4).

22
Quiz Review - Intermediate (continued)

Use the laws of exponents to simplify. Use positive                 428)       48 x2y
exponents only.
414) x1/6 · x5/6
429)       486 y2

y4/5
415)                                                      Simplify.
y3/10
430)        245 k7 q8

416) 6 2/3 · 6 1/4
3
431)       1000 x4 y5
8 8/13
417)
8 -7/13                                                 432)
3
- 64 a 8 b 5

418) (x4/5 )4/5                                           Multiply and simplify.
433) 15 108
419) z -2/5 · z3/5
434)       14m 5 7m17
Use rational exponents to simplify. Do not use fraction
3        3
420)                                                           435)       63       9
6
a2
3                3
436)       64m 3 ·          125m 3
421)
12
x8                                            Simplify by taking the roots of the numerator and the
denominator.
422)                                                                3 256x4
437)
4                                                                4x
x20

423)                                                                  4 r3
438)
8         48                                                     81
ab

7
424)                                                           439)
5                                                       r4
20
7x
Divide and, if possible, simplify.
425)                                                           440)
4              12                                              30a
x5 y3
6a

Simplify by factoring.
441)
426) 48
18ab3
3a
3
427)       54

23
Quiz Review - Intermediate (continued)

442)                                                                                50
457)
3                                                                            x
378a7 z 2
3
14a5 z                                                                 18
458)
x
if possible.
50x3
443) -9 3 - 8 27                                                        459) -
y5

444) 5       12 - 5      75                                         Rationalize the denominator.
29
460)
445)       3 -7     48 - 3         12                                           x3

446)       2a - 3 32a - 2 8a                                        Rationalize the denominator.
461)
Multiply.                                                                            3
5
447)       3( 7 -        5)
3
7
448) 6       5 ( 11 +         5)
9
462)
449) ( 5 +        7 )(    5 -       7)                                          3
y

450) ( 2 - 5 )(          6 + 2)
463)

Solve the problem.                                                                   3       5
451) For f(x) = x +        6 and g(x) = x -   6, find (f ·                            9x2
g)(x).
464)
452) For f(x) = x -        6 and g(x) = x -   6, find (f ·
3       4
g)(x).
9x2

453) For f(x) = x +        2 and g(x) = x -   17, find (f ·
g)(x).                                                                           5
465)
3
36x2
454) For f(x) = 3 -        x and g(x) = 4 -   x, find (f ·
g)(x).
3
466)
4
Rationalize the denominator.                                                               a3
64
455)
5
4
467)
8- 3
16
456)
7

24
Quiz Review - Intermediate (continued)

4                                                    4
468)                                                   484)        2x - 12 + 11 = 23
8- 7

Perform the indicated operation and simplify.
7                                          485) (-5 - 7i) + (12 + 4i)
469)
2+9

486) (13 - 7i) - (2 - 4i)
7
470)
5+4                                    Express in terms of i.
487) -16
7
471)
3 + 10
488)    -196

2-      5                                       489)    -168
472)
2+      5

490)    -25 +      -64
1-        6
473)
1+        6
491)    -3 -      -100

x+2
474)                                              Perform the indicated operation and simplify.
x-2                                         492) (-15 - 3i)(-15 + 3i)

5 x                                         493) (3 - 3i)(3 + 9i)
475)
x-2 y

494) (8 - 2i)2
Solve.
476)       q+ 1=4
6
495)
5i
477)       5q - 4 = 4
5
496)
478)       4q + 5 = 5                                         -3 + 10i

479)       2x + 1 = 13                                        5 + 4i
497)
4 - 2i

480)       8x - 7 - 7 = 0
Find the power of i.
498) i17
3
481)       5x - 3 = 2
499) i14
3
482)       x+8=4
500) i7 - i13
3
483)       t = -1

25
Quiz Review - Intermediate (continued)

Solve using the square root method.                                            8   7
501) x2 + 2 = 146                                           519) 2 = -      -
x x2

502) 4x2 = 60                                                      8   8
520)     +      =1
x x + 12
503) 3x2 = 33
2
521) x - 1 =
x+1
504) (x + 7)2 = 28

Use the discriminant to determine whether the following
505) (x + 7)2 = 20
equations have solutions that are: 1 or 2, real or imaginary
522) s2 + 5s + 6 = 0
506) (p - 9)2 = 17

523) t2 - 10t + 25 = 0
Solve by completing the square.
507) a 2 - 4a - 45 = 0
524) 8y2 = -5y - 5

508) a 2 + 10a - 11 = 0
525) 4 + 6z2 = 4z

509) x2 + 8x = 3
Find the line of symmetry.
526) f(x) = 2x2 - 4x - 0
510) a 2 - 6a - 27 = 0

527) f(x) = 2x2 - 4x + 4
511) x2 + 8x = 5

528) f(x) = 4x2 + 16x + 17
512) x2 = 5 - 8x
Find the vertex.
513) x2 + 4x + 8 = 0                                        529) f(x) = 4x2 + 8x + 6

Solve using the quadratic formula.                               530) f(x) = 3x2 - 6x + 1
514) 4x2 + 8x = - 1

531) f(x) = -2x2 + 4x - 5
515) 4n 2 = -10n - 3
Find the x- and y-intercepts.
516) 3m 2 + 8m + 2 = 0                                      532) f(x) = x2 - 16x + 64

Solve.                                                           533) f(x) = -x2 + 19x - 90
517) x2 - 10x + 74 = 0

534) f(x) = -x2 - 2x - 14
518) x2 + x + 4 = 0

26
Quiz Review - Intermediate (continued)

Graph the quadratic function.                                            538) f(x) = x2 + 2x - 5
535) f(x) = -x2 + 5                                                                              y
y                                                             10
10

5
5

-10     -5             5    10   x
-10     -5              5   10     x
-5
-5

-10
-10

Find the axis of symmetry.
536) f(x) = x2 + 6x                                                 539) f(x) = (x + 4)2
y
10
540) f(x) = (x - 2)2 + 2

5
Find the vertex.
541) f(x) = (x - 1)2 - 1
-10     -5              5   10     x

-5                                           542) f(x) = (x + 4)2 - 1

-10                                      Find the maximum or minimum value.
543) f(x) = (x + 9)2 - 3

Graph.
544) f(x) = -(x + 2)2 - 5
537) f(x) = x2 + 2x - 8
y
10                                       Solve.
545) Which of the pairs of numbers whose sum is 88
has the largest product?
5

546) A gardener is fencing off a rectangular area
-10     -5              5   10     x                             with a fixed perimeter of 20 ft. What is the
maximum area?
-5

547) A projectile is thrown upward so that its
-10                                                distance, in feet, above the ground after t
seconds is h = -10t2 + 340t. What is its
maximum height?

548) A projectile is thrown upward so that its
distance above the ground after t seconds is
h = -15t2 + 630t. After how many seconds does
it reach its maximum height?

27
Quiz Review - Intermediate (continued)

549) John owns a hotdog stand. He has found that                 564) Center at (0, -2), radius 9
his profit is represented by the equation
P = -x2 + 52x + 74, with P being the profit in              565) Center at (9, 7), radius    6
dollars, and x the number of hotdogs sold.
How many hotdogs must he sell to earn the
most profit?                                              566) Center at (0, 10), radius     13

550) Bob owns a watch repair shop. He has found                  567) Center at (2, 0), radius    10
that the cost of operating his shop is given by
c = 2x2 - 192x + 59, where c is the cost in
568) Center at (2, -8), radius 2 5
dollars, and x is the number of watches
repaired. How many watches must he repair to
have the lowest cost?                                Find the center and the radius of the circle.
569) x2 + y2 = 9
Find the distance between the pair of points.
551) (1, -1) and (9, 5)
570) (x + 8)2 + y2 = 16

552) (2, 5) and (-3, -2)
571) (x - 7)2 + (y + 1)2 = 4

553) (7, -1) and (5, -5)
572) x2 + y2 - 14x - 18y + 130 = 36

554) (-5, -4) and (6, -2)
573) x2 + y2 - 12x + 32 = 0
555) (-7, 6) and (7, -4)
574) x2 + y2 - 10x - 75 = 0
Find the midpoint of the segment with the given
endpoints.                                                            575) x2 + y2 + 6x - 16y + 64 = 0
556) (9, 8) and (8, 1)

557) (5, -7) and (-4, 1)

558) (-8, -6) and (9, 7)

559) (-9, 8) and (-3, -4)

5    3      9 11
560)     ,-   and - ,
2    2      2 2

Find an equation of the circle satisfying the given
conditions.
561) Center at (0, 0), radius 14

562) Center at (-7, 3), radius 2

563) Center at (-7, 0), radius 12

28
Testname: QR

1) 12z - 3z 2                                                                    26) (0, 0), (0, 0)
2) 7p2 + 4p3                                                                     27)
y
3) 8x3 - 10x2 + 14x
10
4) 1
5) 1
6) -19                                                                                                  5

7) -16
I
8) r =                                                                                   -10      -5             5   10   x
Pt
3V                                                                                           -5
9) B =
h
10) x = y - wz                                                                                          -10
11) \$22,000
12) 36,966 people                                                                 28)
2 7 r19                                                                                                  y
13)
s18                                                                                              10

24
14)                                                                                                      5
x2 y8
10r5
15)
13                                                                                 -10      -5             5   10   x

y35                                                                                               -5
16)
32x30
17) 1                                                                                                   -10
18) (1, ∞), {x|x > 1}
29)
-7 -6 -5 -4 -3 -2 -1 0          1       2    3   4    5       6    7                                    y
10
19) (-∞, 0], {x|x ≤ 0}

5
-7 -6 -5 -4 -3 -2 -1 0          1       2    3   4    5       6    7

20) (-∞, -8)
-10      -5             5   10   x
-11       -10    -9       -8           -7           -6           -5
-5
21) (7, ∞)
-10
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
22) (-6, ∞)

-9        -8     -7       -6           -5           -4           -3

9
23) , ∞
7

-3       -2    -1    0            1        2            3
24) (-∞, 5)
25) (5, ∞)
29
Testname: QR

30)                                           33) (0, -1), (-4, 0)
y                                                     y
10                                                    10

5                                                     5

-10    -5             5   10   x                  -10       -5              5   10   x

-5                                                    -5

-10                                                   -10

31)                                                   5       49
34) -     ; (0,    )
y                             8       8
10                          35) - 2
4    40
36) y = -         x+
5                                          7    7
37) y = - 7x + 7
38) y = x - 5
-10    -5             5   10   x
10     41
39) y = -     x+
13     13
-5
1     8
40) y = -          x-
10    5
-10
41) Neither
32)                                                   5   3
42) y = x +
y                             7   8
10                                          2    41
43) y = -         x-
3    3
5                                    9    63
44) y =     x+
4    4
5    67
-10    -5             5   10   x        45) y = -         x+
8    8
-5                         46)
y
-10                                                   10

5

-10       -5              5   10   x

-5

-10

30
Testname: QR

47)                                           50)
y                                                y
10                                               10

5                                                5

-10    -5             5   10   x                -10     -5              5    10   x

-5                                               -5

-10                                              -10

48)                                           51) No
y                     52) Yes
10                          53) No
54) Yes
5
55) ℛ the set of all real numbers
56) {x∣ x is a real number and x ≠ -2}
57) {x -3 ≤ x ≤ 3 }
-10    -5             5   10   x        58) {y∣ -4 ≤ y ≤ 2}
59) {x∣ -1 ≤ x ≤ 4}
-5                         60) {x∣ -1 ≤ x ≤ 4}
61) {y∣ -2 ≤ y ≤ 4}
-10                         62) 3
63) -3
49)                                           64) 5
y                     65) 3
10                          66) 28
67) 6x3 - 3x2 + 6x - 3
5                                 8x2 - 7x
68)
x2 - 3x - 28
2
-10    -5             5   10   x        69) x ∣ x is a real number and x ≠
5
-5                         70) 1
71) -1
-10                         72) 5
73) x = 0 and x = 2
74) x = -1 and x = -3
75) 2
76) \$87,350
77) 18,733
78) \$22,667
79) V(x) = -3320x + 15,900
80) V(x) = 347x + 3276
81) N(x) = -40x + 180
82) a) S(x) = 775.8x + 24,269
b) \$27,372.20
83) 44.2%

31
Testname: QR

84) 696.1                                                                 105) {12, 4}
85) 7876 gallons                                                          106) 1, - 2
86) [3, 7)                                                                       3     11
107)     ,-
5     5
-7 -6 -5 -4 -3 -2 -1 0    1   2   3   4   5   6   7                        1    11
108)      ,-
8    8
1
87)    -8 -7 -6 -5 -4 -3 -2 -1 0     1   2   3   4   5   6   7   8        109)      ,-1
3
110) m = 4p
88)    -8 -7 -6 -5 -4 -3 -2 -1 0     1   2   3   4   5   6   7   8                 13
111) y =    x
10
-8 -7 -6 -5 -4 -3 -2 -1 0     1   2   3   4   5   6   7   8        112) 25.6 lb
89)
113) 77.5 cm
114) 10,252 gears
90) -8 -7 -6      -5 -4 -3 -2 -1 0   1   2   3   4   5   6   7   8        115) 5.71 amperes
91) [-2, 2]                                                               116) \$1070.13
90
117) y =
-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
x

92)                                                                                  12
118) y =
x
119) 10.8 amperes
-7 -6 -5 -4 -3 -2 -1 0    1   2   3   4   5   6   7
120) 6.5 ft
121) 2.4 amperes
93)    -7 -6 -5 -4 -3 -2 -1 0    1   2   3   4   5   6   7                122) 11.3 miles per gallon
95
123)       in.
332
94)    -7 -6 -5 -4 -3 -2 -1 0    1   2   3   4   5   6   7
124) 5400 kg
125) 110 cm3
95)    -7 -6 -5 -4 -3 -2 -1 0    1   2   3   4   5   6   7                126)Yes
96)                                                                       127)No
128)No
-7 -6 -5 -4 -3 -2 -1 0   1    2   3   4   5   6   7
129)Yes
130)(0, 1)
97) (-∞, 7)                                                               131)(-2, 6)
132)dependent
-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9                                 133)(0,0)
98) (-∞, ∞)                                                               134)inconsistent
135)(0, 1)
136)(3, 8)
-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9
7     4
137) , -
3     3
99)    -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7                               138)   No solution
139)   (12, -2)
140)   (7, -1)
100)    -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
141)   (-6, 1)
101)   {-9, 9}                                                             142)   (3, 6)
102)   {-2, 14}                                                            143)   (0, 2)
103)   {12, -12}                                                           144)   (3, 0)
104)   {5, -13}
32
Testname: QR

145)   (20, -5)                                                 171)
146)   (7, 8)                                                                                   y
147)   No solution                                                                         4    (0, 4)
148)   (-2, 4)                                                                             3
149)   (-5, -3)                                                                           2
150)   No solution                                                                    (0, 1)
1
151)   28, 10                                                                                                     (2, 0)
152)   19, 57                                                          -4   -3   -2   -1            1         2       3    4   x
153)   111°, 69°                                                                           -1

154)   21°, 69°                                                                            -2
155)   69°, 74°, 37°                                                                       -3
156)   w = 26 ft; l = 61 ft                                                                -4
157)   Width: 5 cm; length: 13 cm
158)   185 tickets                                              172)
159)   505 boxes                                                                                y
160)   Adults: 250; children: 210                                                          5
161)   Reserved: 7000 ; general admission: 30,000                                          4
162)   42 pounds                                                                           3

163)   16 pounds                                                                           2
(0, 1)
1
164)   90 L                                                                                                   (2, 0)
165)   42 ounces                                                       -5 -4 -3 -2 -1               1     2       3    4   5   x
-1
166)   6 lb                                                                                     (1, -1)
-2
167)   \$40,000
-3
168)   9
-4
169)   15                                                                                  -5
170)
173)
(0, 4) y
4                                                                   y
3                                                               5
4
2
3
1                                                               2
(2, 0)
1
-4   -3   -2   -1 (1, 0) 1   2      3     4   x                                                (2, 0)
-1
-5 -4 -3 -2 -1       1 2                   3    4   5   x
-1
-2                                                     (0, -1) (1, -1)
-2
-3
-3
-4                                                               -4
-5

33
Testname: QR

174)                                                               197) x - 4
y                                     198) 9 m - 7
5
3
4                                          199) p - 5 +
p+7
3
2                                                          3
(1, 1)                                200) x + 4 -
1                                                         x+9
(0, 1)           (2, 0)
-5 -4 -3 -2 -1           1     2      3   4   5   x        201) 3m 4(6m 5 + 10m 2 + 5)
-1
202) 16m 5 (10m 4 + 5m 2 - 2)
-2
203) (s - 9)(s + 3)
-3
-4
204) (5x + 6)(4x + 3)
-5                                          205) (p + 8)(p + 6)
206) (2x - 5)(3x + 2)
175)                                                               207) (t + 3)(t + 5)
y                                     208) (a - 5)(a - 8)
6
209) (x + 2)(x - 3)
5
4                                          210) (y - 11)(y - 7)
3                                          211) (x - 5)2
2                                          212) (a - 10)(a - 7)
1
213) (x + 8)(x - 9)
-6 -5 -4 -3 -2 -1
-1        1 2 3 4 5 6 x                     214) (y - 11)(y - 2)
-2                                          215) (x - 9)2
-3                                          216)   (x + 4y)(x - 2y)
-4
217)   (y - 8)(y - 5)
-5
-6                                          218)   (a + 11b)(a + b)
219)   (x + 6y)(x - 2y)
176) 17a 3 + 12a 2                                                 220)   7(x + y)(x - 4y)
177) 18x7 + 10x6 + 13x5 - 4                                        221) 2x(x - 2y)(x + 3y)
178) 2x8 + 8x7 - 3x5 + 3x2 - 4x + 4                                222) (3x + t)(2x - 3t)
179) -15a 5 + 24a 2                                                223) (3x + 2y)(2x - 3y)
180) -3n 5 + 6n 4 - 21                                             224) 2(x - 2y)(x + 5y)
181) -2n 5 - 9n 4 - 10n                                            225) 7(3x - 2y)(2x + 3y)

182) -2x9 - 3x8 + 5x7 + 12                                         226) (4p - 1)(16p2 + 4p + 1)

183) -3x8 - 4x7 - 14x6 + 12                                        227) (2a - 5b)(4a 2 + 10ab + 25b2 )

184) 36x2 - 48x                                                    228) (3s + 1)(9s2 - 3s + 1)

185) 30x11 - 27x7                                                  229) (7c + 5)(49c2 - 35c + 25)
230) (t + 8)(t - 8)
186) 108x14 - 63x12
231)   (5x + 6)(5x - 6)
187) 2x2 + 3x - 20
232)   (xy + 10)(xy - 10)
188) 16x2 - 144                                                    233)   2(6 + a)(6- a)
189) x3 + 2x2 + 5x + 24                                            234)   3(4x + 7)(4x - 7)
190) 7x3 - 34x2 + 3x - 40                                          235) x(9x + 4)(9x - 4)
191) x3 - 2x2 - 8x + 9                                             236) y(y2 + 25)(y + 5)(y - 5)
192) n 2 + 12n + 36                                                237) (x - 5)2(x + 5)
193) w2 - 10w + 25                                                 238) x(x + 4)(x2 + 2)
194) 9m 2 + 48m + 64                                               239) (y + w)(y + 5)(y - 5)
240) 4, -2
195) 2x8 + 4x4
241) 0, -6
196) 3m 3 - 6m 2 n 2 + 2mn 4
34
Testname: QR

242) 7, 2                                        x+2
270) -
243) -15, 0                                      4x + 3
244) -2, 3                                     z -8
245) -7 and 8                           271)
z
246) 10, 11 or -9, -8
(x + 5)(x + 3)
247) 6 cm                               272)
5(x - 9)
248) 12 ft
249) length: 66 ft; width: 22 ft                 y(y2 - 2)
273)
250) height: 15 cm; base: 10 cm                (y - 2)(y + 3)
a-5                                      (a + 7)2 (a - 2)
251)                                    274)
a+2
(a - 7)2 (a + 6)
1
252)                                           x2 - 4x + 16
3x + 2                           275)
(x - 4)2
y+ 5
253)                                            5
y+ 8                             276)
12x
t+2
254)                                           t+ 7
t                               277)
4t
255) -4
7                                       a + 13
256) -                                  278)
6                                       a+1
257) -1                                 279) 3
56y4                             280) m - 6
258)                                           1
x                              281)
x+4
y+ 5
259)                                           x-6
8                               282)
x+5
1
260)                                            2
x+4                              283)
x-2
z-1
261)                                           57
z - 10                           284)
5x
4v
262)                                           5 - 2z
v+3                              285)
z2
8(x + 2)
263)                                           -7x - 12
x-1                             286)
30x
k
264)                                           -3z + 126
k- 4                             287)
40z
(x + 5)(3x + 5)
265)                                           21x + 45
5x                         288)
x-5                                     70x2
266)
8(x + 1)                                15x - 63
289)
a+1                                    70x2
267) -
a+3                                    8x + 6
290)
8p                                      x(x + 6)
268)
3                                       9 r - 28
291)
2x - 5                                  r(r - 7 )
269)
x+3                                       -200
292)
x2 - 100

35
Testname: QR

5x2 - 18x + 8               8a 4 - 9a
293)                        317)
x2 - 16                   9a 4 + 8
5x + 26                     9x2 y3 + 6y2
294)                        318)
(x + 4)2                      x2 + 6x
-x                        x+4
295)                        319)
x + 10                      3 - 8x
-2                            x2 (x + 4)(x - 4)
296)                        320)
x- 1                        (x - 20)(x + 1)(x - 1)
10
297)                               x2 + 9x - 28
1 -y                 321)
-x2 - 8
-3
298)                               x+9
6x - 7               322)
7x - 9
15
299)
8x - 3                      a 2 - 14a - 54
323)
14x + 70                     a 2 - 9a - 9
300)
x2 - 49                          x2 y2
324)
12                          x2 + xy + y2
301)
11
x(x2 + x + 1)
9                    325)
302)                               (x + 1)(x2 + 1)
4
39
1 - 2a               326)
303)                               2
1 - 5a
10
8x2 + 64               327)
304)                               3
9x2                  328) -6, -6
305) -y                     329) -6, 6
306) -(x + 6)                     1
330)
x2 - 12                      5
307)
2x + 12                331) 7
1                332) {-1, 4}
308) -                           25
a                333)
6
309) y2(x + y)
334) -35
4x2 - 7x
310)                             12
5 - 4x2               335)
5
311) 12x                           112
y + 3x                 336)
312)                                5
7x2 y2                 337)   17
8 - 5x2              338)   26
313)
12x2 + 4             339)   - 68
340)   No solution
314) -1
341)   - 81
7a - 4b3            342)   - 10
315)
6b3 + 4a2 b2         343)   3
316) 1                      344)   No solution
345)   -5
346)   5
36
Testname: QR

347) No solution              380) - 22
348) 12                       381) 3
4                        382) -2
349)
3                        383) 8
350) No solution              384) 5
A- P                 385) 4
351) r =                      386) -5
Pt
387) -3
2A - Bh
352) b =                             2
h               388) -
5
a
353) b =                      389) 5x
ac - 1
3
pq                390)
354) f =                           5
p+q
391) z 4
20
355)    hr                    392) 2t
9
393) x2
12
356)      hr                  394) 2a
5
395) b+ 4
11                   396) 2x + 2
357) 2      hr
12                   397) 5
358) 4 hr                     398) -3
359) baker: 20 min            399) -4
assistant: 80 min        400) -7
360) 15 hr                         3
401) x
361) 10 hours
402) 4
1
362) 9 hr                            4
3                      403)       mn
363) 4.3 hr                        3
364) 12 km/h                  404) x8 y8
365) Bike: 12 mph             405) 128
Hike: 2 mph              406) 256
366) 5 hours
407) 27y6
367) 2 hours
408) 171/3
368) 60 mph
369) 14 km/h                  409) x9/2
370) 18 mph                   410) (5x3 y)2/5
371) 105 mph                  411) (3x4 y) 3/5
2                               1
372) 9 kph                    412)
7                             x 4/5
373) 330 mph
p6/7
374) 8 mph                    413)
7
1
375) 1 mph
2                      414) x
376) 10 , - 10                415) y1/2
377) 38 , - 38                416) 6 11/12
378) 11                       417) 8 15/13
16
379)                          418) x16/25
19
419) z 1/5

37
Testname: QR

3                                               8       5
420)       a                                    455)
5
3
421)   x2                                              4       7
456)
422) x5                                                    7
423) (ab)6                                             5 2x
457)
4                                                x
424)   7x
3 2x
425) x15y9                                      458)
x
426) 4 3
5x 2xy
3                                    459) -
y3
427) 3         2
428) 4x 3 y                                            29 x
460)
429) 9 y 6                                              x2
430) ( 7 k3 q4 ) 5 k                                   3
245
3                            461)
431) 10 xy( xy2)                                           7
3                                           3
432) - 4 a 2 b( a 2 b2 )                               9    y2
462)
433) 18 5                                                  y
434) 7m11 2                                            3
15x
3                                    463)
3x
435) 3  21
3
436) 20m 2                                                 12x
464)
437) 4x                                                    3x
4                                                    3
r3                                         5    6x
438)                                            465)
3                                               6x
7                                                 4
439)
r2                                              3       a
466)
a
440) 5
32 + 4 3
441) b 6b                                       467)
61
3
442) 3 a2 z                                            32 + 4 7
468)
443) -33 3                                                57
444) -15 3                                                 14 - 9 7
445) -33 3                                      469)
-79
446) -15 2a
35 - 4 7
447)    21 - 15                                 470)
-11
448) 6 55 + 30
471)  10 - 3
449) -2
9-4 5
450)    12 + 2 2 - 5 6 - 10                     472)
-1
451) (f · g)(x) = x2 - 6
7-2 6
452) (f · g)(x) = x2 - 2x 6 + 6                 473)
-5
453) (f · g)(x) = x2 - x 17 + x 2 -   34
x+4 x+4
454) (f · g)(x) = 12 - 7 x + x                  474)
x-4

38
Testname: QR

5 x( x + 2 y)               -5 ± 13
475)                        515)
x - 4y                       4
476) 15                            -4 ± 10
516)
477) 4                                 3
478) 5                      517) 5 ± 7i
479) 72
-1 ± i 15
480) 7                      518)
2
11
481)                               -4 ± 2
5                     519)
2
482)   56
483)   -1                   520)   -8, 12
484)   10,374               521)     3, - 3
485)   7 - 3i               522)   Two different rational solutions
486)   11 - 3i              523)   Exactly one rational solution
487) 4i                     524)   Two different imaginary solutions
525)   Two different imaginary solutions
488)   14i
526)   x=1
489)   2i 42
527)   x=1
490)   13i
528)   x = -2
491)   i( 3 - 10)           529)   (-1, 2)
492)   234                  530)   (1, -2)
493) 36 + 18i               531)   (1, -3)
494) 60 - 32i               532)   (8, 0), (0, 64)
6                    533)   x-intercepts (9, 0) and (10, 0); y-intercept (0,-90)
495) - i
5                    534)   No x-intercepts, (0, -14)
15   50           535)
496) -       -    i
109 109                                        y
3 13                                           10
497) +   i
5 10
498) i                                              5
499) -1
500) -2i
-10     -5             5     10   x
501) ±12
502) ± 15                                           -5
503) ± 11
504) -7 ± 2 7                                      -10
505) -7 ± 2 5
506) 9 ± 17
507) 9, -5
508) 1, -11
509) -4 ± 19
510) 9, -3
511) -4 ± 21
512) -4 ± 21
513) -2 ± 2i
-2 ± 3
514)
2

39
Testname: QR

536)                                           550) 48 watches
y                     551) 10
10                          552)   74 ≈ 8.602
553) 2 5 ≈ 4.472
5                          554) 5 5 ≈ 11.18
555) 2 74 ≈ 17.205
17 9
-10    -5             5   10   x        556)     ,
2 2
-5                                 1
557)      ,- 3
2
-10                                 1 1
558)     ,
2 2
537)                                           559) - 6, 2
y                     560) - 1, 2
10                          561) x2 + y2 = 196
562) (x + 7)2 + (y - 3)2 = 4
5
563) (x + 7)2 + y2 = 144
564) x2 + (y + 2)2 = 81
-10    -5             5   10   x        565) (x - 9)2 + (y - 7)2 = 6
566) x2 + (y - 10)2 = 13
-5
567) (x - 2)2 + y2 = 10
568)   (x - 2)2 + (y + 8)2 = 20
-10
569)   (0, 0), r = 3
570)   (-8, 0), r = 4
538)
571)   (7, -1), r = 2
y
572)   (7, 9), r = 6
10
573)   (6, 0), r = 2
574)   (5, 0), r = 10
5                          575)   (-3, 8); r = 3

-10    -5             5   10   x

-5

-10

539) x = -4
540) x=2
541) (1, -1)
542) (-4, -1)
543) -3
544) -5
545) 44 and 44
546) 25 ft2
547) 2890 ft
548) 21 sec
549) 26 hotdogs

40

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