Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
1)
A)
2)
B)
3x
2
C)
-
3x + 2
2
D)
-3x + 2
2
2)
2x
3-x
B)
2x
x-3
C)
2(x - 9)
3-x
D)
2(x - 9)
x-3
3)
Solve the rational equation.
x
72
=
+4
2
x + 6 x - 36
A)
4)
3x + 2
2
Subtract.
x-9 x+9
x-3 3-x
A)
3)
1)
Simplify the rational expression.
9x2 - 4
4 - 6x
{4}
In the equation v =
A)
B) -4}
C)
{4, -6}
D)
{-4, 6}
1
w, does v vary directly or inversely with w?
5
4)
B) Inversely
Directly
5)
The recipe for a sheet cake calls for 7 cups of flour and 3 cups of sugar. Suppose you
want to make as much cake batter as you can using all of the flour you have, which is 32
cups. How many cups of sugar would you need? Round to the nearest tenth of a cup.
A) 22.9 cups
B) 9.1 cups
C) 13.7 cups
D) 74.7 cups
5)
6)
Solve the rational equation.
3
3x - 3
3
+
=
x x-2
x-2
6)
A)
7)
-
5 1
,
2 3
B)
C)
{1}
{2, 1}
D)
{}
Nancy shot a 16 on 4 holes of golf. At this rate, what can she expect her score to be if
she plays all 18 holes? Round to nearest whole number.
A) 88 strokes
B) 72 strokes
C) 56 strokes
D) 64 strokes
1
7)
8)
8)
Simplify the rational expression.
y + 19
y2 + 19
9)
A)
1
B)
C)
1
y - 19
D)
1
y
y + 19
y2 + 19
; cannot be simplified
9)
Solve for d1 .
1
1
1
=
+
f d1 d2
A) d1
10)
= f - d2
B) d1
=
fd2
C) d1
d2 - f
d f - d1 f
= 2
d2
D) d1
=
1
f - d2
10)
Solve for d1 .
1
1
1
=
+
f d1 d2
A) d1
11)
1
f - d2
B) d1
C) d1
= f - d2
=
fd2
d2 - f
D) d1
d f - d1 f
= 2
d2
Fill in the blank to make an equivalent fraction with the given denominator.
3
=
y - 2 y3 + y2 - 6y
A)
3y2 + 9y
C) y2
12)
=
B) 3y2
D) 3y3
+ 3y
-3
+ 3y2 - 18y
12)
Solve the rational equation.
t - 2 t + 17
1
=
t - 1 t2 - 1 t + 1
A)
{–4, 5}
B)
11)
-3, -
5
2
C)
2
7,
1
2
D)
{5}
13)
13)
Simplify the rational expression.
35y2 - 5y3
y2 - 6y - 7
A)
-
5y2
y+1
B)
35 - 5y3
C)
-6y - 7
14)
D)
5y2
y+1
35y2 - 5y3
y2 - 6y - 7
; cannot be simplified
14)
Simplify.
3
y-5 5
+
2y
3y2 4y
A)
7y - 20
12y2
B)
y-7
C)
3y2 - 2y
37y - 20
12y2
D)
y3 + 3y2 - 5
24y4
15)
The JUST-SAY-MOW lawn mowing company consists of two people: Lisa and Bob. If
Lisa cuts the lawn by herself, she can do it in 3 hours. If Bob cuts the same lawn
himself, it takes him an hour longer than Lisa. How long would it take them if they
worked together? Round to the nearest hundredth of an hour.
A) 1.71 hours
B) 1.00 hour
C) 4.00 hours
D) 3.50 hours
15)
16)
Competing in a mini-triathlon, Catherine ran 3 miles in the same amount of time she
biked 12 miles. Her average speed on the bike was 18 mph more than her average
running speed. What was her running speed?
A) 5 mph
B) 4 mph
C) 6 mph
D) 8 mph
16)
17)
On a certain map, Detroit and Cleveland are 3" apart. The actual distance from Detroit
to Cleveland is 170 miles. How far apart are two cities that are 11" apart on this map?
Round to the nearest tenth of a mile.
A) 623.3 miles
B) 0.2 miles
C) 717.3 miles
D) 482.3 miles
17)
18)
Add or subtract as indicated and simplify if possible.
39y 14y
+
11x 11x
18)
53y
A)
44x
53y
B)
11x
53y
C)
22x
3
D)
546y2
121x2
19)
19)
Simplify the complex fraction.
w
w+3
w
+w
w+3
A)
20)
1
2
B)
C)
B) (x
D)
x+9
D)
1
w+4
+ 9)(x2 - 81)
x-9
21)
Write the domain of the rational function in interval notation.
5-t
g(t) =
2
t +4
(– , –2) (–2, 2)
C) (– , 5) (5, )
B) (–
(2, )
, –2) (–2, )
D) (– , )
22)
Add or subtract as indicated and simplify if possible.
t2 - 8 -4t + 13
t-3
t-3
t2 + 4t + 5
B)
t-3
t+7
A)
2
23)
w
w+4
20)
- 81
A)
22)
C)
Find the least common denominator (LCD).
9x
-4
,
x + 9 x2 - 81
A) x2
21)
1
1+w
t2 - 4t + 5
C)
t-3
-2y
2y2 + 5y
C)
t+7
23)
Add.
A)
D)
+
y-3
2y2 + y - 10
-y - 3
4y2 + 6y - 10
-2y2 + y - 3
2y3 + 5y2 - 10
4
B)
1-y
(2y + 5)(y - 2)
D)
-3y2 + y + 1
y(2y + 5)(y - 2)
24)
A)
25)
24)
Divide the rational expressions.
8y8 32y2
÷
3x
x10
3x11
B)
256y10
3y6
C)
4x9
3y6
256y10
3x11
25)
B) m(7)
m(7) = 103
C) m(7) = 0
=1
D) m(7) is undefined
26)
Add or subtract as indicated and simplify if possible.
-20x
7
+
-4x + 3 -4x + 3
A)
27)
D)
Evaluate the rational function, if possible.
2y2 + 5
m(y) =
; m(7)
y-7
A)
26)
4x9
-20x + 7
-8x + 6
B)
-20x + 7
-4x + 3
C)
-140x
-4x + 3
x3
A)
C)
-13x
-4x + 3
27)
Simplify the complex fraction.
2x + 3
5x -
D)
x2 + 9
x
2x + 3
B)
x2 (2x - 3)2
(-x2 + 5x + 9)(2x + 3)
D)
x4
5
-5(x2 + 4)
x2
1
x2 (2x - 3)
28)
Write the domain of the function in interval notation and use that information to graph the 28)
function.
3
n(x) =
x+1
A)
(- , 1) (1, )
B) (-
C)
(- , 3) (3, )
D)
, -1) (-1, )
(- , -3) (-3, )
29)
The number of hours it takes to paint a house is inversely proportional to the number of
people painting. If it takes 3 workers 20 hours to paint a certain house, how long would
it take 5 workers? Round to one tenth of an hour.
A) 18.0 hours
B) 22.0 hours
C) 12.0 hours
D) 60.0 hours
29)
30)
Simplify the complex fraction.
2m
-m
n
30)
mA)
m
n
m(2 - n)
n-1
B)
2-n
m(1 - n)
C)
6
2-n
1-n
D)
2-n
n-1
31)
A postal worker can sort a day's worth of mail in 8 hours. With her supervisor helping, it
takes 3 hours. How long would it take the supervisor working alone?
A) 3 hrs. 50 min.
B) 2 hrs. 11 min.
C) 4 hrs. 48 min.
D) 5 hrs. 20 min.
31)
32)
Subtract.
9 t + 12
4t 10t2
32)
A)
43t + 24
20t2
B)
43t - 24
C)
20t2
90 - 12t - t2
40t3
D)
-3 - t
4t - 10t2
33)
The recipe for a holiday punch calls for 7 cups of fruit drink and 3 cups of ginger ale.
Suppose you want to make as much punch as you can using all of the fruit drink you
have, which is 26 cups. How many cups of ginger ale would you need? Round to the
nearest tenth of a cup.
A) 18.6 cups
B) 11.1 cups
C) 60.7 cups
D) 7.4 cups
33)
34)
If a baseball player has a batting average of 0.276, his ratio of hits to at-bats 276 to 1000.
How many base hits would a player with a batting average of 0.276 have if he had 500
at-bats?
A) 110 hits
B) 138 hits
C) 276 hits
D) 362 hits
34)
35)
Subtract.
7x + 9 x + 2
6x - 18 x - 3
35)
A)
36)
B) 6
C)
1
6
D)
x + 11
6(x - 3)
36)
Solve the rational equation.
t2 t
- =1
3 6
A)
37)
x + 21
6(x - 3)
-2,
3
2
B)
C)
{2}
-
3
,2
2
D)
{}
A bus driver follows a morning route and an afternoon route each day. Because there are
more cities on the morning route, the average speed is 12 miles per hour less than the
afternoon route. She covers 70 miles on the morning route in the same amount of time
as she covers 100 miles on the afternoon route. Find her average speed on the afternoon
route.
A) 40 miles per hour
B) 51 miles per hour
C) 28 miles per hour
D) 36 miles per hour
7
37)
38)
38)
Simplify the complex fraction.
12
12
x+h x
h
A)
39)
12
xh(x + h)
B) -
12
x(x + h)
C)
D)
0
39)
Write the domain of the rational function in interval notation.
x(x + 7)
k(x) =
x(x - 10)(x + 7)
A)
B) (-
(- , -7) (-7, 0) (0, )
C) (- , -7) (-7, 0) (0, 10) (10, )
40)
12
x(x + h)
, 10) (10, )
D) (- , )
40)
Solve the proportion.
8 168
=
7
x
A)
{147}
B)
1
21
C)
8
{49}
D)
{1176}
Answer Key
Testname: CH6PRACTICE
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35)
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39)
40)
C
B
A
A
C
B
B
D
B
C
A
A
A
A
A
C
A
B
D
A
D
D
B
B
D
B
D
B
C
D
C
B
B
B
C
C
A
B
C
A
9