Chapter Standardized Test
CHAPTER
ADDITIONAL RESOURCES
• Chapter 7 Resource Book
Chapter Test (3 levels) (p. 106)
SAT/ACT Chapter Test (p. 112)
Alternative Assessment (p. 113)
•
Test and Practice Generator
7
TEST-TAKING STRATEGY Some college entrance exams allow the optional use of calculators.
If you do use a calculator, make sure it is one you are familiar with and have used before.
1. MULTIPLE CHOICE If x4 = 625, what does x equal?
C
A
¡
D
¡
B
¡
E
¡
5
25
C
¡
º5
7. MULTIPLE CHOICE Which function is graphed? C
±5
y
±25
2
2. MULTIPLE CHOICE What is the simplified form of
the expression 兹1苶8苶 + 兹2苶0苶0苶 + 兹2苶 º 兹8苶? A
Qu. Standard
Qu. Standard
A
¡
C
¡
E
¡
B
¡
D
¡
12兹2苶
18兹2苶
14兹2苶 º 兹8苶
4兹2苶 º 4兹8苶
3. MULTIPLE CHOICE What is the simplified form of
the expression 兹5苶4苶苶
x3苶
y6苶
z10苶? (Assume all variables
are positive.) D
3
A
¡
C
¡
E
¡
xy 兹5苶4苶苶
z苶
2 3
10
3
3y3z7兹5苶
B
¡
D
¡
2 33
xy z 兹5苶4苶z苶
3
3xy2z3兹2苶z苶
18xy3z7
4. MULTIPLE CHOICE Which of the following is true
if ƒ(x) = 3xº1/2, g(x) = 6x3/4, and h(x) = 18x1/4? C
A
¡
C
¡
E
¡
h(x) = ƒ(x) + g(x)
h(x) = ƒ(x) • g(x)
B
¡
D
¡
h(x) = ƒ(x) º g(x)
ƒ(x)
g(x)
h(x) = ᎏ
h(x) = ƒ(g(x))
g(x) = x2 + 2, what is ƒ(g(x))? B
x4 + x2 + 17
x4 + x 2 º 9
A
¡
C
¡
E
¡
B
¡
D
¡
x4 + x2 + 5
x4 + x2 º 3
x4 + 7x2 + 5
ƒº1(x) = 2x º 10
E
¡
1
5
ƒº1(x) = ᎏᎏx + ᎏᎏ
2
2
460
460
3
y = 兹x苶º
苶苶
8 +3
3
y = 兹x苶+
苶苶
3 +8
3
y = 兹x苶+
苶苶
8 º3
3
y = 兹x苶+
苶苶
8 +3
8. MULTIPLE CHOICE What is the solution of the
equation (3x + 5)1/2 º 3 = 4? E
A
¡
ºᎏᎏ
B
¡
8
ᎏᎏ
3
D
¡
14
ᎏᎏ
3
E
¡
44
ᎏᎏ
3
4
3
C
¡
11
ᎏᎏ
3
9. MULTIPLE CHOICE What is the solution of the
3
equation 4兹x苶º
苶苶
5 = 20? B
A
¡
D
¡
B
¡
E
¡
120
2005
C
¡
130
220
4101
6, 4, 4, 10, 5, 12, 1? B
A
¡
D
¡
ļ1(x) = 2x + 5
ļ1(x) = 2x + 10
1
2
ƒº1(x) = ᎏᎏx + 5
Chapter 7 Powers, Roots, and Radicals
B
¡
E
¡
4
7
C
¡
5
6
10
11. MULTIPLE CHOICE Which data set matches the
box-and-whisker plot shown? D
6. MULTIPLE CHOICE Which function is the inverse
1
of ƒ(x) = ᎏᎏx º 5? C
2
A
¡
B
¡
C
¡
D
¡
B
¡
D
¡
3
y = 兹x苶º
苶苶
3 +8
10. MULTIPLE CHOICE What is the median of
5. MULTIPLE CHOICE If ƒ(x) = x2 º 3x + 7 and
A
¡
C
¡
E
¡
x
1
14兹2苶
0
¡
C
¡
E
¡
A
1
1
2
3
4
3
1, 1, 3, 5, 6, 7, 9
1, 2, 4, 5, 6, 8, 9
1, 3, 5, 5, 7, 8, 9
5
5
6
¡
D
¡
B
7
7
8
9
10
9
1, 2, 3, 5, 7, 8, 9
1, 3, 4, 5, 6, 7, 9
QUANTITATIVE COMPARISON In Exercises 12 and 13, choose the statement
that is true about the given quantities.
A
¡
B
¡
C
¡
D
¡
The quantity in column A is greater.
The quantity in column B is greater.
The two quantities are equal.
The relationship cannot be determined from the given information.
Column A
Column B
º2/3
ƒ(2) where ƒ(x) = xº2
ƒ(8) where ƒ(x) = x
12.
3
ƒ(ƒ(0)) where ƒ(x) = x + 1
ƒ(ƒ(0)) where ƒ(x) = 5x º 2
13.
14e. Specific metabolic rate
increases as body mass
decreases because the rate is
proportional to m –1/4. In other
words, as mass decreases, the
denominator gets smaller so the
rate increases.
C
B
14. MULTI-STEP PROBLEM The metabolic rate r (in kilocalories per day) of a
mammal can be modeled by r = km3/4 where k is a constant and m is the mass
(in kilograms) of the mammal. The specific metabolic rate s (the rate per unit mass)
km3/4
can be modeled by s = ᎏᎏ. 䉴 Source: Scaling: Why is Animal Size so Important?
m
a. A 922 kilogram cow has a metabolic rate of about 11,700 kilocalories per day.
What is the value of k in the model for metabolic rate? about 69.9
b. Using the k-value from part (a), simplify the model given for specific
69.9
metabolic rate. s = }
m1/4
c. What is the specific metabolic rate of a 922 kilogram cow? about 12.7 kilocalories per day per kilogram
d. What is the specific metabolic rate of a 16 gram mouse? about 197 kilocalories per day per kilogram
e.
Writing How does the specific metabolic rate change with decreasing
body mass? See margin.
15. MULTI-STEP PROBLEM Follow the steps below to find the relationship
between the number of pedal revolutions of a bicycle and the distance traveled.
a. The rear wheel of a bicycle has a diameter of 70 centimeters. Write the
function that describes the distance d traveled by the bicycle in terms of the
number w of rear-wheel revolutions. (Hint: When w = 1, the distance traveled
by the bicycle is equal to the circumference of the rear wheel.) d = ƒ(w) = 220w
b. The gear ratio of a bicycle is calculated by dividing the number of teeth in
the chainwheel by the number of teeth in the freewheel. The number w of rearwheel revolutions is equal to the product of the gear ratio and the number p of
pedal revolutions. A bicycle in first gear has 24 teeth in the chainwheel and 32
# of chainwheel teeth
}}
gear ratio (g) = }
teeth in the freewheel. Write the function that describes w in terms of p.
# of freewheel teeth
c. Use composition of functions to find the relationship between d and p.
so w(p) = gp = 0.75p
d = ƒ(w(p)) = 220gp
d. Shifting gears on a bicycle changes the gear ratio. Use the table below to find
how the distance traveled per pedal revolution changes as you shift gears. 1st gear: about 165 cm per pedal revolution
Gear
Number of teeth in chainwheel
Number of teeth in freewheel
5th
24
19
about 278 cm per pedal revolution
10th
40
22
about 400 cm per pedal revolution
15th
50
19
about 579 cm per pedal revolution
Distance traveled per pedal revolution increases as gear number increases; it becomes harder to pedal.
Chapter Standardized Test
461
461