Download Read each question. Then fill in the correct answer on the answer

Standardized Test Practice - Cumulative, Chapter 5
Read each question. Then fill in the correct answer on the answer document provided by your teacher or
on a sheet of paper.
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1. Simplify the following expression. (5n + 11n – 6) – (2n – 5)
A 3n 2 + 11n – 11
2
B 3n + 11n – 1
C 7n 2 + 11n – 11
2
D 7n + 11n – 1
SOLUTION: Option B is the correct answer.
ANSWER: B
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2. What is the effect on the graph of the equation y = x + 4 when it is changed to y = x – 3?
F The slope of the graph changes.
G The graph widens.
H The graph is the same shape, and the vertex of the graph is moved down.
J The graph is the same shape, and the vertex of the graph is shifted to the left.
SOLUTION: The graph is the same shape, and the vertex of the graph is moved 7 units down.
Therefore, option H is the correct answer.
ANSWER: H
3. Let p represent the price that Ella charges for a necklace. Let f (x) represent the total amount of money that Ella
makes for selling x necklaces. The function f (x) is best represented by
A f (x) = x + p
2
B f (x) =xp
C f (x) =px
D f (x) =x2 + p
SOLUTION: The total amount of money that Ella makes for selling x necklaces is the price of a necklace times x.
That is, f (x) = px .
Therefore, option C is the correct answer.
ANSWER: C
4. Which of the following is not a solution to the cubic equation below?
3
x –Manual
37x – -84
= 0 by Cognero
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F –4
G –3
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That is, f (x) = px .
Therefore, option C is the correct answer.
ANSWER: Standardized
Test Practice - Cumulative, Chapter 5
C
4. Which of the following is not a solution to the cubic equation below?
3
x – 37x – 84 = 0
F –4
G –3
H6
J7
SOLUTION: Solve this equation by factoring. The factors of 84 are 4, 3, and 7.
By the Zero Product Property, the solutions are 7, –3 and –4.
Therefore, option H is the correct answer.
ANSWER: H
5. What is the solution set for the equation
A {–5, 4}
B {–2, 1}
C {2, –1}
D {–3, 3}
?
SOLUTION: Next, solve for x.
The solution set is {–2, 1}.
Option B is the correct answer.
ANSWER: B
6. How many real zeros does the polynomial function graphed below have?
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F2
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The solution set is {–2, 1}.
Option B is the correct answer.
ANSWER: Standardized
Test Practice - Cumulative, Chapter 5
B
6. How many real zeros does the polynomial function graphed below have?
F2
G3
H4
J5
SOLUTION: The graph intersects the x-axis at two points. Therefore, there are two real zeros.
Option F is the correct answer.
ANSWER: F
7. For Marla’s vacation, it will cost $100 to drive her car, plus between $0.50 and $0.75 per mile. If she will drive her
car 400 miles, what is a reasonable conclusion about c, the total cost to drive her car on the vacation?
A 300 < c < 400
B 200 < c ≤ 400
C 100 < c < 400
D 200 ≤ c ≤ 300
SOLUTION: The total cost to drive her car is represented by the inequality:
.
That is,
.
Therefore, option A is the correct answer.
ANSWER: A
can be used to approximate the population of Ling’s home country
8. The function
between 1960 and 2000. The domain of the function x represents the number of years since 1960, and P is given in
millions of people. Evaluate P(20) to estimate the population of the country in 1980.
F about 2 million people
G about 2.5 million people
H about 3 million people
J about 3.5 million people
SOLUTION: Substitute 20 for x in the function and evaluate.
Therefore, option J is the correct answer.
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ANSWER: J
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That is,
.
Therefore, option A is the correct answer.
ANSWER: Standardized
Test Practice - Cumulative, Chapter 5
A
can be used to approximate the population of Ling’s home country
8. The function
between 1960 and 2000. The domain of the function x represents the number of years since 1960, and P is given in
millions of people. Evaluate P(20) to estimate the population of the country in 1980.
F about 2 million people
G about 2.5 million people
H about 3 million people
J about 3.5 million people
SOLUTION: Substitute 20 for x in the function and evaluate.
Therefore, option J is the correct answer.
ANSWER: J
9. Solve 4x – 5 = 2x + 5 – 3x for x.
A –2
B –1
C1
D2
SOLUTION: Option D is the correct answer.
ANSWER: D
Record your answers on the answer sheet provided by your teacher or on a sheet of paper.
10. A stone path that is x feet wide is built around a rectangular flower garden. The garden is 12 feet wide and 25 feet
long as shown below.
If the combined area of the garden and the stone path is 558 square feet, what is the width of the walkway? Express
your answer in feet.
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SOLUTION: The dimensions of the combined area are 25 + 2x and 12 + 2x.
Therefore, the combined area of the garden and the stone path is:
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Option D is the correct answer.
ANSWER: Standardized
Test Practice - Cumulative, Chapter 5
D
Record your answers on the answer sheet provided by your teacher or on a sheet of paper.
10. A stone path that is x feet wide is built around a rectangular flower garden. The garden is 12 feet wide and 25 feet
long as shown below.
If the combined area of the garden and the stone path is 558 square feet, what is the width of the walkway? Express
your answer in feet.
SOLUTION: The dimensions of the combined area are 25 + 2x and 12 + 2x.
Therefore, the combined area of the garden and the stone path is:
.
Since the combined area is 558 square feet, this equation can be written:
.
Simplify.
Solve for x.
The value of x cannot be negative.
Therefore, the width of the walkway is 3 ft.
ANSWER: 3 ft
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3
11. Factor 64a + ab completely. Show your work.
SOLUTION: eSolutions Manual - Powered by Cognero
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The value of x cannot be negative.
Therefore, the width of the walkway is 3 ft.
ANSWER: Standardized
Test Practice - Cumulative, Chapter 5
3 ft
4
3
11. Factor 64a + ab completely. Show your work.
SOLUTION: ANSWER: 2
2
a(4a + b)(16a – 4ab + b )
12. Simplify
Give your answer in factored form. Show your work.
SOLUTION: ANSWER: (3x + 2)(x – 4)
13. GRIDDED RESPONSE What is the value of a in the matrix equation below?
SOLUTION: Solve the system of equations.
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ANSWER: Standardized
Test Practice - Cumulative, Chapter 5
(3x + 2)(x – 4)
13. GRIDDED RESPONSE What is the value of a in the matrix equation below?
SOLUTION: Solve the system of equations.
ANSWER: 7.5
14. GRIDDED RESPONSE Matt has a cubic aquarium as shown below. He plans to fill it by emptying cans of water
with the dimensions as shown.
About how many cylindrical cans will it take to fill the aquarium?
SOLUTION: 3
The volume of the aquarium is 15 × 15 × 15 = 3375 in .
3
The volume of the cylinder is π × 2 × 2 × 6 = 24π in .
The ratio between the volume of the aquarium and the cylinder is
.
It will take about 45 cylindrical cans to fill the aquarium.
ANSWER: 45
15. What are the slope and y-intercept of the equation of the line graphed at the right?
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The ratio between the volume of the aquarium and the cylinder is
.
It will take about 45 cylindrical cans to fill the aquarium.
ANSWER: Standardized
Test Practice - Cumulative, Chapter 5
45
15. What are the slope and y-intercept of the equation of the line graphed at the right?
SOLUTION: The coordinates of the intercepts are (–6, 0) and (0, 3).
The slope m =
.
The slope of the line is
.
The y-intercept of the line is b = 3.
ANSWER: Record your answers on a sheet of paper. Show your work.
16. The volume of a rectangular prism is 864 cubic centimeters. The length is 1 centimeter less than the height, and the
width is 3 centimeters more than the height.
a. Write a polynomial equation that can be used to solve for the height of the prism h.
b. How many possible roots are there for h in the polynomial equation you wrote? Explain.
c. Solve the equation from part a for all real roots h. What are the dimensions of the prism?
SOLUTION: a. Let h be the height of the prism.
Therefore, the dimensions are h, h – 1,h + 3.
The volume of the prism is
.
Therefore,
.
b. Sample answer: The order of the equation is 3, so there are up to 3 possible solutions to the equation.
c.
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The y-intercept of the line is b = 3.
ANSWER: Standardized Test Practice - Cumulative, Chapter 5
Record your answers on a sheet of paper. Show your work.
16. The volume of a rectangular prism is 864 cubic centimeters. The length is 1 centimeter less than the height, and the
width is 3 centimeters more than the height.
a. Write a polynomial equation that can be used to solve for the height of the prism h.
b. How many possible roots are there for h in the polynomial equation you wrote? Explain.
c. Solve the equation from part a for all real roots h. What are the dimensions of the prism?
SOLUTION: a. Let h be the height of the prism.
Therefore, the dimensions are h, h – 1,h + 3.
The volume of the prism is
.
Therefore,
.
b. Sample answer: The order of the equation is 3, so there are up to 3 possible solutions to the equation.
c.
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The expression h + 11h + 96 is a prime. So, the value of h is 9.
Therefore, the prism is 9 cm tall, 8 cm long and 12 cm wide.
ANSWER: 3
2
a. h + 2h – 3h = 864
b. Sample answer: The order of the equation is 3, so there are up to 3 possible solutions to the equation.
c. h = 9, the prism is 9 centimeters tall, 8 centimeters long, and 12 centimeters wide.
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17. Scott launches a model rocket from ground level. The rocket’s height h in meters is given by the equation h = –4.9t
+ 56t, where t is the time in seconds after the launch.
a. What is the maximum height the rocket will reach? Round to the nearest tenth of a meter. Show each step and
explain your method.
b. How long after it is launched will the rocket reach its maximum height? Round to the nearest tenth of a second.
SOLUTION: a. Write the function in the vertex form of the equation.
Solve by completing the square.
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ANSWER: 3
2
a. h + 2h – 3h = 864
b. Sample answer: The order of the equation is 3, so there are up to 3 possible solutions to the equation.
Standardized
Test
Practice
- Cumulative,
5 long, and 12 centimeters wide.
c. h = 9, the
prism
is 9 centimeters
tall, 8 Chapter
centimeters
2
17. Scott launches a model rocket from ground level. The rocket’s height h in meters is given by the equation h = –4.9t
+ 56t, where t is the time in seconds after the launch.
a. What is the maximum height the rocket will reach? Round to the nearest tenth of a meter. Show each step and
explain your method.
b. How long after it is launched will the rocket reach its maximum height? Round to the nearest tenth of a second.
SOLUTION: a. Write the function in the vertex form of the equation.
Solve by completing the square.
Therefore, the vertex of the function is
.
The maximum height the rocket will reach is 160 m.
b. The rocket will reach its maximum height at
s or about 5.7 s.
ANSWER: a. 160 m; Sample answer: the vertex form of the equation is
so the vertex is at b. 5.7 s
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