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

Standardized Test Practice - Cumulative, Chapter 4
Read each question. Then fill in the correct answer on the answer document provided by your teacher or
on a sheet of paper.
1. A rental store charges $32 per day to rent a bicycle. At this rate, the store rents about 200 bikes per month. The
owner of the store estimates that they will rent 5 fewer bikes per month for each $2 increase in the rental price.
What price will maximize the income of the store?
A $46
B $51
C $56
D $57
SOLUTION: Multiply the expressions for the new price and new number of customers after x price increases to write a quadratic
equation.
The function f (x) reaches the maximum at:
So,
will maximize the income of the store. The correct choice is C.
ANSWER: C
2. What are the solutions of the quadratic equation graphed below?
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F –4, –1
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ANSWER: C
Standardized
Test Practice - Cumulative, Chapter 4
2. What are the solutions of the quadratic equation graphed below?
F –4, –1
G 1, 4
H –1, 4
J –4, 1
SOLUTION: The graph intersects the horizontal axis at x = –4, 1. Therefore the solutions are x = –4 and 1. The correct choice is
J.
ANSWER: J
3. Peyton works as a nanny. She charges at least $10 to drive to a home and $10.50 per hour. Which inequality best
represents the relationship between the number of hours working n and the total charge c?
A c ≥ 10 + 10.50n
B c ≥ 10.50 + 10n
C c ≤ 10.50 + 10
D c ≤ 10n + 10.50n
SOLUTION: Therefore the correct choice is A.
ANSWER: A
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4. Leo sells T-shirts at a local swim meet. It costs him $250 to set up the stand and rent the machine. It costs him an
additional $5 to make each T-shirt. If he sells each T-shirt for $15, how many T-shirts does he have to sell before he
can make a profit?
ANSWER: J
Standardized
Test Practice - Cumulative, Chapter 4
3. Peyton works as a nanny. She charges at least $10 to drive to a home and $10.50 per hour. Which inequality best
represents the relationship between the number of hours working n and the total charge c?
A c ≥ 10 + 10.50n
B c ≥ 10.50 + 10n
C c ≤ 10.50 + 10
D c ≤ 10n + 10.50n
SOLUTION: Therefore the correct choice is A.
ANSWER: A
4. Leo sells T-shirts at a local swim meet. It costs him $250 to set up the stand and rent the machine. It costs him an
additional $5 to make each T-shirt. If he sells each T-shirt for $15, how many T-shirts does he have to sell before he
can make a profit?
F 10
G 15
H 25
J 50
SOLUTION: Let n be the number of T-shirts he sells to make a profit.
The correct choice is H.
ANSWER: H
2
x – -2x
= 15 by
completing
5. Solve
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A –4, –1
the square.
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ANSWER: H
Standardized
Test Practice - Cumulative, Chapter 4
2
5. Solve x – 2x = 15 by completing the square.
A –4, –1
B –3, 5
C –2, 3
D 5, 7
SOLUTION: The correct choice is B.
ANSWER: B
6. The graph of
is translated down 5 units to produce the graph of the function h(x). Which of the
following could be h(x)?
F
G
H
J SOLUTION: The value of y decreases 5 units in the translation.
Therefore,
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ANSWER: B
Standardized
Test Practice - Cumulative, Chapter 4
6. The graph of
is translated down 5 units to produce the graph of the function h(x). Which of the
following could be h(x)?
F
G
H
J SOLUTION: The value of y decreases 5 units in the translation.
Therefore,
The answer is choice G.
ANSWER: G
7. Which of the following points is not a vertex of the feasible region for the system of linear inequalities below?
A B
C
D SOLUTION: Graph the inequalities and locate the vertices.
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The answer is choice G.
ANSWER: G
Standardized
Test Practice - Cumulative, Chapter 4
7. Which of the following points is not a vertex of the feasible region for the system of linear inequalities below?
A B
C
D SOLUTION: Graph the inequalities and locate the vertices.
The vertices of the reason are (0, 6), (3, 0), and (0, 0).
Therefore,
is not a vertex of the feasible region for the system of linear inequalities so G is the correct
answer.
ANSWER: G
2
8. The function P(t) = –0.068t + 7.85t + 56 can be used to approximate the population, in thousands, of Clarksville
between 1960 and 2000. The domain t of the function is the number of years since 1960.
According to the model, in what year did the population of Clarksville reach 200,000 people?
F 1974
G 1977
H 1981
J 1983
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SOLUTION: Substitute P(t) = 200 in the expression.
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answer.
ANSWER: G
Standardized
Test Practice - Cumulative, Chapter 4
2
8. The function P(t) = –0.068t + 7.85t + 56 can be used to approximate the population, in thousands, of Clarksville
between 1960 and 2000. The domain t of the function is the number of years since 1960.
According to the model, in what year did the population of Clarksville reach 200,000 people?
F 1974
G 1977
H 1981
J 1983
SOLUTION: Substitute P(t) = 200 in the expression.
Solve the equation for t.
The population reaches 200,000 in the year (1960 + 23) or 1983.
is not possible since the domain is between 1960 and 2000.
The correct choice is J.
ANSWER: J
Record your answers on the answer sheet provided by your teacher or on a sheet of paper.
9. GRIDDED RESPONSE What is the y-coordinate of the solution of the system of equations below?
SOLUTION: Graph the equations.
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ANSWER: J
Standardized
Test Practice - Cumulative, Chapter 4
Record your answers on the answer sheet provided by your teacher or on a sheet of paper.
9. GRIDDED RESPONSE What is the y-coordinate of the solution of the system of equations below?
SOLUTION: Graph the equations.
The lines intersect at (2, 1). Therefore, the y-coordinate of the solution is 1.
ANSWER: 1
10. GRIDDED RESPONSE Simplify
SOLUTION: ANSWER: 10
11. Use the quadratic function below to answer each question.
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ANSWER: 10
Standardized
Test Practice - Cumulative, Chapter 4
11. Use the quadratic function below to answer each question.
a. How many real roots does the quadratic function have?
b. How many complex roots does the function have?
c. What do you know about the discriminant of the quadratic equation? Explain.
SOLUTION: a. The graph has no x-intercepts. Thus the function has no real solution.
b. The function has (1 + 1) or 2 solutions because there is only one turning point for the graph. Since there is no real
solution, both the roots are complex.
c. Sample answer: The discriminant is negative because the roots are complex.
ANSWER: a. 0
b. 2
c. Sample answer: The discriminant is negative because the roots are complex.
2
12. If one of the roots of x + k x – 12 = 0 is 4, what is the value of k?
SOLUTION: Let x be the second root of the equation.
Sum of the roots is equal to –k and the product of the root is –12. That is,
Substitute x = –3 in the expression for k.
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b. 2
c. Sample Test
answer:
The discriminant
is negative
because
the roots are complex.
Standardized
Practice
- Cumulative,
Chapter
4
2
12. If one of the roots of x + k x – 12 = 0 is 4, what is the value of k?
SOLUTION: Let x be the second root of the equation.
Sum of the roots is equal to –k and the product of the root is –12. That is,
Substitute x = –3 in the expression for k.
ANSWER: –1
2
2
13. Describe the translation of the graph of y = (x + 5) – 1 to the graph of y = (x – 1) + 3.
SOLUTION: Sample answer: It is a translation 6 units right and 4 units up.
ANSWER: Sample answer: It is a translation 6 units right and 4 units up.
Record your answers on a sheet of paper. Show your work.
2
2
14. For a given quadratic equation y = ax + bx + c, describe what the discriminant b – 4ac tells you about the roots of
the equation.
SOLUTION: Sample answer: If negative, there are 2 complex roots; if 0, there is 1 real, rational root; if positive and a perfect
square, there are 2 real, rational roots; if positive but not a perfect square, there are 2 real, irrational roots.
ANSWER: Sample answer: If negative, there are 2 complex roots; if 0, there is 1 real, rational root; if positive and a perfect
square, there are 2 real, rational roots; if positive but not a perfect square, there are 2 real, irrational roots.
is checking
shipment
15. Craig
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of ink jet printers that cost $200 each and laser printers that cost $500 each. There
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are 40 boxes in the shipment, and the invoice total is $11,600.
ANSWER: Sample answer: If negative, there are 2 complex roots; if 0, there is 1 real, rational root; if positive and a perfect
square, there are 2 real, rational roots; if positive but not a perfect square, there are 2 real, irrational roots.
Standardized
Test Practice - Cumulative, Chapter 4
15. Craig is checking in a shipment of ink jet printers that cost $200 each and laser printers that cost $500 each. There
are 40 boxes in the shipment, and the invoice total is $11,600.
a. Write a system of equations to model the situation. Let x represent the number of ink jet printers, and let y
represent the number of laser printers.
b. Write a matrix equation that can be used to solve the system of equations you wrote in part a.
c. Find the inverse of the coefficient matrix and solve the matrix equation. How many ink jet printers and laser
printers were included in the shipment?
SOLUTION: a. The system of equation represents the situation is:
b.
c. The inverse of the coefficient matrix is:
Now, multiply both sides of the matrix equation by the inverse of the coefficient matrix.
Thus, there were 28 ink jet printers and 12 laser printers included in the shipment.
ANSWER: a. x + y = 40; 200x + 500y = 11,600
b.
c. 28 ink jet printers and 12 laser printers
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16. If Robert kicks a football straight up into the air with an initial velocity of 100 feet per second, the function h(t) = –
2
16t + 100t gives the height, in feet, of the ball after t seconds.
b.
Standardized
Practice - Cumulative, Chapter 4
c. 28 ink jetTest
printers and 12 laser printers
16. If Robert kicks a football straight up into the air with an initial velocity of 100 feet per second, the function h(t) = –
2
16t + 100t gives the height, in feet, of the ball after t seconds.
a. Graph the quadratic function on a coordinate grid.
b. What is the maximum height reached by the football? Round to the nearest foot.
c. How long is the football in the air before it hits the ground?
SOLUTION: a. Graph the equation.
b. From the graph, the maximum height reached by the football is about 156 ft.
c. Substitute 0 for h(t) in the function
.
The football is in the air for 6.25 seconds.
ANSWER: a.
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The football is in the air for 6.25 seconds.
Standardized Test Practice - Cumulative, Chapter 4
ANSWER: a.
b. 156 ft
c. 6.25 seconds
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