Download wk 9 and 10 practice problems

TEST NAME: Week 9 and Week 10 Practice Problems
TEST ID: 486405
GRADE: 09
SUBJECT: Mathematics
TEST CATEGORY: My Classroom
Week 9 and Week 10 Practice Problems
Page 1 of 36
Student: Class:
Date:
1.
Which system of equations has the same solutions as the system below?
A.
B.
C.
D.
2.
Arthur was solving the system of equations below:
Arthur multiplied the first equation (I) by 2 and added the product to the
second equation (II). The sum was the equation seen below: When Arthur solved for y, he got 3. Substituting 3 into the first equation
(I), he found that x was 2. Use Arthur's answers to show that his solution works for the second
equation (II).
Week 9 and Week 10 Practice Problems
Page 2 of 36
3.
Which systems of equations have the same solutions?
A.
L and M
B.
L and N
C.
M and N
D.
L, M, and N
4.
Which statement explains that the systems of equations shown below
have the same solution?
System A:
System B:
A.
One of the equations in B is the sum of both of the original equations
in A.
B.
One of the equations in B is the product of both of the original
equations in A.
C.
One of the equations in B is obtained from multiplying an equation in
A by 3 and then adding both equations in A.
D.
One of the equations in B is obtained from multiplying an equation in
A by –3 and then adding both equations in A.
Week 9 and Week 10 Practice Problems
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5.
Use the system of equations for each part of the problem.
Part A. Find the equation that results from adding the first equation to
three times the second equation. Then find the equation that results
from taking the first equation minus two times the second equation. Part B. Show that the values of x and y obtained from solving these new
equations are also the solutions of the original system of equations.
Use words, numbers, and/or pictures to show your work.
6.
In order to solve the system of equations using the
elimination method, which of the following steps could be used?
A.
Multiply the first equation by 2 and then add that result to the second
equation.
B.
Multiply the first equation by 3 and then add that result to the second
equation.
C.
Multiply the second equation by 2 and then add that result to the first
equation.
D.
Multiply the second equation by 3 and then add that result to the first
equation.
Week 9 and Week 10 Practice Problems
Page 4 of 36
7.
Jolene is solving the system of equations shown below.
Which of these systems of equations has the same solution?
A.
B.
C.
D.
8.
A system of equations is shown below.
2x + y = 9
–
x + y = 6
What is the solution to the system?
A.
(1, 7)
B.
(2, 5)
C.
(3, 3)
D.
(4, 1)
Week 9 and Week 10 Practice Problems
Page 5 of 36
A system of equations is shown below.
9.
2x − y = 0
x + 2y = 5
What is the solution to the system?
A.
(0, 0)
B.
(1, 2)
C.
(2, 4)
D.
(3, 1)
10.
What is the x­coordinate of the solution to this system of linear
equations?
A.
B.
C.
D.
11.
Sue paid $46 for 2 adult and 4 child tickets to a play. Karen paid $86 for
4 adult and 7 child tickets to the same play. What is the cost of 1 adult
and 1 child ticket?
A.
$17.00
B.
$17.50
C.
$18.50
D.
$19.00
Week 9 and Week 10 Practice Problems
Page 6 of 36
12.
A system of equations is shown below.
3x + 2y = 15
2x – 10 = y
What is the solution to the system?
A.
(5, –20)
B.
(–5, –20)
C.
(–35, –80)
D.
(5, 0)
13.
The Smith family paid a total of $25.50 for 2 adult and 3 child movie
tickets. The Jones family paid a total of $22.00 for 2 adult and 2 child
movie tickets. How much more did 1 adult ticket cost than a child ticket?
A.
$6
B.
$4
C.
$2
D.
$1
14.
The sum of the digits of a two­digit number is 7. If the digits are
reversed the number is increased by 27. What is the number?
A.
25
B.
34
C.
43
D.
61
15.
A hardware store sold 10 hammers and 120 packages of nails for
$950.50. If it sells one hammer and one package of nails for $12, how
much does one package of nails cost?
A.
$2.00
B.
$4.45
C.
$7.55
D.
$7.92
Week 9 and Week 10 Practice Problems
Page 7 of 36
16.
A store sells pencils and erasers.
5 pencils and 10 erasers cost $1.05.
2 pencils and 5 erasers cost $0.44.
How much would 7 pencils and 7 erasers cost?
A.
$1.49
B.
$1.33
C.
$1.19
D.
$1.03
17.
What is the x­coordinate of the solution to the system of equations
shown below?
A.
B.
C.
D.
18.
Marcus buys 2 hamburgers and 3 drinks for $8.75. Pam buys 4
hamburgers and 2 drinks for $12.50. How much does 1 hamburger cost?
A.
$1.25
B.
$1.75
C.
$2.25
D.
$2.50
Week 9 and Week 10 Practice Problems
Page 8 of 36
19.
What is the solution to the system of equations below?
A.
B.
C.
D.
20.
What is the approximate solution to the system of equations graphed
below?
A.
B.
C.
D.
Week 9 and Week 10 Practice Problems
Page 9 of 36
21.
Bella is solving a system of equations. She evaluates the equations and
decides to solve them by the graphing method. The graph she
constructed to solve the system of equations is shown below.
Which of these is the best approximated solution for this system of
equations?
A.
B.
C.
D.
22.
Which system of equations has exactly one solution?
A.
B.
C.
D.
Week 9 and Week 10 Practice Problems
Page 10 of 36
23.
Which of these correctly explains the solution of the system of equations
shown below?
A.
The equations have y­intercepts at 2 and 4; therefore, solution.
B.
The equations have x­intercepts at 3 and 12; therefore, solution.
C.
The values of and is the solution.
D.
The lines representing the equations intersect at therefore, is the solution.
is the
is the
satisfy both the equations; therefore, and 24.
Taylor bought 2 hotdogs and 2 sodas for $3.50. Jacob bought 3 hotdogs
and 1 soda for $4.25. What is the cost of 1 soda?
A.
$0.25
B.
$0.50
C.
$1.25
D.
$1.50
25.
Michael is 12 years older than Lynn. The sum of Lynn’s and Michael’s
ages is 84. How old is Michael?
A.
36
B.
38
C.
42
D.
48
Week 9 and Week 10 Practice Problems
Page 11 of 36
26.
Karen paid $1.20 for 6 pencils and 4 erasers at the school store. Trey
paid $1.10 for 8 pencils and 2 erasers at the school store. How much
does an eraser cost?
A.
$0.08
B.
$0.10
C.
$0.15
D.
$0.18
27.
A movie theater sells small and large boxes of popcorn. A small box of popcorn costs $1.50.
A large box of popcorn costs $4.00.
A total of 25 boxes of popcorn were sold totaling $75.00.
How many large boxes of popcorn were sold?
A.
6
B.
10
C.
12
D.
15
28.
A system of equations is shown below.
5y + 15x = 10 y − 3x = 8
What is the y­value in the solution to the system?
A.
–
B.
0
C.
1
D.
5
1
Week 9 and Week 10 Practice Problems
Page 12 of 36
29.
What is the solution of the system of equations that
contains the equation and the equation of the line shown on
the graph below?
A.
B.
C.
no solution
D.
infinitely many solutions
30.
Which system of equations would have no solution?
A.
B.
C.
D.
Week 9 and Week 10 Practice Problems
Page 13 of 36
31.
What is the solution to the system of equations shown below?
y = 6x – 9
8x + 6y = 12
A.
(0, –9)
B.
(0.5, –6)
C.
(1, –3)
D.
(1.5, 0)
32.
A system of equations is shown below.
2x + 3y = 8 x + 2y = 8
What is the solution to the system?
A.
(–8, 8)
B.
(–2, –3)
C.
(2, 3)
D.
(8, –8)
Week 9 and Week 10 Practice Problems
Page 14 of 36
33.
The graph below represents a system of linear equations.
Based on the graph, which is the apparent solution to the system of
equations?
A.
B.
C.
D.
34.
Michael has a jar of dimes and nickels. There are 152 dimes and nickels
in the jar that total $11. If d represents the number of dimes and
n represents the number of nickels, which system of equations below
represents the situation?
A.
B.
C.
D.
Week 9 and Week 10 Practice Problems
Page 15 of 36
35.
A barbershop purchased 15 hair brushes and 5 blow dryers for $215. The
barbershop then purchased 5 more hair brushes and 7 more blow dryers
from the same company for $189. How much does one blow dryer cost?
A.
$7
B.
$17
C.
$22
D.
$26
36.
A store sells jars of peanut butter that cost p dollars and jars of jelly
that cost j dollars.
Winston purchased 3 jars of peanut butter and 2 jars of jelly for
$11.50.
Peter purchased 2 jars of peanut butter and 4 jars of jelly for $13.00.
How much does 1 jar of peanut butter cost?
A.
$2.00
B.
$2.50
C.
$3.00
D.
$3.50
37. A system of equations is shown.
What is thevalue of x in the solution for the system of equations?
A.
2
B.
3
C.
4
D.
5
Week 9 and Week 10 Practice Problems
Page 16 of 36
38.
A system of equations is shown below.
3x + 2y = 18
1.5x + 0.75y = 7.5
What is the y­value of the solution to the system?
A.
2
B.
4
C.
6
D.
8
39.
A system of equations is shown below.
7x − 4y = 0
2x + 7y = 57
What is the y­value in the solution to the system?
A.
0
B.
2
C.
4
D.
7
40.
A system of equations is shown below.
3 – 2y = x
2x – 3y = 6
What is the solution to the system?
A.
(0, –2)
B.
(1, 1)
C.
(3, 0)
D.
(5, –1)
Week 9 and Week 10 Practice Problems
Page 17 of 36
41.
A hardware store sells screws and bolts.
For 8 screws and 4 bolts, the cost is $1.12.
For 9 screws and 6 bolts, the cost is $1.44.
How much does 1 bolt cost?
A.
$0.04
B.
$0.12
C.
$0.15
D.
$0.20
42.
On Tuesday, Wendy and her friend purchased 3 sandwiches and 2 drinks
for $15.75. On Friday, Wendy purchased 2 sandwiches and 1 drink at the
same restaurant for $9.85. How much does 1 sandwich cost?
A.
$5.90
B.
$3.95
C.
$3.25
D.
$1.95
43.
The sum of two numbers is 59. The difference between the two numbers
is 11. Which is the smaller of the two numbers?
A.
20
B.
22
C.
24
D.
26
44.
Company 1 earned $0.546 million more than Company 2. The companies
earned a total of $9.454 million. How much did Company 2 earn?
A.
$4.454 million
B.
$5.000 million
C.
$5.091 million
D.
$8.908 million
Week 9 and Week 10 Practice Problems
Page 18 of 36
45.
Joe and Charlie ate at the same restaurant. Joe bought 4 hamburgers
and 2 sodas for $12.50. Charlie bought 3 hamburgers and 3 sodas for
$11.25. What was the price of one hamburger?
A.
$1.25
B.
$1.50
C.
$2.25
D.
$2.50
46.
Kaitlyn bought 2 pieces of gum and 3 candy bars for $3.25. Jordan bought
4 pieces of gum and 1 candy bar for $2.75 at the same store. What is the
cost of 1 piece of gum and 1 candy bar?
A.
$0.25
B.
$0.50
C.
$0.75
D.
$1.25
47.
In the following system of equations, what is the y­value of the solution?
48.
The system of equations What is the value of has the solutions A.
B.
C.
D.
Week 9 and Week 10 Practice Problems
Page 19 of 36
49.
The sum of two numbers is 41.4. The difference between the two
numbers is 7.6. What is the value of the larger of the two numbers?
A.
13.1
B.
16.9
C.
24.5
D.
28.3
50.
Sheila bought several bags of balloons and boxes of candles. The candles
cost $15 per box, and the balloons cost $8 per bag. She bought a total of
17 bags and boxes and paid a total of $192. How many bags of balloons
did Sheila buy?
A.
6 B.
7 C.
8 D.
9 51.
A system of equations is shown below.
3x – y = 14
x = 2y – 2
What is the solution to the system?
A.
(4, –2)
B.
(3, –5)
C.
(6, 4)
D.
(4, 3)
52.
Ron bought 8 pencils and 2 erasers for $1.66. Sarah bought 12 pencils
and 5 erasers for $3.19. What is the cost for 1 pencil and 1 eraser?
A.
$0.25
B.
$0.31
C.
$0.32
D.
$0.47
Week 9 and Week 10 Practice Problems
Page 20 of 36
53.
A system of equations is shown below.
5x − 2y = 11
3x + 5y = 19
What is the solution to the system of equations?
A.
B.
C.
D.
no solution
54.
The sum of two positive numbers is 45. The difference between the
numbers is 9. What is the value of the larger number?
A.
9
B.
18
C.
27
D.
36
Week 9 and Week 10 Practice Problems
Page 21 of 36
55. Tom graphed a system of equations on a sheet of 1­quadrant grid paper as shown.
Which system of equations could be shown on this grid paper?
A.
B.
C.
D.
Week 9 and Week 10 Practice Problems
Page 22 of 36
56.
A 4­pound box of rice, which is a mixture of white rice and wild rice, sells
for $1.80 per pound. White rice sells for $0.75 per pound.
Wild rice sells for $2.25 per pound.
How much white rice is in the mixture?
A.
1.2 pounds
B.
1.4 pounds
C.
2.8 pounds
D.
3.6 pounds
57.
Joe bought 2 pairs of jeans and 1 shirt for $120. Sam bought 1 pair of
jeans and 3 shirts for $135. How much does 1 shirt cost?
A.
$45.00
B.
$40.00
C.
$33.75
D.
$30.00
58.
The difference between two numbers is one. Three times the larger
number minus two times the smaller number is 9. What is the value of
the larger number?
A.
5
B.
6
C.
7
D.
8
59.
On Saturday, Carrie went to the store and bought 4 loaves of bread and 1
gallon of milk for a total of $12.50. The next weekend, she went to the
same store and spent $11.50 on 2 loaves of bread and 2 gallons of milk.
The prices had not changed. What is the price for one gallon of milk?
A.
$2.25
B.
$2.50
C.
$3.50
D.
$4.80
Week 9 and Week 10 Practice Problems
Page 23 of 36
60.
A system of equations is shown below.
3x + 6 = 4y
3x − 2y = 0
What is the x­value in the solution to the system?
A.
B.
C.
D.
61.
Which ordered pair represents the solution to the system of equations
shown below?
A.
B.
C.
D.
62.
At the same store, Leigh bought 2 pairs of pants and 5 shirts for $61,
and Jessica bought 3 pairs of pants and 2 shirts for $64. How much does
1 pair of pants cost?
A.
$5.00
B.
$9.00
C.
$10.00
D.
$18.00
Week 9 and Week 10 Practice Problems
Page 24 of 36
63.
Two functions, intersect each other at the points What values are solutions of the equation A.
0 and 2
B.
0 and 4
C.
2 and 32
D.
4 and 32
64. A system of equations is shown below.
y = 7x – 5
y = 3x
Which is a y­value of a solution to the system?
A.
2
B.
3
C.
9
D.
16
65.
Two functions are shown below.
What is the approximate value of x when f(x) = g(x)?
A.
2.98
B.
3.54
C.
4.12
D.
5.38
Week 9 and Week 10 Practice Problems
Page 25 of 36
66.
If and , what is the approximate solution to
g(x) = h(x)?
A.
– 0.21
B.
1.27
C.
6.05
D.
7.15
67.
The table below shows the values of f(x) and g(x) for different values of
x. What is/are the solution(s) of the equation 68.
If f(x) = 5(2)x and g(x) = –2x + 46, for what positive value of x does
f(x) = g(x)?
A.
3
B.
5
C.
40
D.
46
Week 9 and Week 10 Practice Problems
Page 26 of 36
69.
Two functions are shown below. For approximately what value of x does f(x) = g(x)?
A.
–
B.
– 0.15
C.
0.29
D.
0.51
0.37
70.
If y = 6x + 8 and y = –4x – 2, what is the value of x + y when the two
equations are equal?
A.
–
B.
–1
C.
1
D.
2
2
71.
Given:
f(x) = 3x
g(x) = –2x + 13
For which x­value does f(x) = g(x)?
A.
B.
C.
D.
Week 9 and Week 10 Practice Problems
Page 27 of 36
72.
When does the value of A.
x = –2
B.
x = –1
C.
x = 2
D.
x = 4
equal the value of ?
73.
Given:
f(x) = –x + 6
g(x) = 2x – 4
What is the approximate value of x when f(x) = g(x)?
A.
2.8
B.
3.2
C.
4
D.
6
74.
Two functions are shown below.
y = –2x + 3
y = 4x – 9
What is the value of x + ywhen the two functions are equal?
A.
–
B.
–1
C.
1
D.
3
3
Week 9 and Week 10 Practice Problems
Page 28 of 36
75.
Two functions are shown below.
f(x) = 2(3)x
g(x) = 4x + 2
What is the difference in the y­values of the two unique points where
f(x) = g(x)?
A.
0
B.
2
C.
4
D.
6
76.
If f(x) = 2(3)x and g(x) = 6x + 6, for what positive value of x does
f(x) = g(x)?
A.
0
B.
1
C.
2
D.
3
Week 9 and Week 10 Practice Problems
Page 29 of 36
77.
The functions and are shown on the graph below.
Which approximate values best represent the solutions of the equation A.
B.
C.
D.
78.
Two functions are shown below.
f(x) = 2x – 6
g(x) = –x + 9
What is the value of x when f(x) = g(x)?
A.
3
B.
4
C.
5
D.
9
Week 9 and Week 10 Practice Problems
Page 30 of 36
79.
The function f(x) = 0.85x + 3.99 models the total cost of purchasing x
key chains from an Internet company that charges shipping. The function
g(x) = 1.10x models the total cost of purchasing x number of the same
key chains from an Internet company that does not charge shipping.
What is the best approximation of the number of key chains for which
the two companies charge the same amount?
A.
14
B.
15
C.
16
D.
17
80.
The functions f(x) and g(x) are defined below.
What is the difference in the x values for the two points where
f(x) = g(x)?
A.
48
B.
36
C.
4
D.
2
81.
Which statement is true about the equation given and A.
It has two solutions at B.
It has two solutions at C.
It has four solutions at D.
It has four solutions at .
Week 9 and Week 10 Practice Problems
Page 31 of 36
82.
The graphs of the functions described below have at least one point of
intersection.
To the nearest 0.01, what is the x­coordinate of the leftmost
intersection?
A.
5.02
B.
6.00
C.
10.25
D.
14.41
83.
Two functions are shown below.
f(x) = 4(2)x
g(x) = –3x – 1
What is the value of x when f(x) = g(x)?
A.
B.
C.
D.
Week 9 and Week 10 Practice Problems
Page 32 of 36
84.
Functions and are shown on the graph below.
What is/are the solution(s) of the equation 85.
The population of one type of algae can be modeled by the equation
P = 3(1.75)t, where t is time in days. A second type of algae has a
population modeled by the equation P = 500 + 100t, where t is time in
days. After approximately how many days are the populations equal?
A.
4
B.
5
C.
10
D.
11
86.
A company is selling two new products. Weekly sales of product one can
be modeled by the function f(x) = 100(1.108)x after x weeks. Weekly
sales of product two can be modeled by the function g(x) = 10x + 200
after x weeks. After approximately how many weeks will the weekly
sales of the two products be the same?
A.
9 weeks
B.
11 weeks
C.
15 weeks
D.
19 weeks
Week 9 and Week 10 Practice Problems
Page 33 of 36
87.
The table below shows values for two functions, f(x) and g(x).
x –3 –2 –1 0 1 2 3 f(x) –5 –2 1 4 7 10 13 g(x) 16 8 4 2 1 0.5 0.25 For what value of x does f(x) approximately equal g(x)?
A.
2.7
B.
0.6
C.
D.
–0.2
– 0.4
88.
The figure below shows the graph of the functions value(s) of x does and For which
A.
B.
C.
D.
Week 9 and Week 10 Practice Problems
Page 34 of 36
89.
The graphs of functions and are shown below.
Which statement is true about the real solutions of the equation A.
It has only one real solution, B.
It has two real solutions, C.
It has two real solutions, D.
It has three real solutions, .
Week 9 and Week 10 Practice Problems
Page 35 of 36
90. On the coordinate plane, and are graphed.
Between which 2 consecutive integers is there a solution to A.
and B.
and C.
0 and 1
D.
1 and 2
?
Week 9 and Week 10 Practice Problems
Page 36 of 36