School Name: Teacher Name: Student Name: Grade 8 Math March Packet Subject: Mathematics State: Massachusetts
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Subject: Mathematics
State: Massachusetts
2 What is the value of 2 + 2 + 2 ?0 -1 -2
-6(A)
-5(A)
-(B)
(C)
5(D)
1 5
1 5
3 4
4 Which of the following is equivalent to the expression below? (2 )(2 )5 6
2(A) 11
2(B) 30
4(C) 11
4(D) 30
3 Simplify:
5 In this problem represents a positive number. c
The quotient rule for exponents says that if and are positive integers with > , then = c m n m n m-n
After explaining to yourself why this is true, complete the following exploration of the quotient rule when m ≤ :n
a. What expression does the quotient rule provide for when = ?m n
b. If = , simplify without using the quotient rule.m n
c. What do parts (a) and (b) above suggest is a good definition for c ?0
d. What expression does the quotient rule provide for ?
e. What expression do we get for if we use the value for found in part (c)?c0
f. Using parts (d) and (e), propose a definition for the expression − .c n
cm
cn
cm
cn
cm
cn
c0
cn
c0
cn
6 (a) An ant has a mass of approximately 4 × 10 grams and an elephant has a mass of approximately 8 −3
metric tons. How many ants does it take to have the same mass as an elephant?
(b) An ant is 10 cm long. If you put all the ants from your answer to part (a) in line front to back, how long −1
would the line be?
(c) Find two cities in the United States that are a similar distance apart to illustrate the length in part (b).
Note: 1 kg = 1000 grams, 1 metric ton = 1000 kg, 1 m = 100 cm, 1 km = 1000 m.
8 The body of a 154-pound person contains approximately 2 × 10 milligrams of gold and 6 × 10-1 1
milligrams of aluminum. Based on this information, the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body?
7 A dollar bill is about 3 × 10 inches thick. A penny is about 6 × 10 inches thick.-4 -3
Which statement correctly compares these measurements?
(A) The thickness of a dollar bill is the thickness of a penny.
(B) The thickness of a dollar bill is the thickness of a penny.
(C) The thickness of a dollar bill is 10 times the thickness of a penny.
(D) The thickness of a dollar bill is 20 times the thickness of a penny.
1 10
1 20
9 It is said that the average person blinks about 1000 times an hour. This is an order-of-magnitude estimate, that is, it is an estimate given as a power of ten. Consider:
100 blinks per hour, which is about two blinks per minute.
10,000 blinks per hour, which is about three blinks per second.
Neither of these are reasonable estimates for the number of blinks a person makes in an hour. Make order-of- magnitude estimates for each of the following:
a. Your age in hours.
b. The number of breaths you take in a year.
c. The number of heart beats in a lifetime.
d. The number of basketballs that would fill your classroom.
Can you think of others questions like these?
10 3908 Nyx is an asteroid between Mars and Jupiter. Let represent the approximate distance from 3908 d Nyx to the Sun.
The average distance from Venus to the Sun is about 7 × 10 miles. The average distance from Jupiter to the 7
Sun is about 5 × 10 miles.8
At a certain time of year, the square of the distance from 3908 Nyx to the Sun is equal to the product of the average distance from Venus to the Sun and the average distance from Jupiter to the Sun. This equation can be used to find the distance from 3908 Nyx to the Sun, , at this time of year.d
= (7 × 10 )(5 × 10 )d 2 7 8
Which of the following numbers is equal to ?d 2
1.2 × 10(A) 16
3.5 × 10(B) 16
1.2 × 10(C) 57
3.5 × 10(D) 57
11 A company’s profit of $1.71 ×10 will be shared equally by its 3,800 employees. How much money 6
will each employee receive?
$4.5 ×10(A) 2
$4.5 ×10(B) 1
$4.5 ×10(C) 3
$4.5 ×10(D) 5
12 The figure shows a spreadsheet Shona made to record the mass, in grams, of several samples of cells.
Her spreadsheet automatically converts the masses into scientific notation.
List the four samples from least mass to greatest mass.
13 The total cost in dollars, , of a membership at each of four health clubs is represented below in terms y of , the number of months of the membership.x
Which representation has the greatest rate of change?
Health Club A(A)
Health Club B(B)
Health Club C(C)
Health Club D(D)
14 John and Kim wrote down two different functions that have the same rate of change.
John’s function is represented by the table shown below.
Graph a function that could be Kim’s function.
15 The students at a middle school want to hire a DJ for an end-of-the-year dance. The information below can be used to find the total cost of hiring a DJ at each of four different companies.
Which company’s cost has the greatest rate of change?
Awesome Entertainers(A)
Cool Beats(B)
Turntable Tunes(C)
Rock-N-Sounds(D)
16 Samir was assigned to write an example of a linear functional relationship. He wrote this example for the assignment.
(a) Fill in the table above to create an example of the populations of a certain county that is increasing in population by 10% each year.
(b) State whether Samir's relationship represents a linear functional relationship. Explain your reasoning.
17 Classify each equation as defining as a linear or non-linear function of . Check one cell per column.y x
18 Which of the following graphs shows a linear function?
(A)
(B)
(C)
(D)
19 Which of these equations define as a nonlinear function of ? y x
Select correct answer.each
= + 3(B) y x2
= 12 − (F) y x2
20 A student has had a collection of baseball cards for several years. Suppose that , the number of B baseball cards in the collection, can be described as a function of , which is the time in years since the t collection was started. Explain what each of the following equations would tell us about the number of cards in the collection over time.
(a) = 200 + 100 B t
(b) = 100 + 200 B t
(c) = 2000 − 100 B t
(d) = 100 − 200B t
21 A car is traveling down a long, steep hill. The elevation, , above sea level (in feet) of the car when it is E miles from the top of the hill is given by the equation = 7500 − 250 , where can be any number from 0 d E d d
to 6.
Find the slope and intercepts of the graph of this function and explain what they mean in the context of the moving car.
22 The prices and sizes of several houses for sale in a neighborhood are shown in the scatter plot below.
Which equation represents the line of best fit?
y = 100x(A)
y = 1,000x + 50,000(D)
23 The graph below shows Carlos’s speed on his trip to school.
Based on the graph, when is Carlos’s speed decreasing most rapidly?
for times between B and C(A)
for times between D and E(B)
for times between E and F(C)
for times between H and I(D)
24 The school is 100 meters from Jason's house. The following describes his most recent trip:
He walked 50 meters toward school in 2 minutes. He realized he left a book at home.
He turned around and walked home at the same speed.
He spent 1 minute looking for his book before he found it.
He walked all the way to school at twice his original speed.
Finish the graph to accurately represent Jason's trip.
25 Aqua Water Company purchased a new water tank. The tank is a cylinder with a diameter of 14 feet and a height of 24 feet. What is the volume of the tank in cubic feet?
168π cubic feet(A)
336π cubic feet(B)
1,176π cubic feet(C)
4,704π cubic feet(D)
26 The sphere below has a 3-inch radius. The right cylinder has a radius of 3 inches and a height of 4 inches.
(a) What is the volume, in cubic inches, of the sphere?
(b) What is the volume, in cubic inches, of the cylinder?
(c) Lin claims that the volume of any sphere with radius inches is always to the volume of a cylinder r equal
with a radius of inches and a height of inches, when = . Show all work necessary to justify Lin's r h h r
claim.
4 3
28 A square is drawn on a coordinate plane. Which transformation would change the perimeter of the square?
a translation of 2 units down(A)
a reflection across the x-axis(B)
a dilation with a scale factor of 2(C)
a 90 clockwise rotation about the origin(D)
27 The figure below shows a cylindrical tank that is to be filled with gasoline. How many cubic feet of gasoline will be required to fill the tank?
(A) 8π ft3
(B) 16π ft3
(C) 18π ft3
(D) 32π ft3
29 Pentagon is shown on the coordinate plane. CDEFG
Pentagon is translated 7 units up and 5 units left, resulting in pentagon ' ' ' ' ' (not shown).CDEFG C D E F G
Complete the statements below using “greater than”, “less than” or “equal to”.
The length of is ____________________ to the length of . FG ’ ’F C
The perimeter of pentagon is ____________________ the perimeter of pentagon ’ ’ ’ ’ ’.CDEFG C D E F G
30 Lines and are parallel on a coordinate plane. Lines and are transformed by the same rotation‚ m n m n resulting in image lines and . Which statement describes the relationship between lines and ?s t s t
Lines and are parallel.(A) s t
Lines and are perpendicular.(B) s t
Lines and are intersecting but not perpendicular.(C) s t
The relationship between lines and cannot be determined without knowing the angle of (D) s t the rotation.
31 Parallelogram is shown on the coordinate plane.WXYZ
Parallelogram (not shown) is the reflection of parallelogram across the -axis. Which W′X′Y′Z′ WXYZ y statement is true?
Line is parallel to line (A) W’X’ W’Z’
Line is parallel to line (B) W’X’ Z’Y’
Line is perpendicular to line (C) W’X’ W’Z’
Line is perpendicular to line (D) W’X’ Z’Y’
32 Consider the equation 5 − 2 = 3. If possible, write a second linear equation to create a system of x y equations that has:
(a) Exactly 1 solution.
(b) Exactly 2 solutions.
(d) Infinitely many solutions.
For each of these cases, how many such equations are possible?
33 Let (x, y) be the solution of the system of equations below. 4x + 3y = 17 3x + 2y = 12 What is the value of − x y?
-11(A)
-1(B)
5(C)
9(D)
35 The equation of line is = −2 + 8 .j y x
The equation of line is y = 3 − 7 .k x
34 The table below shows two systems of linear equations.
Indicate whether each system of equations has no solution, one solution or infinitely many solutions by selecting the correct cell in the table. Select one cell per column.
Graph the system of equations on the coordinate plane
Plot point on the graph. P
36 A transformation of Pentagon 1 resulted in Pentagon 2.
37 Below is a picture of two congruent rectangles:
Which transformation was used?
a translation 10 units to the right(B)
a translation 5 units to the right(C)
a reflection across the x-axis(D)
(a) Show that the rectangles are congruent by finding a translation followed by a rotation which maps one of the rectangles onto the other.
(b) Explain why the congruence of the two rectangles can not be shown by translating Rectangle 1 to Rectangle 2.
(c) Can the congruence of the two rectangles be shown with a single reflection? Explain.
38 Triangles and are shown below in the coordinate plane:ABC PQR
(a) Show that Δ is congruent to Δ with a reflection followed by a translation.ABC PQR
(b) If you reverse the order of your reflection and translation in part (a) does it still map Δ to Δ ?ABC PQR
(c) Find a second way, different from your work in part (a), to map Δ to Δ using translations, ABC PQR rotations, and/or reflections.
39 In a park, the locations of a drinking fountain, a streetlight, and a flagpole form a right triangle. The drinking fountain is 12 yards north of the streetlight, and the flagpole is 5 yards east of the drinking fountain, as shown in this diagram.
What is the shortest distance from the streetlight to the flagpole?
7 yards(A)
11 yards(B)
13 yards(C)
17 yards(D)
40 You are a representative for a cell phone company and it is your job to promote different cell phone plans.
Your boss asks you to visually display the costs of three plans and compare them so you can point out the advantages of each plan to your customers.
The information on the plans is shown in the boxes below.
(a) Use this information to write equations for each plan, and then graph the equations and estimate their intersections.
(b) A customer wants to know how to decide which plan will save her the most money. Describe which plan has the lowest cost for each possible range of numbers of text messages a customer might send.
41 The local swim center is making a special offer. They usually charge $7 per day to swim at the pool. This month swimmers can pay an enrollment fee of $30 and then the daily pass will only be $4 per day.
(a) Suppose you do not take the special offer. Write an equation that represents the amount of money you would spend based on how many days you go to the pool if the passes were bought at full price.
(b) Write a second equation that represents the amount of money you would spend if you decided to take the special offer.
(c) Graph your two equations from parts (a) and (b).
(d) After how many days of visiting the pool will the special offer be a better deal? How can you tell algebraically? How can you see this graphically?
(e) You only have $60 to spend for the summer on visiting the pool. Which offer would you take? Explain.
42 The coordinate plane shown below has a figure in the third quadrant.
Which of the following shows the same figure after it has been reflected across the y-axis and then reflected across the x-axis?
(A)
(B)
(C)
(D)
43 Triangle is shown on this coordinate grid.ABC
Triangle is dilated with the origin as the center of the dilation. Which ordered pair could represent the ABC image of point (5, 2) after the dilation?C
(2.5, 1)(A)
(5, −2)(B)
(7.5, 4.5)(C)
(−1, −4)(D)
ii. Center and scale factor 3.B
iii. Center and scale factor .C
b. For each dilation, answer the following questions:
i. By what factor do the base and height of the triangle change? Explain.
ii. By what factor does the area of the triangle change? Explain.
iii. How do the angles of the scaled triangle compare to the original? Explain.
1 2
45 Seven line segments are shown on the coordinate plane.
Which of these segments could be the image of segment after a sequence of reflections, rotations, and/or AB translations?
Select correct answer. each
line segment (A) CD
line segment (B) EF
line segment (C) GH
line segment (D) JK
line segment (E) LM
line segment (F) NP
46 For each linear equation in this table, indicate whether the equation has no solution, one solution, or infinitely many solutions.
47 Consider the equation 3(2 + 5) = + .x ax b
(a) Find one value for and one value for so that there is exactly one value of that makes the equation a b x true. Explain your reasoning.
(b) Find one value for and one value for so that there are infinitely many values of that make the a b x equation true. Explain your reasoning.
48 Which ordered pair is the solution of the system of equations below?
x + 2 = 6 y
3 + 8 = 4x y
(2, 2)(A)
(4, 10)(B)
(10, −2)(C)
(20, −7)(D)
49 Ted has some red blocks and some green blocks. • Each red block weighs the same number of ounces.
• Each green block weighs the same number of ounces.
• The total weight of 2 red blocks and 6 green blocks is 23 ounces.
• The total weight of 3 red blocks and 4 green blocks is 22 ounces
What is the total weight of 1 red block 1 green block?and
3 ounces (A)
6 ounces (B)
6.5 ounces (C)
13.5 ounces (D)
50 What is the coordinate of the solution to this system of equations?y
−2 + 3 = −6x y
5 − 6 = 15x y
Write your answer below.
51 Three students solved the equation 3(5 − 14) = 18 in different ways, but each student arrived at the x correct answer. Circle YES or NO to indicate whether each solution shows a correct method for solving the equation.
52 Consider the equation 3(2 + 5) = + .x ax b
(a) Find one value for and one value for so that there is exactly one value of that makes the equation a b x true. Explain your reasoning.
(b) Find one value for and one value for so that there are infinitely many values of that make the a b x equation true. Explain your reasoning.
53 A history club sold rolls of wrapping paper as a fundraiser. The wrapping paper was sold in small rolls and large rolls.
The club earned $3.00 for every small roll sold.
The club earned $4.50 for every large roll sold.
The club sold 10 more large rolls than small rolls.
How many small rolls did the history club sell?
54 A company uses a new machine and an old machine to print booklets. Each machine prints booklets at a constant rate. The graph and the equation represent the relationships between , the number of minutes the x machines print, and , the number of booklets printed.y
The company uses both machines to print a total of 1,250 booklets. Both machines start printing at the same time. During printing, the old machine breaks down and stops printing. The new machine continues printing for an additional 14 minutes and completes the order.
What is the total number of minutes the new machine prints? Show or explain all your work.
Write your answer and your work below.
55 An equation is incorrectly solved below.
Equation: 2 + 3 = −4x
Step 2: 2 = −1x
Step 3: = − 1 2
Step 4: = −x 1 2
What is the first step that shows an error in the solution to the equation?
Step 1(A)
Step 2(B)
Step 3(C)
Step 4(D)
2x 2
1 2
1 2
(a) What is the cost per pound of this coffee?
(b) How many pounds of coffee could Lena buy for $1.00?
(c) Draw a graph in the coordinate plane of the relationship between the number of pounds of coffee and the total cost. If you can, use technology to do this.
(d) In this situation, what is the meaning of the slope of the line you drew in part (3)?
57 Amanda graphed line and line on a coordinate plane, as shown below.m n
Which of the following statements is true?
The slope of line is greater than the slope of line .(A) m n
The slope of line is greater than the slope of line .(B) n m
The -intercept of line is greater than the -intercept of line .(C) x m x n
The -intercept of line is greater than the -intercept of line .(D) y n y m
58 The graph below represents , the cost in dollars of pounds of salad at a salad bar.y x
What is the unit rate for the cost of a salad at the salad bar?
$0.50 per pound(A)
$1.00 per pound(B)
$2.00 per pound(C)
$4.00 per pound(D)
59 Mindy is saving money She started with $0. After 6 weeks, she had $90 saved. Mindy is not sure exactly how much money she saved each week. She assumes that she saved money at a constant rate from when she started saving money through week 6.
Part A: Create a graph that can be used to model the number of dollars, , Mindy saves in weeks.y x
Part B: Explain what the slope of the line you drew represents.
Part C: Explain how the line you drew can be used to predict the number of weeks it will take Mindy to save $150. Include in your explanation any assumptions that must be made in order to make the prediction.
60 The table below shows two coordinate pairs that satisfy the equation for some (x, y) y = mx + b numbers and .m b
(a) If = 7, determine possible values for and . Explain your choices.m y 1 y 2
(b) Find another pair of -values that could work for = 7. Explain why they would work. How do these -y m y values compare to the first pair you found for = 7?m
(c) Use the same -values in the table and find possible values for and if = 3. Explain your choices.x y 1 y 2 m
(d) Find another pair of -values that could work for = 3. Explain why they would work. How do these -y m y values compare to the first pair you found for = 3?m
61 John and Kim wrote down two different functions that have the same rate of change. John's function is shown in the table below.
Graph a function on the grid that could be Kim's function.
62 Use the graph shown below to answer the question.
Which statement is true?not
(A) The slope of the line is .
(B) The slope of the line is - .
(C) The smaller triangle and the larger triangle shown are similar.
(D) The simplified ratio of the vertical side length to the horizontal side length of each triangle
is .
3 5
3 5
3 5
63 A function machine takes an input, does something to this input according to a rule, and returns a unique output.
Given below are tables of input-output pairs for different function machines. Fill in the remaining table entries and describe each function rule in words.
64 The table below shows a relationship between x and y that is a function.not
Write one ordered pair that can be removed from the table to make the relationship between and a x y function.
65 Which of the following tables shows a relationship that is a function?not
(A)
(B)
(C)
(D)
State: Massachusetts
2 What is the value of 2 + 2 + 2 ?0 -1 -2
-6(A)
-5(A)
-(B)
(C)
5(D)
1 5
1 5
3 4
4 Which of the following is equivalent to the expression below? (2 )(2 )5 6
2(A) 11
2(B) 30
4(C) 11
4(D) 30
3 Simplify:
5 In this problem represents a positive number. c
The quotient rule for exponents says that if and are positive integers with > , then = c m n m n m-n
After explaining to yourself why this is true, complete the following exploration of the quotient rule when m ≤ :n
a. What expression does the quotient rule provide for when = ?m n
b. If = , simplify without using the quotient rule.m n
c. What do parts (a) and (b) above suggest is a good definition for c ?0
d. What expression does the quotient rule provide for ?
e. What expression do we get for if we use the value for found in part (c)?c0
f. Using parts (d) and (e), propose a definition for the expression − .c n
cm
cn
cm
cn
cm
cn
c0
cn
c0
cn
6 (a) An ant has a mass of approximately 4 × 10 grams and an elephant has a mass of approximately 8 −3
metric tons. How many ants does it take to have the same mass as an elephant?
(b) An ant is 10 cm long. If you put all the ants from your answer to part (a) in line front to back, how long −1
would the line be?
(c) Find two cities in the United States that are a similar distance apart to illustrate the length in part (b).
Note: 1 kg = 1000 grams, 1 metric ton = 1000 kg, 1 m = 100 cm, 1 km = 1000 m.
8 The body of a 154-pound person contains approximately 2 × 10 milligrams of gold and 6 × 10-1 1
milligrams of aluminum. Based on this information, the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body?
7 A dollar bill is about 3 × 10 inches thick. A penny is about 6 × 10 inches thick.-4 -3
Which statement correctly compares these measurements?
(A) The thickness of a dollar bill is the thickness of a penny.
(B) The thickness of a dollar bill is the thickness of a penny.
(C) The thickness of a dollar bill is 10 times the thickness of a penny.
(D) The thickness of a dollar bill is 20 times the thickness of a penny.
1 10
1 20
9 It is said that the average person blinks about 1000 times an hour. This is an order-of-magnitude estimate, that is, it is an estimate given as a power of ten. Consider:
100 blinks per hour, which is about two blinks per minute.
10,000 blinks per hour, which is about three blinks per second.
Neither of these are reasonable estimates for the number of blinks a person makes in an hour. Make order-of- magnitude estimates for each of the following:
a. Your age in hours.
b. The number of breaths you take in a year.
c. The number of heart beats in a lifetime.
d. The number of basketballs that would fill your classroom.
Can you think of others questions like these?
10 3908 Nyx is an asteroid between Mars and Jupiter. Let represent the approximate distance from 3908 d Nyx to the Sun.
The average distance from Venus to the Sun is about 7 × 10 miles. The average distance from Jupiter to the 7
Sun is about 5 × 10 miles.8
At a certain time of year, the square of the distance from 3908 Nyx to the Sun is equal to the product of the average distance from Venus to the Sun and the average distance from Jupiter to the Sun. This equation can be used to find the distance from 3908 Nyx to the Sun, , at this time of year.d
= (7 × 10 )(5 × 10 )d 2 7 8
Which of the following numbers is equal to ?d 2
1.2 × 10(A) 16
3.5 × 10(B) 16
1.2 × 10(C) 57
3.5 × 10(D) 57
11 A company’s profit of $1.71 ×10 will be shared equally by its 3,800 employees. How much money 6
will each employee receive?
$4.5 ×10(A) 2
$4.5 ×10(B) 1
$4.5 ×10(C) 3
$4.5 ×10(D) 5
12 The figure shows a spreadsheet Shona made to record the mass, in grams, of several samples of cells.
Her spreadsheet automatically converts the masses into scientific notation.
List the four samples from least mass to greatest mass.
13 The total cost in dollars, , of a membership at each of four health clubs is represented below in terms y of , the number of months of the membership.x
Which representation has the greatest rate of change?
Health Club A(A)
Health Club B(B)
Health Club C(C)
Health Club D(D)
14 John and Kim wrote down two different functions that have the same rate of change.
John’s function is represented by the table shown below.
Graph a function that could be Kim’s function.
15 The students at a middle school want to hire a DJ for an end-of-the-year dance. The information below can be used to find the total cost of hiring a DJ at each of four different companies.
Which company’s cost has the greatest rate of change?
Awesome Entertainers(A)
Cool Beats(B)
Turntable Tunes(C)
Rock-N-Sounds(D)
16 Samir was assigned to write an example of a linear functional relationship. He wrote this example for the assignment.
(a) Fill in the table above to create an example of the populations of a certain county that is increasing in population by 10% each year.
(b) State whether Samir's relationship represents a linear functional relationship. Explain your reasoning.
17 Classify each equation as defining as a linear or non-linear function of . Check one cell per column.y x
18 Which of the following graphs shows a linear function?
(A)
(B)
(C)
(D)
19 Which of these equations define as a nonlinear function of ? y x
Select correct answer.each
= + 3(B) y x2
= 12 − (F) y x2
20 A student has had a collection of baseball cards for several years. Suppose that , the number of B baseball cards in the collection, can be described as a function of , which is the time in years since the t collection was started. Explain what each of the following equations would tell us about the number of cards in the collection over time.
(a) = 200 + 100 B t
(b) = 100 + 200 B t
(c) = 2000 − 100 B t
(d) = 100 − 200B t
21 A car is traveling down a long, steep hill. The elevation, , above sea level (in feet) of the car when it is E miles from the top of the hill is given by the equation = 7500 − 250 , where can be any number from 0 d E d d
to 6.
Find the slope and intercepts of the graph of this function and explain what they mean in the context of the moving car.
22 The prices and sizes of several houses for sale in a neighborhood are shown in the scatter plot below.
Which equation represents the line of best fit?
y = 100x(A)
y = 1,000x + 50,000(D)
23 The graph below shows Carlos’s speed on his trip to school.
Based on the graph, when is Carlos’s speed decreasing most rapidly?
for times between B and C(A)
for times between D and E(B)
for times between E and F(C)
for times between H and I(D)
24 The school is 100 meters from Jason's house. The following describes his most recent trip:
He walked 50 meters toward school in 2 minutes. He realized he left a book at home.
He turned around and walked home at the same speed.
He spent 1 minute looking for his book before he found it.
He walked all the way to school at twice his original speed.
Finish the graph to accurately represent Jason's trip.
25 Aqua Water Company purchased a new water tank. The tank is a cylinder with a diameter of 14 feet and a height of 24 feet. What is the volume of the tank in cubic feet?
168π cubic feet(A)
336π cubic feet(B)
1,176π cubic feet(C)
4,704π cubic feet(D)
26 The sphere below has a 3-inch radius. The right cylinder has a radius of 3 inches and a height of 4 inches.
(a) What is the volume, in cubic inches, of the sphere?
(b) What is the volume, in cubic inches, of the cylinder?
(c) Lin claims that the volume of any sphere with radius inches is always to the volume of a cylinder r equal
with a radius of inches and a height of inches, when = . Show all work necessary to justify Lin's r h h r
claim.
4 3
28 A square is drawn on a coordinate plane. Which transformation would change the perimeter of the square?
a translation of 2 units down(A)
a reflection across the x-axis(B)
a dilation with a scale factor of 2(C)
a 90 clockwise rotation about the origin(D)
27 The figure below shows a cylindrical tank that is to be filled with gasoline. How many cubic feet of gasoline will be required to fill the tank?
(A) 8π ft3
(B) 16π ft3
(C) 18π ft3
(D) 32π ft3
29 Pentagon is shown on the coordinate plane. CDEFG
Pentagon is translated 7 units up and 5 units left, resulting in pentagon ' ' ' ' ' (not shown).CDEFG C D E F G
Complete the statements below using “greater than”, “less than” or “equal to”.
The length of is ____________________ to the length of . FG ’ ’F C
The perimeter of pentagon is ____________________ the perimeter of pentagon ’ ’ ’ ’ ’.CDEFG C D E F G
30 Lines and are parallel on a coordinate plane. Lines and are transformed by the same rotation‚ m n m n resulting in image lines and . Which statement describes the relationship between lines and ?s t s t
Lines and are parallel.(A) s t
Lines and are perpendicular.(B) s t
Lines and are intersecting but not perpendicular.(C) s t
The relationship between lines and cannot be determined without knowing the angle of (D) s t the rotation.
31 Parallelogram is shown on the coordinate plane.WXYZ
Parallelogram (not shown) is the reflection of parallelogram across the -axis. Which W′X′Y′Z′ WXYZ y statement is true?
Line is parallel to line (A) W’X’ W’Z’
Line is parallel to line (B) W’X’ Z’Y’
Line is perpendicular to line (C) W’X’ W’Z’
Line is perpendicular to line (D) W’X’ Z’Y’
32 Consider the equation 5 − 2 = 3. If possible, write a second linear equation to create a system of x y equations that has:
(a) Exactly 1 solution.
(b) Exactly 2 solutions.
(d) Infinitely many solutions.
For each of these cases, how many such equations are possible?
33 Let (x, y) be the solution of the system of equations below. 4x + 3y = 17 3x + 2y = 12 What is the value of − x y?
-11(A)
-1(B)
5(C)
9(D)
35 The equation of line is = −2 + 8 .j y x
The equation of line is y = 3 − 7 .k x
34 The table below shows two systems of linear equations.
Indicate whether each system of equations has no solution, one solution or infinitely many solutions by selecting the correct cell in the table. Select one cell per column.
Graph the system of equations on the coordinate plane
Plot point on the graph. P
36 A transformation of Pentagon 1 resulted in Pentagon 2.
37 Below is a picture of two congruent rectangles:
Which transformation was used?
a translation 10 units to the right(B)
a translation 5 units to the right(C)
a reflection across the x-axis(D)
(a) Show that the rectangles are congruent by finding a translation followed by a rotation which maps one of the rectangles onto the other.
(b) Explain why the congruence of the two rectangles can not be shown by translating Rectangle 1 to Rectangle 2.
(c) Can the congruence of the two rectangles be shown with a single reflection? Explain.
38 Triangles and are shown below in the coordinate plane:ABC PQR
(a) Show that Δ is congruent to Δ with a reflection followed by a translation.ABC PQR
(b) If you reverse the order of your reflection and translation in part (a) does it still map Δ to Δ ?ABC PQR
(c) Find a second way, different from your work in part (a), to map Δ to Δ using translations, ABC PQR rotations, and/or reflections.
39 In a park, the locations of a drinking fountain, a streetlight, and a flagpole form a right triangle. The drinking fountain is 12 yards north of the streetlight, and the flagpole is 5 yards east of the drinking fountain, as shown in this diagram.
What is the shortest distance from the streetlight to the flagpole?
7 yards(A)
11 yards(B)
13 yards(C)
17 yards(D)
40 You are a representative for a cell phone company and it is your job to promote different cell phone plans.
Your boss asks you to visually display the costs of three plans and compare them so you can point out the advantages of each plan to your customers.
The information on the plans is shown in the boxes below.
(a) Use this information to write equations for each plan, and then graph the equations and estimate their intersections.
(b) A customer wants to know how to decide which plan will save her the most money. Describe which plan has the lowest cost for each possible range of numbers of text messages a customer might send.
41 The local swim center is making a special offer. They usually charge $7 per day to swim at the pool. This month swimmers can pay an enrollment fee of $30 and then the daily pass will only be $4 per day.
(a) Suppose you do not take the special offer. Write an equation that represents the amount of money you would spend based on how many days you go to the pool if the passes were bought at full price.
(b) Write a second equation that represents the amount of money you would spend if you decided to take the special offer.
(c) Graph your two equations from parts (a) and (b).
(d) After how many days of visiting the pool will the special offer be a better deal? How can you tell algebraically? How can you see this graphically?
(e) You only have $60 to spend for the summer on visiting the pool. Which offer would you take? Explain.
42 The coordinate plane shown below has a figure in the third quadrant.
Which of the following shows the same figure after it has been reflected across the y-axis and then reflected across the x-axis?
(A)
(B)
(C)
(D)
43 Triangle is shown on this coordinate grid.ABC
Triangle is dilated with the origin as the center of the dilation. Which ordered pair could represent the ABC image of point (5, 2) after the dilation?C
(2.5, 1)(A)
(5, −2)(B)
(7.5, 4.5)(C)
(−1, −4)(D)
ii. Center and scale factor 3.B
iii. Center and scale factor .C
b. For each dilation, answer the following questions:
i. By what factor do the base and height of the triangle change? Explain.
ii. By what factor does the area of the triangle change? Explain.
iii. How do the angles of the scaled triangle compare to the original? Explain.
1 2
45 Seven line segments are shown on the coordinate plane.
Which of these segments could be the image of segment after a sequence of reflections, rotations, and/or AB translations?
Select correct answer. each
line segment (A) CD
line segment (B) EF
line segment (C) GH
line segment (D) JK
line segment (E) LM
line segment (F) NP
46 For each linear equation in this table, indicate whether the equation has no solution, one solution, or infinitely many solutions.
47 Consider the equation 3(2 + 5) = + .x ax b
(a) Find one value for and one value for so that there is exactly one value of that makes the equation a b x true. Explain your reasoning.
(b) Find one value for and one value for so that there are infinitely many values of that make the a b x equation true. Explain your reasoning.
48 Which ordered pair is the solution of the system of equations below?
x + 2 = 6 y
3 + 8 = 4x y
(2, 2)(A)
(4, 10)(B)
(10, −2)(C)
(20, −7)(D)
49 Ted has some red blocks and some green blocks. • Each red block weighs the same number of ounces.
• Each green block weighs the same number of ounces.
• The total weight of 2 red blocks and 6 green blocks is 23 ounces.
• The total weight of 3 red blocks and 4 green blocks is 22 ounces
What is the total weight of 1 red block 1 green block?and
3 ounces (A)
6 ounces (B)
6.5 ounces (C)
13.5 ounces (D)
50 What is the coordinate of the solution to this system of equations?y
−2 + 3 = −6x y
5 − 6 = 15x y
Write your answer below.
51 Three students solved the equation 3(5 − 14) = 18 in different ways, but each student arrived at the x correct answer. Circle YES or NO to indicate whether each solution shows a correct method for solving the equation.
52 Consider the equation 3(2 + 5) = + .x ax b
(a) Find one value for and one value for so that there is exactly one value of that makes the equation a b x true. Explain your reasoning.
(b) Find one value for and one value for so that there are infinitely many values of that make the a b x equation true. Explain your reasoning.
53 A history club sold rolls of wrapping paper as a fundraiser. The wrapping paper was sold in small rolls and large rolls.
The club earned $3.00 for every small roll sold.
The club earned $4.50 for every large roll sold.
The club sold 10 more large rolls than small rolls.
How many small rolls did the history club sell?
54 A company uses a new machine and an old machine to print booklets. Each machine prints booklets at a constant rate. The graph and the equation represent the relationships between , the number of minutes the x machines print, and , the number of booklets printed.y
The company uses both machines to print a total of 1,250 booklets. Both machines start printing at the same time. During printing, the old machine breaks down and stops printing. The new machine continues printing for an additional 14 minutes and completes the order.
What is the total number of minutes the new machine prints? Show or explain all your work.
Write your answer and your work below.
55 An equation is incorrectly solved below.
Equation: 2 + 3 = −4x
Step 2: 2 = −1x
Step 3: = − 1 2
Step 4: = −x 1 2
What is the first step that shows an error in the solution to the equation?
Step 1(A)
Step 2(B)
Step 3(C)
Step 4(D)
2x 2
1 2
1 2
(a) What is the cost per pound of this coffee?
(b) How many pounds of coffee could Lena buy for $1.00?
(c) Draw a graph in the coordinate plane of the relationship between the number of pounds of coffee and the total cost. If you can, use technology to do this.
(d) In this situation, what is the meaning of the slope of the line you drew in part (3)?
57 Amanda graphed line and line on a coordinate plane, as shown below.m n
Which of the following statements is true?
The slope of line is greater than the slope of line .(A) m n
The slope of line is greater than the slope of line .(B) n m
The -intercept of line is greater than the -intercept of line .(C) x m x n
The -intercept of line is greater than the -intercept of line .(D) y n y m
58 The graph below represents , the cost in dollars of pounds of salad at a salad bar.y x
What is the unit rate for the cost of a salad at the salad bar?
$0.50 per pound(A)
$1.00 per pound(B)
$2.00 per pound(C)
$4.00 per pound(D)
59 Mindy is saving money She started with $0. After 6 weeks, she had $90 saved. Mindy is not sure exactly how much money she saved each week. She assumes that she saved money at a constant rate from when she started saving money through week 6.
Part A: Create a graph that can be used to model the number of dollars, , Mindy saves in weeks.y x
Part B: Explain what the slope of the line you drew represents.
Part C: Explain how the line you drew can be used to predict the number of weeks it will take Mindy to save $150. Include in your explanation any assumptions that must be made in order to make the prediction.
60 The table below shows two coordinate pairs that satisfy the equation for some (x, y) y = mx + b numbers and .m b
(a) If = 7, determine possible values for and . Explain your choices.m y 1 y 2
(b) Find another pair of -values that could work for = 7. Explain why they would work. How do these -y m y values compare to the first pair you found for = 7?m
(c) Use the same -values in the table and find possible values for and if = 3. Explain your choices.x y 1 y 2 m
(d) Find another pair of -values that could work for = 3. Explain why they would work. How do these -y m y values compare to the first pair you found for = 3?m
61 John and Kim wrote down two different functions that have the same rate of change. John's function is shown in the table below.
Graph a function on the grid that could be Kim's function.
62 Use the graph shown below to answer the question.
Which statement is true?not
(A) The slope of the line is .
(B) The slope of the line is - .
(C) The smaller triangle and the larger triangle shown are similar.
(D) The simplified ratio of the vertical side length to the horizontal side length of each triangle
is .
3 5
3 5
3 5
63 A function machine takes an input, does something to this input according to a rule, and returns a unique output.
Given below are tables of input-output pairs for different function machines. Fill in the remaining table entries and describe each function rule in words.
64 The table below shows a relationship between x and y that is a function.not
Write one ordered pair that can be removed from the table to make the relationship between and a x y function.
65 Which of the following tables shows a relationship that is a function?not
(A)
(B)
(C)
(D)
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