2016: NY Grade 8 - Math - Sara Cowley | Laabri | Nneɛma a ɛma wotumi yɛ ade

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From the New York State Education Department. New York State Testing Program Grade 8 Common Core Mathematics Test Released Questions May 2016. Internet. Available from https://www.nysedregents.org/ei/math/2016/english/2016-released-items-math-g8.pdf; accessed 3, May, 2023.

1

Mr. Thomsen is buying two types of gift cards to give as prizes to employees as a company meeting. He will buy restaurant gift cards that each cost $50. He will also buy movie theater gift cards that each cost $20. He has $450 to buy a total of 15 gift cards. How many of each type of gift card can Mr. Thomsen buy?

He can buy 5 restaurant gift cards and 10 movie theater gift cards.

He can buy 8 restaurant gift cards and 7 movie theater gift cards.

He can buy 10 restaurant gift cards and 5 movie theater gift cards.

He can buy 12 restaurant gift cards and 3 movie theater gift cards.

8.EE.8.c

1

The relationship between temperature in degrees Fahrenheit and degrees Celsius is shown in the graph below.
What is the meaning of the y-intercept?

the change in degrees Fahrenheit for every change of one degree Celsius

the change in degrees Celsius for every change of one degree Fahrenheit

the temperature in degrees Fahrenheit for when the temperature is zero degrees Celsius

the temperature in degrees Celsius when the temperature is zero degrees Fahrenheit

8.F.4

1

Kevin moved from a city to a small town. The population of the city is 6\times10^{5}, which is about 15 times as great as the small town. Which expression could represent the approximate population of the small town?

4\times10^{3}

4\times10^{4}

9\times10^{5}

9\times10^{6}

8.EE.3

1

Pentagon P and pentagon Q, shown below, are congruent.
Which sequence could be used to transform pentagon P to pentagon Q?

a 180\degree clockwise rotation about the origin

a translation four units left and then a reflection over the x-axis

a reflection over the y-axis and then a translation seven units down

a translation seven units down and then a 90\degree clockwise rotation about the origin

8.G.2

1

The graph of a system of equations is shown below.
What system of equations represents the graph?

y=-2x+10

y=-\frac{1}{3}x

y=-2x+10

y=-\frac{1}{2}x

y=-\frac{1}{2}x+10

y=-2x

y=-\frac{1}{3}x+10

y=-2x

8.EE.8.b

1

A cylinder and a cone have congruent heights and radii. What is the ratio of the volume of the cone to the volume of the cylinder?

1:1

1:3

1:6

1:9

8.G.9

1

Which of the equations listed below are linear equations?
Equation I: C=2\pi r
Equation II: A=\pi r^2
Equation III: V=\frac{4}{3}\pi r^{3}

equation I only

equation II only

equations I and III

equations II and III

8.F.3

1

The scatter plot below shows the points scored and the points allowed by the Bulldogs football team for several games.
Which association (correlation) best describes the data?

no association (correlation)

positive association (correlation)

negative association (correlation)

nonlinear association (correlation)

8.SP.1

1

The graph below shows the relationship between the distances run and the time for three people in a 100-yard race.
The relationship between the distance run and the time for Kofi can be represented by the equation y=15.55x, where he ran y yards in x seconds. Which two equations could be used to represent this relationship for Bella and Elsie?

Bella: y=15.15x; Elsie: y=15.85x

Bella: y=15.85x; Elsie: y=15.65x

Bella: y=15.45x; Elsie: y=15.15x

Bella: y=15.85x; Elsie: y=15.15x

8.EE.5

1

Which table of values represents a linear function?

null

8.F.3

1

Simplify.
5^-8\times5^4

\frac{1}{5^4}

\frac{1}{5^{32}}

-5^2

-5^12

8.EE.1

1

What is the value of t that satisfies the equation below?

-\frac{11}{3}

-\frac{4}{5}

10

11

8.EE.7.b

1

Ellentown College has approximately 3\times10^3 students and Pengrove University has approximately 30,000 students. How many times as much is the number of students at Pengrove University as the number of students at Ellentown College?

1

10

30

100

8.EE.3

1

A series of transformations on quadrilateral S resulted in quadrilateral T.
The angle measures of quadrilateral T are congruent to those of quadrilateral S.
The side lengths of quadrilateral T are twice as long as those of quadrilateral S.
Which transformation on quadrilateral S must be included to result in quadrilateral T?

dilation

rotation

reflection

translation

8.G.4

1

Function 1 is represented by the equation y=-\frac{4}{5}x-2, and function 2 is represented by the graph below.
For which of the functions are all the output values less than -1?

both functions

only function 1

only function 2

neither function

8.F.2

1

Rectangle FGHJ, shown below, is translated 6 units right and 1 unit up to produce rectangle F'G'H'J'.
Which statement about the side lengths of rectangle F'G'H'J' is true?

F'G'=3 and G'H'=5

F'G'=3 and G'H'=6

F'G'=9 and G'H'=5

F'G'=9 and G'H'=6

8.G.1.a

1

Solve the system of equations below.
2x+4y=10
2x+4y=-10

x=3, y=1

x=6, y=-4

No solution

Infinitely many solutions

8.EE.8.b

1

Mia enlarged a plan for an outdoor stage. The original plan is shown below.
She dilated the outdoor stage by a scale factor of four with the center of dilation at the origin. Which ordered pair will be the coordinates of one of the new vertices?

(2,1)

(8,16)

(32,4)

(32,16)

8.G.3

1

Bianca and Nick are both musicians who sell their songs online. During the same year, Bianca sold 8\times10^5 downloads of her songs and Nick sold 4\times10^6 downloads of his songs. How many times as much is the number of songs that Nick sold than the number of songs that Bianca sold?

2

5

20

40

8.EE.3

1

Which table represents a relation that is not a function?

null

8.F.1

1

The Ecology Club was planning to take a field trip either to the seacoast or the mountains. The club president surveyed all of the members to determine the preferred trip. The results are displayed in the table below.
Which statement is true about the results of the survey?

20% of eighth-grade students preferred the seacoast

32% of seventh-grade students preferred the mountains

40% of students preferred the mountains

48% of students preferred the seacoast

8.SP.4

1

A cylinder has a radius of 3 inches and a height of 4\frac{3}{4} inches. A sphere has a radius of 3 inches. What is the difference between the volumes, to the nearest tenth of a cubic inch, of the cylinder and the sphere?

21.2

51.8

68.3

96.6

8.G.9

1

Two friends work at different companies, P and S. Both companies use the number of hours that an employee works to calculate that employee's vacation hours. The relationship between the number of hours worked and the number of vacation hours for employees at each company is shown in the table and graph, respectively.
Which statement describes the difference in each friend's vacation hours if both work 2,080 hours?

The friend at company S will have about 42 more vacation hours than the friend at company P

The friend at company S will have about 46 more vacation hours than the friend at company P.

The friend at company P will have about eight more vacation hours than the friend at company S.

The friend at company P will have about nine more vacation hours than the friend at company S.

8.EE.5

1

Which equation represents a nonlinear function?

y=-3x+1

y=x^{2}+1

y=\frac{x}{2}+1

y=2x+\frac{1}{2}

8.F.3

1

What is the value of the expression below?
\frac{(4.8\times10^8)}{(1.2\times10^4)}\times(2.2\times10^-6)

0.88

0.088

0.0088

0.00088

8.EE.4

1

A crane is lowering a concrete block from a height of 270 feet above the ground at a constant rate of 2.5 feet per second. Which function can be used to determine h, the height, in feet, above the ground of the concrete block after s seconds?

h=270s+2.5

h=2.5s+270

h=270-2.5s

h=2.5s-270

8.F.4

1

Function P is a linear function with a y-intercept of 5. Function Q is defined by the equation y=-\frac{1}{3}x+4. Which statement must be true about functions P and Q?

Both functions have the same slope.

Both functions have a negative slope.

The functions will have the same input when y=0.

The functions will have different outputs when x=0.

8.F.2

1

Line k is the line of best fit for a set of data on a scatter plot. The data show a strong linear association. Which scatter plot best represents these data and line k?

null

8.SP.2

1

In the diagram below, lines MN and JK are parallel and are intersected by line QT.
Which transformation could be used to show that \angle MRS is congruent to \angle JST?

reflect \angle MRS over the x-axis

rotate \angle MRS about the origin

translate \angle MRS down and to the right

dilate \angle MRS by a scale factor of two with the center at point R

8.G.5

1

What is the equation of the line that passes through points (-3,0.5) and (3,-0.5)?

y=-\frac{1}{6}x

y=-6x

y=-\frac{1}{6}x+1

y=-6x-17.5

8.EE.6

1

Function J is shown on the coordinate grid below.
If the y-intercept of Function R is 3/2 greater than the y-intercept of Function J, which equation could represent Function R?

y=-x+4.5

y=0.5x+3

y=3x+0.5

y=4.5x-1

8.F.2

2

Jude incorrectly simplified the expression (1/2)^2\times 1/2\times(1/2)^3, as shown below:
A. Describe the mistake that Jude made (use the typing capability within the Show Your Work space), AND
B. Correctly simplify the expression:

8.EE.1

2

Congruent rectangles HJKL and H'J'K'L' are shown on the coordinate grid below.
Describe a sequence of transformations on rectangle HJKL that would result in rectangle H'J'K'L'.

8.G.2

2

Write an equation of a function that is not linear.
Use your equation to explain why your function is not linear.

8.F.3

2

8.EE.7.a

2

A reporter collected data on y, the current market value, in dollars, of a certain car for various years, x, after it had been purchased new. The equation below was fit to the data.
y=16,500-1,500x
A. What does the slope of the graph of this equation represent?
B. What does the y-intercept of the graph of this equation represent?

8.SP.3

2

A triangle with vertices at A(-1,1), B(-2,1), and C(-1,4) is translated. The image of vertex A has coordinates at (3,-1).
Determine the coordinates of either the image of vertex B or the image of vertex C.
Show your work.

8.G.3

3

Stanley drove his car on a business trip. When he left, the mileage was 840 miles, and when he returned, the mileage was 1,200 miles. The car used 12 gallons of gasoline for this trip.
A. Draw a graph on the grid provided to show the relationship between gasoline used, x, and the distance traveled, y, during Stanley's trip.
Carla made the same trip as Stanley, but her car used only 10 gallons of gasoline.
B. Graph the gasoline usage of Carla's car on the same grid as Stanley's car.
C. How do the slopes for Stanley's and Carla's cars compare?
Explain your answer in terms of the unit rate.

8.EE.5

3

Tim is selling tickets to a school sporting event to raise money for his club. He put some extra money in his box before he began. As he sells tickets, he records the number of tickets he has sold and the total amount of money in the box. Some of his data are shown below.
Assuming all the tickets are the same price, write an equation that represents the situation in the table. Explain how to use your equation to determine the amount of money originally in the box before any tickets were sold and the price of each ticket.
Show your work.

8.F.4

3

Rectangle JKLM is shown on the coordinate grid below.
Rectangle JKLM undergoes a sequence of transformations, resulting in rectangle J'K'L'M'.
The length of side K'L' is 6 units. The coordinates of vertex K' are (-3,2), and the coordinates of vertex M' are (3,-2).
Describe a sequence of transformations to rectangle JKLM that would result in rectangle J'K'L'M'.
Show your work.

8.G.4

3

Oliver works at a bookstore. He packed 20 identical paperbacks and 9 identical textbooks in a box. The total mass of the books was 44.4 pounds. After he put 1 more textbook and 5 more paperbacks in the box, the total mass of the books was 51 pounds.
A. Write a system of equations that can be used to determine p, the mass, in pounds, of one paperback, and t, the mass, in pounds, of one textbook.
B. Solve the system of equations to find the two masses.
Show your work.

8.EE.8.c

2016: NY Grade 8 - Math

2016: NY Grade 8 - Math

The relationship between temperature in degrees Fahrenheit and degrees Celsius is shown in the graph below.What is the meaning of the y-intercept?

Kevin moved from a city to a small town. The population of the city is 6\times10^{5}, which is about 15 times as great as the small town. Which expression could represent the approximate population of the small town?

Pentagon P and pentagon Q, shown below, are congruent.Which sequence could be used to transform pentagon P to pentagon Q?

The graph of a system of equations is shown below.What system of equations represents the graph?

A cylinder and a cone have congruent heights and radii. What is the ratio of the volume of the cone to the volume of the cylinder?

Which of the equations listed below are linear equations?Equation I: C=2\pi rEquation II: A=\pi r^2Equation III: V=\frac{4}{3}\pi r^{3}

The scatter plot below shows the points scored and the points allowed by the Bulldogs football team for several games.Which association (correlation) best describes the data?

Which table of values represents a linear function?

Simplify.5^-8\times5^4

What is the value of t that satisfies the equation below?

Ellentown College has approximately 3\times10^3 students and Pengrove University has approximately 30,000 students. How many times as much is the number of students at Pengrove University as the number of students at Ellentown College?

Function 1 is represented by the equation y=-\frac{4}{5}x-2, and function 2 is represented by the graph below.For which of the functions are all the output values less than -1?

Rectangle FGHJ, shown below, is translated 6 units right and 1 unit up to produce rectangle F'G'H'J'.Which statement about the side lengths of rectangle F'G'H'J' is true?

Solve the system of equations below.2x+4y=102x+4y=-10

Mia enlarged a plan for an outdoor stage. The original plan is shown below.She dilated the outdoor stage by a scale factor of four with the center of dilation at the origin. Which ordered pair will be the coordinates of one of the new vertices?

Bianca and Nick are both musicians who sell their songs online. During the same year, Bianca sold 8\times10^5 downloads of her songs and Nick sold 4\times10^6 downloads of his songs. How many times as much is the number of songs that Nick sold than the number of songs that Bianca sold?

Which table represents a relation that is not a function?

The Ecology Club was planning to take a field trip either to the seacoast or the mountains. The club president surveyed all of the members to determine the preferred trip. The results are displayed in the table below.Which statement is true about the results of the survey?

A cylinder has a radius of 3 inches and a height of 4\frac{3}{4} inches. A sphere has a radius of 3 inches. What is the difference between the volumes, to the nearest tenth of a cubic inch, of the cylinder and the sphere?

Which equation represents a nonlinear function?

What is the value of the expression below?\frac{(4.8\times10^8)}{(1.2\times10^4)}\times(2.2\times10^-6)

A crane is lowering a concrete block from a height of 270 feet above the ground at a constant rate of 2.5 feet per second. Which function can be used to determine h, the height, in feet, above the ground of the concrete block after s seconds?

Function P is a linear function with a y-intercept of 5. Function Q is defined by the equation y=-\frac{1}{3}x+4. Which statement must be true about functions P and Q?

Line k is the line of best fit for a set of data on a scatter plot. The data show a strong linear association. Which scatter plot best represents these data and line k?

In the diagram below, lines MN and JK are parallel and are intersected by line QT.Which transformation could be used to show that \angle MRS is congruent to \angle JST?

What is the equation of the line that passes through points (-3,0.5) and (3,-0.5)?

Function J is shown on the coordinate grid below.If the y-intercept of Function R is 3/2 greater than the y-intercept of Function J, which equation could represent Function R?

Jude incorrectly simplified the expression (1/2)^2\times 1/2\times(1/2)^3, as shown below:A. Describe the mistake that Jude made (use the typing capability within the Show Your Work space), AND B. Correctly simplify the expression:

Congruent rectangles HJKL and H'J'K'L' are shown on the coordinate grid below.Describe a sequence of transformations on rectangle HJKL that would result in rectangle H'J'K'L'.

Write an equation of a function that is not linear. Use your equation to explain why your function is not linear.

A triangle with vertices at A(-1,1), B(-2,1), and C(-1,4) is translated. The image of vertex A has coordinates at (3,-1).Determine the coordinates of either the image of vertex B or the image of vertex C.Show your work.

The relationship between temperature in degrees Fahrenheit and degrees Celsius is shown in the graph below.What is the meaning of the y-intercept?

Kevin moved from a city to a small town. The population of the city is 6\times10^{5}, which is about 15 times as great as the small town. Which expression could represent the approximate population of the small town?

Pentagon P and pentagon Q, shown below, are congruent.Which sequence could be used to transform pentagon P to pentagon Q?

The graph of a system of equations is shown below.What system of equations represents the graph?

A cylinder and a cone have congruent heights and radii. What is the ratio of the volume of the cone to the volume of the cylinder?

Which of the equations listed below are linear equations?Equation I: C=2\pi rEquation II: A=\pi r^2Equation III: V=\frac{4}{3}\pi r^{3}

The scatter plot below shows the points scored and the points allowed by the Bulldogs football team for several games.Which association (correlation) best describes the data?

Which table of values represents a linear function?

Simplify.5^-8\times5^4

What is the value of t that satisfies the equation below?

Ellentown College has approximately 3\times10^3 students and Pengrove University has approximately 30,000 students. How many times as much is the number of students at Pengrove University as the number of students at Ellentown College?

Function 1 is represented by the equation y=-\frac{4}{5}x-2, and function 2 is represented by the graph below.For which of the functions are all the output values less than -1?

Rectangle FGHJ, shown below, is translated 6 units right and 1 unit up to produce rectangle F'G'H'J'.Which statement about the side lengths of rectangle F'G'H'J' is true?

Solve the system of equations below.2x+4y=102x+4y=-10

Mia enlarged a plan for an outdoor stage. The original plan is shown below.She dilated the outdoor stage by a scale factor of four with the center of dilation at the origin. Which ordered pair will be the coordinates of one of the new vertices?

Bianca and Nick are both musicians who sell their songs online. During the same year, Bianca sold 8\times10^5 downloads of her songs and Nick sold 4\times10^6 downloads of his songs. How many times as much is the number of songs that Nick sold than the number of songs that Bianca sold?

Which table represents a relation that is not a function?

The Ecology Club was planning to take a field trip either to the seacoast or the mountains. The club president surveyed all of the members to determine the preferred trip. The results are displayed in the table below.Which statement is true about the results of the survey?

A cylinder has a radius of 3 inches and a height of 4\frac{3}{4} inches. A sphere has a radius of 3 inches. What is the difference between the volumes, to the nearest tenth of a cubic inch, of the cylinder and the sphere?

Which equation represents a nonlinear function?

What is the value of the expression below?\frac{(4.8\times10^8)}{(1.2\times10^4)}\times(2.2\times10^-6)

A crane is lowering a concrete block from a height of 270 feet above the ground at a constant rate of 2.5 feet per second. Which function can be used to determine h, the height, in feet, above the ground of the concrete block after s seconds?

Function P is a linear function with a y-intercept of 5. Function Q is defined by the equation y=-\frac{1}{3}x+4. Which statement must be true about functions P and Q?

Line k is the line of best fit for a set of data on a scatter plot. The data show a strong linear association. Which scatter plot best represents these data and line k?

In the diagram below, lines MN and JK are parallel and are intersected by line QT.Which transformation could be used to show that \angle MRS is congruent to \angle JST?

What is the equation of the line that passes through points (-3,0.5) and (3,-0.5)?

Function J is shown on the coordinate grid below.If the y-intercept of Function R is 3/2 greater than the y-intercept of Function J, which equation could represent Function R?

Jude incorrectly simplified the expression (1/2)^2\times 1/2\times(1/2)^3, as shown below:A. Describe the mistake that Jude made (use the typing capability within the Show Your Work space), AND B. Correctly simplify the expression:

Congruent rectangles HJKL and H'J'K'L' are shown on the coordinate grid below.Describe a sequence of transformations on rectangle HJKL that would result in rectangle H'J'K'L'.

Write an equation of a function that is not linear. Use your equation to explain why your function is not linear.

A triangle with vertices at A(-1,1), B(-2,1), and C(-1,4) is translated. The image of vertex A has coordinates at (3,-1).Determine the coordinates of either the image of vertex B or the image of vertex C.Show your work.

The relationship between temperature in degrees Fahrenheit and degrees Celsius is shown in the graph below.
What is the meaning of the y-intercept?

Pentagon P and pentagon Q, shown below, are congruent.
Which sequence could be used to transform pentagon P to pentagon Q?

The graph of a system of equations is shown below.
What system of equations represents the graph?

Which of the equations listed below are linear equations?
Equation I: C=2\pi r
Equation II: A=\pi r^2
Equation III: V=\frac{4}{3}\pi r^{3}

The scatter plot below shows the points scored and the points allowed by the Bulldogs football team for several games.
Which association (correlation) best describes the data?

Simplify.
5^-8\times5^4

Function 1 is represented by the equation y=-\frac{4}{5}x-2, and function 2 is represented by the graph below.
For which of the functions are all the output values less than -1?

Rectangle FGHJ, shown below, is translated 6 units right and 1 unit up to produce rectangle F'G'H'J'.
Which statement about the side lengths of rectangle F'G'H'J' is true?

Solve the system of equations below.
2x+4y=10
2x+4y=-10

Mia enlarged a plan for an outdoor stage. The original plan is shown below.
She dilated the outdoor stage by a scale factor of four with the center of dilation at the origin. Which ordered pair will be the coordinates of one of the new vertices?

The Ecology Club was planning to take a field trip either to the seacoast or the mountains. The club president surveyed all of the members to determine the preferred trip. The results are displayed in the table below.
Which statement is true about the results of the survey?

What is the value of the expression below?
\frac{(4.8\times10^8)}{(1.2\times10^4)}\times(2.2\times10^-6)

In the diagram below, lines MN and JK are parallel and are intersected by line QT.
Which transformation could be used to show that \angle MRS is congruent to \angle JST?

Function J is shown on the coordinate grid below.
If the y-intercept of Function R is 3/2 greater than the y-intercept of Function J, which equation could represent Function R?

Jude incorrectly simplified the expression (1/2)^2\times 1/2\times(1/2)^3, as shown below:
A. Describe the mistake that Jude made (use the typing capability within the Show Your Work space), AND
B. Correctly simplify the expression:

Congruent rectangles HJKL and H'J'K'L' are shown on the coordinate grid below.
Describe a sequence of transformations on rectangle HJKL that would result in rectangle H'J'K'L'.

Write an equation of a function that is not linear.
Use your equation to explain why your function is not linear.

A triangle with vertices at A(-1,1), B(-2,1), and C(-1,4) is translated. The image of vertex A has coordinates at (3,-1).
Determine the coordinates of either the image of vertex B or the image of vertex C.
Show your work.

The relationship between temperature in degrees Fahrenheit and degrees Celsius is shown in the graph below.
What is the meaning of the y-intercept?

Pentagon P and pentagon Q, shown below, are congruent.
Which sequence could be used to transform pentagon P to pentagon Q?

The graph of a system of equations is shown below.
What system of equations represents the graph?

Which of the equations listed below are linear equations?
Equation I: C=2\pi r
Equation II: A=\pi r^2
Equation III: V=\frac{4}{3}\pi r^{3}

The scatter plot below shows the points scored and the points allowed by the Bulldogs football team for several games.
Which association (correlation) best describes the data?

Simplify.
5^-8\times5^4

Function 1 is represented by the equation y=-\frac{4}{5}x-2, and function 2 is represented by the graph below.
For which of the functions are all the output values less than -1?

Rectangle FGHJ, shown below, is translated 6 units right and 1 unit up to produce rectangle F'G'H'J'.
Which statement about the side lengths of rectangle F'G'H'J' is true?

Solve the system of equations below.
2x+4y=10
2x+4y=-10

Mia enlarged a plan for an outdoor stage. The original plan is shown below.
She dilated the outdoor stage by a scale factor of four with the center of dilation at the origin. Which ordered pair will be the coordinates of one of the new vertices?

The Ecology Club was planning to take a field trip either to the seacoast or the mountains. The club president surveyed all of the members to determine the preferred trip. The results are displayed in the table below.
Which statement is true about the results of the survey?

What is the value of the expression below?
\frac{(4.8\times10^8)}{(1.2\times10^4)}\times(2.2\times10^-6)

In the diagram below, lines MN and JK are parallel and are intersected by line QT.
Which transformation could be used to show that \angle MRS is congruent to \angle JST?

Function J is shown on the coordinate grid below.
If the y-intercept of Function R is 3/2 greater than the y-intercept of Function J, which equation could represent Function R?

Jude incorrectly simplified the expression (1/2)^2\times 1/2\times(1/2)^3, as shown below:
A. Describe the mistake that Jude made (use the typing capability within the Show Your Work space), AND
B. Correctly simplify the expression:

Congruent rectangles HJKL and H'J'K'L' are shown on the coordinate grid below.
Describe a sequence of transformations on rectangle HJKL that would result in rectangle H'J'K'L'.

Write an equation of a function that is not linear.
Use your equation to explain why your function is not linear.

A triangle with vertices at A(-1,1), B(-2,1), and C(-1,4) is translated. The image of vertex A has coordinates at (3,-1).
Determine the coordinates of either the image of vertex B or the image of vertex C.
Show your work.