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2017: NY Grade 8 - Math

Last updated 3 months ago

48 questions

Instructions

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NY-8.EE.3

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From the New York State Education Department. New York State Testing Program Grade 8 Common Core Mathematics Test Released Questions June 2017. Internet. Available from https://www.nysedregents.org/ei/math/2017/english/2017-released-items-math-g8cr.pdf; accessed 3, May, 2023.

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Question 39

39.

Determine the solution to the equation below.

Show your work.

Question 40

40.

A cylinder and a cone have the same volume. The cylinder has a radius of 2 inches and a height of 3 inches. The cone has a radius of 3 inches. What is the height of the cone?

Question 41

41.

Determine the solution, if any, to the system of equations below.
8x - 2y = 1
-4x + y = 3

Show your work.

Answer: _______ 

Question 42

42.

The hypotenuses of similar triangles ABC and DFA both lie on line k, as shown below.
Demonstrate whether the slope of line k is constant between points C and D. Use the leg lengths of triangles ABC and DFA in your answer.

Question 43

43.

The values in the table below represent Function B, which is a linear function.
Function L is represented by the equation y=6x+4. Compare Functions B and L by determining which one has the greater rate of change and which one has the greater y-intercept.

Explain why your answers are correct.

Show your work.

Question 44

44.

The values given in the table below lie on the graph of a linear function.
What equation represents this linear function?

Show your work.

Question 45

45.

The circular base of the cone below has center C. Another circle, with center B, is parallel to the base. This circle is the base of a smaller cone with height AB. The measurements in the diagram are given in inches.
Triangle ABD is similar to triangle ACE.
The smaller cone is removed to create a new object, as shown below.
What is the volume of this new object? Round your answer to the nearest tenth.

Show your work.

Answer: _______ cubic inches

Question 46

46.

The table and the graph below show Josie's and Salvador's wages, respectively, based on the number of hours worked.
In 2010, Josie and Salvador each worked an eight-hour day for five days each week. How many weeks did it take Josie to earn $1,000 more than Salvador?

Show your work.

Answer: _______ weeks

Question 47

47.

In the figure below, line DE is parallel to line FG, with transversal AG.
Write and solve a system of linear equations to determine the values of x and y.

Show your work.

Answer: x = _______  and y = _______ 

Question 48

48.

Four equations are shown below.

Equation 1: y=2^{x}
Equation 2: y=2x-5
Equation 3: y=x^{2}+6
Equation 4: y=\frac{x}{2}

Identify one linear equation and one nonlinear equation from the list. 
State a reason why each equation you identified is linear or nonlinear.

Linear equation: _______ . Reason: _______ 
Nonlinear equation: _______ . Reason: _______ 

A certain human red blood cell has a diameter of 0.000007 meters. Which expression represents this diameter, in meters, in scientific notation?

A function has the following properties:
It is increasing and linear when the value of x is between -5 and -3.
It remains constant when the value of x is between -3 and 0.
It is decreasing and linear when the value of x is between 0 and 3.
It is increasing and nonlinear when the value of x is between 3 and 5.
Which graph best represents this function?

The figure shown below consists of a square pyramid on top of a cube. A vertical plane passes through point X and is perpendicular to the bases of both shapes, slicing the figure into equal halves.
What shape is created by the intersection of the vertical plane and these three-dimensional shapes?

square

triangle

hexagon

pentagon

Ms. Gibson made an initial deposit of $500 when opening a bank account. After the initial deposit, she deposited the same amount of money each month. The table below shows the total amount of money, a, she deposited into the account after a certain number of months, t, since opening it.

Which equation models the relationship between a and t ?

a = 250t

a = 500t

a = 250t + 500

a = 500t + 250

Triangle F and triangle G are shown below.
Which sequence does not transform triangle F to triangle G?

a 180\degree clockwise rotation about the origin

a 180\degree counterclockwise rotation about the origin

a reflection over the x-axis and then a reflection over the y-axis

a reflection over the y-axis and then a 90\degree clockwise rotation about the origin

Which statement explains the type of function that is represented by the equation y = x^{2} + 9

The function is linear because it contains more than one term.

The function is linear because the variable x is raised to the second power.

The function is nonlinear because it contains more than one term.

The function is nonlinear because the variable x is raised to the second power.

Line n is shown on the grid below.
Line q will be graphed on the same grid. The only solution to the system of linear equations formed by lines n and q occurs when x = 3/2 and y = 0. Which equation could represent line q?

y = 3/2x

y = 4/3x - 2

y = -5/2x + 1

y = -2/3x + 3/2

The table represents linear Function F.
The equation y = 4x + 2 represents Function G.

Which statement is true?

The rate of change of Function G is less than the rate of change of Function F because 2 < 3.

The rate of change of Function G is less than the rate of change of Function F because 4 < 9.

The rate of change of Function G is greater than the rate of change of Function F because 2 > 9/7.

The rate of change of Function G is greater than the rate of change of Function F because 4 > 3.

What is the solution to the equation shown below?

x = -6

x=4

x=-4.5

x=9

A company performed power tests on a set of batteries of the same type. The company 10 determined that the equation y = 100 - 8.9x, where x is the number of hours of use and y is the percent of battery power remaining, models the battery life. Based on the equation, what is the best prediction of the percent of remaining power for a battery after 11 hours of use?

1.2%

2.1%

10%

97.9%

A cook uses 2.5 cups of flour for each ounce of butter in a recipe. Which graph represents the relationship between the amount of flour and the amount of butter in the recipe?

Two rectangles are shown below. Rectangle P has a perimeter of 20 inches. Rectangle Q has a perimeter of 30 inches.
What are the values of j and h?

j=3 and h=3

j=10 and h=4

j=2 and h=4

j=9.5 and h=6.5

A school club had a T-shirt sale to raise money. After the sale, an inventory showed that 108 blue T-shirts and 96 green T-shirts had been sold. The sizes of these T-shirts included 60 small, 86 medium, and 58 large. Which table correctly represents these data?

The vertices of a triangle are located at F(-4,-2), G(2,2), and H(0,-4). A sequence of transformations to triangle FGH results in triangle F'G'H', as shown below.
Which sequence of transformations to triangle FGH results in triangle F'G'H'?

a 90\degree clockwise rotation about the origin, then a dilation by a scale factor of 2 with a center of dilation at the origin

a 90\degree counterclockwise rotation about the origin, then a dilation by a scale factor of 2 with a center of dilation at the origin

a 90\degree counterclockwise rotation about the origin, then a dilation by a scale factor of 1/2 with a center of dilation at the origin

a 90\degree clockwise rotation about the origin, then a dilation by a scale factor of 1/2 with a center of dilation at the origin

What is the value of n in the equation shown below?

5

6

10

12

Which set of ordered pairs represents a function?

{(2, 7), (2, 8), (3, 8)}

{(3, 2), (3, 3), (3, 4)}

{(4, 1), (5, 1), (4, 4)}

{(5, 6), (8, 6), (9, 6)}

A parallelogram with vertices at (0, 3), (2, 0), (4, 2), and (2, 5) is reflected over the y-axis. Which vertex of the parallelogram will have the same x-coordinate before and after the reflection?

(0, 3)

(2, 0)

(4, 2)

(2, 5)

The graph of a function is shown below.
Which statement is true about a section of the graph?

In Section N, the function is linear and decreasing.

In Section P, the function is linear and increasing.

In Section Q, the function is nonlinear and decreasing.

In Section R, the function is nonlinear and increasing.

The owner of a coffee shop compared the amount of hot coffee per day, in fluid ounces, sold and the daily high temperature, in degrees Fahrenheit, per day. Her data are shown in the scatter plot below.
If these data are modeled by the line y=-5.9x+850, which statement best describes a valid prediction the owner could make?

For each temperature increase of 10\degree F, the shop can expect to sell about 60 fluid ounces more hot coffee.

For each temperature decrease of 10\degree F, the shop can expect to sell about 6 fluid ounces more hot coffee.

On a day with a high temperature of 0\degree F, the shop can expect to sell about 145 fluid ounces of hot coffee.

On a day with a high temperature of 0\degree F, the shop can expect to sell about 850 fluid ounces of hot coffee.

Squares PQRS and TUVW are shown below.
Which sequence of transformations of square PQRS shows that square PQRS is congruent to square TUVW?

a translation 2 units up and 2 units to the right, then a reflection over the x-axis

a translation 2 units up and 2 units to the right, then a reflection over the y-axis

a translation 2 units down and 2 units to the left, then a reflection over the x-axis

a translation 2 units down and 2 units to the left, then a reflection over the y-axis

Two types of shipping boxes are shown below.

What is the difference in the surface areas, in square feet, of the two boxes?

2

3

21

30

Which expression is equivalent to 2^{2} \cdot \frac{2}{2^{4}} ?

2^{-2}

2^{-1}

2^{6}

2^{7}

The object below was made by placing a cone on top of a cylinder. The base of the cone is congruent to the base of the cylinder.
What is the volume, in cubic centimeters, of the object?

Lily wants to define a transformation (or series of transformations) using only rotations, reflections, or translations that takes Figure A to Figure B.
Which statement about the transformation that Lily wants to define is true?

It can be defined with two reflections.

It can be defined with one rotation and one translation.

It cannot be defined because Figure A and Figure B are not congruent.

It cannot be defined because the longest side of Figure B is on the bottom.

What is the solution to the system of equations below?

2x+3y=6
x-3y=9

(-1, \frac{8}{3})

(-3,-4)

(5,-\frac{4}{3})

(8,-\frac{1}{3})

As part of a training program for a triathlon, Marcie completes a three-mile run a few times each week. The scatter plot below shows the times in which Marcie completes this run for each week that she has been in the training program.
Based on these data, which statement best describes the relationship between the number of weeks Marcie has been in the training program and her running times?

There is a negative linear association with no outliers.

There is a negative linear association with one outlier.

There is a positive linear association with no outliers.

There is a positive linear association with one outlier.

What is the solution to the equation below?

Which statement best explains whether these ordered pairs represent a function?
(-4,2), (6,7), (-8,3), (9,10), (12,14), (6,9)

The ordered pairs represent a function because no output values are repeated.

The ordered pairs represent a function because each output value is greater than each input value.

The ordered pairs do not represent a function because one input value has two different output values.

The ordered pairs do not represent a function because the difference between the input and output of each ordered pair is not the same.

The amount of revenue in dollars, y, that Jason receives from selling x posters is given by the equation y = 4x. The cost of producing x posters is given by the equation y = \frac{1}{2}x + 280. How many posters does Jason need to sell so that the cost and revenue are equal?

40

80

140

320

A car traveled 36 miles in 45 minutes. The car traveled at a constant speed. If the car continues to travel at this rate, which equation can be used to determine y, the total number of miles the car will travel, in x hours?

y=48x

y=x+48

48y=x

48+y=x

The mass of a dust particle is approximately 7.5  \times   10^{-10} kilograms and the mass of an electron is 9.1 \times  10^{-31} kilograms. Approximately how many electrons have the same mass as one dust particle?

Two photographers offer different pricing plans for their services. The graph below models the prices Photographer A charges. The table below shows the prices Photographer B charges. Each photographer charges a one-time equipment fee and an hourly rate.
Which statement about the two pricing plans is true?

Photographer A charges $15 per hour more than Photographer B.

Photographer B charges $15 per hour more than Photographer A.

Photographer A's equipment fee is $25 less than Photographer B's.

Photographer B's equipment fee is $25 less than Photographer A's.

Acute \triangle ABC is rotated about a point and then dilated by a scale factor of 1/2 to produce \triangle A'B'C'. Which statement correctly compares \triangle A'B'C' to \triangle ABC?

The angle measures and side lengths of \triangle A'B'C' are half the size of those of \triangle ABC.

The angle measures of \triangle A'B'C' are the same as those of \triangle ABC, but the side lengths of \triangle A'B'C' are half the size of those of \triangle ABC.

The angle measures of \triangle A'B'C' are the same as those of \triangle ABC, but the side lengths of \triangle A'B'C' are twice the size of those of \triangle ABC.

The angle measures of \triangle A'B'C' depend on the angle of rotation, but the side lengths of \triangle A'B'C' are half the size of those of \triangle ABC.

Which expression is equivalent to (4.5 \times 10^{2}) + (6.0 \times 10^{3}) and written in scientific notation?

The points (2, -2) and (-4, 13) lie on the graph of a linear function of x. Which point also lies on the graph of this function?

(-6,18)

(-1,5)

(7,14.5)

(13,-4)

What value for the constant, h, in the equation shown below will result in an infinite number of solutions?

The graphs below show the relationship between elapsed time and distance traveled by airplane A and airplane B after each airplane reaches its cruising speed.
Airplane C is traveling at a different cruising speed. The equation y= \frac{27}{6}x can be used to determine y, the number of miles traveled by airplane C in x minutes. Which statement accurately compares the cruising speed of airplane C to airplanes A and B?

The cruising speed of airplane C is less than the cruising speeds of both airplanes A and B.

The cruising speed of airplane C is greater than the cruising speeds of both airplanes A and B.

The cruising speed of airplane C is greater than the cruising speed of airplane A and less than the cruising speed of airplane B.

The cruising speed of airplane C is less than the cruising speed of airplane A and greater than the cruising speed of airplane B.

Two transformations are performed on a figure on a coordinate plane. The first transformation is a translation 8 units to the left. Which second transformation will result in an image that is similar to, but not congruent to, the original figure?

a clockwise rotation of 90 \degree about the center

a clockwise rotation of 180 \degree about the center

a dilation by a scale factor of 1 with the origin as the center of dilation

a dilation by a scale factor of 1/2 with the origin as the center of dilation