2016: NY Grade 8 - Math

Mr. Thomsen is buying two types of gift cards to give as prizes to employees at 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 $50 to buy a total of 15 gift cards. How many of each type of gift card can Mr. Thomsen buy?

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{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?

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?

Which table of values represents a linear function?

Simplify.

5^{-8}\times5^4

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

3(t+4)-2(2t+3)=-4

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?

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?

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?

Bianca and Nick are both musicians who sell their songs online. During the same year, Biance 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?

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?

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 \frac{3}{2} greater than the y-intercept of Function J, which equation could represent Function R?

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'.

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.

-Draw a graph on the grid in the Show Your Work space 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.

-Graph the gasoline usage of Carla's car on the same grid as Stanley's car.

How do the slopes for Stanley's and Carla's cars compare?

-Explain your answer in terms of the unit rate.

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.

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.