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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1.
A certain human red blood cell has a diameter of 0.000007 meters. Which expression represents this diameter, in meters, in scientific notation?
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2.
A function has the following properties:
It is increasing and linear when the value of xis 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?
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3.
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?
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4.
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 ?
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5.
Triangle F and triangle G are shown below.
Which sequence does not transform triangle F to triangle G?
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6.
Which statement explains the type of function that is represented by the equation y = x^{2} + 9
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7.
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?
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8.
The table represents linear Function F.
The equation y = 4x + 2 represents Function G.
Which statement is true?
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9.
What is the solution to the equation shown below?
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10.
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?
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11.
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?
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12.
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?
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13.
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?
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14.
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'?
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15.
What is the value of n in the equation shown below?
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16.
Which set of ordered pairs represents a function?
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17.
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?
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18.
The graph of a function is shown below.
Which statement is true about a section of the graph?
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19.
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?
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20.
Squares PQRS and TUVW are shown below.
Which sequence of transformations of square PQRS shows that square PQRS is congruent to square TUVW?
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21.
Two types of shipping boxes are shown below.
What is the difference in the surface areas, in square feet, of the two boxes?
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22.
Which expression is equivalent to 2^{2} \cdot \frac{2}{2^{4}} ?
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23.
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?
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24.
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?
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25.
What is the solution to the system of equations below?
2x+3y=6
x-3y=9
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26.
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?
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27.
What is the solution to the equation below?
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28.
Which statement best explains whether these ordered pairs represent a function?
(-4,2), (6,7), (-8,3), (9,10), (12,14), (6,9)
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29.
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?
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30.
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?
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31.
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?
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32.
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?
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33.
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?
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34.
Which expression is equivalent to (4.5 \times 10^{2}) + (6.0 \times 10^{3}) and written in scientific notation?
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35.
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?
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36.
What value for the constant, h, in the equation shown below will result in an infinite number of solutions?
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37.
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?
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38.
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?
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39.
Determine the solution to the equation below.
Show your work.
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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?
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41.
Determine the solution, if any, to the system of equations below.
8x - 2y = 1
-4x + y = 3
Show your work.
Answer: _______
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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.
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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.
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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.
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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
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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
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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 = _______
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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.
