PARCC Grade 08 Mathematics Practice Test Released April,

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1 Non-Calculator Part 1. Solve for. Enter your answer in the space provided. Enter only your solution. ( ) ( ) 2. Which decimal is equivalent to? Select your answer. A. B. C. D. 3. Two lines are graphed on the same coordinate plane. The lines only intersect at the point ( ). Which of these systems of linear equations could represent the two lines? Select all that apply. A. { B. { C. { D. { E. { 4. A relationship between and is defined by the equation, where is the input and is the output. Which statements about the relationship are true? Select each correct statement. A. is a function of. B. The graph of the relationship is a line. C. When the input is, the output is 4. D. When the input is, the output is 3. E. The -intercept of the relationship is ( ). 5. The body of a 154-pound person contains approximately milligrams of gold and 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? Enter your answer in the box. Page 1 of 22

2 Non-Calculator Part (continued) 6. The graph shows as a function of. For each interval in the table, indicate whether the function is increasing, decreasing or neither increasing nor decreasing over the interval. Interval Increasing Decreasing Neither Increasing not Decreasing 7. The table 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. System of Equations { { ( ) No Solution One Solution Infinitely Many Solutions Page 2 of 22

3 Non-Calculator Part (continued) 8. Parallelogram is shown in the coordinate plane. Parallelogram (not shown) is the image of parallelogram after a rotation of about the origin. Which statements about parallelogram are true? Select each correct statement. A. is parallel to B. is parallel to C. is parallel to D. is parallel to E. is parallel to 9. Which equation has both 4 and as possible values of? A. B. C. D. Page 3 of 22

4 Non-Calculator Part (continued) 10. When the input to a function is, the output is 4. Which statement about this function must be true? A. An input of has infinitely many possible outputs. B. An input of has exactly one possible output. C. An output of 4 has infinitely many inputs. D. An output of 4 has exactly one input. 11. A system of equations is shown. { What is the solution ( ) of the system of equations? Enter your answers in the boxes. ( ) Page 4 of 22

5 Non-Calculator Part (continued) 12. Three congruent figures are shown on the coordinate plane. Part A Select a transformation from each drop-down menu to make the statement true. Figure 1 can be transformed onto figure 2 by Choose a reflection across the -axis a rotation clockwise about the origin a translation 2 units to the left followed by Choose a reflection across the -axis a rotation clockwise about the origin a translation 3 units to the right Part B Figure 3 can also be created by transforming figure 1 with a sequence of two transformations. Select a transformation from each drop-down menu to make the statement true. Figure 1 can be transformed onto figure 3 by Choose a reflection across the -axis a rotation clockwise about the origin a translation 7 units to the right followed by Choose a reflection across the -axis a rotation clockwise about the origin a translation 3 units to the left Page 5 of 22

6 Non-Calculator Part (continued) 13. Which expressions are equivalent to? Select all that apply. A. B. C. D. E. F. 14. The graph of a nonlinear function is shown on the coordinate plane. In the graph, is a function of. When the input of the function is, what is the output of the function? A. B. C. 1 D. 5 Page 6 of 22

7 Non-Calculator Part (continued) 15. A scatter plot is shown in the coordinate plane. Which of these most closely approximates a line of best fit for the data in the scatter plot? Page 7 of 22

8 Non-Calculator Part (continued) 16. The equation of line is. The equation of line is. The equations of lines s and t form a system of equations. The solution to the system of equations is located at point P. To graph a line, select Line and plot two points on the coordinate plane. A line will be drawn through the points. In similar fashion, select Line and plot two points on the coordinate plane. A line will be drawn through the points. Select Point P and plot the point on the coordinate plane. 17. Classify each equation as defining a linear or nonlinear function of. Select one cell per column. function ( ) linear non-linear Page 8 of 22

9 Non-Calculator Part (continued) 18. Solve for. ( ) ( ) Enter your answer in the space provided. Enter only your solution. 19. Select the point on the number line that best approximates the location of Note: After clicking on some interval of 0.5 units on the number line, a zoom-in window opens below the original number line allowing the student to place their point to accuracy within 0.05 units. Page 9 of 22

10 Calculator Part In this part of the session, a calculator is provided in the toolbar for your use. If you prefer, you may use your own hand-held calculator during this part of the session. 1. In, is perpendicular to. The dimensions are shown in centimeters. What is the length of? Enter your answer in the box. centimeters Note: The Pythagorean Theorem is provided on the PARCC Formula Chart for this grade level. 2. Filipo is building a rectangular sandbox for his younger brother. The length of the sandbox is 1 foot longer than twice the width of the sandbox. The perimeter of the sandbox is 29 feet. Part A Which equation could be used to determine A. B., the width, in feet, of the sandbox? C. ( ) D. ( ) Part B What is the width, in feet, of the sandbox? Enter your answer in the space provided. Page 10 of 22

11 Calculator Part (continued) 3. The table shows the results of a random survey of students in grade 7 and grade 8. Every student surveyed gave a response. Each student was asked if he or she exercised less than 5 hours last week or 5 or more hours last week. Less than 5 hours 5 or more hours Grade 7 Students Grade 8 Students Based on the results of the survey, which statements are true? Select each correct statement. A. More grade 8 students were surveyed than grade 7 students. B. A total of 221 students were surveyed. C. Less than 50% of the grade 8 students surveyed exercised 5 or more hours last week. D. More than 50% of the students surveyed exercised less than 5 hours last week. E. A total of 107 grade 7 students were surveyed. Page 11 of 22

12 Calculator Part (continued) 4. A school is selling t-shirts and sweatshirts for a fund-raiser. The table shows the number of t-shirts and the number of sweatshirts in each of three recent orders. The total cost of orders A and B are given. Each t-shirt has the same cost, and each sweatshirt has the same cost. Order Number of Number of Total Cost of Order T-shirts Sweatshirts (dollars) A B C 1 2? The system of equations shown can be used to represent this situation. { Part A What is the cost of 1 t-shirt and 1 sweatshirt? Enter your answer in the box. Part B Select a choice from each drop-down menu to correctly complete the statement. In the system of equations, represents Choose the number of t-shirts in the order the number of sweatshirts in the order the cost, in dollars, of each t-shirt the cost, in dollars, of each sweatshirt and represents Choose the number of t-shirts in the order the number of sweatshirts in the order the cost, in dollars, of each t-shirt the cost, in dollars, of each sweatshirt Part C If the system of equations is graphed in a coordinate plane, what are the coordinates ( ) of the intersection of the two lines? ( ) Part D What is the total cost, in dollars, of order C? $ Page 12 of 22

13 Calculator Part (continued) 5. Functions W and Z are both linear functions of. Which statement comparing the functions is true? (Note: This should read Which statements comparing the functions are true? ) A. The slope of Function W is less than the slope of Function Z. B. The slope of Function W is greater than the slope of Function Z. C. The -intercept of Function W is equal to the -intercept of Function Z. D. The -intercept of Function W is less than the -intercept of Function Z. E. The -value when for Function W is greater than the -value when for Function Z. F. The -value when for Function W is equal to the -value when for Function Z. Page 13 of 22

14 Calculator Part (continued) 6. Line t and and are shown on the coordinate grid. Which statements are true? Select all that apply. A. The slope of is equal to the slope of. B. The slope of is equal to the slope of. C. The slope of is equal to the slope of line t. D. The slope of line t is equal to. E. The slope of line t is equal to. F. The slope of line t is equal to. Page 14 of 22

15 Calculator Part (continued) 7. A pool cleaning service drained a full pool. The following table shows the number of hours it drained and the amount of water remaining in the pool at that time. Part A Part B Part C Part D Page 15 of 22 Pool Draining Time (hours) Water Remaining (gallons) 13,200 12,000 10,800 9,600 8,400 Plot the points that show the relationship between the number of hours elapsed and the number of gallons of water left in the pool. Select a place on the grid to plot each point. The data suggests a linear relationship between the number of hours the pool has been draining and the number of gallons of water remaining in the pool. Assuming the relationship is linear, what does the rate of change represent in the context of this relationship? A. The number of gallons of water in the pool after 1 hour. B. The number of hours it took to drain 1 gallon of water. C. The number of gallons drained each hour D. The number of gallons of water in the pool when it is full. What does the y intercept of the linear function represent in the context of this relationship? A. The number of gallons of water in the pool after 1 hour. B. The number of hours it took to drain 1 gallon of water. C. The number of gallons drained each hour D. The number of gallons of water in the pool when it is full. Which equation describes the relationship between the time elapsed and the number of gallons of water remaining in the pool? A. B. C. D.

16 Calculator Part (continued) 8. Two different proportional relationships are represented by the equation and the table. Proportion A Proportion B Use the drop-down menus to complete the sentence, comparing the rates of change of the proportional relationships. The rate of change in Proportion A is Choose Choose more less than the rate of change in Proportion B. 9. Eric planted a seedling in his garden and recorded it height each week. The equation shown can be used to estimate the height, h, in inches, of the seedling after w, weeks since Eric planted the seedling. Part A What does the slope of the graph of the equation represent? A. the height, in inches, of the seedling after w weeks B. the height, in inches, of the seedling when Eric first planted it C. the increase in the height, in inches, of the seedling each week D. the total increase in the height, in inches, of the seedling after w weeks Part B The equation estimates the height of the seedling to be 8.25 inches after how many weeks? Enter your answer in the box. Page 16 of 22

17 Calculator Part (continued) 10. Functions A, B, and C are linear functions. Some values of Function A are shown in the table. Function A x y The graph of Function B has a y intercept of ( ) and an x intercept of ( ). Function C is defined by the equation ( ). Order the linear functions based on rate of change, from least to greatest. Least Rate of Change Greatest Rate of Change 11. The figure shows a right-circular cylinder and a right-circular cone. The cylinder and the cone have the same base and the same height. Part A What is the volume of the cone, in cubic feet? Part B A. B. C. D. What is the ratio of the cone s volume to the cylinder s volume? Enter your answer in the space provided. Enter only your fraction. (Note: formulas for the volumes of cylinders and cones are provided on the PARCC formula chart.) Page 17 of 22

18 Calculator Part (continued) 12. A solution is 20% bleach. Create a graph that represents all possible combinations of the number of liters of bleach, contained in number of liters of solution. To graph a line, select two points on the coordinate plane. A line will be drawn through the points. 13. Liz saw the number shown on the calculator screen. Which number represents the number Liz saw? A B C. D. Page 18 of 22

19 Practice Test Answer and Alignment Document Mathematics: Grade 8 End-of-Year Assessment M A T Item Number Answer Key Part 1: Non-Calculator Evidence Statement Keys 1 or equivalent 8.EE.7b 2 D 8.NS.1 3 A, E 8.EE.8a 4 A, B, D 8.F EE.3 H 6 8.F EE.8b-3 8 C, D 8.G.1c 9 C 8.EE.2 10 B 8.F (10, -2) 8.EE.8b-1 Part A: Part B: 12 8.G.2 PARCC EOY Assessment: Grade 8 Mathematics Practice Test - Answer and Alignment Document 1

20 Practice Test Answer and Alignment Document Mathematics: Grade 8 End-of-Year Assessment M 13 B, E 8.EE.1 14 D 8.F A 8.SP.2 A T H 16 8.EE.8b F EE.7b 19 8.NS.2 Part 2: Calculator G Part A: D Part B: 4.5 or equivalent 8.EE.C.Int.1 3 B, C 8.SP.4 Part A: 19 Part B: 4 Part C: (8, 11) Part D: 30 8.EE.8c PARCC EOY Assessment: Grade 8 Mathematics Practice Test - Answer and Alignment Document 2

21 Practice Test Answer and Alignment Document Mathematics: Grade 8 End-of-Year Assessment M 5 B, F 8.F.2 6 A, B, C, E 8.EE.6-1 Part A: A T H 7 Part B: C Part C: D Part D: A 8.F EE Part A: C Part B: 8 8.SP F.2 11 Part A: B Part B: 8.G.9 PARCC EOY Assessment: Grade 8 Mathematics Practice Test - Answer and Alignment Document 3

22 Practice Test Answer and Alignment Document Mathematics: Grade 8 End-of-Year Assessment M A T H 12 8.EE A 8.EE.4-2 PARCC EOY Assessment: Grade 8 Mathematics Practice Test - Answer and Alignment Document 4

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