CTB/McGraw-Hill. Math Grade 8 Fall Benchmark Assessment Test ID: 87738

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1 Page 1 of 39 Developed and published by CTB/McGraw-Hill LLC, a subsidiary of The McGraw-Hill Companies, Inc., 20 Ryan Ranch Road, Monterey, California All rights reserved. Only authorized customers may copy, download and/or print the document. Any other use or reproduction of this document, in whole or in part, requires written permission of the publisher. Test Name: Math Grade 8 Fall Benchmark Assessment Test ID: CTB/McGraw-Hill Math Grade 8 Fall Benchmark Assessment Test ID: 87738

2 Test Directions Materials: CR Answer Sheet (optional) General Offline Instructions: Today you will take the Acuity Assessment. Read each question carefully and decide which answer is correct. Using your scan sheet, fill in the bubble that contains the letter for the answer you choose. Page 2 of 39

3 1. The quadrilateral ABCD is rotated 90 degrees counterclockwise about the origin to form quadrilateral PQRS. Which statement is true for the quadrilaterals? A Angle PQR is congruent to angle BAD. B Quadrilateral PQRS is congruent to quadrilateral ABCD. C The lengths of the sides of quadrilateral ABCD are longer than the lengths of the corresponding sides of quadrilateral PQRS. D The lengths of the sides of quadrilateral ABCD are shorter than the lengths of the corresponding sides of quadrilateral PQRS. Page 3 of 39

4 2. Look at this table and this graph. x y How much larger is the y-intercept for the table of values than the y-intercept represented in the graph? A 2 B 0 C 2 D 4 Page 4 of 39

5 3. Look at this table. x y Which of these explains why the table does or does not represent a function? A The table does represent a function because each y-value is positive. B The table does not represent a function because each x-value is negative. C The table does represent a function because each x-value has exactly one y-value. D The table does not represent a function because there are two different x-values that have the same y-value. 4. Look at triangles ABC and DEF. Which sequence of transformations can map ΔABC onto ΔDEF? A a counterclockwise rotation by 90 about the origin followed by a reflection across the y-axis B a counterclockwise rotation by 90 about the origin followed by a translation down by 2 units C a counterclockwise rotation by 180 about the origin followed by a reflection across the y-axis D a counterclockwise rotation by 180 about the origin followed by a translation down by 2 units Page 5 of 39

6 5. The coordinates of the vertices of ΔABC are A(2, 0), B(4, 3), and C(1, 5). The triangle is reflected across the x-axis to obtain ΔA'B'C'. What are the coordinates of ΔA'B'C'? You can use the blank grid to find the answer. A A'(2, 0), B'(4, 3), C'(1, 5) B A'(0, 2), B'( 3, 4), C'( 5, 1) C A'( 2, 0), B'( 4, 3), C'( 1, 5) D A'(0, 2), B'( 3, 4),C'( 5, 1) Page 6 of 39

7 6. Look at these four scatter plots. Which scatter plot shows a positive association between the variables x and y? A Scatter Plot 1 B Scatter Plot 2 C Scatter Plot 3 D Scatter Plot 4 Page 7 of 39

8 7. Look at ΔXYZ. Which sequence of transformations would result in a figure that is similar but not congruent? A translate 3 to the left and reflect over the y-axis B reflect across the x-axis and reflect across the y-axis C reflect across the x-axis and dilate by a scale factor of 2 D translate 3 to the right and rotate 90 degrees clockwise around the origin Page 8 of 39

9 8. Which graph represents a function? A C B D Page 9 of 39

10 9. Look at polygons ABCD and PQRS. Which sequence of transformations will map polygon ABCD onto polygon PQRS? A a counterclockwise rotation by 90 about the origin followed by a translation right by 1 unit B a counterclockwise rotation by 90 about the origin followed by a translation right by 4 units C a counterclockwise rotation by 180 about the origin followed by a translation right by 1 unit D a counterclockwise rotation by 180 about the origin followed by a translation right by 4 units Page 10 of 39

11 10. Look at quadrilateral PQRS. Which transformation would result in quadrilateral P'Q'R'S' being formed with P'(1, 2), Q'(4, 2), R'(5, 2), and S' (2, 2)? A Quadrilateral PQRS is reflected over the x-axis. B Quadrilateral PQRS is dilated by a scale factor of about the origin. C Quadrilateral PQRS is translated to the left and down. D Quadrilateral PQRS is rotated around the origin 90 degrees clockwise. Page 11 of 39

12 11. Which table represents a function? A x y C x y B x y D x y Page 12 of 39

13 12. Look at rectangles ABCD and PQRS. Which of these best represents the sequence of transformations that will map rectangle ABCD onto rectangle PQRS? A 90º clockwise rotation about the origin reflection across the y-axis B reflection across the x-axis 90º counterclockwise rotation about the origin C 180º counterclockwise rotation about the origin reflection across the y-axis D reflection across the x-axis 180º counterclockwise rotation about the origin Page 13 of 39

14 13. Maya plays 10 tennis matches each month. She plotted the number of hours she practiced each day of a month and the number of tennis matches she won that month. Based on the graph, which of these best describes the association between the number of hours Maya practiced and the number of tennis matches she won that month? A There is no association between the number of hours Maya practiced and the number of tennis matches she won that month. B There is a weak association between the number of hours Maya practiced and the number of tennis matches she won that month. C There is a positive association between the number of hours Maya practiced and the number of tennis matches she won that month. D There is a negative association between the number of hours Maya practiced and the number of tennis matches she won that month. Page 14 of 39

15 14. ΔABC has its vertices at A(0, 2), B(1, 1), and C(2, 2), and ΔPQR has its vertices at P(0, 4), Q( 2, 2), and R( 4, 4). What transformations were used to map ΔABC to ΔPQR? You can use the blank grid to find the answer. A translation 3 units up and reflection over the y-axis B dilation by a factor of 2 and reflection over the y-axis C rotation of 180 degrees and reflection over the y-axis D reflection over the x-axis and reflection over the y-axis Page 15 of 39

16 15. The graph and table show the number of cartons that two machines seal in different intervals of time. Which statement is correct? A Machine A and Machine B will seal the same number of cartons in 8 minutes. B Machine A and Machine B will seal the same number of cartons in 10 minutes. C The rate at which Machine A seals the cartons is less than the rate at which Machine B seals the cartons. D The rate at which Machine A seals the cartons is greater than the rate at which Machine B seals the cartons. Page 16 of 39

17 16. Look at ΔPQR. ΔPQR is rotated by 180 in a counterclockwise direction about the origin to obtain ΔP'Q'R'. What are the coordinates of ΔP'Q'R'? A P'(1, 4), Q'(0, 2), and R'(5, 3) B P'( 4, 1), Q'( 2, 0), and R'( 3, 5) C P'( 1, 4), Q'(0, 2), and R'( 5, 3) D P'( 4, 1), Q'( 2, 0), and R'( 3, 5) Page 17 of 39

18 17. Look at ΔABC. Which sequence of transformations on ΔABC will result in a figure that is congruent to ΔABC? A reflection across the y-axis followed by dilation by a scale factor of 2 B rotation of 180 counterclockwise about the origin followed by reflection across the y-axis C dilation by a scale factor of 2 followed by rotation of 180 counterclockwise about the origin D rotation of 180 counterclockwise about the origin followed by dilation by a scale factor of 3 Page 18 of 39

19 18. Look at ΔDEF. ΔDEF is translated up 4 units to obtain ΔD'E'F'. What are the coordinates of ΔD'E'F'? A D'(3, 1), E'(5, 2), F'(0, 4) B D'(3, 3), E'(5, 2), F'(0, 0) C D'( 3, 3), E'( 5, 2), F'(0, 0) D D'( 3, 1), E'( 5, 2), F'(0, 4) 19. Look at the table and the equation. x y y = 8x Which statement best compares the y-intercepts? A The y-intercept is greater for the table than the equation. B The y-intercept is greater for the equation than the table. C The y-intercept is 12 more for the equation than the table. D The y-intercept is 12 more for the table than the equation. Page 19 of 39

20 20. Dan drew square ABCD on a coordinate grid. He transformed the square in four different ways, as shown in this table. Transformation Description 1 reflection across y-axis 2 translation by 2 units downward 3 rotation of 90 about the origin in a conterclockwise direction 4 dilation by a scale factor of Which transformation will not produce an image congruent to square ABCD? A Transformation 1 B Transformation 2 C Transformation 3 D Transformation 4 Page 20 of 39

21 21. The coordinates of ΔXYZ are X( 6, 0), Y(0, 8), and Z( 8, 10). ΔXYZ is translated up 3 units and then rotated 180 about the origin to obtain ΔX'Y'Z'. What are the coordinates of ΔX'Y'Z'? You can use the blank grid to find the answer. A X'(6, 3), Y'(0, 5), Z'(8, 7) B X'(6, 3), Y'(0, 5), Z'(8, 7) C X'(3, 0), Y'( 3, 8), Z'(5, 10) D X'(6, 3), Y'(0, 11), Z'(8, 13) 22. Which argument accurately justifies that the congruence of only two pairs of angles are required to determine similarity of two triangles? A If two pairs of angles are congruent, then the third angles must be right angles. B If two pairs of angles are congruent, then the third angles must also be congruent. C If two pairs of angles are congruent, then the sides between them must also be congruent. D If two pairs of angles are congruent, then the sum of the lengths of the sides must be congruent. Page 21 of 39

22 23. The scatter plot shows the relationship between the number of days required to paint a house and the number of painters who paint the house. Which statement is true for the scatter plot? A It shows one outlier. B It shows five outliers. C There is no association between the number of days required to paint a house and the number of painters who paint the house. D There is a positive association between the number of days required to paint a house and the number of painters who paint the house. 24. Given any shape, which series of transformations would result in an image being similar but not congruent to its preimage? A reflection over the x-axis, reflection over the y-axis, translation up 3 B reflection over the x-axis, reflection over the y-axis, reflection over the x-axis C reflection over the x-axis, reflection over the y-axis, dilation by a scale factor of 3 D reflection over the x-axis, reflection over the y-axis, rotation of 180 counterclockwise Page 22 of 39

23 25. This graph and equation each show the distances, in kilometers, of two different cars from a destination after x hours. What is the difference between the cars' initial distance, in kilometers, from their destination? A 10 B 60 C 170 D Quadrilateral PQRS has vertices P( 2, 2), Q(2, 2), R(2, 4), and S(0, 4). The quadrilateral is translated 4 units to the right. It is then dilated by a scale factor of The final image created is quadrilateral EFGH. What is true about the shape formed after each transformation as compared to the original shape? A Both shapes are congruent to the original shape. B Neither shape is congruent to the original shape. C The first shape is similar and the second shape is congruent to the original shape. D The first shape is congruent and the second shape is similar to the original shape. Page 23 of 39

24 If you are taking this assessment in one session, please turn the page and continue working. If you are taking this assessment in two sessions, please stop here.

25 27. A tutoring agency has two teachers. Teacher A charges $75.00 for 3 hours of tutoring. Teacher B's fees are represented in the table below. Teacher B Number of Hours Fees (in dollars) What is the difference, in dollars, between the rates per hour charged by the two teachers? Show your work. Page 24 of 39

26 28. Look at quadrilateral ABCD. Quadrilateral ABCD is reflected across the x-axis and then dilated by a scale factor of PQRS. to create image Draw the image PQRS. Explain your steps to find this image. Page 25 of 39

27 What is the relationship between quadrilateral ABCD and quadrilateral PQRS? Page 26 of 39

28 29. The coordinates of the vertices of triangle ABC are A( 9, 9), B( 3, 6), and C( 6, 3). Triangle ABC is dilated by a scale factor of PQR. and then rotated counterclockwise about the origin by 180 to create triangle On the coordinate grid, draw triangle ABC and triangle PQR. Explain how you found the coordinates of the image after the dilation and the effect of the rotation on these coordinates. If triangle PQR is reflected across the x-axis to create triangle XYZ, what are the coordinates of the points X, Y, and Z? Page 27 of 39

29 30. Wendy transformed figure ABCD to create figure PQRS. The coordinates of the figure PQRS are P( 3, 1), Q( 1, 1), R( 2, 0), and S( 4, 0), as shown. Describe the sequence of two transformations Wendy used to create figure PQRS from figure ABCD. Give the coordinates of the figure after the first transformation. Explain how the coordinates were determined. Page 28 of 39

30 31. Joe kept track of the number of vegetables picked from his garden each day and recorded them in the table below. Vegetables Picked Day Tomatoes Peppers Part A: Is the number of peppers a function of the number of tomatoes? Explain your answer. Part B: What change(s) could you make to the data in order to get a different answer for Part A? Page 29 of 39

31 32. Look at this figure. Part A.1 Write an equation that shows the relationship between,, and. Part A.2 Use the definition of supplementary angles to explain the relationship between,, and. Part B. Arnie states that if = 50 and = 110, then = 80. Is Arnie correct? Explain why Arnie is correct or incorrect. Part C. If = 100 and = 85, what is? Explain your answer. Page 30 of 39

32 33. The table shows the temperature of Jack's city and the number of people at his ice cream shop. Temperature and Ice Cream Sales Temperature ( C) Number of People at Jack's Ice Cream Shop Part A1. Make a scatter plot on the grid to represent the data in the table. Title and label the scatter plot. Page 31 of 39

33 Part A2. Based on the scatter plot, describe the association between the temperature of Jack's city and the number of people at his ice cream shop. Explain your answer. Part B1. Jack states that there would be fewer than 30 people at his ice cream shop if the temperature was greater than 50 C. Explain why Jack's statement is incorrect. Part B2. State one possible reason for the presence of the outlier. Page 32 of 39

34 Written Response Answer Sheet Page 33 of 39

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40 Written Response Answer Sheet This is the end of the test. Page 39 of 39

CTB/McGraw-Hill. 5-2 wks Test ID:

CTB/McGraw-Hill. 5-2 wks Test ID: CTB/McGraw-Hill 5-2 wks 26-27 Test ID: 814161 Page 1 of 13 Developed and published by CTB/McGraw-Hill LLC, a subsidiary of The McGraw-Hill Companies, Inc., 20 Ryan Ranch Road, Monterey, California 93940-5703.