ctb/mcgraw-hill math grade 8 fall benchmark assessment

CTB/McGraw-Hill

Math Grade 8 Fall BenchmarkAssessment

Test ID: 87738

Test Name: Math Grade 8 Fall Benchmark Assessment Test ID: 87738

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of 39 Developed and published by CTB/McGraw-Hill LLC, a subsidiary of The McGraw-Hill Companies, Inc., 20 Ryan Ranch Road, Monterey, California 93940-5703. Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights

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Materials: • CR Answer Sheet (optional)

General Offline Instructions:

Today you will take the Acuity Assessment. Read each question carefully and decide whichanswer is correct. Using your scan sheet, fill in the bubble that contains the letter for the answeryou choose.


Test Directions

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of 39 Copyright © 2012 by The McGraw-Hill Companies, Inc.

1.

The quadrilateral ABCD is rotated 90 degrees counterclockwise about the origin to form quadrilateralPQRS.

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 correspondingsides of quadrilateral PQRS.

D The lengths of the sides of quadrilateral ABCD are shorter than the lengths of the correspondingsides of quadrilateral PQRS.


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2.

Look at this table and this graph.

x y

0 6

1 9

2 12

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


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3.

Look at this table.

x y

−1 1

−2 2

−3 3

−4 1

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 samey-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


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5.

The coordinates of the vertices of ΔABC are A(2, 0), B(4, 3), and C(1, 5). The triangle is reflected acrossthe 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)


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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


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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


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8.

Which graph represents a function?

A C

B D


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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


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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.


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11.

Which table represents a function?

Ax y

1 3

1 5

1 7

1 9

Cx y

1 2

1 4

2 6

2 8

Bx y

4 1

4 3

6 4

7 8

Dx y

1 3

2 6

3 9

4 12


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12.

Look at rectangles ABCD and PQRS.

Which of these best represents the sequence of transformations that will map rectangle ABCD ontorectangle 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


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13.

Maya plays 10 tennis matches each month. She plotted the number of hours she practiced each day of amonth 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 Mayapracticed 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 tennismatches she won that month.

B There is a weak association between the number of hours Maya practiced and the number of tennismatches she won that month.

C There is a positive association between the number of hours Maya practiced and the number oftennis matches she won that month.

D There is a negative association between the number of hours Maya practiced and the number oftennis matches she won that month.


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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), andR(−4, 4). What transformations were used to map ΔABC to ΔPQR?


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


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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 thecartons.

D The rate at which Machine A seals the cartons is greater than the rate at which Machine B seals thecartons.


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16.

Look at ΔPQR.

ΔPQR is rotated by 180° in a counterclockwise direction about the origin to obtain ΔP'Q'R'. What are thecoordinates 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)


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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


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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

3 60

6 120

9 180

y = 8x − 16

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.


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20.

Dan drew square ABCD on a coordinate grid. He transformed the square in four different ways, as shownin 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


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21.

The coordinates of ΔXYZ are X(–6, 0), Y(0, –8), and Z(–8, –10). ΔXYZ is translated up 3 units and thenrotated 180° about the origin to obtain ΔX'Y'Z'. What are the coordinates of ΔX'Y'Z'?


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 todetermine 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.


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23.

The scatter plot shows the relationship between the number of days required to paint a house and thenumber 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 ofpainters who paint the house.

D There is a positive association between the number of days required to paint a house and thenumber of painters who paint the house.

24.

Given any shape, which series of transformations would result in an image being similar but not congruentto 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


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25.

This graph and equation each show the distances, in kilometers, of two different cars from a destinationafter x hours.

What is the difference between the cars' initial distance, in kilometers, from their destination?

A 10

B 60

C 170

D 180

26.

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.


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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.

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)

3 120

6 240

9 360

What is the difference, in dollars, between the rates per hour charged by the two teachers?

Show your work.


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Page 24 of 39 Copyright © 2012 by The McGraw-Hill Companies, Inc.

28.

Look at quadrilateral ABCD.

Quadrilateral ABCD is reflected across the x-axis and then dilated by a scale factor of to create image

PQRS.

Draw the image PQRS.

Explain your steps to find this image.


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What is the relationship between quadrilateral ABCD and quadrilateral PQRS?


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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 and then rotated counterclockwise about the origin by 180° to create triangle

PQR.

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 onthese coordinates.

If triangle PQR is reflected across the x-axis to create triangle XYZ, what are the coordinates of the pointsX, Y, and Z?


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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.


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31.

Joe kept track of the number of vegetables picked from his garden each day and recorded them in the tablebelow.

Vegetables Picked

Day 1 2 3 4 5 6

Tomatoes 7 8 10 6 7 9

Peppers 12 13 10 9 8 16

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?

___________________________________________________________________________


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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 ?



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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

5 0

10 40

15 6

20 15

25 17

30 30

35 40

40 42

45 50

Part A1. Make a scatter plot on the grid to represent the data in the table. Title and label the scatter plot.


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Part A2. Based on the scatter plot, describe the association between the temperature of Jack's city and thenumber of people at his ice cream shop.


Part B1. Jack states that there would be fewer than 30 people at his ice cream shop if the temperature wasgreater than 50°C. Explain why Jack's statement is incorrect.

Part B2. State one possible reason for the presence of the outlier.


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ctb/mcgraw-hill math grade 8 fall benchmark assessment

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