grade 8 mathematics · 2019-11-07 · •graph the system of equations on the coordinate plane. to...

Colorado Measures ofAcademic Success

Mathematics

Grade 8

Paper Practice Resource for Students

Paper Practice Resource for Students

The Colorado Measures of Academic Success (CMAS) is Colorado’s standards-based assessment program designed to measure the Colorado AcademicStandards (CAS) in the content areas of science, social studies, English languagearts, and mathematics. The sample items included in this resource providestudents with an opportunity to become familiar with the format of test itemsthat appear in the paper-based test books. The sample items are not intended tobe a complete test, nor are they intended to cover all assessed content or itemtypes.

While the use of the sample items is not required, it is strongly encouraged tohelp ensure students are familiar with the types of items they may encounterwhile taking the paper-based test.

Item Types:

Selected Response Items

Selected response items are multiple choice questions. To respond, the studentindicates their response in an answer grid or by filling in the circle(s) next totheir answer choice.

Constructed Response Items

Constructed response items are questions or prompts that require anindependent, written response. To respond, the student writes his or her answerin the response box in the test book.

A»CD

Correct Mark: Incorrect Marks:

ððððE

Converted Online Technology-Enhanced Item Types

Online technology-enhanced items converted to the paper testing format mayask students to:

• Circle the correct answer

• Complete a table with checkmarks, Xs, or letters from a list of answerchoices

• Fill in the blank

• Draw lines from boxes to correct answers

• Complete a bar graph or histogram

• Interact with a number line

• Graph points and lines on a coordinate grid

• Divide and shade shapes to indicate fractions

Directions for Completing the Answer Grids

1. Work the problem and find an answer.

2. Write your answer in the boxes at the top of the grid.

3. Print only one number or symbol in each box. Do not leave a blank box in themiddle of an answer.

4. Under each box, fill in the circle that matches the number or symbol youwrote above. Make a solid mark that completely fills the circle.

5. Do not fill in a circle under an unused box.

6. Fractions cannot be entered into an answer grid and will not be scored. Enterfractions as decimals.

7. See below for examples on how to correctly complete an answer grid.

EXAMPLES

To answer –3 in a question, fill inthe answer grid as shown below.

To answer .75 in a question, fill inthe answer grid as shown below.

OR

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ITEM SET 1 -SECTION 1

(Non-Calculator)Directions:

This Item Set has two sections: a non-calculator section and a calculator section.

You will now take the non-calculator section. You may not use a calculator.

1. What fraction is equivalent to

Enter your answer in the space provided. Enter only your answer.

.0 4?

2. Solve this equation for x.

Enter your answer in the box.

. − = − +x x0 5(5 7 ) 8 (4 6)

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Use the information provided to answer Part A and Part B for question 3.

Three congruent figures are shown on the coordinate plane.

1-1-2-3-4-5-6-7-8-9 20 3 4 5 6 7 8 9

987654321

-1-2-3-4-5-6-7-8-9

x

yy

1

2

3

3. Part A

Circle the correct answer option from each drop-down menu to make thestatement true.

Figure 1 can be transformed onto figure 2 by ____________________________________ ,

followed by ___________________________________.

a reflection across the y-axis

a rotation 90° clockwise about the origin

a translation 3 units to the right

a reflection across the x-axis


a translation 2 units to the left

Part B

Figure 3 can also be created by transforming figure 1 with a sequence oftwo transformations.

Circle the correct answer option from each drop-down menu to make thestatement true.

Figure 1 can be transformed onto figure 3 by ____________________________________ ,

followed by ___________________________________.

a reflection across the x-axis


a translation 3 units to the left

a reflection across the y-axis


a translation 7 units right

4. Which equation has both and as possible values of 4 −4 y?

A

B

C

D

=y 82

=y 83

=y 162

=y 643

5. The equation of line j is .

The equation of line k is .

The equations of lines j and k form a system of equations. The solutionto the system of equations is located at point P.

• Graph the system of equations on the coordinate plane. To grapheach line, plot two points on the grid and draw a line through thepoints.

• Plot point P on the graph. Label point P.

= − +y x2 8

= −y x3 7

-1-2-3-4-5-6-7-8-9-10 0 1 2 3 4 5 6 7 8 9 10x

y

-1-2-3-4-5-6-7-8-9

-10

10

9

8

7

6

5

4

3

2

1

6. Which table represents a non-linear relationship between x and y?

A

B

C

D

x y

0

1

4

9

0

1

2

3

x y

0

8

10

16

–1

3

4

7

x y

3

3

3

3

–3

–2

–1

0

x y

0

5

10

17

0

5

10

17

7. A partially filled input-output table is shown. Complete the table so thatit represents a function.

Write each number from the list in the correct Input or Output box. Useeach number only once.

1

5

4

6

10

Input Output

851

8. The graph shows as a function of

For each interval in the table, place a check mark (✔) in the circle toindicate whether the function is increasing, decreasing, or neitherincreasing nor decreasing over the interval.

y x.

1-1-2-3-4-5-6-7 20 3 4 5 6 7

7654321

-1-2-3-4-5-6

-1-2-3-4-5-6-7

x

y

Interval Increasing Decreasing

7 3− < < −x

3 1− < < −x

1 1− < <x

1 3< <x

3 5< <x

5 7< <x

Neither Increasingnor Decreasing

9.

Seven line segments are shown on the coordinate plane.

Which of these segments could be the image of segment after asequence of reflections, rotations, and/or translations?

Select each correct answer.

1-1-2-3-4-5-6-7-8-9 20 3 4 5 6 7 8 9

987654321

-1-2-3-4-5-6-7-8-9

x

yy

C

D

K

J

A B

E F

H

G

P N

M L

AB

A

B

C

D

E

F

line segment CD

line segment EF

line segment GH

line segment JK

line segment LM

line segment NP


Triangle PQR is shown on the coordinate plane.

Triangle PQR is rotated 90° counterclockwise about the origin to form theimage triangle (not shown). Then triangle is reflected across thex-axis to form triangle (not shown).

10. Part A

What are the signs of the coordinates of point ?

y

x0 1

1234

-4

-3

-2

-1-1-2-3-4 2 3 4

Q

RP

P Q R′ ′ ′ P Q R′ ′ ′P Q R″ ″ ″

x y( , ) P′

Part B

What are the signs of the coordinates of point ?x y( , ) Q″

A

B

C

D

Both and are positive.x y

is negative and is positive.x y

Both and are negative.x y

is positive and is negative.x y

A

B

C

D

Both and are positive.x y

is negative and is positive.x y

Both and are negative.x y

is positive and is negative.x y

11. Which expressions are equivalent to

Select all that apply.

−− ?3 8

3 4

12. A scatter plot is shown on the coordinate plane.

987654321

0 1 2 3 4 5 6 7 8 9

A

B

C

D

E

F

−3 12

3 4−

32

312

314

3112

B

C

987654321

0 1 2 3 4 5 6 7 8 9

987654321

0 1 2 3 4 5 6 7 8 9

D

987654321

0 1 2 3 4 5 6 7 8 9

A

987654321

0 1 2 3 4 5 6 7 8 9

Which of these most closely approximates a line of best fit for the datain the scatter plot?

13. Select a point on the number line that best approximates the location of

Fill in one circle on the number line to plot the point.

10.

3 4 5

This is the end of Item Set 1 Section 1.

ITEM SET 1 -SECTION 2(Calculator)

You may use a calculator for Item Set 1 - Section 2.

14. The number of bottles a machine fills is proportional to the number ofminutes the machine operates. The machine fills 250 bottles every 20 minutes. Create a graph that shows the number of bottles, y, themachine fills in x minutes.

To graph a line, plot two points on the coordinate plane, and then draw aline to connect the points.

175

150

125

100

75

50

25

0

Number of Minutes1 2 3 4

Num

ber

of B

ottles

Fill

ed

5 6 7 8 9x

y

This is the end of Item Set 1 Section 2.

15. A car manufacturer provided information about two different car models.

The graph and table each show a proportional relationship between thenumber of miles traveled and the advertised number of gallons of gasused for the two car models, A and B, respectively. Based on the graphand table, car A can travel how many times the distance car B can travelwhen both cars use 1 gallon of gas? Write your answer as a decimal.


35030025020015010050

0 1 2 3 4 5 6 7 8 9 10 11Gas (gallons)

Dis

tanc

e (m

iles)

Car Ay

x

Car B

Gas(gallons)

Distance(miles)

0

3

5

7

10

0

60

100

140

200

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ITEM SET 2(Calculator)

You may use a calculator for Item Set 2.

1. Line and and are shown on the coordinate plane.

Which statements are true?

Select all that apply.

t ECA FDB

1-1-2-3-4-5-6-7-8-9 20 3 4 5 6 7 8 9

987654321

-1-2-3-4-5-6-7-8-9

x

t

yy

A

FE

BC

D

A

B

C

D

E

F

The slope of is equal to the slope of AC BC.

The slope of is equal to the slope of AC BD.

The slope of is equal to the slope of line AC t.

The slope of line is equal to t .ECAE

The slope of line is equal to t .FBFD

The slope of line is equal to t .AEFD

2. Two utility companies sell electricity in units of kilowatt-hours. The costof electricity for company P is shown in the table. The cost of electricityfor company M can be found by using the equation shown, where yrepresents the total cost in dollars for x kilowatt-hours of electricity.

• Use the information provided to find the unit rate, in dollars perkilowatt-hour, for each company. Show your work or explain youranswers.

• Find the total cost, in dollars, of buying 2,375 kilowatt-hours ofelectricity from the least expensive company.

Enter your answers and your work or explanation in the space provided.

Company P Company M

Electricity Costs

y = 0.15xNumber ofKilowatt-hours

1250

1650

Total Cost(dollars)

150.00

198.00

Use the information provided to answer Part A through Part D for question 3.

At a fall festival, a student council sold two types of drinks: hot chocolate andapple cider. The student council earned $1.25 for every cup of hot chocolate itsold and $0.75 for every cup of apple cider it sold.

There were 375 cups of drinks sold, and the total amount of money earnedfrom selling drinks was $393.75.

The system of equations shown can be used to represent this situation.

3. Part A

What does the variable x represent in this system of equations?

. . .

x y

x y

3751 25 0 75 393 75

+ =+ =

⎧⎨⎪

⎩⎪

Part B

What does the expression represent in this system of equations?y0.75

A

B

C

D

the number of dollars earned from selling one cup of hot chocolate

the number of dollars earned from selling one cup of apple cider

the number of cups of hot chocolate sold

the number of cups of apple cider sold

A

B

C

D

the number of dollars earned from selling one cup of hot chocolate

the number of dollars earned from selling one cup of apple cider

the total number of dollars earned from selling hot chocolate

the total number of dollars earned from selling apple cider

Part C

How many cups of apple cider were sold?

Enter your answer in the box. Your answer must be a whole number or adecimal.

cups of apple cider

Part D

How much money did the student council earn from selling hotchocolate?

Enter your answer in the box. Your answer must be a whole number or adecimal.

$


The figure shows a right-circular cylinder and a right-circular cone. Thecylinder and the cone have the same base and the same height.

4. Part A

What is the volume, in cubic feet, of the cone?

h = 3 ft h = 3 ft

r = 4 ftr = 4 ft

Part B

What is the ratio of the cone′s volume to the cylinder′s volume?

Enter your answer in the box. Enter only your fraction.

A

B

C

D

π12

π16

π36

π48

TURN THE PAGE ANDCONTINUE WORKING


In the coordinate plane shown, triangle is congruent to triangle .

Triangle is similar to triangle .

ABC ′ ′ ′ABC

′ ′ ′ABC ′′ ′′ ′′A B C

10 2 3 4 5 6 7

1234567

-1-2-3-4-5-6-7

-1-2-3-4-5-6-7

A

B

y

x

B” C”

A”

A’

B’ CC’

Part B

Describe a sequence of transformations that shows that triangle is similar to triangle . Include all the necessary information tocomplete each transformation.

Enter your description in the space provided.

′′ ′′ ′′A B C′ ′ ′ABC

5. Part A

Describe a single transformation that shows that triangle iscongruent to triangle . Include all the necessary information tocomplete the transformation.

Enter your description in the space provided.

′ ′ ′ABCABC

This is the end of Item Set 2.

6. The table shows the results of a random survey of students in grade 7and grade 8. Every student surveyed gave a response. Each student wasasked if he or she exercised less than 5 hours last week or 5 or morehours last week.

Based on the results of the survey, which statements are true?

Select each correct statement.

5 or More HoursLess than 5 Hours

A

B

C

D

E

More grade 8 students were surveyed than grade 7 students.

A total of 221 students were surveyed.

Less than 50% of the grade 8 students surveyed exercised 5 or morehours last week.

More than 50% of the students surveyed exercised less than 5 hourslast week.

A total of 107 grade 7 students were surveyed.

ITEM SET 3(Calculator)

You may use a calculator for Item Set 3.

1. Functions W and Z are both linear functions of x.

Which statement comparing the functions is true?

1-1-2-3-4 20 3 4

4

3

2

1

-1-2-3-4

x

yFunction W Function Z

yx

0

2

4

−2 −2.5

−2

−1.5

−1

A

B

C

D

E

F

The slope of Function W is less than the slope of Function Z.

The slope of Function W is greater than the slope of Function Z.

The y-intercept of Function W is equal to the y-intercept of Function Z.

The y-intercept of Function W is less than the y-intercept of Function Z.

The y-value when for Function W is greater than the y-valuewhen for Function Z.

= −x 4= −x 4

The y-value when for Function W is equal to the y-valuewhen for Function Z.

= −x 4= −x 4

Use the information provided to answer Part A through Part C for question 2.

Martin is considering the expressions and .

He wants to know if one expression is greater than the other for all values

of x.

2. Part A

Which statement about the relationship between the expressions is true?

+x(7 48)12 − − + +x x( 3) 4( 5)1

2

A

B

C

D

The value of the expression is always equal to the value

of the expression .

+x(7 48)12

− − + +x x( 3) 4( 5)12

The value of the expression is always less than the value

of the expression .

+x(7 48)12

− − + +x x( 3) 4( 5)12

The value of the expression is always greater than the

value of the expression .

+x(7 48)12

− − + +x x( 3) 4( 5)12

The value of the expression is sometimes greater than

and sometimes less than the value of the expression

.

+x(7 48)12

− − + +x x( 3) 4( 5)12

Part B

Show or explain how you found your answer to Part A.

Enter your work or your explanation in the space provided.

Part C

Write a new expression that always has a greater value than both ofthese expressions.

Enter your expression in the space provided.


A pool cleaning service drained a full pool. The table shows the number ofhours it drained and the amount of water remaining in the pool at that time.

3. Part A

The data suggest a linear relationship between the number of hours thepool had been draining and the number of gallons of water remaining inthe pool. Assuming the relationship is linear, what does the rate ofchange represent in the context of this relationship?

Part B

Which equation describes the relationship between the time elapsed andthe number of gallons of water remaining in the pool?

A

B

C

D

the number of gallons of water in the pool when it is full

the number of gallons of water in the pool after 1 hour

the number of hours it took to drain 1 gallon of water

the number of gallons drained each hour

A

B

C

D

= − +y x600 15,000

= − +y x600 13,200

= − +y x1,200 13,200

= − +y x1,200 15,000


The owner of a computer store is offering a discount on a computer sold inthe store.

4. Part A

The owner offers a payment plan where the total cost of the computer ispaid in 6 equal monthly payments.

• Determine the amount of each monthly payment.

• Show your work or explain your answer.

Enter the monthly payment and your work or explanation in the spaceprovided.

Computer Sale!

Original Price: $598.0025% off original price

8% tax applied after discount

Part B

A different computer is advertised as 40% off of the original price. Afterthe discount, the tax is $44.64.

• Determine the total price of this computer after the discount andtax are applied.


• Determine the original price of this computer.


Enter your answers and your work or explanations in the space provided.

5. The graph of Function 1 is shown on the coordinate plane.

The equations of three other functions are given. Indicate whether theslope of each function is greater than, equal to, or less than the slope ofFunction 1.

Draw a line from each equation to the correct statement.

-1-2-3-4-5-6 0 1 2 3 4 5 6x

y

-1-2-3-4-5-6

6

5

4

3

2

1

Function 1

= +32

6y x= 2y= +3 2y x

Slope of the functionis less than the slope

of Function 1

Slope of the functionis equal to the slope

of Function 1

Slope of the functionis greater than theslope of Function 1


The figure shows line RS parallel to line UV. The lines are intersected by 2 transversals. All lines are in the same plane.

6. Part A

Explain why triangle RTS is similar to triangle VTU.

Enter your explanation in the space provided.

SR

V

T

U

Part B

Given that determine Show yourwork or explain your answer.

Enter your answer and your work or explanation in the space provided.

∠ =m STV 108°, ∠ + ∠m SRT m TUV.

This is the end of Item Set 3.

7. In is perpendicular to The dimensions are shown incentimeters.

What is the length, in centimeters, of


ABC, BD AC.

810

B

DA C

10

AC?

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1119838 ISD319351 2 3 4 5 A B C D E Printed in the USA

grade 8 mathematics · 2019-11-07 · •graph the system of equations on the coordinate plane. to...

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