Select the equation that represents the graph of the line below.

Full text

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1 TEACHER READS:

Read the question to yourself and select the best answer.

Select the equation that represents the graph of the line below.

A. y = x – 1 B.

y =

1 2

x – 1

C.

y =

1 2

x + 2

D. y = x + 2

Master ID: 498921 Revision: 1 Correct: B

Rationale:

A. Student(s) may not have understood that the slope can be multiplied by a number to create a steeper or flatter line.

B. Correct answer

C. Student(s) may have believed that b was the point at which the line crosses the x–axis.

D. Student(s) may not have understood that the slope of the line can be multiplied by a number to make it steeper or flatter.

Student(s) may have believed that b was where the line crossed the x–axis.

Standards:

CCSS.MA.8.8.EE

CCSS.MA.8.8.EE.6

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Read the question to yourself and select the best answer.

A system of two linear equations is shown below.

5x + 2y = –4 5x + 2y = 1

Which statement is true regarding the solution to this system of linear equations?

A. The system has no solution.

B. The system has one unique solution at (5, 2).

C. The system has one unique solution at (–4, 1).

D. The system has an infinite number of solutions.

Master ID: 449878 Revision: 1 Correct: A

Rationale:

A. Correct answer

B. Student(s) may have used the coefficients of x and y in the two equations to form a solution.

C. Student(s) may have used the right sides of the two equations to form a solution.

D. Student(s) may have confused equations of the form ax + by = c and ax + by = d as having an infinite number of solutions, rather than no solution.

Standards:

CCSS.MA.8.8.EE CCSS.MA.8.8.EE.8.b

Read the question to yourself and select the best answer.

What is the product of (8.8 × 10

6

)(5 × 10

2

)?

A. 4.4 × 10

8

B. 4.4 × 10

9

C. 4.4 × 10

12

D. 4.4 × 10

10

Master ID: 433552 Revision: 1 Correct: B

Rationale:

A. Student(s) may not have accounted for the increase of 1 in the exponent when converting 44 to 4.4.

B. Correct answer

C. Student(s) may have multiplied exponents, rather than add the exponents.

D. Student(s) may have multiplied exponents, rather than add the exponents, but correctly accounted for the increase of 1 in the exponent when converting 44 to 4.4.

Standards:

CCSS.MA.8.8.EE

CCSS.MA.8.8.EE.4

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4 TEACHER READS:

Read the question to yourself and select the best answer.

The graph below will allow you to determine the solution to which of these systems of linear equations?

A. –2x + y = –2 –x + y = –4

B. –2x + y = 2 –x + y = 4

C. 2x + y = –2 x + y = –4

D. 2x + y = 2

x + y = 4

Master ID: 182444 Revision: 1 Correct: B

Rationale:

A. Student(s) may have mixed up the signs of the constants on the right sides of the equations.

B. Correct answer

C. Student(s) may have mixed up the signs of the coefficients of the x–terms on the left sides of the equations, and they may have mixed up the signs of the constants on the right sides of the equations.

D. Student(s) may have mixed up the signs of the coefficients of the x–terms on the left sides of the equations.

Standards:

CCSS.MA.8.8.EE CCSS.MA.8.8.EE.8.b

5 TEACHER READS:

Read the question to yourself and select the best answer.

Hannah is at the supermarket to buy carrots and potatoes. If she buys 2 pounds of carrots and 3 pounds of potatoes, it will cost her a total of $8, and if she buys 4 pounds of carrots and 4 pounds of potatoes, it will cost her a total of $13. Which of these statements is correct?

A. Carrots cost $1.50 a pound, which is less than potatoes cost.

B. Carrots cost $1.50 a pound, which is more than potatoes cost.

C. Carrots cost $1.75 a pound, which is less than potatoes cost.

D. Carrots cost $1.75 a pound, which is more than potatoes cost.

Master ID: 179588 Revision: 1 Correct: D

Rationale:

A. Student(s) may have mistakenly attributed the cost per pound of potatoes to carrots, and they may have mistakenly determined that potatoes are more expensive than carrots.

B. Student(s) may have correctly determined that carrots are more expensive than potatoes, but they may have mistakenly attributed the cost per pound of potatoes to carrots.

C. Student(s) may have correctly determined the cost per pound of carrots, but they may have mistakenly determined that potatoes are more expensive than carrots.

D. Correct answer

Standards:

CCSS.MA.8.8.EE

CCSS.MA.8.8.EE.8.c

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Read the question to yourself and select the best answer.

Which of these systems of equations has an infinite number of solutions?

A. –6c + 11d = 20 –6c + 11d = 20

B. –6c + 11d = 20 –5c + 8d = 22

C. –6c + 11d = 22 –5c + 8d = 22

D. –5c + 8d = 20 –5c + 8d = 22

Master ID: 179585 Revision: 1 Correct: A

Rationale:

A. Correct answer

B. Student(s) may have mistakenly reasoned that when the sides of the equations with the variables are different and the sides without the variables are different, the system of equations has an infinite number of solutions.

C. Student(s) may have mistakenly reasoned that when the sides of the equations with the variables are different and the sides without the variables are the same, the system of equations has an infinite number of solutions.

D. Student(s) may have mistakenly reasoned that when the sides of the equations with the variables are the same and the sides without the variables different, the system of equations has an infinite number of solutions.

Standards:

CCSS.MA.8.8.EE CCSS.MA.8.8.EE.8.b

Read the question to yourself and select the best answer.

Is √ 15 located between points M and N on the number line below?

A. No, because it is not greater than 3 and less than 4.

B. No, because it is not greater than 9 and less than 16.

C. Yes, because it is greater than 3 and less than 4.

D. Yes, because it is greater than 9 and less than 16.

Master ID: 179408 Revision: 1 Correct: C

Rationale:

A. Student(s) may have mistakenly determined that

√ 15 is not greater than 3 and less than 4, but they may have correctly determined what this would have meant.

B. Student(s) may have correctly determined that

√ 15 is not greater than 9 and less than 16, but they may have misinterpreted what this means.

C. Correct answer

D. Student(s) may have correctly determined that

√ 15 is between points M and N on the number line, but they may have misidentified the reason why.

Standards:

CCSS.MA.8.8.NS

CCSS.MA.8.8.NS.2

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8 TEACHER READS:

Read the question to yourself and select the best answer.

Travis converted some repeating decimals into fractions as follows. Based upon what he has seen so far, which of the following equations must be correct?

A.

0.9 =

8 9

B.

0.9 =

8 9

C. 0.9 = 1 D. 0.9 = 1

Master ID: 179333 Revision: 1 Correct: D

Rationale:

A. Student(s) may not have noticed that there is no bar above the 9, and they may have then confused 0.9 with 0.8.

B. Student(s) may have confused 0.9 with 0.8

C. Student(s) may not have noticed that there is no bar above the 9.

D. Correct answer

Standards:

CCSS.MA.8.8.NS CCSS.MA.8.8.NS.1

9 TEACHER READS:

Read the question to yourself and select the best answer.

The diameter of a speck of dust is about 0.00002 in.

Which of these is an appropriate estimate for the diameter of the speck of dust?

A. 2 × 10

–5

in.

B. 2 × 10

–4

in.

C. 2 × 10

4

in.

D. 2 × 10

5

in.

Master ID: 179295 Revision: 1 Correct: A

Rationale:

A. Correct answer

B. Student(s) may have counted the number of zeros after the decimal point in 0.00002 and mistakenly assumed that the exponent in the expression should be the additive inverse of this number.

C. Student(s) may have counted the number of zeros after the decimal point in 0.00002 and mistakenly assumed that the exponent in the expression should be this number.

D. Student(s) may have mistakenly made the exponent in the expression the additive inverse of what it should be.

Standards:

CCSS.MA.8.8.EE

CCSS.MA.8.8.EE.3

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Read the question to yourself and select the best answer.

Which of these equations has no solutions?

A. –10 + 8x – 7x + 10 = x + 6 – x – 6

B. 21 – 9 + 4x – 5x = 8x – 7x + 4 + 6

C. x – 4 + 1 – 7x = –8x + 4 + 2x – 7

D. 3x + 5 – 10x + 8 = x – 8x – 16 – 3

Master ID: 179234 Revision: 1 Correct: D

Rationale:

A. Student(s) may have first simplified each side of the equation separately and arrived at x = 0, thinking that the equation x = 0 has 0 solutions.

B. Student(s) may have subtracted 4x from 5x instead of subtracting 5x from 4x on the left side of the equation.

C. Student(s) may have confused an equation that has an infinite number of solutions with an equation that has no solutions.

D. Correct answer

Standards:

CCSS.MA.8.8.EE CCSS.MA.8.8.EE.7.a

Read the question to yourself and select the best answer.

Why does the equation

9 – 2x – 9 – 16x = –14x – 7 – 4x – 11 have no solutions?

A. because if you add 18x to both sides of the equation and simplify, you get –18 = –18

B. because if you add 18x to both sides of the equation and simplify, you get 0 = –18

C. because if you subtract 18x from both sides of the equation and simplify, you get –18 = –18

D. because if you subtract 18x from both sides of the equation and simplify, you get 0 = –18

Master ID: 179221 Revision: 1 Correct: B

Rationale:

A. Student(s) may have mistakenly calculated the equation that would result if 18x were added to both sides, and they may have confused an equation that has an infinite number of solutions with an equation that has no solutions.

B. Correct answer

C. Student(s) may have mistakenly calculated the equation that would result if 18x were subtracted from both sides, in part because they confused adding 18x to both sides of the equation with subtracting 18x from both sides, and they may have confused an equation that has an infinite number of solutions with an equation that has no solutions.

D. Student(s) may have confused the result if 18x were added to both sides of the equation with the result if 18x were subtracted from both sides of the equation.

Standards:

CCSS.MA.8.8.EE

CCSS.MA.8.8.EE.7.a

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12 TEACHER READS:

Read the question to yourself and select the best answer.

A weightlifter is using a weightlifting bar that weighs 45 pounds. If x represents the amount of weight that the weightlifter puts on the bar and y represents the total amount that the weightlifter lifts, with the weight of the bar included, which of these functions models this situation, and why?

A. y = x – 45, because the rate of change of the function should be –45 and the initial value should be 1

B. y = x – 45, because the rate of change of the function should be 1 and the initial value should be –45

C. y = x + 45, because the rate of change of the function should be 1 and the initial value should be 45

D. y = x + 45, because the rate of change of the function should be 45 and the initial value should be 1

Master ID: 176039 Revision: 1 Correct: C

Rationale:

A. Student(s) may have mistakenly determined that the function should be y = x – 45, and they may have misinterpreted the rate of change and the initial value of this incorrect function.

B. Student(s) may have mistakenly determined that the function should be y = x – 45, but they may have correctly interpreted the rate of change and the initial value of this incorrect function.

C. Correct answer

D. Student(s) may have correctly determined that the function should be y = x + 45, but they may have misinterpreted the rate of change and the initial value of this function.

Standards:

CCSS.MA.8.8.F CCSS.MA.8.8.F.4

13 TEACHER READS:

Read the question to yourself and select the best answer.

Natasha got a raise on her hourly wage, and the graph below shows the amount of money she has made this year since her rate of pay was increased. Which of these statements must be correct based on the graph?

A. Before her raise, Natasha made $12.50 an hour.

B. Before her raise, Natasha made $25.00 an hour.

C. After her raise, Natasha makes $12.50 an hour.

D. After her raise, Natasha makes $25.00 an hour.

Master ID: 176029 Revision: 1 Correct: C

Rationale:

A. Student(s) may have confused Natasha's rate of pay after her raise with her rate of pay before her raise.

B. Student(s) may have divided the y–intercept of the graph by 10, since the x–axis is in increments of 10, and mistakenly assumed that this was Natasha's rate of pay before her raise.

C. Correct answer

D. Student(s) may have divided the y–intercept of the graph by 10, since the x–axis is in increments of 10, and mistakenly assumed that this was Natasha's rate of pay after her raise.

Standards:

CCSS.MA.8.8.F

CCSS.MA.8.8.F.4

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Read the question to yourself and select the best answer.

A movie distributor found that the relationship between the amount it spends on advertisements for a particular movie and the amount of money the movie takes in can be modeled by the equation y = 1.2x + 24, where x is the amount spent on advertisements in millions of dollars and y is the amount taken in by the movie in millions of dollars. According to the model, how much should the movie distributor spend on advertisements if it wants the movie to take in $36,000,000?

A. $10,000,000

B. $20,000,000

C. $30,000,000

D. $50,000,000

Master ID: 175947 Revision: 1 Correct: A

Rationale:

A. Correct answer

B. Student(s) may have mistakenly divided the y–

intercept of the model equation by the slope of the model equation to arrive at the answer.

C. Student(s) may have mistakenly divided the amount the movie distributor wants the movie to take in by the slope of the model equation to arrive at the answer.

D. Student(s) may have correctly substituted 36 for y in the model equation to arrive at 36 = 1.2x + 24, but they may have added 24 to 36 instead of subtracting 24 from 36 on the left side of the equation when

eliminating the 24 on the right side of the equation and then solved the equation.

Standards:

CCSS.MA.8.8.SP CCSS.MA.8.8.SP.3

Read the question to yourself and select the best answer.

A hot air balloon was flying at an altitude of 300 meters when the pilot decided to land by descending at a rate of 2 meters per second. For which of these functions does

y represent the altitude of the hot air balloon if x

represents the number of seconds since the pilot started her landing?

A. y = –2x – 300

B. y = –2x + 300

C. y = 2x – 300

D. y = 2x + 300

Master ID: 175946 Revision: 1 Correct: B

Rationale:

A. Student(s) may have correctly made the slope of the model equation negative, but they may have mistakenly also made the y–intercept of the equation negative.

B. Correct answer

C. Student(s) may have mixed up the signs of the slope and y–intercept of the model equation.

D. Student(s) may have correctly made the y–intercept of the model equation positive, but they may have mistakenly also made the slope of the equation positive.

Standards:

CCSS.MA.8.8.F

CCSS.MA.8.8.F.4

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16 TEACHER READS:

Read the question to yourself and select the best answer.

The table of values below shows the amount of water in a watering can and the weight of the can. Based on this information, how much does a gallon of water weigh?

Amount of Water in Can (gallons) Weight of Cans (pounds)

0 2

0.5 6.2

1 10.4

1.5 14.6

2 18.8

A. 4.2 pounds B. 6.2 pounds C. 8.4 pounds D. 10.4 pounds

Master ID: 175937 Revision: 1 Correct: C

Rationale:

A. Student(s) may have confused the weight of the watering can when it contains a half–gallon of water with the weight of the can when it contains a gallon of water, but they may have then correctly subtracted the weight of the can.

B. Student(s) may have confused the weight of the watering can when it contains a half–gallon of water with the weight of the can when it contains a gallon of water, and they may have then forgotten to subtract the weight of the can.

C. Correct answer

D. Student(s) may have correctly determined the weight of the watering can when it contains a gallon of water, but they may have then forgotten to subtract the weight of the can.

Standards:

CCSS.MA.8.8.F

CCSS.MA.8.8.F.4

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Read the question to yourself and select the best answer.

Which of these functions has a greater rate of change than the function graphed below, and why?

A. y = 2x + 12, because the rate of change of the graphed function is 3

B. y = 2x + 12, because the rate of change of the graphed function is 9

C. y = 10x + 1, because the rate of change of the graphed function is 3

D. y = 10x + 1, because the rate of change of the graphed function is 9

Master ID: 175896 Revision: 1 Correct: C

Rationale:

A. Student(s) may have correctly determined the rate of change of the graphed function, but they may have mistakenly compared the rate of change to the y–

intercept of the function y = 2x + 12.

B. Student(s) may have incorrectly determined the rate of change of the graphed function by not realizing that the ticks on the x–axis each represent 3 units, and they may have mistakenly compared the rate of change to the y–intercept of the function y = 2x + 12.

C. Correct answer

D. Student(s) may have incorrectly determined the rate of change of the graphed function by not realizing that the ticks on the x–axis each represent 3 units.

Standards:

CCSS.MA.8.8.F CCSS.MA.8.8.F.2

Read the question to yourself and select the best answer.

Olivia added the linear equations –4x + 9y = 19 and 5x – 9y = –17 together and got x = 2. She then

substituted the value of x back into one of the equations and simplified to get y = 3. How many solutions are there to the system of equations?

A. 0 B. 1 C. 2 D. 3

Master ID: 170985 Revision: 1 Correct: B

Rationale:

A. Student(s) may have mistakenly concluded that since the terms with y in them drop out when the two equations are added together, the system of equations has no solution.

B. Correct answer

C. Student(s) may have mistakenly chosen the value of x as the number of solutions to the system of equations.

D. Student(s) may have mistakenly chosen the value of y as the number of solutions to the system of equations.

Standards:

CCSS.MA.8.8.EE

CCSS.MA.8.8.EE.7.a

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19 TEACHER READS:

Read the question to yourself and select the best answer.

Suppose that a number written as a decimal has an infinite number of non–repeating digits after the decimal point. What is this number called?

A. irrational B. natural C. rational D. unnatural

Master ID: 170257 Revision: 1 Correct: A

Rationale:

A. Correct answer

B. Student(s) may have confused a positive number that has no digits after the decimal point with a positive number that has an infinite number of non–repeating digits after the decimal point.

C. Student(s) may have confused a number that can be written with a finite number of digits after the decimal point with a number that has an infinite number of non–repeating digits after the decimal point.

D. Student(s) may have mistakenly concluded that since a number with an infinite number of non–repeating digits after the decimal point is not natural, it must be the opposite of natural.

Standards:

CCSS.MA.8.8.NS CCSS.MA.8.8.NS.1

20 TEACHER READS:

Read the question to yourself and select the best answer.

What is the distance between the points (10, 12) and (–4, –36)?

A. 14 units B. 22 units C. 48 units D. 50 units

Master ID: 169974 Revision: 1 Correct: D

Rationale:

A. Student(s) may have confused the horizontal distance between the points with the straight–line distance between the points.

B. Student(s) may have mistakenly added the x– and y–

coordinates of the first point to arrive at the answer.

C. Student(s) may have confused the vertical distance between the points with the straight–line distance between the points.

D. Correct answer

Standards:

CCSS.MA.8.8.G

CCSS.MA.8.8.G.8

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Read the question to yourself and select the best answer.

Which relation is a not function?

A. {(2, 3), (4, 5), (10, 12), (15, 16)}

B. {(-5, 20), (6, 13), (8, 20), (11, 8)}

C. {(0, 8), (0, -4), (7, 4), (12, 1)}

D.

{(4,

1 4

), (9,

1 9

), (17,

1 17

), (18,

1 18

)}

Master ID: 43806 Revision: 1 Correct: C

Rationale:

A. Student(s) may have chosen this option because (10, 12) doesn't follow the y = x + 1 rule implied by the other three points.

B. Student(s) may have believed the same y–value could not be paired with different x–values.

C. Correct answer

D. Student(s) may have believed both coordinates must be integers.

Standards:

CCSS.MA.8.8.F CCSS.MA.8.8.F.1

Read the question to yourself and select the best answer.

Which equation is equivalent to 3 + 5(x + 2) = 12?

A. 8x + 16 = 12

B. 8x + 2 = 12

C. 5x + 5 = 12

D. 5x + 13 = 12

Master ID: 43210 Revision: 1 Correct: D

Rationale:

A. Student(s) may have combined 3 and 5 before distributing.

B. Student(s) may have combined the 3 and 5 and not distributed that any value to the 2.

C. Student(s) may have forgotten to distribute the 5 to the 2.

D. Correct answer

Standards:

CCSS.MA.8.8.EE CCSS.MA.8.8.EE.7.b

23 TEACHER READS:

Read the question to yourself and select the best answer.

Which value of x will make this expression true?

7

5

• 7

x

= 7

15

A. 3 B. 4

C. 10

D. 20

Master ID: 42235 Revision: 1 Correct: C

Rationale:

A. Student(s) solved as though an exponent were being placed on an already exponentiated number instead of multiplying the two exponentiated numbers.

B. Student(s) did not know how to proceed with the

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24 TEACHER READS:

Read the question to yourself and select the best answer.

Which scatterplot shows a positive correlation?

A.

B.

C.

D.

Master ID: 37190 Revision: 1 Correct: C

Rationale:

A. Student(s) may have misunderstood what it meant for two values to have a positive correlation and chosen this option because the all the data points have positive coordinates and because the point with the least y–value is on the left side of the graph and the point with the greatest y–value is on the right side.

B. Student(s) may have confused positive and negative correlations.

C. Correct answer

D. Student(s) may have believed "positive correlation" meant the data points were widely dispersed.

(14)

Read the question to yourself and select the best answer.

Simplify:

(4x

2

y)(4x

2

y)

A. 8x

4

y

B. 8x

4

y

2

C. 16x

4

y

D. 16x

4

y

2

Master ID: 30744 Revision: 2 Correct: D

Rationale:

A. Student(s) may have added the constants and ignored the implied power of 1.

B. Student(s) may have added the constants.

C. Student(s) may have mishandled the implied powers of 1 for y.

D. Correct answer

Standards:

CCSS.MA.8.8.EE CCSS.MA.8.8.EE.1

Read the question to yourself and select the best answer.

Matthew must solve the following question on a quiz.

Leah has 4 times as many nickels as she has dimes. All together, her nickels and dimes have a value of $1.20.

How many of each coin does she have?

Which of the following systems of equations can he use to answer this question if n represents the number of nickels and d represents the number of dimes?

A. n = 4d

n + d = 120

B. d = 4n

n + d = 120

C. n = 4d

5n + 10d = 120

D. d = 4n

5n + 10d = 120

Master ID: 24706 Revision: 1 Correct: C

Rationale:

A. Student(s) may have forgotten to use the values of the coins as coefficients in the second equation.

B. Student(s) may have incorrectly modeled the phrase "4 times as many nickels as dimes" and forgotten to use the values of the coins as coefficients in the second equation.

C. Correct answer

D. Student(s) may have incorrectly modeled the phrase "4 times as many nickels as dimes."

Standards:

CCSS.MA.8.8.EE

CCSS.MA.8.8.EE.8.a

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27 TEACHER READS:

Read the question to yourself and select the best answer.

Rick is using the substitution method to solve the system.

5x – 2y = –11 x + 3y = 20

Which of the following equations can he create from this system?

A. 5x – 2y = x + 3y

B. 5x – 2(20 – x) = –11

C. 5(20 – 3y) – 2y = –11

D. 20 – 3y – 2y = –11

Master ID: 24692 Revision: 1 Correct: C

Rationale:

A. Student(s) may have previously used the substitution method with equations written in slope–intercept form and believed the correct use of this strategy always involved replacing the right side of one equation with the left side of another.

B. Student(s) may have incorrectly solved for y in the second equation prior to substituting.

C. Correct answer

D. Student(s) may have incorrectly replaced the entire x–

term in the first equation, having forgotten to keep the coefficient.

Standards:

CCSS.MA.8.8.EE CCSS.MA.8.8.EE.8.a

28 TEACHER READS:

Read the question to yourself and select the best answer.

Evaluate:

5

0

• 5

2

A. 0

B. 10

C. 25

D. 625

Master ID: 22219 Revision: 1 Correct: C

Rationale:

A. Student(s) may have thought a zero exponent equaled zero.

B. Student(s) may have multiplied instead of simplifying the exponent.

C. Correct answer

D. Student(s) may have multiplied the bases before adding the powers.

Standards:

CCSS.MA.8.8.EE

CCSS.MA.8.8.EE.1

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Read the question to yourself and select the best answer.

Which of the following has the GREATEST value?

A. 2

–3

B. 3

–2

C.

1

2–3

D.

1

3–2

Master ID: 21697 Revision: 1 Correct: D

Rationale:

A. Student(s) may have made computational errors when evaluating the expressions and believed this had the greatest value.

B. Student(s) may have understood that the negative power moved the value into the denominator but also believed the negative stayed as part of the value and chosen this because –1/9 was the greatest of the values they obtained.

C. Student(s) may have made known 1/8 was greater than 1/9 and mistakenly arrived at the conclusion that

1

1 8

was greater than

1

1 9

.

D. Correct answer

Standards:

CCSS.MA.8.8.EE CCSS.MA.8.8.EE.1

Read the question to yourself and select the best answer.

Which pair of lines will intersect at the origin?

A. y = 2

y = 3

B. y = 2x

y = 3x

C. x = 2

y = 3

D. None of these systems represent lines that intersect at the origin.

Master ID: 18140 Revision: 1 Correct: B

Rationale:

A. Student(s) may have misunderstood the phrase

"intersect at the origin" or not recognized this system shows parallel vertical lines which never intersect.

B. Correct answer

C. Student(s) may not have recognized this system shows perpendicular lines which intersect at (2 , 3).

D. Student(s) may have believed that the system would have to use equations with 0's in them or misevaluated the correct answer, Option B.

Standards:

CCSS.MA.8.8.EE

CCSS.MA.8.8.EE.8.a

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31 TEACHER READS:

Read the question to yourself and select the best answer.

Simplify the expression:

–4(3x + 2y) + 6(–2x – 5y)

A. –62xy B. –24x – 3y C. –24x + 13y D. –24x – 38y

Master ID: 10683 Revision: 1 Correct: D

Rationale:

A. Student(s) may have combined the unlike terms within the parentheses prior to multiplication and combining like terms.

B. Student(s) may not have applied the distribution property prior to combining like terms.

C. Student(s) may not have multiplied the negative signs on the y terms correctly.

D. Correct answer

Standards:

CCSS.MA.8.8.EE CCSS.MA.8.8.EE.7.b

32 TEACHER READS:

Read the question to yourself and select the best answer.

Which set of ordered pairs below is a function?

I. {(3 , 3), (6 , 1), (2 , 3)}

II. {(4 , 7), (2 , 8), (4 , 2)}

III. {(9 , 6), (3 , 1), (7 , 3)}

A. I only B. II only C. III only D. I and III

Master ID: 764 Revision: 1 Correct: D

Rationale:

A. Student(s) may not have considered all options and may not have realized that there is another function.

B. Student(s) may have misunderstood the question and identified the only set of ordered pairs that is NOT a function.

C. Student(s) may have recognized III was a function and mistakenly believed it was not because the number 3 is used twice as a y–value.

D. Correct answer

Standards:

CCSS.MA.8.8.F

CCSS.MA.8.8.F.1

(18)

Read the question to yourself and select the best answer.

How could you convert 0.123 into a fraction?

A. Subtract the equation x = 0.123 from the equation 100x = 12.3 and solve for x.

B. Subtract the equation x = 0.123 from the equation 1000x = 123.3 and solve for x.

C. Subtract the equation 10x = 1.23 from the equation 100x = 12.3 and solve for x.

D. Subtract the equation 100x = 12.3 from the equation 1000x

= AD 123.3 and solve for x.

Master ID: 182482 Revision: 1 Correct: D

Rationale:

A. Student(s) may not have realized that another one of the steps is multiplying both sides of the equation x = 0.123 by 1000.

B. Student(s) may have correctly recognized that one of the steps in converting 0.123 to a fraction is multiplying both sides of the equation x = 0.123 by 100.

C. Student(s) may have correctly recognized that both sides of the equation x = 0.123 must be multiplied by a constant to get one equation, and then both sides of the equation x = 0.123 must be multiplied by a different constant to get another equation, but they may have been off by a factor of 10 with the constant each time.

D. Correct answer

Standards:

CCSS.MA.8.8.NS CCSS.MA.8.8.NS.1

Read the question to yourself and select the best answer.

Which of these cylinders has a height that is equal to the length of its radius?

A. A cylinder with a volume of 16 π in

3

and a height of 2 in.

B. A cylinder with a volume of 27 π in

3

and a height of 3 in.

C. A cylinder with a volume of 34 π in

3

and a height of 8 in.

D. A cylinder with a volume of 72 π in

3

and a height of 6 in.

Master ID: 182457 Revision: 1 Correct: B

Rationale:

A. Student(s) may have mistakenly used the formula V = π r

3

h for the volume of a cylinder.

B. Correct answer

C. Student(s) may have mistakenly used the formula V = π rh for the volume of a cylinder.

D. Student(s) may have mistakenly used the formula V = 1/3 π r

2

h for the volume of a cylinder.

Standards:

CCSS.MA.8.8.G

CCSS.MA.8.8.G.9

(19)

35 TEACHER READS:

Read the question to yourself and select the best answer.

The volume of a cone with a height of 6 cm is 18 π cm

3

. If the cone's radius increases by 3 cm, by how much will the cone's volume increase?

A. by 9 π cm

3

B. by 27 π cm

3

C. by 54 π cm

3

D. by 72 π cm

3

Master ID: 182441 Revision: 1 Correct: C

Rationale:

A. Student(s) may have mistakenly chose the amount by which the cone's volume increases if the height, and not the radius, increases by 3 cm.

B. Student(s) may have mistakenly chosen the volume of the cone when the height increases by 3 cm instead of the amount by which the cone's volume increases when the radius increases by 3 cm.

C. Correct answer

D. Student(s) may have mistakenly chosen the volume of the cone when the radius increases by 3 cm instead of the amount by which the cone's volume increases when the radius increases by 3 cm.

Standards:

CCSS.MA.8.8.G CCSS.MA.8.8.G.9

36 TEACHER READS:

Read the question to yourself and select the best answer.

Suppose a pentagon graphed on a coordinate plane will undergo a dilation. Which of these is a true statement?

A. The resulting pentagon will be similar to the original pentagon only if the center of the dilation is the origin.

B. The resulting pentagon will be similar to the original pentagon only if the center of the dilation is a vertex of the original pentagon.

C. The resulting pentagon will be similar to the original pentagon regardless of the center of the dilation.

D. The resulting pentagon will not be similar to the original pentagon regardless of the center of the dilation.

Master ID: 91393 Revision: 1 Correct: C

Rationale:

A. Student(s) may have incorrectly determined that the center of the dilation matters, and they may have mistakenly concluded that the center must be the origin in order for the original and resulting pentagons to be similar.

B. Student(s) may have incorrectly determined that the center of the dilation matters, and they may have mistakenly concluded that the center must be a vertex in order for the original and resulting pentagons to be similar.

C. Correct answer

D. Student(s) may have correctly determined that the center of the dilation does not matter, but they may have misidentified the effect of the dilation on the similarity of the original and resulting pentagons.

Standards:

CCSS.MA.8.8.G

CCSS.MA.8.8.G.4

(20)

Read the question to yourself and select the best answer.

Simplify:

54 • 8–6 • 9–12 5–2 • 83 • 9–4

A.

52

83 • 916

B.

93

52 • 82

C.

56

89 • 98

D.

58

818 • 93

Master ID: 22747 Revision: 1 Correct: C

Rationale:

A. Student(s) may have added the powers of the exponents with the same base together instead of subtracting them.

B. Student(s) may have divided the powers of the exponents with the same base instead of subtracting them.

C. Correct answer

D. Student(s) may have placed terms in the numerator with negative exponents in the denominator and terms in the denominator with negative exponents in the

numerator (

5

4 • 52 • 94 83 • 86 • 912

), and then multiplied or

divided the powers of the terms with a common base instead of adding them.

Standards:

CCSS.MA.8.8.EE CCSS.MA.8.8.EE.1

Read the question to yourself and select the best answer.

Which pair of equations would represent lines that are PERPENDICULAR to each other?

I. 3x – 2y = 12 II. 3x + 2y = –12 III. 2x – 3y = –12

A. I and II B. II and III C. I and III

D. None of these lines are perpendicular to each other.

Master ID: 17085 Revision: 1 Correct: B

Rationale:

A. Student(s) may have remembered that perpendicular lines have opposite slopes but forgotten about them also being reciprocals. Student(s) may have answered the question without changing the equations to slope- intercept form.

B. Correct answer

C. Student(s) may have remembered that perpendicular lines have reciprocal slopes but forgotten about them also being opposites.

D. Student(s) may not have incorrectly calculated the slopes of one or more lines.

Standards:

CCSS.MA.9-12.G-GPE.5

(21)

39 TEACHER READS:

Read the question to yourself and select the best answer.

Look at Triangle QRS and Triangle Q'R'S' on the coordinate plane.

Which transformation performed on Triangle QRS will produce the image of Triangle Q'R'S'?

A. a translation of 6 units to the right

B. a clockwise rotation of 90 degrees about the origin

C. a reflection over the x–axis

D. a reflection over the y–axis

Master ID: 33453 Revision: 1 Correct: D

Rationale:

A. Student(s) may have focused on the positions of points along the top of the triangle (Q, R, Q', and R').

B. Student(s) may have had a sense of the approximate location where the image Q'R'S' would fall (in quadrant 1) but not realized the orientation and relative position of the points would be different.

C. Student(s) may have confused which axis was reflected over: choosing the x–axis because there is a

40 TEACHER READS:

Read the question to yourself and select the best answer.

Which of the following graphs represents a proportional relationship?

A.

B.

C.

D.

(22)

Correct: B Rationale:

A. Student(s) may have noticed that the graph goes through the origin (0, 0) and that y is 1 bigger than x each time and assumed it's a proportional relationship.

B. Correct answer

C. Student(s) may have noticed that y is 3 larger than x each time, but did not realize that the graph needs to go through the origin (0, 0) in order to be proportional.

D. Student(s) may have noticed that the graph is linear and assumed that all linear relationships are also proportional relationships.

Standards:

CCSS.MA.7.7.RP.2.a

Figure

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References

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