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Common Core: 8th Grade Math : Grade 8

Study concepts, example questions & explanations for Common Core: 8th Grade Math

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All Common Core: 8th Grade Math Resources

7 Diagnostic Tests 75 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #11 : Understand Functions: Ccss.Math.Content.8.F.A.1

Select the table that properly represents a function.

Possible Answers:

Screen shot 2016 03 14 at 9.47.13 am

Screen shot 2016 03 14 at 9.44.41 am

Screen shot 2016 03 14 at 9.45.26 am

Screen shot 2016 03 14 at 9.44.51 am

Correct answer:

Screen shot 2016 03 14 at 9.44.41 am

Explanation:

Each of the tables provided contains sets of ordered pairs. The input column represents the x-variables, and the output column represents the y-variables. We can tell if a set of ordered pairs represents a function when we match x-values to y-values.

In order for a table to represents a function, there must be one and only one input for every output. This means that our correct answer will have all unique input values:

Screen shot 2016 03 14 at 9.44.41 am

Functions cannot have more than one input value that is the same; thus, the following tables do not represent a function:

Screen shot 2016 03 14 at 9.45.07 am

Screen shot 2016 03 14 at 9.45.40 am

Screen shot 2016 03 14 at 9.47.29 am

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Example Question #1 : Compare Properties Of Two Functions: Ccss.Math.Content.8.F.A.2

The table and the equation provided represent two different functions. Which of these two functions—either table or equation form—has the greater rate of change, and what is the rate of change?

Screen shot 2016 03 14 at 8.52.05 am

y=2x+15

Possible Answers:

$\textup{Equation, }4$

$\textup{Table, }2$

$\textup{Equation, }2$

$\textup{Table, }3$

Correct answer:

$\textup{Table, }3$

Explanation:

The rate of change is also known as the slope. As we have learned we can use the following equation to solve for the slope of the table:

$\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

An input/output table displays sets of ordered pairs. The input column represents the x-values and the output column represents the y-values. We can select two sets of ordered pairs from the table to solve for the slope:

$\frac{12-3}{4-1}=\frac{9}{3}=3$

The slope for our table is

In order to determine the slope of the equation, we need to make sure the equation is in slope-intercept form:

y=mx+b

In this equation, the variables and are defined as the following:

$\textup{m=slope}$

$\textup{b=y-intercept}$

The given formula for this problem was provided in slope-intercept form; thus, the slope for the equation is

The function with the greatest rate of change will possess the greatest slope. In this case, the greater slope is , which was displayed in the function written in table form; thus, the following answer is correct:

$\textup{Table, }3$

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Example Question #2 : Compare Properties Of Two Functions: Ccss.Math.Content.8.F.A.2

The table and the equation provided represent two different functions. Which of these two functions—either table or equation form—has the greater rate of change, and what is the rate of change?

Screen shot 2016 03 14 at 9.44.41 am

y=3x-1

Possible Answers:

$\textup{Equation, }2$

$\textup{Table, }5$

$\textup{Table, }3$

$\textup{Equation, }3$

Correct answer:

$\textup{Equation, }3$

Explanation:

The rate of change is also known as the slope. As we have learned we can use the following equation to solve for the slope of the table:

$\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$\frac{30-10}{15-5}=\frac{20}{10}=2$

The slope for our table is

In order to determine the slope of the equation, we need to make sure the equation is in slope-intercept form:

y=mx+b

In this equation, the variables and are defined as the following:

$\textup{m=slope}$

$\textup{b=y-intercept}$

The given formula for this problem was provided in slope-intercept form; thus, the slope for the equation is

The function with the greatest rate of change will possess the greatest slope. In this case, the greater slope is , which was displayed in the function written in equation form; thus, the following answer is correct:

$\textup{Equation, }3$

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Example Question #3 : Compare Properties Of Two Functions: Ccss.Math.Content.8.F.A.2

The table and the equation provided represent two different functions. Which of these two functions—either table or equation form—has the greater rate of change, and what is the rate of change?

Screen shot 2016 03 14 at 11.40.24 am

y=4x+12

Possible Answers:

$\textup{Table, }5$

$\textup{Equation, }2$

$\textup{Table, }10$

$\textup{Equation, }4$

Correct answer:

$\textup{Table, }5$

Explanation:

The rate of change is also known as the slope. As we have learned we can use the following equation to solve for the slope of the table:

$\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$\frac{9-(-1)}{3-1}=\frac{10}{2}=5$

The slope for our table is

In order to determine the slope of the equation, we need to make sure the equation is in slope-intercept form:

y=mx+b

In this equation, the variables and are defined as the following:

$\textup{m=slope}$

$\textup{b=y-intercept}$

The given formula for this problem was provided in slope-intercept form; thus, the slope for the equation is

$\textup{Table, }5$

Report an Error

Example Question #4 : Compare Properties Of Two Functions: Ccss.Math.Content.8.F.A.2

The table and the equation provided represent two different functions. Which of these two functions—either table or equation form—has the greater rate of change, and what is the rate of change?

Screen shot 2016 03 14 at 11.50.11 am

y=x+9

Possible Answers:

$\textup{Equation, }1$

$\textup{Table, }\frac{1}{3}$

$\textup{Equation, }2$

$\textup{Table, }1$

Correct answer:

$\textup{Equation, }1$

Explanation:

The rate of change is also known as the slope. As we have learned we can use the following equation to solve for the slope of the table:

$\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$\frac{5-4}{6-3}=\frac{1}{3}$

The slope for our table is $\frac{1}{3}$

In order to determine the slope of the equation, we need to make sure the equation is in slope-intercept form:

y=mx+b

In this equation, the variables and are defined as the following:

$\textup{m=slope}$

$\textup{b=y-intercept}$

The given formula for this problem was provided in slope-intercept form; thus, the slope for the equation is

$\textup{Equation, }1$

Report an Error

Example Question #261 : Grade 8

The table and the equation provided represent two different functions. Which of these two functions—either table or equation form—has the greater rate of change, and what is the rate of change?

Screen shot 2016 03 14 at 12.03.31 pm

y=2x+18

Possible Answers:

$\textup{Table, }6$

$\textup{Equation, }2$

$\textup{Table, }4$

$\textup{Equation, }4$

Correct answer:

$\textup{Table, }4$

Explanation:

The rate of change is also known as the slope. As we have learned we can use the following equation to solve for the slope of the table:

$\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$\frac{4-0}{5-4}=\frac{4}{1}=4$

The slope for our table is

In order to determine the slope of the equation, we need to make sure the equation is in slope-intercept form:

y=mx+b

In this equation, the variables and are defined as the following:

$\textup{m=slope}$

$\textup{b=y-intercept}$

The given formula for this problem was provided in slope-intercept form; thus, the slope for the equation is

$\textup{Table, }4$

Report an Error

Example Question #6 : Compare Properties Of Two Functions: Ccss.Math.Content.8.F.A.2

The table and the equation provided represent two different functions. Which of these two functions—either table or equation form—has the greater rate of change, and what is the rate of change?

Screen shot 2016 03 14 at 11.50.11 am

y=3x-9

Possible Answers:

$\textup{Equation, }3$

$\textup{Equation, }2$

$\textup{Table, }6$

$\textup{Table, }4$

Correct answer:

$\textup{Equation, }3$

Explanation:

The rate of change is also known as the slope. As we have learned we can use the following equation to solve for the slope of the table:

$\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$\frac{5-4}{6-3}=\frac{1}{3}$

The slope for our table is $\frac{1}{3}$

In order to determine the slope of the equation, we need to make sure the equation is in slope-intercept form:

y=mx+b

In this equation, the variables and are defined as the following:

$\textup{m=slope}$

$\textup{b=y-intercept}$

The given formula for this problem was provided in slope-intercept form; thus, the slope for the equation is

$\textup{Equation, }3$

Report an Error

Example Question #7 : Compare Properties Of Two Functions: Ccss.Math.Content.8.F.A.2

The table and the equation provided represent two different functions. Which of these two functions—either table or equation form—has the greater rate of change, and what is the rate of change?

Screen shot 2016 03 14 at 1.11.15 pm

y=6x+2

Possible Answers:

$\textup{Table, }5$

$\textup{Equation, }6$

$\textup{Equation, }7$

$\textup{Table, }7$

Correct answer:

$\textup{Table, }7$

Explanation:

The rate of change is also known as the slope. As we have learned we can use the following equation to solve for the slope of the table:

$\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$\frac{15-8}{5-4}=\frac{7}{1}=7$

The slope for our table is

In order to determine the slope of the equation, we need to make sure the equation is in slope-intercept form:

y=mx+b

In this equation, the variables and are defined as the following:

$\textup{m=slope}$

$\textup{b=y-intercept}$

The given formula for this problem was provided in slope-intercept form; thus, the slope for the equation is

$\textup{Table, }7$

Report an Error

Example Question #8 : Compare Properties Of Two Functions: Ccss.Math.Content.8.F.A.2

The table and the equation provided represent two different functions. Which of these two functions—either table or equation form—has the greater rate of change, and what is the rate of change?

Screen shot 2016 03 14 at 1.50.59 pm

y=9x+15

Possible Answers:

$\textup{Equation, }9$

$\textup{Table, }10$

$\textup{Equation, }6$

$\textup{Table, }6$

Correct answer:

$\textup{Equation, }9$

Explanation:

The rate of change is also known as the slope. As we have learned we can use the following equation to solve for the slope of the table:

$\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$\frac{9-3}{3-2}=\frac{6}{1}=6$

The slope for our table is

In order to determine the slope of the equation, we need to make sure the equation is in slope-intercept form:

y=mx+b

In this equation, the variables and are defined as the following:

$\textup{m=slope}$

$\textup{b=y-intercept}$

The given formula for this problem was provided in slope-intercept form; thus, the slope for the equation is

The function with the greatest rate of change will possess the greatest slope. In this case, the greater slope is , which was displayed in the equation written in table form; thus, the following answer is correct:

$\textup{Equation, }9$

Report an Error

Example Question #9 : Compare Properties Of Two Functions: Ccss.Math.Content.8.F.A.2

The table and the equation provided represent two different functions. Which of these two functions—either table or equation form—has the greater rate of change, and what is the rate of change?

Screen shot 2016 03 14 at 1.54.16 pm

y=4x+15

Possible Answers:

$\textup{Table, }5$

$\textup{Equation, }10$

$\textup{Table, }10$

$\textup{Equation, }5$

Correct answer:

$\textup{Table, }5$

Explanation:

The rate of change is also known as the slope. As we have learned we can use the following equation to solve for the slope of the table:

$\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$\frac{62-37}{10-5}=\frac{25}{5}=5$

The slope for our table is

In order to determine the slope of the equation, we need to make sure the equation is in slope-intercept form:

y=mx+b

In this equation, the variables and are defined as the following:

$\textup{m=slope}$

$\textup{b=y-intercept}$

The given formula for this problem was provided in slope-intercept form; thus, the slope for the equation is

$\textup{Table, }5$

Report an Error

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All Common Core: 8th Grade Math Resources

7 Diagnostic Tests 75 Practice Tests Question of the Day Flashcards Learn by Concept

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Common Core: 8th Grade Math : Grade 8

Study concepts, example questions & explanations for Common Core: 8th Grade Math

All Common Core: 8th Grade Math Resources

Example Questions

Example Question #11 : Understand Functions: Ccss.Math.Content.8.F.A.1

Example Question #1 : Compare Properties Of Two Functions: Ccss.Math.Content.8.F.A.2

Example Question #2 : Compare Properties Of Two Functions: Ccss.Math.Content.8.F.A.2

Example Question #3 : Compare Properties Of Two Functions: Ccss.Math.Content.8.F.A.2

Example Question #4 : Compare Properties Of Two Functions: Ccss.Math.Content.8.F.A.2

Example Question #261 : Grade 8

Example Question #6 : Compare Properties Of Two Functions: Ccss.Math.Content.8.F.A.2

Example Question #7 : Compare Properties Of Two Functions: Ccss.Math.Content.8.F.A.2

Example Question #8 : Compare Properties Of Two Functions: Ccss.Math.Content.8.F.A.2

Example Question #9 : Compare Properties Of Two Functions: Ccss.Math.Content.8.F.A.2

All Common Core: 8th Grade Math Resources

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