IAR Grade 8: Math - In progress! - Sara Cowley | Library

1

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

Utilize the drawing tools in the Show Your Work space to plot two points and draw a line.
[Calculator permitted]

1

Two different proportional relationships are represented by the equation and the table.

Use the drop-down menus to complete the sentence comparing the rates of change of the proportional relationships.

The rate of change in Proportion A is __________ __________ than the rate of change in Proportion B.
[Calculator permitted]

1

Eric planted a seedling in his garden and recorded its height each week. The equation shown can be used to estimate the height, h, in inches, of the seedling by the end of each week, w, after it was planted.
[Calculator permitted]

Part A
What does the slope of the graph of the equation h=\frac{3}{4}w+\frac{9}{4} represent? Choose from the answers below and enter the letter in the box: _______ 
a. the height, in inches, of the seedling after w weeks
b. the height, in inches, of the seedling with Eric first planted it
c. the increase in the height, in inches, of the seedling each week
d. the total increase in the height, in inches, of the seedling after w weeks

Part B
The equation h=\frac{3}{4}w+\frac{9}{4} estimates the height of the seedling to be 8.25 inches after how many weeks? Enter your answer in the box: _______ 

1

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

Input                        Output
   1                                  4
__________          6
   5                          __________ 
__________  __________ 

Select each number from the list within each dropdown.

1

Solve this equation for x.

0.5(5-7x)=8-(4x+6)

1

The graph shows y as a function of x.

For each interval in the table, indicate whether the function is increasing, decreasing, or neither increasing nor decreasing over the interval.

1

Select the point on the number line that best approximates the location of \sqrt{14}.
[vertical positioning of the points are irrelevant]

1

Functions A, B, and C are linear functions.
Some values of Function A are shown in the table.
The graph of Function B has a y-intercept of (0,3) and an x-intercept of (-5,0).
Function C is defined by the equation y=(3x+1).

Order the linear functions based on rate of change, from least to greatest:
[Calculator permitted]

Least Rate of Change _______________ 
Neither Least or Greatest Rate of Change _______________ 
Greatest Rate of Change ______________________ 

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

1

A system of equations is shown.

x=10\\ 3x+5y=20

What is the solution (x,y) of the system of equations?
Enter your answers in the boxes.
(_______ ,_______ )

1

Classify each equation as defining y as a linear or nonlinear function of x.
Drag or click the equation into the appropriate category.

y=7\times{4x}
y=(2x+5)^2
y=10x^2
y=5x-3
y=\frac{x}{2}
y=2x^{3}+1

linear
nonlinear

1

Consider the system of equations.

y=2x+2\\y=6x+2

Select from the drop-down menus to correctly complete each statement.
The graph of the system consists of lines that have __________ of intersection. Therefore, the system has __________ solution.

1

Which of these equations represent functions where x is the input and y is the output? Select each correct answer.

1

Solve this equation for x.
0.5(5-7x)=8-(4x+6)

1

Three congruent figures are shown on the coordinate plane.
Part A
Select a transformation from each drop-down menu to make the statement true.
Figure 1 can be transformed onto figure 2 by __________, followed by __________.

Part B
Figure 3 can also be created by transforming figure 1 with a sequence of two transformations.
Select a transformation from each drop-down menu to make the statement true.
Figure 1 can be transformed onto figure 3 by __________, followed by __________.

1

The graph represents y as a function of x. Place one additional point on the coordinate plane so that the graph continues to represent y as a function of x.

Use the drawing tools in the Show Your Work space to plot the point on the coordinate plane.

1

The graph shows y as a function of x.

For which intervals is the function decreasing?
Select all that apply.

1

The equation of line s is y=\frac{1}{3}x-3.
The equation of line t is y=-x+5.
The equations of lines s and t form a system of equations. The solution to the system of equations is located at point P.

a. Graph lines s and t using the graphing tool below.
b. In the Show Your Work space, plot Point P and write its coordinates.

Instructions

Click the graph tab.
Click on the graph background to add a point. Add two points to create a graph. Drag a point or type in x and y coordinates to edit its position. Click on a point to delete it.

1

Which statement best describes the value of \sqrt{8}?

1

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

1

A system of equations is shown.

{x=10}\\{3x+5y+20}

In the system of equations, what is the value of y?

1

Which equations define y as a nonlinear function of x?
Select all that apply.

1

Consider the system of equations.

{y=2x+2}\\{y=6x+2}

Which statements are true about the system of equations?
Select each correct answer.

1

Which decimal is the equivalent of \frac{6}{11}?

1

Seven line segments are shown on the coordinate plane.

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

Select each correct answer.

1

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

Three congruent figures are shown in the coordinate plane.
Part A
Which statement describes a possible sequence of transformations that transforms figure 1 into figure 2?
__________

Part B
Figure 3 can also be created by transforming figure 1 with a sequence of two transformations. 
Which statement describes a possible sequence of transformations that transforms figure 1 into figure 3?
__________

1

The graph represents y as a function of x.
Which additional point can be plotted so that the graph continues to represent y as a function of x?

1

Which expressions are equivalent to \frac{3^{-8}}{3^{-4}}?
Select all that apply.

1

The equation of line s is y=\frac{1}{3}x-3.

The equation of line t is y=-x+5.

The equations of lines s and t form a system of equations. The solution to the system of equations is located at point P.

Which graph correctly shows line s, line t, and point P?

1

A scatter plot is shown on the coordinate plane.

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

1

The body of a 154-pound person contains approximately 2\times10^{-1} milligrams of gold and 6\times10^{1} milligrams of aluminum. Based on this information, the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body?

The use of a calculator is allowed for questions 17 to 22.

1

A solution is 20% bleach.

Which graph represents the number of liters of bleach, y, contained in x liters of solution?
[Calculator permitted]

1

Use the information provided to answer Part A and Part B for this question. 
[Calculator permitted]

Filipo is building a rectangular sandbox for his younger brother. The length of the sandbox is 1 foot longer than twice the width of the sandbox. The perimeter of the sandbox is 29 feet.

Part A
Which equation could be used to determine w, the width, in feet, of the sandbox? Enter the corresponding letter in the answer box.
a. w+w+2=29
b. w+2w+1=29
c. 2w+2(w+2)=29
d. 2w+2(2w+1)=29
_______

Part B
What is the width, in feet, of the sandbox?
_______ 

1

The gasoline mileage for two cars can be compared by finding the distance each car traveled and the amount of gasoline used. The table shows the distance that car M traveled using x gallons of gasoline. The graph shows the distance, y, that car P traveled using x gallons of gasoline.

Based on the information in the table and the graph, compare the approximate miles per gallon of car M to car P. Show your work or explain your answer.
[Calculator permitted]

1

Use the information provided to answer Part A and Part B for this question.
[Calculator permitted]

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

Part A
Explain why triangle RTS is similar to triangle VTU.
_______ 

Part B
Given that m\angle{STV}=108\degree, determine m\angle{SRT}+m\angle{TUV}. Show your work or explain your answer.
_______ 

1

Use the information provided to answer Part A through Part D for this question.
[Calculator permitted]

Line t is shown in the coordinate plane.


Part A
What is the slope of line t? __________

Part B
What is the y-intercept of line t? __________

Part C
Line s (not shown) has the same slope and passes through the point (0,4). Which table represents 4 points on line s? __________

Part D
Which equation could represent line s? __________

1

Use the information provided to answer Part A through Part C for this question.
[Calculator permitted]

Martin is considering the expressions \frac{1}{2}(7x+48) and -(\frac{1}{2}x-3)+4(x+5). He wants to know if one expression is greater than the other for all values of x.

Part A
Which statement about the relationship between the expressions is true? Enter the corresponding letter of the correct statement. _______
a. The value of the expression \frac{1}{2}(7x+48) is always equal to the value of the expression -(\frac{1}{2}x-3)+4(x+5).
b. The value of the expression \frac{1}{2}(7x+48) is always less than the value of the expression -(\frac{1}{2}x-3)+4(x+5).
c. The value of the expression \frac{1}{2}(7x+48) is always greater than the value of the expression -(\frac{1}{2}x-3)+4(x+5).
d. The value of the expression \frac{1}{2}(7x+48) is sometimes greater than and sometimes less than the value of the expression -(\frac{1}{2}x-3)+4(x+5).

Part B
Show or explain how you found your answer to Part A. 
Enter your work or your explanation in the Show Your Work Space.

Part C
Write a new expression that always has a greater value than both of these expressions. _______ 

1

Use the information provided to answer Part A and Part B for this question.
[Calculator permitted]

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

Part A
What is the volume, in cubic feet, of the cone? __________

Part B
What is the ratio of the cone's volume to the cylinder's volume? __________

1

In \triangle{ABC}, \overline{BD} is perpendicular to \overline{AC}. The dimensions are shown in centimeters.
What is the length, in centimeters, of \overline{AC}?
[Calculator permitted]

1

Relationship A is defined by the equation y=9x.
Some values of relationship B are shown in the table.

Both relationships represent a direct proportion between x and y. The rate of change of relationship B is how many units greater than the rate of change of relationship A?

1

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


Use the information provided to find the unit rate, in dollars per kilowatt-hour, for each company. _______ Show your work or explain your answers in the Show Your Work space.
Find the total cost, in dollars, of buying 2,375 kilowatt-hours of electricity from the least expensive company.  _______ 
[Calculator permitted]

1

Use the information provided to answer Part A and Part B for this question.
[Calculator permitted]

In a system of two linear equations, the lines represented by each equation have the same slope.

Part A
Which could be the total number of solutions to the system of equations?
Select each correct answer from the list below.

Part B
Explain why you chose your answer(s) in Part A in the Show Your Work space.

1

Line t and \triangle{ECA} and \triangle{FDB} are shown on the coordinate plane.

Which statements are true? Select all that apply.
[Calculator permitted]

1

Use the information provided to answer Part A and Part B for this question. 
[Calculator permitted]

The owner of a computer store is offering a discount on a computer sold in the store.
Part A
The owner offers a payment plan where the total cost of the computer is paid in 6 equal monthly payments.
Determine the amount of each monthly payment: _______ 
Show your work or explain your answer in the Show Your Work space.
Part B
A different computer is advertised as 40% off of the original price. After the discount, the tax is $44.64.
Determine the total price of this computer after the discount and tax are applied: _______ 
Show your work or explain your answer in the Show Your Work space.
Determine the original price of this computer: _______ 
Show your work or explain your answer in the Show Your Work space.

1

Function A is a linear function. Some values of Function A are shown in the table.

Function B is a linear function with a y-intercept of and an x-intercept of -5.

Which statement is true?
[Calculator permitted]

	Increasing	Decreasing	Neither Increasing nor Decreasing
-7<x<-3
-3<x<-1
-1<x<1
1<x<3
3<x<5
5<x<7

	Increasing	Decreasing	Neither Increasing nor Decreasing
-7<x<-3
-3<x<-1
-1<x<1
1<x<3
3<x<5
5<x<7

IAR Grade 8: Math - In progress!

IAR Grade 8: Math - In progress!

Solve this equation for x.0.5(5-7x)=8-(4x+6)

The graph shows y as a function of x.For each interval in the table, indicate whether the function is increasing, decreasing, or neither increasing nor decreasing over the interval.

Select the point on the number line that best approximates the location of \sqrt{14}.[vertical positioning of the points are irrelevant]

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

Classify each equation as defining y as a linear or nonlinear function of x. Drag or click the equation into the appropriate category.

Which of these equations represent functions where x is the input and y is the output? Select each correct answer.

Solve this equation for x. 0.5(5-7x)=8-(4x+6)

The graph represents y as a function of x. Place one additional point on the coordinate plane so that the graph continues to represent y as a function of x.Use the drawing tools in the Show Your Work space to plot the point on the coordinate plane.

The graph shows y as a function of x.For which intervals is the function decreasing?Select all that apply.

Which statement best describes the value of \sqrt{8}?

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

A system of equations is shown.{x=10}\\{3x+5y+20}In the system of equations, what is the value of y?

Which equations define y as a nonlinear function of x?Select all that apply.

Consider the system of equations.{y=2x+2}\\{y=6x+2}Which statements are true about the system of equations?Select each correct answer.

Which decimal is the equivalent of \frac{6}{11}?

Seven line segments are shown on the coordinate plane.Which of these segments could be the image of segment AB after a sequence of reflections, rotations, and/or translations?Select each correct answer.

The graph represents y as a function of x.Which additional point can be plotted so that the graph continues to represent y as a function of x?

Which expressions are equivalent to \frac{3^{-8}}{3^{-4}}?Select all that apply.

The equation of line s is y=\frac{1}{3}x-3.The equation of line t is y=-x+5.The equations of lines s and t form a system of equations. The solution to the system of equations is located at point P.Which graph correctly shows line s, line t, and point P?

A scatter plot is shown on the coordinate plane.Which of these most closely approximates a line of best fit for the data in the scatter plot?

The body of a 154-pound person contains approximately 2\times10^{-1} milligrams of gold and 6\times10^{1} milligrams of aluminum. Based on this information, the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body?

A solution is 20% bleach.Which graph represents the number of liters of bleach, y, contained in x liters of solution?[Calculator permitted]

In \triangle{ABC}, \overline{BD} is perpendicular to \overline{AC}. The dimensions are shown in centimeters.What is the length, in centimeters, of \overline{AC}?[Calculator permitted]

Relationship A is defined by the equation y=9x. Some values of relationship B are shown in the table.Both relationships represent a direct proportion between x and y. The rate of change of relationship B is how many units greater than the rate of change of relationship A?

Line t and \triangle{ECA} and \triangle{FDB} are shown on the coordinate plane.Which statements are true? Select all that apply.[Calculator permitted]

Function A is a linear function. Some values of Function A are shown in the table.Function B is a linear function with a y-intercept of and an x-intercept of -5. Which statement is true?[Calculator permitted]

Solve this equation for x.0.5(5-7x)=8-(4x+6)

The graph shows y as a function of x.For each interval in the table, indicate whether the function is increasing, decreasing, or neither increasing nor decreasing over the interval.

Select the point on the number line that best approximates the location of \sqrt{14}.[vertical positioning of the points are irrelevant]

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

Classify each equation as defining y as a linear or nonlinear function of x. Drag or click the equation into the appropriate category.

Which of these equations represent functions where x is the input and y is the output? Select each correct answer.

Solve this equation for x. 0.5(5-7x)=8-(4x+6)

The graph represents y as a function of x. Place one additional point on the coordinate plane so that the graph continues to represent y as a function of x.Use the drawing tools in the Show Your Work space to plot the point on the coordinate plane.

The graph shows y as a function of x.For which intervals is the function decreasing?Select all that apply.

Which statement best describes the value of \sqrt{8}?

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

A system of equations is shown.{x=10}\\{3x+5y+20}In the system of equations, what is the value of y?

Which equations define y as a nonlinear function of x?Select all that apply.

Consider the system of equations.{y=2x+2}\\{y=6x+2}Which statements are true about the system of equations?Select each correct answer.

Which decimal is the equivalent of \frac{6}{11}?

Seven line segments are shown on the coordinate plane.Which of these segments could be the image of segment AB after a sequence of reflections, rotations, and/or translations?Select each correct answer.

The graph represents y as a function of x.Which additional point can be plotted so that the graph continues to represent y as a function of x?

Which expressions are equivalent to \frac{3^{-8}}{3^{-4}}?Select all that apply.

The equation of line s is y=\frac{1}{3}x-3.The equation of line t is y=-x+5.The equations of lines s and t form a system of equations. The solution to the system of equations is located at point P.Which graph correctly shows line s, line t, and point P?

A scatter plot is shown on the coordinate plane.Which of these most closely approximates a line of best fit for the data in the scatter plot?

The body of a 154-pound person contains approximately 2\times10^{-1} milligrams of gold and 6\times10^{1} milligrams of aluminum. Based on this information, the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body?

A solution is 20% bleach.Which graph represents the number of liters of bleach, y, contained in x liters of solution?[Calculator permitted]

In \triangle{ABC}, \overline{BD} is perpendicular to \overline{AC}. The dimensions are shown in centimeters.What is the length, in centimeters, of \overline{AC}?[Calculator permitted]

Relationship A is defined by the equation y=9x. Some values of relationship B are shown in the table.Both relationships represent a direct proportion between x and y. The rate of change of relationship B is how many units greater than the rate of change of relationship A?

Line t and \triangle{ECA} and \triangle{FDB} are shown on the coordinate plane.Which statements are true? Select all that apply.[Calculator permitted]

Function A is a linear function. Some values of Function A are shown in the table.Function B is a linear function with a y-intercept of and an x-intercept of -5. Which statement is true?[Calculator permitted]

Solve this equation for x.

0.5(5-7x)=8-(4x+6)

The graph shows y as a function of x.

For each interval in the table, indicate whether the function is increasing, decreasing, or neither increasing nor decreasing over the interval.

Select the point on the number line that best approximates the location of \sqrt{14}.
[vertical positioning of the points are irrelevant]

Classify each equation as defining y as a linear or nonlinear function of x.
Drag or click the equation into the appropriate category.

Solve this equation for x.
0.5(5-7x)=8-(4x+6)

The graph represents y as a function of x. Place one additional point on the coordinate plane so that the graph continues to represent y as a function of x.

Use the drawing tools in the Show Your Work space to plot the point on the coordinate plane.

The graph shows y as a function of x.

For which intervals is the function decreasing?
Select all that apply.

A system of equations is shown.

{x=10}\\{3x+5y+20}

In the system of equations, what is the value of y?

Which equations define y as a nonlinear function of x?
Select all that apply.

Consider the system of equations.

{y=2x+2}\\{y=6x+2}

Which statements are true about the system of equations?
Select each correct answer.

Seven line segments are shown on the coordinate plane.

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

Select each correct answer.

The graph represents y as a function of x.
Which additional point can be plotted so that the graph continues to represent y as a function of x?

Which expressions are equivalent to \frac{3^{-8}}{3^{-4}}?
Select all that apply.

The equation of line s is y=\frac{1}{3}x-3.

The equation of line t is y=-x+5.

The equations of lines s and t form a system of equations. The solution to the system of equations is located at point P.

Which graph correctly shows line s, line t, and point P?

A scatter plot is shown on the coordinate plane.

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

A solution is 20% bleach.

Which graph represents the number of liters of bleach, y, contained in x liters of solution?
[Calculator permitted]

In \triangle{ABC}, \overline{BD} is perpendicular to \overline{AC}. The dimensions are shown in centimeters.
What is the length, in centimeters, of \overline{AC}?
[Calculator permitted]

Relationship A is defined by the equation y=9x.
Some values of relationship B are shown in the table.

Both relationships represent a direct proportion between x and y. The rate of change of relationship B is how many units greater than the rate of change of relationship A?

Line t and \triangle{ECA} and \triangle{FDB} are shown on the coordinate plane.

Which statements are true? Select all that apply.
[Calculator permitted]

Function A is a linear function. Some values of Function A are shown in the table.

Function B is a linear function with a y-intercept of and an x-intercept of -5.

Which statement is true?
[Calculator permitted]

Solve this equation for x.

0.5(5-7x)=8-(4x+6)

The graph shows y as a function of x.

For each interval in the table, indicate whether the function is increasing, decreasing, or neither increasing nor decreasing over the interval.

Select the point on the number line that best approximates the location of \sqrt{14}.
[vertical positioning of the points are irrelevant]

Classify each equation as defining y as a linear or nonlinear function of x.
Drag or click the equation into the appropriate category.

Solve this equation for x.
0.5(5-7x)=8-(4x+6)

The graph represents y as a function of x. Place one additional point on the coordinate plane so that the graph continues to represent y as a function of x.

Use the drawing tools in the Show Your Work space to plot the point on the coordinate plane.

The graph shows y as a function of x.

For which intervals is the function decreasing?
Select all that apply.

A system of equations is shown.

{x=10}\\{3x+5y+20}

In the system of equations, what is the value of y?

Which equations define y as a nonlinear function of x?
Select all that apply.

Consider the system of equations.

{y=2x+2}\\{y=6x+2}

Which statements are true about the system of equations?
Select each correct answer.

Seven line segments are shown on the coordinate plane.

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

Select each correct answer.

The graph represents y as a function of x.
Which additional point can be plotted so that the graph continues to represent y as a function of x?

Which expressions are equivalent to \frac{3^{-8}}{3^{-4}}?
Select all that apply.

The equation of line s is y=\frac{1}{3}x-3.

The equation of line t is y=-x+5.

The equations of lines s and t form a system of equations. The solution to the system of equations is located at point P.

Which graph correctly shows line s, line t, and point P?

A scatter plot is shown on the coordinate plane.

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

A solution is 20% bleach.

Which graph represents the number of liters of bleach, y, contained in x liters of solution?
[Calculator permitted]

In \triangle{ABC}, \overline{BD} is perpendicular to \overline{AC}. The dimensions are shown in centimeters.
What is the length, in centimeters, of \overline{AC}?
[Calculator permitted]

Relationship A is defined by the equation y=9x.
Some values of relationship B are shown in the table.

Both relationships represent a direct proportion between x and y. The rate of change of relationship B is how many units greater than the rate of change of relationship A?

Line t and \triangle{ECA} and \triangle{FDB} are shown on the coordinate plane.

Which statements are true? Select all that apply.
[Calculator permitted]

Function A is a linear function. Some values of Function A are shown in the table.

Function B is a linear function with a y-intercept of and an x-intercept of -5.

Which statement is true?
[Calculator permitted]