End-of-Grade 8 (EOG8) Math

Last updated 12 months ago

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End-of-Grade 8 (EOG8) Math

Last updated 12 months ago

45 Nsɛmmisa

This is the start of the calculator inactive test questions.

null

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What is the equation of the line graphed below?

y = \frac{2}{3} x - 2

y = \frac{2}{3} x + 3

y = \frac{3}{2} x - 2

y = \frac{3}{2} x + 3

NC.8.F.4

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2 Which graph has a slope that is \frac{1}{4} unit greater than the slope of the graph of y = x - 2?

null

NC.8.F.2

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Susan recorded the time she ate dinner and the number of calories she consumed during dinner for six consecutive days. The results are shown in the table.
Which best describes the association between the time Susan ate dinner and the number of calories she consumed?

positive

negative

irrational

almost none

NC.8.SP.1

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Which choice is an irrational number?

\frac{4\pi}{\pi}

\sqrt{6^2}

\sqrt{18}

21.989

NC.8.NS.1

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In which choice is y a nonlinear function of x?

y = \frac{x}{4} + 5

y = 10 + x

y = \frac{x+3}{4} - 2x

y = \frac{2}{x+3} - 5

NC.8.F.3

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Mr. Jones determined that the equation y = 98 - \frac{16}{5} x could be used to predict his students’ unit test scores, based on the number of days, x, a student was absent during the unit. What is the meaning of the y-intercept of the function?

A student who was not absent during the unit should score about 98.

A student who was not absent during the unit should score about 94.5.

A student’s test score should increase by about 3.2 points for each day the student is absent.

A student’s test score should decrease by about 3.2 points for each day the student is absent.

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Which is the graph of the linear equation y = -x?

null

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In which choice is y a nonlinear function of x?

null

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Which choice is both the square of an integer and the cube of an integer?

121

100

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In which choice do all three points lie on the same straight line?

(0, 1), (-1, 3), (1, 3)

(4, 2), (2, 1), (4, -2)

(0, 0), (8, 0), (0,8)

(1, 2), (2, 4), (4, 8)

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The area of a square is 49 \, \text{cm}^2. What is the perimeter, in cm, of the square?

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What is the slope of the line that passes through the points (2, 3) and (8, 6)?

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The table shows four quantities. Each quantity is assigned a numeric label.
Order the quantities from least to greatest.
Next, write the sequence of numeric labels in the same order as their corresponding quantities.
This sequence of numeric labels is your answer.
Enter your answer. (For example, if the order of the numeric labels were “1, 2, 3, 4,” enter the answer as “1234.”)

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What is the value of x in the equation shown below?
x^{3} + 1 = 9

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What positive integer is closest to the value of \sqrt{230}?

NC.8.NS.2

This is the end of the calculator inactive test questions.

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A square is drawn below.
What is the value of x?

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What is the value of x in the equation shown below?
0.25x + 7 = 4(x - 2)

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What is the rate of change of the linear function that has a graph that passes through the points (2, 9) and (-1, 3)?

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What value of x satisfies the equation below?
12(x - 2) + 3x = \frac{1}{2}(x + 6) + 2

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In the diagram, parallel lines P and Q are cut by transversal R.
What is the value of x?

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A light year is defined as the distance light travels in one year. One light year is 9.46 \times 10^{12} kilometers. A galaxy is about 150,000 light years wide. About how many kilometers wide is the galaxy?

1.419 \times 10^{16}

1.419 \times 10^{17}

1.419 \times 10^{18}

1.419 \times 10^{19}

NC.8.EE.4

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Rectangle JKLM is shown.
To the nearest tenth of a centimeter, what is the distance from J to M?

5.0 cm

10.2 cm

15.3 cm

21.0 cm

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The value in dollars, y, of a car x years after it was purchased can be modeled by the function y = 14,000 - 875x. What is the meaning of the y-intercept of the linear model?

The initial value of the car is $14,000.

The average value of the car is $14,000.

The car’s value decreases by $875 each year after it was purchased.

The car’s value decreases by $16 each year after it was purchased.

NC.8.SP.3

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Alexis has a cylindrical trash can with a diameter of 24 cm and a height of 42 cm. What is the approximate volume of the can?

1,008 cm³

3,167 cm³

19,000 cm³

76,000 cm³

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Which equation best models the data shown in the scatterplot below?

y = 3x + 10

y = 3x + 60

y = 4x + 5

y = 4x + 35

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In which choice is y a function of x?

(1, 3), (3, 4), (4, 5), (5, 6)

(2, 0), (2, 3), (4, 5), (6, 7)

(2,5), (4,8), (6, 10), (2, 12)

(6, 2), (4, 1), (6,8), (8, 10)

NC.8.F.1

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Carly went for a walk and jog.
She started walking.
After a few minutes, Carly began jogging at a faster speed than she was walking.
Carly then got tired and slowed down to a slower speed than she was jogging.
Which graph best represents the distance Carly went?

null

NC.8.F.5

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In the figure, JLK is a right triangle, point P is the midpoint of side JK, and segment PQ is parallel to segment JL.
The length of segment PK is 4 units and the length of segment PQ is 2 units. What is the approximate perimeter of shaded triangle PQL?

10.0 units

9.5 units

9.0 units

8.5 units

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A car rental company charges $34 per day for a rented car and $0.50 for every mile driven. A second car rental company charges $20 per day and $0.75 for every mile driven. What is the number of miles at which both companies charge the same amount for a one-day rental?

56 miles

54 miles

36 miles

24 miles

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A cylindrical barrel has a height of 8 feet and a diameter of 6 feet. What is the approximate volume of the barrel?

151 cubic feet

226 cubic feet

603 cubic feet

905 cubic feet

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ΔLMN will be dilated with respect to the origin by a scale factor of \frac{1}{2}.
What will be the coordinates of ΔL'M'N'?

L'(-6, -8), M'(6,8), N'(6, 1)

L'(-3, 2), M'(3, 2), N'(3, 0.5)

L'(-1.5, 2), M'(1.5, 2), N'(1.5, 0.5)

L'(-1, 2), M'(1, 2), N'(1, 1)

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The scatterplot shows the amount of sunlight some tomato plants received and the amount each plant grew.
What is the meaning of the slope of the trend line shown on the scatterplot?

A plant grows about 3 inches for every 2 hours of sunlight it receives.

A plant grows about 2 inches for every 3 hours of sunlight it receives.

A plant grows about 3 inches for every 1 hour of sunlight it receives.

A plant grows about 1 inch for every 3 hours of sunlight it receives.

NC.8.SP.3

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The table shows the number of hours Jake studied for his math tests and his corresponding grade.
Another student, Howie, increased his test scores 6 points for each hour he studied.
Which statement correctly describes the rate of change between hours studied and corresponding test scores of the two students?

Jake’s test scores increased by 1 point more than Howie’s test scores for each hour studied.

Jake’s test scores increased by 3 points more than Howie’s test scores for each hour studied.

Howie’s test scores increased by 1 point more than Jake’s test scores for each hour studied.

Howie’s test scores increased by 3 points more than Jake’s test scores for each hour studied.

NC.8.F.2

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A figure is shown.
What is the length of the dotted line, to the nearest inch?

10 inches

11 inches

12 inches

13 inches

NC.8.G.7

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A group of students were asked if they are in the Math Club and if they are in the Literature Club. Partial results are shown in the table.
Of the students in the Math Club, 67% (rounded) are not in the Literature Club.
Of the students not in the Math Club, 78% (rounded) are not in the Literature Club.
What is the value of x + y?

NC.8.SP.4

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ΔXYZ with vertices X(1, 1), Y(3, 5), and Z(5, 1) will be rotated 180° about the origin. What will be the coordinates of Y'?

(-5, 3)

(-3, -5)

(5, -3)

(5, 3)

NC.8.G.3

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Which function has the same slope as the linear function graphed below?

y = 4x + 3

y = \frac{1}{4}x + 3

y = 2 - 4x

y = 2 - \frac{1}{4}x

NC.8.F.2

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A line passes through the points (1, 4) and (5,8). A second line passes through the points (2, 10) and (6, 4). At what point do the two lines intersect?

(2, 10)

(3, 6)

(4, 7)

(5,8)

NC.8.EE.8

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In which set of points is y a function of x?

{(2, 4), (4, 16), (5, 25), (6, 36)}

{(4, 2), (4, -2), (16, 4), (16, -4)}

{(2, 1), (2, 0), (1, -1), (3, 1)}

{(2, 3), (1, 3), (0, 3), (0, 2)}

NC.8.F.1

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The points P(3, -2), Q(10, -2), and R(3, -8) are the vertices of a triangle. What is the approximate length of side RQ?

7 units

9 units

11 units

13 units

NC.8.G.8

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In the expressions, x and y represent positive integers.
expression one: \ 2 \cdot 10^x
expression two: \ 4 \cdot 10^{x+y}
The value of expression two is 20,000 times greater than the value of expression one. What is the value of y?

NC.8.EE.3

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Segment XY is graphed in the coordinate plane.
Which could be the coordinates of the third vertex, Z, of triangle XYZ so that it would have a hypotenuse with a length of \sqrt{45} units?

(-1, 5)

(-1, -1)

(6, -1)

(8, 5)

NC.8.G.8

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Paula and Julia went walking. The equation y = 3x models the distance Paula walked in x hours. Julia walked at a pace one mile per hour faster than Paula. Which graph correctly models Julia’s walking distance as a function of time?

null

NC.8.F.2

Ɛhia

The diameter of a sphere is 6 cm. What is the volume of the sphere?
(Note: v = \frac{4}{3} \pi r^3)

8 \pi \text{ cm}^3

36 \pi \text{ cm}^3

144 \pi \text{ cm}^3

288 \pi \text{ cm}^3

NC.8.G.9

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Henry made the scatterplot shown.
The scatterplot shows the data points, and it also shows the linear model that Henry drew. Which statement best describes the linear model?

The linear model describes the data well because points are scattered above and below the line.

The linear model describes the data well because all the points are close to the line.

The linear model does not describe the data well because the line does not go through any of the points.

The linear model does not describe the data well because most of the points are located above the line.

NC.8.SP.2

End-of-Grade 8 (EOG8) Math

End-of-Grade 8 (EOG8) Math

What is the equation of the line graphed below?

2 Which graph has a slope that is \frac{1}{4} unit greater than the slope of the graph of y = x - 2?

Susan recorded the time she ate dinner and the number of calories she consumed during dinner for six consecutive days. The results are shown in the table.Which best describes the association between the time Susan ate dinner and the number of calories she consumed?

Which choice is an irrational number?

In which choice is y a nonlinear function of x?

Mr. Jones determined that the equation y = 98 - \frac{16}{5} x could be used to predict his students’ unit test scores, based on the number of days, x, a student was absent during the unit. What is the meaning of the y-intercept of the function?

Which is the graph of the linear equation y = -x?

In which choice is y a nonlinear function of x?

Which choice is both the square of an integer and the cube of an integer?

In which choice do all three points lie on the same straight line?

The area of a square is 49 \, \text{cm}^2. What is the perimeter, in cm, of the square?

What is the slope of the line that passes through the points (2, 3) and (8, 6)?

What is the value of x in the equation shown below?x^{3} + 1 = 9

What positive integer is closest to the value of \sqrt{230}?

A square is drawn below.What is the value of x?

What is the value of x in the equation shown below?0.25x + 7 = 4(x - 2)

What is the rate of change of the linear function that has a graph that passes through the points (2, 9) and (-1, 3)?

What value of x satisfies the equation below?12(x - 2) + 3x = \frac{1}{2}(x + 6) + 2

In the diagram, parallel lines P and Q are cut by transversal R.What is the value of x?

A light year is defined as the distance light travels in one year. One light year is 9.46 \times 10^{12} kilometers. A galaxy is about 150,000 light years wide. About how many kilometers wide is the galaxy?

Rectangle JKLM is shown. To the nearest tenth of a centimeter, what is the distance from J to M?

The value in dollars, y, of a car x years after it was purchased can be modeled by the function y = 14,000 - 875x. What is the meaning of the y-intercept of the linear model?

Alexis has a cylindrical trash can with a diameter of 24 cm and a height of 42 cm. What is the approximate volume of the can?

Which equation best models the data shown in the scatterplot below?

In which choice is y a function of x?

Carly went for a walk and jog.She started walking.After a few minutes, Carly began jogging at a faster speed than she was walking.Carly then got tired and slowed down to a slower speed than she was jogging.Which graph best represents the distance Carly went?

In the figure, JLK is a right triangle, point P is the midpoint of side JK, and segment PQ is parallel to segment JL.The length of segment PK is 4 units and the length of segment PQ is 2 units. What is the approximate perimeter of shaded triangle PQL?

A car rental company charges $34 per day for a rented car and $0.50 for every mile driven. A second car rental company charges $20 per day and $0.75 for every mile driven. What is the number of miles at which both companies charge the same amount for a one-day rental?

A cylindrical barrel has a height of 8 feet and a diameter of 6 feet. What is the approximate volume of the barrel?

ΔLMN will be dilated with respect to the origin by a scale factor of \frac{1}{2}.What will be the coordinates of ΔL'M'N'?

The scatterplot shows the amount of sunlight some tomato plants received and the amount each plant grew.What is the meaning of the slope of the trend line shown on the scatterplot?

A figure is shown.What is the length of the dotted line, to the nearest inch?

ΔXYZ with vertices X(1, 1), Y(3, 5), and Z(5, 1) will be rotated 180° about the origin. What will be the coordinates of Y'?

Which function has the same slope as the linear function graphed below?

A line passes through the points (1, 4) and (5,8). A second line passes through the points (2, 10) and (6, 4). At what point do the two lines intersect?

In which set of points is y a function of x?

The points P(3, -2), Q(10, -2), and R(3, -8) are the vertices of a triangle. What is the approximate length of side RQ?

In the expressions, x and y represent positive integers.expression one: \ 2 \cdot 10^xexpression two: \ 4 \cdot 10^{x+y}The value of expression two is 20,000 times greater than the value of expression one. What is the value of y?

Segment XY is graphed in the coordinate plane.Which could be the coordinates of the third vertex, Z, of triangle XYZ so that it would have a hypotenuse with a length of \sqrt{45} units?

Paula and Julia went walking. The equation y = 3x models the distance Paula walked in x hours. Julia walked at a pace one mile per hour faster than Paula. Which graph correctly models Julia’s walking distance as a function of time?

The diameter of a sphere is 6 cm. What is the volume of the sphere?(Note: v = \frac{4}{3} \pi r^3)

Henry made the scatterplot shown. The scatterplot shows the data points, and it also shows the linear model that Henry drew. Which statement best describes the linear model?

What is the equation of the line graphed below?

2 Which graph has a slope that is \frac{1}{4} unit greater than the slope of the graph of y = x - 2?

Susan recorded the time she ate dinner and the number of calories she consumed during dinner for six consecutive days. The results are shown in the table.Which best describes the association between the time Susan ate dinner and the number of calories she consumed?

Which choice is an irrational number?

In which choice is y a nonlinear function of x?

Mr. Jones determined that the equation y = 98 - \frac{16}{5} x could be used to predict his students’ unit test scores, based on the number of days, x, a student was absent during the unit. What is the meaning of the y-intercept of the function?

Which is the graph of the linear equation y = -x?

In which choice is y a nonlinear function of x?

Which choice is both the square of an integer and the cube of an integer?

In which choice do all three points lie on the same straight line?

The area of a square is 49 \, \text{cm}^2. What is the perimeter, in cm, of the square?

What is the slope of the line that passes through the points (2, 3) and (8, 6)?

What is the value of x in the equation shown below?x^{3} + 1 = 9

What positive integer is closest to the value of \sqrt{230}?

A square is drawn below.What is the value of x?

What is the value of x in the equation shown below?0.25x + 7 = 4(x - 2)

What is the rate of change of the linear function that has a graph that passes through the points (2, 9) and (-1, 3)?

What value of x satisfies the equation below?12(x - 2) + 3x = \frac{1}{2}(x + 6) + 2

In the diagram, parallel lines P and Q are cut by transversal R.What is the value of x?

A light year is defined as the distance light travels in one year. One light year is 9.46 \times 10^{12} kilometers. A galaxy is about 150,000 light years wide. About how many kilometers wide is the galaxy?

Rectangle JKLM is shown. To the nearest tenth of a centimeter, what is the distance from J to M?

The value in dollars, y, of a car x years after it was purchased can be modeled by the function y = 14,000 - 875x. What is the meaning of the y-intercept of the linear model?

Alexis has a cylindrical trash can with a diameter of 24 cm and a height of 42 cm. What is the approximate volume of the can?

Which equation best models the data shown in the scatterplot below?

In which choice is y a function of x?

Carly went for a walk and jog.She started walking.After a few minutes, Carly began jogging at a faster speed than she was walking.Carly then got tired and slowed down to a slower speed than she was jogging.Which graph best represents the distance Carly went?

In the figure, JLK is a right triangle, point P is the midpoint of side JK, and segment PQ is parallel to segment JL.The length of segment PK is 4 units and the length of segment PQ is 2 units. What is the approximate perimeter of shaded triangle PQL?

A car rental company charges $34 per day for a rented car and $0.50 for every mile driven. A second car rental company charges $20 per day and $0.75 for every mile driven. What is the number of miles at which both companies charge the same amount for a one-day rental?

A cylindrical barrel has a height of 8 feet and a diameter of 6 feet. What is the approximate volume of the barrel?

ΔLMN will be dilated with respect to the origin by a scale factor of \frac{1}{2}.What will be the coordinates of ΔL'M'N'?

The scatterplot shows the amount of sunlight some tomato plants received and the amount each plant grew.What is the meaning of the slope of the trend line shown on the scatterplot?

A figure is shown.What is the length of the dotted line, to the nearest inch?

ΔXYZ with vertices X(1, 1), Y(3, 5), and Z(5, 1) will be rotated 180° about the origin. What will be the coordinates of Y'?

Which function has the same slope as the linear function graphed below?

A line passes through the points (1, 4) and (5,8). A second line passes through the points (2, 10) and (6, 4). At what point do the two lines intersect?

In which set of points is y a function of x?

Susan recorded the time she ate dinner and the number of calories she consumed during dinner for six consecutive days. The results are shown in the table.
Which best describes the association between the time Susan ate dinner and the number of calories she consumed?

What is the value of x in the equation shown below?
x^{3} + 1 = 9

A square is drawn below.
What is the value of x?

What is the value of x in the equation shown below?
0.25x + 7 = 4(x - 2)

What value of x satisfies the equation below?
12(x - 2) + 3x = \frac{1}{2}(x + 6) + 2

In the diagram, parallel lines P and Q are cut by transversal R.
What is the value of x?

Rectangle JKLM is shown.
To the nearest tenth of a centimeter, what is the distance from J to M?

Carly went for a walk and jog.
She started walking.
After a few minutes, Carly began jogging at a faster speed than she was walking.
Carly then got tired and slowed down to a slower speed than she was jogging.
Which graph best represents the distance Carly went?

In the figure, JLK is a right triangle, point P is the midpoint of side JK, and segment PQ is parallel to segment JL.
The length of segment PK is 4 units and the length of segment PQ is 2 units. What is the approximate perimeter of shaded triangle PQL?

ΔLMN will be dilated with respect to the origin by a scale factor of \frac{1}{2}.
What will be the coordinates of ΔL'M'N'?

The scatterplot shows the amount of sunlight some tomato plants received and the amount each plant grew.
What is the meaning of the slope of the trend line shown on the scatterplot?

A figure is shown.
What is the length of the dotted line, to the nearest inch?

In the expressions, x and y represent positive integers.
expression one: \ 2 \cdot 10^x
expression two: \ 4 \cdot 10^{x+y}
The value of expression two is 20,000 times greater than the value of expression one. What is the value of y?

Segment XY is graphed in the coordinate plane.
Which could be the coordinates of the third vertex, Z, of triangle XYZ so that it would have a hypotenuse with a length of \sqrt{45} units?

The diameter of a sphere is 6 cm. What is the volume of the sphere?
(Note: v = \frac{4}{3} \pi r^3)

Henry made the scatterplot shown.
The scatterplot shows the data points, and it also shows the linear model that Henry drew. Which statement best describes the linear model?

Susan recorded the time she ate dinner and the number of calories she consumed during dinner for six consecutive days. The results are shown in the table.
Which best describes the association between the time Susan ate dinner and the number of calories she consumed?

What is the value of x in the equation shown below?
x^{3} + 1 = 9

A square is drawn below.
What is the value of x?

What is the value of x in the equation shown below?
0.25x + 7 = 4(x - 2)

What value of x satisfies the equation below?
12(x - 2) + 3x = \frac{1}{2}(x + 6) + 2

In the diagram, parallel lines P and Q are cut by transversal R.
What is the value of x?

Rectangle JKLM is shown.
To the nearest tenth of a centimeter, what is the distance from J to M?

Carly went for a walk and jog.
She started walking.
After a few minutes, Carly began jogging at a faster speed than she was walking.
Carly then got tired and slowed down to a slower speed than she was jogging.
Which graph best represents the distance Carly went?

In the figure, JLK is a right triangle, point P is the midpoint of side JK, and segment PQ is parallel to segment JL.
The length of segment PK is 4 units and the length of segment PQ is 2 units. What is the approximate perimeter of shaded triangle PQL?

ΔLMN will be dilated with respect to the origin by a scale factor of \frac{1}{2}.
What will be the coordinates of ΔL'M'N'?

The scatterplot shows the amount of sunlight some tomato plants received and the amount each plant grew.
What is the meaning of the slope of the trend line shown on the scatterplot?

A figure is shown.
What is the length of the dotted line, to the nearest inch?

In the expressions, x and y represent positive integers.
expression one: \ 2 \cdot 10^x
expression two: \ 4 \cdot 10^{x+y}
The value of expression two is 20,000 times greater than the value of expression one. What is the value of y?

Segment XY is graphed in the coordinate plane.
Which could be the coordinates of the third vertex, Z, of triangle XYZ so that it would have a hypotenuse with a length of \sqrt{45} units?

The diameter of a sphere is 6 cm. What is the volume of the sphere?
(Note: v = \frac{4}{3} \pi r^3)

Henry made the scatterplot shown.
The scatterplot shows the data points, and it also shows the linear model that Henry drew. Which statement best describes the linear model?