8th Grade Benchmark C
This benchmark will count as a test grade!
Questions and Answers
- 1.
Which segment is QR congruent to?
- A.
P'S'
- B.
P'Q'
- C.
Q'R'
- D.
R'S'
Correct Answer
C. Q'R'Explanation
Q'R' is the segment that is congruent to QR. This means that Q'R' and QR have the same length.Rate this question:
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- 2.
Which of the following is the graph of a function?
- A.
- B.
- C.
- D.
Correct Answer
D.Explanation
The correct answer is the first graph. It represents a function because for every input value (x-coordinate), there is only one output value (y-coordinate). In other words, there are no vertical lines that intersect the graph at more than one point.Rate this question:
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- 3.
In the coordinate plane below, quadrilateral ABCD is reflected over the y-axis to form quadrilateral EFGH.Which angle is angle B congruent to?
- A.
E
- B.
F
- C.
G
- D.
H
Correct Answer
B. FExplanation
When a figure is reflected over the y-axis, the x-coordinates of the points remain the same, but the y-coordinates change sign. In this case, angle B is a vertex of quadrilateral ABCD, and when it is reflected over the y-axis, it becomes angle F in quadrilateral EFGH. Therefore, angle B is congruent to angle F.Rate this question:
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- 4.
Below is the graph of the linear equation y= -3x+4.what are the slope and y-intercept of this graph?
- A.
Slope of -3, y-intercept of 4
- B.
Slope of 1/3, y-intercept of -4
- C.
Slope of -3, y-intercept of -4
- D.
Slope of -1/3, y-intercept of 4
Correct Answer
A. Slope of -3, y-intercept of 4Explanation
The slope of a linear equation represents the rate of change of the dependent variable (y) with respect to the independent variable (x). In this case, the slope is -3, indicating that for every 1 unit increase in x, y decreases by 3 units. The y-intercept represents the value of y when x is equal to 0. In this case, the y-intercept is 4, meaning that the graph intersects the y-axis at the point (0, 4). Therefore, the correct answer is slope of -3, y-intercept of 4.Rate this question:
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- 5.
- A.
2 in cubed
- B.
5 in cubed
- C.
7 in cubed
- D.
21 in cubed
Correct Answer
C. 7 in cubedExplanation
The answer is 7 in cubed because "in cubed" refers to raising a number to the power of 3. So, 7 in cubed means 7^3, which equals 343.Rate this question:
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- 6.
- A.
A
- B.
B
- C.
C
- D.
D
Correct Answer
D. D -
- 7.
Of which of the following perfect squares is 4 the square root?
- A.
8
- B.
16
- C.
25
- D.
36
Correct Answer
B. 16Explanation
The square root of a number is the value that, when multiplied by itself, gives the original number. In this case, the square root of 4 is 2, because 2 multiplied by itself equals 4. Among the given options, the only perfect square for which 2 is the square root is 16, because 2 multiplied by itself equals 16. Therefore, the correct answer is 16.Rate this question:
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- 8.
- A.
A
- B.
B
- C.
C
- D.
D
Correct Answer
B. B -
- 9.
- A.
A
- B.
B
- C.
C
- D.
D
Correct Answer
D. D -
- 10.
- A.
A
- B.
B
- C.
C
- D.
D
Correct Answer
A. A -
- 11.
Point K (2,1) and J(-4,-7) are shown on the coordinate plane below.What is the distance between point K and J?
- A.
4 units
- B.
8 units
- C.
10 units
- D.
16 units
Correct Answer
C. 10 unitsExplanation
The distance between two points in a coordinate plane can be found using the distance formula, which is derived from the Pythagorean theorem. The formula is: distance = sqrt((x2-x1)^2 + (y2-y1)^2). In this case, the x-coordinates of K and J are 2 and -4 respectively, and the y-coordinates are 1 and -7 respectively. Plugging these values into the formula, we get: distance = sqrt(((-4)-(2))^2 + ((-7)-(1))^2) = sqrt((-6)^2 + (-8)^2) = sqrt(36 + 64) = sqrt(100) = 10 units. Therefore, the distance between point K and J is 10 units.Rate this question:
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- 12.
Quincy created a scatter plot showing the relationship between age and height in his middle school. Which of the following graphs is mostly likely the scatter plot he created?
- A.
A
- B.
B
- C.
C
- D.
D
Correct Answer
A. AExplanation
Graph A is the most likely scatter plot that Quincy created because it shows a random distribution of points with no clear pattern or trend. In a scatter plot, the points represent individual data points, and in this case, the points are scattered across the graph without any obvious relationship between age and height. Graphs B, C, and D show either a positive or negative correlation between age and height, which is not indicated in the question.Rate this question:
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- 13.
In the coordinate plane below, figure LMN is rotated 180 degrees about the origin.What are the coordinates of the new figure?L(-6,8) M( -4,2) N(-9, 3)
- A.
A
- B.
B
- C.
C
- D.
D
Correct Answer
B. BExplanation
The coordinates of the new figure after rotating 180 degrees about the origin can be found by changing the signs of both x and y coordinates of each point. The new coordinates are L(6,-8), M(4,-2), and N(9,-3).Rate this question:
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- 14.
Which is the product of (1.35X105)(4.89X103)?A. 6.24X108B. 6.6015X105C. 6.6015X108 D. 66.015X107
- A.
A
- B.
B
- C.
C
- D.
D
Correct Answer
C. C -
- 15.
Which of the following functions is linear?
- A.
A
- B.
B
- C.
C
- D.
D
Correct Answer
D. DExplanation
The correct answer is D because a linear function is a function that can be represented by a straight line on a graph. Option D is the only option that represents a straight line when graphed, indicating that it is a linear function.Rate this question:
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- 16.
Two points on the graph of a line are (-2,6) and (1,-2). what is the rate of change of the line?***Answers below are fraction
- A.
-4/3
- B.
4/3
- C.
-3/4
- D.
3/4
Correct Answer
A. -4/3Explanation
The rate of change of a line can be found by calculating the difference in the y-coordinates divided by the difference in the x-coordinates of two points on the line. In this case, the difference in the y-coordinates is -2 - 6 = -8, and the difference in the x-coordinates is 1 - (-2) = 3. Therefore, the rate of change is -8/3, which can be simplified to -4/3.Rate this question:
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- 17.
Marcela has the lid from a can of cherries that her friend Lily used to make a pie. The radius of the lid measures 1.5 inches and the formula for the volume of a cylinder is V= (pi)r2h. If the recipe calls for cherries that fill a 22-cubic inch can, which is the height to the nearest inch of the can of cherries needed to make a pie?
- A.
1.5 in
- B.
3 in
- C.
4 in
- D.
6.75 in
Correct Answer
B. 3 inExplanation
The formula for the volume of a cylinder is V= (pi)r^2h. Since the radius of the lid is given as 1.5 inches, we can substitute this value into the formula. We are also given that the volume of the can of cherries needed is 22 cubic inches. By rearranging the formula to solve for h, we can find the height. Plugging in the values, we have 22 = (pi)(1.5^2)h. Solving for h gives us h ≈ 3 inches. Therefore, the height of the can of cherries needed to make a pie is 3 inches.Rate this question:
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- 18.
What is the slope of the line that passes through the points (-7, -6) and (3,0)?***The numbers below are fractions
- A.
-8/3
- B.
-2
- C.
-5/3
- D.
3/5
Correct Answer
D. 3/5Explanation
To find the slope of a line passing through two points, we can use the formula (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points. In this case, the coordinates are (-7, -6) and (3, 0). Plugging these values into the formula, we get (0 - (-6)) / (3 - (-7)), which simplifies to 6 / 10 or 3/5. Therefore, the slope of the line passing through these points is 3/5.Rate this question:
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- 19.
On the coordinate plane below, the figure DART is dilated by a factor of 2.D(-3,4) A( 4, 3)R( 4, -3)T( -3, -4)
- A.
A
- B.
B
- C.
C
- D.
D
Correct Answer
A. AExplanation
The figure DART is dilated by a factor of 2, which means that each point in the figure is multiplied by 2 in both the x and y coordinates. Therefore, the new coordinates for point D would be (-3*2, 4*2) = (-6, 8). Comparing this with the given answer choices, we can see that the new coordinates (-6, 8) match with point A. Therefore, the correct answer is A.Rate this question:
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- 20.
Below is a graph representing the price per pound of cheese at Kramer's Grocery and Sophie's Supermarket. Based on the graph, which of the following statements is true?
- A.
Kramer's cheese is $1 less per pound than Sophie's cheese.
- B.
Kramer's cheese is $3 more per pound than Sophie's cheese.
- C.
Sophie's cheese is $4 more per pound than Kramer's cheese.
- D.
Sophie's cheese is $2 less per pound than Kramer's cheese.
Correct Answer
D. Sophie's cheese is $2 less per pound than Kramer's cheese.Explanation
According to the graph, the price of Kramer's cheese is higher than Sophie's cheese. The difference between the prices is $2, with Sophie's cheese being $2 less per pound than Kramer's cheese.Rate this question:
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- 21.
Ray tells his friend Danny that he can bicycle 5 miles to the local pool in 20 minutes. Danny then shows Ray a graph of his bicycle ride to the local YMCA, pictured below.
- A.
Ray, because he bicycles 15 miles an hour and Danny bicycles 12 miles an hour.
- B.
Ray, because he bicycles 20 miles an hour and Danny bicycles 12 miles an hour.
- C.
Danny, because he bicycles 10 miles an hour and Ray bicycles 5 miles an hour.
- D.
Danny, because he bicycles 5 miles an hour and Ray bicycles 4 miles an hour.
Correct Answer
A. Ray, because he bicycles 15 miles an hour and Danny bicycles 12 miles an hour.Explanation
Based on the given information, Ray claims that he can bicycle 5 miles to the local pool in 20 minutes. Looking at the graph provided by Danny, it shows that Ray's ride to the local YMCA took 20 minutes as well. Since the distance is the same for both rides, but Ray's ride took the same amount of time at a faster speed, it can be concluded that Ray bicycles at a faster speed than Danny. Therefore, the correct answer is Ray, because he bicycles 15 miles an hour and Danny bicycles 12 miles an hour.Rate this question:
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- 22.
Solve for y:11(y-2)+3y=-7y+14***The following are fractions
- A.
7/12
- B.
12/7
- C.
14
- D.
21
Correct Answer
B. 12/7Explanation
To solve the equation, we need to simplify both sides. First, distribute 11 to (y-2), which gives us 11y - 22. Then, combine like terms by adding 3y and 7y on the right side, which gives us 10y. Simplifying further, we have 11y + 10y - 22 = 14. Combining like terms again, we get 21y - 22 = 14. To isolate y, we add 22 to both sides, resulting in 21y = 36. Finally, we divide both sides by 21, giving us y = 36/21, which simplifies to 12/7. Therefore, the answer is 12/7.Rate this question:
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- 23.
Quadrilateral PQRS is transformed to create quadrilateral P'Q'R'S'.Which of the following best describes the transformation from PQRS to P'Q'R'S' below?
- A.
Reflection over the y-axis
- B.
Rotation 90 clockwise
- C.
Translation 4 units down
- D.
Reflection over the x-axis
Correct Answer
D. Reflection over the x-axisExplanation
The given answer, "reflection over the x-axis," best describes the transformation from PQRS to P'Q'R'S'. This is because a reflection over the x-axis would result in the points being mirrored across the x-axis. In other words, any point above the x-axis would be reflected to a point below the x-axis, and vice versa. This transformation would change the orientation of the quadrilateral, flipping it upside down.Rate this question:
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- 24.
Each week, Herbie receives an allowance for helping with tasks around the house. Below is a graph that represents this situation. Based on the graph, how much allowance does Herbie receive each mount? (Assume that 4 weeks are in a month.)
- A.
$24
- B.
$48
- C.
$60
- D.
$72
Correct Answer
B. $48Explanation
Based on the graph, the y-axis represents the allowance received by Herbie and the x-axis represents the number of weeks. The graph shows that for every 4 weeks, the allowance received by Herbie is $48. Therefore, the correct answer is $48.Rate this question:
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- 25.
Which of the following sequences transforms PODS into P'O'D'S'?
- A.
Horizontal shift 3 units to the right, vertical shift 1 unit down
- B.
Horizontal shift 11 units to the right, vertical shift 3 units down
- C.
Horizontal shift 11 units to the left, vertical shift 4 units up
- D.
Horizontal shift 4 units to the right, vertical shift 11 units down
Correct Answer
B. Horizontal shift 11 units to the right, vertical shift 3 units downExplanation
The correct answer is the sequence that involves a horizontal shift of 11 units to the right and a vertical shift of 3 units down. This transformation will move each letter in the word "PODS" to the right by 11 units and downward by 3 units, resulting in the word "P'O'D'S'".Rate this question:
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- 26.
What is the solution to the following system of linear equations?2x-7y=12-2x+6y=-10
- A.
(1,2)
- B.
(2,-1)
- C.
(-1,-2)
- D.
(-2,-1)
Correct Answer
C. (-1,-2)Explanation
The solution to the given system of linear equations can be found by solving the equations simultaneously. By adding the two equations, we can eliminate the x variable and solve for y. The resulting equation is -y = 2, which gives us y = -2. Substituting this value of y into either of the original equations, we can solve for x. Plugging in y = -2 into the first equation, we get 2x - 7(-2) = 12, which simplifies to 2x + 14 = 12. Solving for x, we find x = -1. Therefore, the solution to the system of equations is (-1, -2).Rate this question:
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- 27.
In the figure below, lines HI and JK are parallel.If angle HBA measures 63 degrees, what is the measure of angle BCK?
- A.
27
- B.
90
- C.
117
- D.
153
Correct Answer
C. 117Explanation
Since lines HI and JK are parallel, angle HBA and angle BCK are corresponding angles. Corresponding angles are congruent when the lines are parallel. Therefore, the measure of angle BCK is also 63 degrees. However, the options provided do not include 63 degrees. Therefore, the answer is not available.Rate this question:
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- 28.
- A.
A
- B.
B
- C.
C
- D.
D
Correct Answer
B. B -
- 29.
- A.
A
- B.
B
- C.
C
- D.
D
Correct Answer
B. B -
- 30.
- A.
A
- B.
B
- C.
C
- D.
D
Correct Answer
C. C -
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