Math Quizzes Questions and
Answers Grade Level 2023
What is the perimeter of the figure provided? - -29 cm
The perimeter of the figure is 2 × (l + w) = 2 × (5.5 + 9) = 29 cm.
-As shown below, a figure was cut along the dotted line to form a second figure.
What statement is true about the figures? - -The area of the 2 figures is congruent, but the
perimeter of the second figure is greater.
The area is the same because the shapes occupy the same amount of space, but the perimeter is
greater for the second figure because it has 2 new external lines where it was cut.
-A student is instructed to draw a four-pointed geometric shape on an xy-plane. After the shape
is drawn, the student is instructed to add 5 to each x-coordinate and add 3 to each y-coordinate.
Which of the following did the student perform? - -translation
A translation is simply moving the object from one point on a plane to another point on the
plane. The shape of the object remains the same; the object is simply moved along the plane.
-What is the area of the figure provided? - -49.5 cm2
The area of the figure is l × w = 5.5 × 9 = 49.5 \text{ cm}^2l×w=5.5×9=49.5 cm2.
-What is the volume of the triangular prism pictured? - -60 in3
The volume of a prism is in general B*h. The base of this prism is a triangle. The area of a
triangle is ½ × b × h. The area of the base is ½ × 3 × 4 = 6 and then it is multiplied by the heights
so 6 × 10 = 60.
-Mrs. Blue wants her students to be able to write two column geometric proofs. Which is the
most appropriate way to determine their mastery? - -Give students an open ended exam where
they write multiple two column proofs.
Asking students to write a proof is the best way to determine if they can write a proof.
-Which of the following terms best describes a polygon with 4 sides with only 2 angles of equal
measure? - -Quadrilateral
A quadrilateral is a shape with 4 sides and 4 vertices. It can have any combination of equal angle
measures.
-What is the volume of a ball that is 12 cm in diameter? - -288π cm3
,The volume of a sphere is equal to 4/3 × π × r3. Since the diameter of the ball is 12 cm, the
radius of the ball is 6 cm. Therefore the volume of the sphere is equal to 4/3 × π × 63, which
equals 288π cm3.
-What is the area of the shaded region? - -34 in2
One way to find the area is to find the area of the large rectangle, then subtract the area that is cut
out.
A=A_{\text{large rectangle}}-A_{\text{ small rectangle}}=(11\times 8)-(9\times 6)=88-54=34\
text{ in}^2A=Alarge rectangle−A small rectangle=(11×8)−(9×6)=88−54=34 in2
Similarly, the shape could be divided into 4 rectangles, then the areas can be added together.
A=2A_{rectangle_{1}}+2A_{rectangle_{2}}=2(11\times 1)-2(6\times 1)=22+12=34\
text{ in}^2A=2Arectangle1+2Arectangle2=2(11×1)−2(6×1)=22+12=34 in2.
-Triangle ABC has been plotted on a coordinate graph with the points A (-3, 1), B (-1, 3), and C
(-1, 1). If the triangle is translated 5 units right and 2 units down, what are the new coordinates of
point A? - -(2, -1)
A translation of a geometric figure moves the entire figure to a new location in the same
coordinate plane. If the movement is a shift to the right, the x-coordinate (first coordinate) should
be increased. If the movement includes a shift down, the y-coordinate (second coordinate) should
be decreased.
Therefore, if the point (-3, 1) is shifted 5 units to the right and 2 units down, the new point will
be (-3 + 5, 1 - 2) = (2, -1).
-The images below are similar triangles. Solve for the missing value, x. - -12
Since the triangles are similar, this question is best solved by setting up a proportion: \frac{15}
{20} = \frac{x}{16}2015=16x
Solving leads to 20x = 24020x=240.
This reduces to x = 12x=12
-There are 9 regular parallelograms that compose a single large one.
If the perimeter of each of the regular parallelograms is 14, what is the perimeter of the large
figure? - -42
If the perimeter is 14 then each side is 3.5 (14 ÷ 4 = 3.5).
There are 12 sides used to compose the larger parallelogram. 12 × 3.5 = 42
-Ms. Trask wants to create an authentic assessment to test her students about angles in triangles.
Which of the following should she do first? - -Look at the standards to determine what a
meaningful task that students could complete to demonstrate their knowledge.
Looking at the standards to design the assessment is a great first step.
-A fifth-grade teacher wants to assess students' ability to calculate the area of nonstandard
polygons. Which of the following figures would assess a student's ability to find the area of non-
standard polygons? - -Figure 5
,Figure 5 is a non-standard polygon because it does not have a standard geometric structure, such
as a triangle, square, or rectangle do.
-What is the perimeter of the shaded portion of the figure? - -$$68 \text{ in}$
To find the perimeter, add the perimeter of the outside with the perimeter of the inside.
P=[2(11)+2(8)]+[2(9)+2(6)]=38+30=68 \text{ in}P=[2(11)+2(8)]+[2(9)+2(6)]=38+30=68 in
-The ΔABC in the coordinate plane will be translated 3 units to the right and then 4 units down.
Which of the following points correctly expresses the location of vertex C after the translations?
- -(-2, -2)
The original coordinates of point C are (-5, 2). A translation to the right increases the first
coordinate, in this case, by 3 units: -5 + 3 = -2. A translation down decreases the second
coordinate, in this case, by 4 units: 2 - 4 = -2.
-Which of the following best describes the polygon shown? - -a convex pentagon
A pentagon has 5 sides. A convex polygon has no angles greater than 180°. Another way to think
of how to identify a convex pentagon is that it has no angles pointing inward.
-A rectangle has a length that is twice the size of its width. If the perimeter of the rectangle is 48
inches, what is the area of the rectangle in square inches? - -128 in2
Since the length is twice the size of the width, the equation for the perimeter would be
P=w+w+l+l=w+w_{}+2w+2wP=w+w+l+l=w+w+2w+2w.
Since the perimeter is 48, 48=6w48=6w so the width is 8 and the length must be 16.
The area would then be A=lw= \left( 16 \right) \left( 8 \right) =128A=lw=(16)(8)=128 in2.
-Miguel is playing with his model cars. Which transformation is represented in the picture of his
cars? - -rotation
This is a rotation because the top car has been rotated 180° about the point at the center, which is
the transformation between the two cars, leaving you with this position and orientation of the
bottom car.
-How many faces does a rectangular prism have? - -6
A rectangular prism has 6 faces.
-A child is using a geoboard and creates a shape with 3 angles. What is the name of this shape? -
-Triangle
A triangle has 3 sides and 3 angles.
-The cement pipe used in a storm drain system is an 8-foot long right circular cylinder with a
wall thickness of 3 inches and an outside diameter of 24 inches. Which of the values below best
approximates the volume, in cubic feet, of the interior of the pipe? (The formula for the volume,
V, of a right circular cylinder with radius r and height h is V = πr2h.) - -14.1
If the diameter of the pipe is 24 inches, then the radius of the pipe is 12 inches (because d = 2r,
where d = diameter and r = radius). If the wall of the pipe has a thickness of 3 inches, then the
interior of the pipe has a radius of 12 - 3 = 9 inches. Because the calculation is to be performed in
, cubic feet and not in inches, 9 inches must be converted to feet. This can be done using the
conversion factor 1 foot/12 inches to cancel inches and bring in feet. 9 inches × 1 foot/12 inches
= 9 feet/12, which reduces to ¾ feet, or 0.75 feet. Therefore, the radius to use in the volume
calculation is 0.75 feet. The length of the cement pipe was given as 8 feet. Accordingly, the
value to use as the height of the right circular cylinder is 8 feet. Finally, substitutions can be
made and the appropriate calculations performed, using 3.14 as an approximation for π in the
formula V = πr2h so that the volume of the interior of the pipe is discovered to be approximately
14.13 cubic feet. The best answer to select from the options, therefore, is 14.1.
V = π(0.75)2(8)= π(0.5625)(8)= π(4.5)≈14.13 cubic feet
-Which of the following terms would be used to describe a polygon with six sides whose angles
are all of equal measure? - -a regular hexagon
Since all angles are of equal measure, the polygon is regular. Since it has six sides it is a
hexagon.
-A tennis ball has a diameter of about 3 inches. The container that holds a stack of three such
balls is a right cylinder with a circular base. What is the approximate volume, in cubic inches, of
the container that holds three tennis balls? - -64
To find the volume of a right cylinder with a circular base, the area of the base of the cylinder is
multiplied by its height. The area of the base of this container is a circle and so the calculation
for its area should follow the formula A = πr2, where A = the area of the circular base and r = the
radius of the base. The radius of the circular base of the can should be approximately equal to
(though slightly larger than) the radius of the tennis ball. The diameter of the ball is given as
"about 3 inches". Because diameter is twice radius, the radius of the tennis ball must be
approximately half of that amount, or about 1.5 inches. Therefore, the area of the base of the
cylindrical can with a circular base can be calculated as A = π(1.5)2 = 2.25π ≈ 7.07 square
inches. It was given that the can for the tennis balls fits a stack of three tennis balls. Therefore,
the height of the can should equal the height of three 3-inch diameter balls stacked on top of each
other: 3(3 inches) = 9 inches. Therefore, the height of the can must be about 9 inches. Now the
volume of the container can be calculated by multiplying the area of the circular base, ~7.07
inches, with the height of the can, ~9 inches. 7.07(9) = 63.63 in³. This answer can be rounded to
approximately 64 cubic inches for the best approximate answer to this question.
-The Huang family is building a circular swimming pool in their backyard with a diameter of 8
meters. They wish to place a decorative rock border along the edge of the pool from point A to
point B, as shown by the dotted curve in the diagram. As seen in the diagram, points A and B are
directly across from one another. Approximately how many linear meters of rock will be needed
to form the decorative border along the edge of the pool from point A to point B? - -12.6 m
The length of the edge of the pool from point A to point B is a portion of the perimeter of the
pool. Because points A and B are directly across from each other and the segment which
connects them passes through the center of the circular swimming pool, the segment AB is a
diameter, and so the portion of the perimeter of the pool that will have a decorative rock border
is exactly half. Because the pool is in the shape of a circle, its perimeter is calculated using the
formula for C, the circumference of a circle. C = πd. The circumference of the swimming pool is
simply C = π×8 ≈ 3.14×8 ≈ 25.12 meters. Given that the circumference is ~25.12 meters, half
that amount is 12.56 meters. Therefore, the best answer option is 12.6.
Answers Grade Level 2023
What is the perimeter of the figure provided? - -29 cm
The perimeter of the figure is 2 × (l + w) = 2 × (5.5 + 9) = 29 cm.
-As shown below, a figure was cut along the dotted line to form a second figure.
What statement is true about the figures? - -The area of the 2 figures is congruent, but the
perimeter of the second figure is greater.
The area is the same because the shapes occupy the same amount of space, but the perimeter is
greater for the second figure because it has 2 new external lines where it was cut.
-A student is instructed to draw a four-pointed geometric shape on an xy-plane. After the shape
is drawn, the student is instructed to add 5 to each x-coordinate and add 3 to each y-coordinate.
Which of the following did the student perform? - -translation
A translation is simply moving the object from one point on a plane to another point on the
plane. The shape of the object remains the same; the object is simply moved along the plane.
-What is the area of the figure provided? - -49.5 cm2
The area of the figure is l × w = 5.5 × 9 = 49.5 \text{ cm}^2l×w=5.5×9=49.5 cm2.
-What is the volume of the triangular prism pictured? - -60 in3
The volume of a prism is in general B*h. The base of this prism is a triangle. The area of a
triangle is ½ × b × h. The area of the base is ½ × 3 × 4 = 6 and then it is multiplied by the heights
so 6 × 10 = 60.
-Mrs. Blue wants her students to be able to write two column geometric proofs. Which is the
most appropriate way to determine their mastery? - -Give students an open ended exam where
they write multiple two column proofs.
Asking students to write a proof is the best way to determine if they can write a proof.
-Which of the following terms best describes a polygon with 4 sides with only 2 angles of equal
measure? - -Quadrilateral
A quadrilateral is a shape with 4 sides and 4 vertices. It can have any combination of equal angle
measures.
-What is the volume of a ball that is 12 cm in diameter? - -288π cm3
,The volume of a sphere is equal to 4/3 × π × r3. Since the diameter of the ball is 12 cm, the
radius of the ball is 6 cm. Therefore the volume of the sphere is equal to 4/3 × π × 63, which
equals 288π cm3.
-What is the area of the shaded region? - -34 in2
One way to find the area is to find the area of the large rectangle, then subtract the area that is cut
out.
A=A_{\text{large rectangle}}-A_{\text{ small rectangle}}=(11\times 8)-(9\times 6)=88-54=34\
text{ in}^2A=Alarge rectangle−A small rectangle=(11×8)−(9×6)=88−54=34 in2
Similarly, the shape could be divided into 4 rectangles, then the areas can be added together.
A=2A_{rectangle_{1}}+2A_{rectangle_{2}}=2(11\times 1)-2(6\times 1)=22+12=34\
text{ in}^2A=2Arectangle1+2Arectangle2=2(11×1)−2(6×1)=22+12=34 in2.
-Triangle ABC has been plotted on a coordinate graph with the points A (-3, 1), B (-1, 3), and C
(-1, 1). If the triangle is translated 5 units right and 2 units down, what are the new coordinates of
point A? - -(2, -1)
A translation of a geometric figure moves the entire figure to a new location in the same
coordinate plane. If the movement is a shift to the right, the x-coordinate (first coordinate) should
be increased. If the movement includes a shift down, the y-coordinate (second coordinate) should
be decreased.
Therefore, if the point (-3, 1) is shifted 5 units to the right and 2 units down, the new point will
be (-3 + 5, 1 - 2) = (2, -1).
-The images below are similar triangles. Solve for the missing value, x. - -12
Since the triangles are similar, this question is best solved by setting up a proportion: \frac{15}
{20} = \frac{x}{16}2015=16x
Solving leads to 20x = 24020x=240.
This reduces to x = 12x=12
-There are 9 regular parallelograms that compose a single large one.
If the perimeter of each of the regular parallelograms is 14, what is the perimeter of the large
figure? - -42
If the perimeter is 14 then each side is 3.5 (14 ÷ 4 = 3.5).
There are 12 sides used to compose the larger parallelogram. 12 × 3.5 = 42
-Ms. Trask wants to create an authentic assessment to test her students about angles in triangles.
Which of the following should she do first? - -Look at the standards to determine what a
meaningful task that students could complete to demonstrate their knowledge.
Looking at the standards to design the assessment is a great first step.
-A fifth-grade teacher wants to assess students' ability to calculate the area of nonstandard
polygons. Which of the following figures would assess a student's ability to find the area of non-
standard polygons? - -Figure 5
,Figure 5 is a non-standard polygon because it does not have a standard geometric structure, such
as a triangle, square, or rectangle do.
-What is the perimeter of the shaded portion of the figure? - -$$68 \text{ in}$
To find the perimeter, add the perimeter of the outside with the perimeter of the inside.
P=[2(11)+2(8)]+[2(9)+2(6)]=38+30=68 \text{ in}P=[2(11)+2(8)]+[2(9)+2(6)]=38+30=68 in
-The ΔABC in the coordinate plane will be translated 3 units to the right and then 4 units down.
Which of the following points correctly expresses the location of vertex C after the translations?
- -(-2, -2)
The original coordinates of point C are (-5, 2). A translation to the right increases the first
coordinate, in this case, by 3 units: -5 + 3 = -2. A translation down decreases the second
coordinate, in this case, by 4 units: 2 - 4 = -2.
-Which of the following best describes the polygon shown? - -a convex pentagon
A pentagon has 5 sides. A convex polygon has no angles greater than 180°. Another way to think
of how to identify a convex pentagon is that it has no angles pointing inward.
-A rectangle has a length that is twice the size of its width. If the perimeter of the rectangle is 48
inches, what is the area of the rectangle in square inches? - -128 in2
Since the length is twice the size of the width, the equation for the perimeter would be
P=w+w+l+l=w+w_{}+2w+2wP=w+w+l+l=w+w+2w+2w.
Since the perimeter is 48, 48=6w48=6w so the width is 8 and the length must be 16.
The area would then be A=lw= \left( 16 \right) \left( 8 \right) =128A=lw=(16)(8)=128 in2.
-Miguel is playing with his model cars. Which transformation is represented in the picture of his
cars? - -rotation
This is a rotation because the top car has been rotated 180° about the point at the center, which is
the transformation between the two cars, leaving you with this position and orientation of the
bottom car.
-How many faces does a rectangular prism have? - -6
A rectangular prism has 6 faces.
-A child is using a geoboard and creates a shape with 3 angles. What is the name of this shape? -
-Triangle
A triangle has 3 sides and 3 angles.
-The cement pipe used in a storm drain system is an 8-foot long right circular cylinder with a
wall thickness of 3 inches and an outside diameter of 24 inches. Which of the values below best
approximates the volume, in cubic feet, of the interior of the pipe? (The formula for the volume,
V, of a right circular cylinder with radius r and height h is V = πr2h.) - -14.1
If the diameter of the pipe is 24 inches, then the radius of the pipe is 12 inches (because d = 2r,
where d = diameter and r = radius). If the wall of the pipe has a thickness of 3 inches, then the
interior of the pipe has a radius of 12 - 3 = 9 inches. Because the calculation is to be performed in
, cubic feet and not in inches, 9 inches must be converted to feet. This can be done using the
conversion factor 1 foot/12 inches to cancel inches and bring in feet. 9 inches × 1 foot/12 inches
= 9 feet/12, which reduces to ¾ feet, or 0.75 feet. Therefore, the radius to use in the volume
calculation is 0.75 feet. The length of the cement pipe was given as 8 feet. Accordingly, the
value to use as the height of the right circular cylinder is 8 feet. Finally, substitutions can be
made and the appropriate calculations performed, using 3.14 as an approximation for π in the
formula V = πr2h so that the volume of the interior of the pipe is discovered to be approximately
14.13 cubic feet. The best answer to select from the options, therefore, is 14.1.
V = π(0.75)2(8)= π(0.5625)(8)= π(4.5)≈14.13 cubic feet
-Which of the following terms would be used to describe a polygon with six sides whose angles
are all of equal measure? - -a regular hexagon
Since all angles are of equal measure, the polygon is regular. Since it has six sides it is a
hexagon.
-A tennis ball has a diameter of about 3 inches. The container that holds a stack of three such
balls is a right cylinder with a circular base. What is the approximate volume, in cubic inches, of
the container that holds three tennis balls? - -64
To find the volume of a right cylinder with a circular base, the area of the base of the cylinder is
multiplied by its height. The area of the base of this container is a circle and so the calculation
for its area should follow the formula A = πr2, where A = the area of the circular base and r = the
radius of the base. The radius of the circular base of the can should be approximately equal to
(though slightly larger than) the radius of the tennis ball. The diameter of the ball is given as
"about 3 inches". Because diameter is twice radius, the radius of the tennis ball must be
approximately half of that amount, or about 1.5 inches. Therefore, the area of the base of the
cylindrical can with a circular base can be calculated as A = π(1.5)2 = 2.25π ≈ 7.07 square
inches. It was given that the can for the tennis balls fits a stack of three tennis balls. Therefore,
the height of the can should equal the height of three 3-inch diameter balls stacked on top of each
other: 3(3 inches) = 9 inches. Therefore, the height of the can must be about 9 inches. Now the
volume of the container can be calculated by multiplying the area of the circular base, ~7.07
inches, with the height of the can, ~9 inches. 7.07(9) = 63.63 in³. This answer can be rounded to
approximately 64 cubic inches for the best approximate answer to this question.
-The Huang family is building a circular swimming pool in their backyard with a diameter of 8
meters. They wish to place a decorative rock border along the edge of the pool from point A to
point B, as shown by the dotted curve in the diagram. As seen in the diagram, points A and B are
directly across from one another. Approximately how many linear meters of rock will be needed
to form the decorative border along the edge of the pool from point A to point B? - -12.6 m
The length of the edge of the pool from point A to point B is a portion of the perimeter of the
pool. Because points A and B are directly across from each other and the segment which
connects them passes through the center of the circular swimming pool, the segment AB is a
diameter, and so the portion of the perimeter of the pool that will have a decorative rock border
is exactly half. Because the pool is in the shape of a circle, its perimeter is calculated using the
formula for C, the circumference of a circle. C = πd. The circumference of the swimming pool is
simply C = π×8 ≈ 3.14×8 ≈ 25.12 meters. Given that the circumference is ~25.12 meters, half
that amount is 12.56 meters. Therefore, the best answer option is 12.6.
