Question 1

What is the value of $n$ in the diagram below?

Accepted Answer

24

Answer

42

Answer

18

Answer

48

Question 2

Triangle M is similar to triangle N. Triangle M has two angles with measures of $32^\circ$ and $93^\circ$. Which two angle measures could be included in triangle N?

Accepted Answer

$93^\circ$ and $55^\circ$

Answer

$32^\circ$ and $58^\circ$

Answer

$93^\circ$ and $87^\circ$

Answer

$32^\circ$ and $74^\circ$

Question 3

Figure X and figure Y are shown on the coordinate grid below.

Which statement about figures X and Y MUST be true?

Accepted Answer

A series of translations will transform figure X to figure Y, and the figures will be congruent.

Answer

A series of translations will transform figure X to figure Y, but the figures will not be congruent.

Answer

A $180^\circ$ clockwise rotation will transform figure X to figure Y, but the figures will not be congruent.

Answer

A $180^\circ$clockwise rotation will transform figure X to figure Y, and the figures will be congruent.

Question 4

A cone has a radius of 1.2 inches and a height of 2.9 inches. What is the volume, to the nearest tenth of a cubic inch, of the cone?

Accepted Answer

4.4

Answer

10.6

Answer

13.1

Answer

3.6

Question 5

A solid object was sliced to form two new objects. Each of the two new objects had a circular base. Which shape could NOT have been the original object?

Accepted Answer

prism

Answer

cone

Answer

sphere

Answer

cylinder

Question 6

A cylinder has a diameter of $14$ centimeters and a volume of $112\pi$ cubic centimeters.
What is the height, in centimeters, of the cylinder?

Accepted Answer

$\frac{16}{7}$

Answer

$4$

Answer

$16$

Answer

$\frac{4}{7}$

Question 7

Maria wants to transform figure L to figure M using only rotations, reflections, and translations. Which statement is true?

Accepted Answer

The transformation cannot be done because figure L is not congruent to figure M.

Answer

The transformation can be done with a reflection followed by a translation.

Answer

The transformation can be done with a reflection followed by a rotation.

Answer

The transformation cannot be done because figures L and M are in different quadrant.

Question 8

An above-ground swimming pool in the shape of a cylinder has a diameter of $18\, 	ext {feet}$ and a height of $4.5\,  	ext {feet}$. If the pool is filled with water to $6\, 	ext {inches}$ from the top of the pool, what is the volume, to the nearest cubic foot, of the water in the pool?

Accepted Answer

$1,018$

Answer

$4,072$

Answer

$226$

Answer

$452$

Question 9

The figure shown below consists of a square pyramid on top of a cube. A vertical plane passes through point $	ext X$ and is perpendicular to the bases of both shapes, slicing the figure into equal halves.

What shape is created by the intersection of the vertical plane and these three-dimensional shapes?

Accepted Answer

pentagon

Answer

hexagon

Answer

square

Answer

triangle

Question 10

Triangle F and triangle G are shown below.

Which sequence does NOT transform triangle F to triangle G?

Accepted Answer

a reflection over the $y	ext{-axis}$ and then a $90^\circ$ clockwise rotation about the origin

Answer

a $180^\circ$  counterclockwise rotation about the origin

Answer

a reflection over the $x	ext{-axis}$ and then a reflection over the $y	ext{-axis}$

Answer

a $180^\circ$ clockwise rotation about the origin

Question 11

The vertices of a triangle are located at $	ext F(- 4, -2), 	ext G(2, 2),$ and $	ext H(0, -4).$ A sequence of transformations to triangle $	ext{FGH}$ results in triangle as shown below.

Which sequence of transformations to triangle $	ext{FGH}$ results in triangle $	ext{F'G'H'}?$

Accepted Answer

a $90^\circ$ clockwise rotation about the origin, then a dilation by a scale factor of $\frac{1}{2}$with a
center of dilation at the origin

Answer

a $90^\circ$  clockwise rotation about the origin, then a dilation by a scale factor of $2$ with a
center of dilation at the origin

Answer

a $90^\circ$  counterclockwise rotation about the origin, then a dilation by a scale factor of $2$ with
a center of dilation at the origin

Answer

a $90^\circ$ counterclockwise rotation about the origin, then a dilation by a scale factor of
$\frac{1}{2}$with a center of dilation at the origin

Question 12

A parallelogram with vertices at $(0, 3), (2, 0), (4, 2),$ and $(2, 5)$ is reflected over the $y	ext{-axis}.$ Which vertex of the parallelogram will have the same $ x	ext{-coordinate}$ before and after the reflection?

Accepted Answer

$(0, 3)$

Answer

$(2, 5)$

Answer

$(2, 0)$

Answer

$(4, 2)$

Question 13

Squares $	ext{PQRS}$ and $	ext {TUVW}$ are shown below.

Which sequence of transformations of square $	ext{PQRS}$ shows that square $	ext{PQRS}$ is congruent to square $	ext{TUVW}?$

Accepted Answer

a translation $2$ units down and $2$ units to the left, then a reflection over the $x	ext{-axis}$

Answer

a translation $2$ units up and $2$ units to the right, then a reflection over the $y	ext{-axis}$

Answer

a translation $2$ units up and $2$ units to the right, then a reflection over the $x	ext{-axis}$

Answer

a translation $2$ units down and $2$ units to the left, then a reflection over the $y	ext{-axis}$

Question 14

Two types of shipping boxes are shown below.

What is the difference in the surface areas, in square feet, of the two boxes?

Accepted Answer

3

Answer

21

Answer

30

Answer

2

Question 15

The object below was made by placing a cone on top of a cylinder. The base of the cone is congruent to the base of the cylinder.

What is the volume, in cubic centimeters, of the object?

Accepted Answer

$32\pi$

Answer

$44\pi$

Answer

$40\pi$

Answer

$128\pi$

Question 16

Lily wants to define a transformation (or series of transformations) using only rotations, reflections, or translations that takes Figure $A$ to Figure $B.$

Which statement about the transformation that Lily wants to define is true?

Accepted Answer

It cannot be defined because Figure $A$ and Figure $B$ are not congruent.

Answer

It can be defined with two reflections.

Answer

It can be defined with one rotation and one translation.

Answer

It cannot be defined because the longest side of Figure $B$ is on the bottom.

Question 17

Acute $	riangle 	ext{ABC}$ is rotated about a point and then dilated by a scale factor of $\frac{1}{2}$ to produce  $	riangle 	ext{A'B'C'}.$Which statement correctly compares   $	riangle 	ext{A'B'C'}$ to $	riangle 	ext{ABC}?$

Accepted Answer

The angle measures of $	riangle 	ext{A'B'C'}$ are the same as those of $	riangle 	ext{ABC},$ but the side
lengths of $	riangle 	ext{A'B'C'}$ are half the size of those of $	riangle 	ext{ABC}.$

Answer

The angle measures and side lengths of $	riangle 	ext{A'B'C'}$ are half the size of those
of  $	riangle 	ext{ABC}.$

Answer

The angle measures of $	riangle 	ext{A'B'C'}$ are the same as those of $	riangle 	ext{ABC},$ but the side
lengths of $	riangle 	ext{A'B'C'}$ are twice the size of those of $	riangle 	ext{ABC}.$

Answer

The angle measures of $	riangle 	ext{A'B'C'}$ depend on the angle of rotation, but the side
lengths of $	riangle 	ext{A'B'C'}$ half the size of those of$	riangle 	ext{ABC}.$

Question 18

Two transformations are performed on a figure on a coordinate plane. The first transformation is a translation 8 units to the left. Which second transformation will result in an image that is similar to, but not congruent to, the original figure?

Accepted Answer

a dilation by a scale factor of $\frac{1}{2}$ with the origin as the center of dilation

Answer

a dilation by a scale factor of $1$ with the origin as the center of dilation

Answer

clockwise rotation of $90^\circ$  about the center

Answer

a clockwise rotation of $180^\circ$about the center

Question 19

On the coordinate plane below, rectangle $ABCD$ is rotated $90\degree$ clockwise about the origin to form rectangle $WXYZ$ .
Which statement about the relationship between rectangle $ABCD$ and rectangle $WXYZ$ is true?

Accepted Answer

$\overline{AB} \cong \overline{WX}$

Answer

$\overline{DA} \cong \overline{YZ}$

Answer

$\overline{BC} \cong \overline{YZ}$

Answer

$\overline{DC} \cong \overline{XY}$

Question 20

On a coordinate plane, vertex $A$ for triangle $ABC$ is located at $(6, 4)$. Triangle $ABC$ is dilated by a scale factor of 0.5 with the center of dilation at the origin. The resulting image is triangle $A'B'C'$. What are the coordinates of vertex $A'$?

Accepted Answer

(3, 2)

Answer

(12,8)

Answer

(6.5,4.5)

Answer

(5.5, 3.5)

Question 21

Triangle $BCD$ is rotated $180\degree$ clockwise and then dilated by a factor of 4 centered at the origin. The resulting image is triangle $B'C'D'$. Which statement about the two triangles is true?

Accepted Answer

The corresponding angles of $\Delta BCD$ and $\Delta B'C'D'$ are congruent.

Answer

The perimeter of $\Delta BCD$ is 4 times the perimeter of $\Delta B'C'D'$.

Answer

The corresponding sides of $\Delta BCD$ and $\Delta B'C'D'$ are congruent.

Answer

The area of $\Delta BCD$ is 4 times the area of $\Delta B'C'D'$.

Question 22

The object below is made of solid plastic. It is a cylinder with an indentation at the top in the shape of a cone.
What is the volume, to the nearest tenth of a cubic inch, of the plastic object?

Accepted Answer

97.6

Answer

100.4

Answer

91.7

Answer

103.5

Question 23

What is the volume, in terms of $\pi$, for a cylindrical container with a radius of 3.25 centimeters and a height of 10 centimeters?

Accepted Answer

$105.625 \pi cm^3$

Answer

$422.5 \pi cm^3$

Answer

$331.83 \pi cm^3$

Answer

$65 \pi cm^3$

Question 24

Mya claims $(m\angle 3 + m\angle 4) = m\angle 1$, as shown in the triangle below.
Which equations explain why Mya's claim must be true?

Accepted Answer

$(m\angle1+m\angle2)=180 \degree$ and $(m\angle3+m\angle4+m\angle2)180 \degree$

Answer

$(m\angle1+m\angle2)=90 \degree$ and $(m\angle3+m\angle4+m\angle2)90 \degree$

Answer

$(m\angle1+m\angle2)=90 \degree$ and $(m\angle3+m\angle4)90 \degree$

Answer

$(m\angle1+m\angle2)=180 \degree$ and $(m\angle3+m\angle4)180 \degree$

Question 25

A company makes two different sized ice cream cones. The smaller cones are 3.5 inches tall and have a diameter of 3 inches. The larger cones are 5.1 inches tall and have a diameter of 4.5 inches. About how much greater, to the nearest tenth of a cubic inch, is the volume of the larger cone than the volume of the smaller cone?

Accepted Answer

18.8

Answer

225.5

Answer

56.4

Answer

75.2

Question 26

Triangle $A$ and triangle $B$ are graphed on the coordinate plane below.

Which sequence of transformations will map triangle $A$onto its congruent image, triangle $B?$

Accepted Answer

a reflection over the $x$-axis, then a translation $6$ units to the left

Answer

a rotation $90^\circ$ clockwise about the origin, then a translation $6$ units to the left

Answer

a translation $8$ units down, then a reflection over the $y$-axis

Answer

a reflection over the $x$-axis, then a reflection over the $y$-axis

Question 27

Rectangle $A'B'C'D'$ is similar to rectangle $ABCD$, as shown on the coordinate plane below.

Which sequence of transformations maps rectangle $ABCD$ onto rectangle $A'B'C'D'?$

Accepted Answer

a reflection over the $y$-axis, then a dilation by a scale factor of $\frac{1}{2}$ with a center of dilation at the origin

Answer

a dilation by a scale factor of $\frac{1}{2}$with a center of dilation at the origin, then a $90^\circ$ counterclockwise rotation about the origin

Answer

a  $90^\circ$ counterclockwise rotation about the origin, then a dilation by a scale factor of $\frac{1}{2}$ with a center of dilation at the origin

Answer

a translation $8$ units to the left, then a dilation by a scale factor of $\frac{1}{2}$ with a center of dilation at the origin

Question 28

Patty has a flower box in the shape of a rectangular prism with interior dimensions that are $15$ inches in length, $8$ inches in width, and $6$ inches in height. Patty will fill the flower box $\frac{3}{4}$full of soil. How many cubic inches of soil will be in the flower box?

Accepted Answer

$540$

Answer

$516$

Answer

$720$

Answer

$387$

Question 29

The measures of the angles in triangle UVW are shown in the diagram below.

What is the value of $x?$

Accepted Answer

$45$

Answer

$21$

Answer

$126$

Answer

$39$

Question 30

Two solids are described in the list below.
$\bullet\enspace$ One solid is a sphere and has a radius of $6$ inches.
$\bullet\enspace$ The other solid is a cylinder with a radius of $6$ inches and a height of $6$ inches.

What is the difference between the volumes, in cubic inches, of the solids in terms of $\pi$?

Accepted Answer

$72\pi$

Answer

$144\pi$

Answer

$288\pi$

Answer

$216\pi$

Question 31

Triangle ABC is graphed on a coordinate plane, as shown below.

Triangle ABC is dilated by a scale factor of 2 with a center of dilation at the origin to create $	riangle$A'B'C' . What are the coordinates of the vertices of $	riangle$ A'B'C' ?

Accepted Answer

$(4,4),\,(8,8),\,(-8,4)$

Answer

$(4,2),\,(8,6),\,(-8,2)$

Answer

$(4,4),\,(6,6),\,(-2,4)$

Answer

$(1,1),\,(2,2),\,(-2,1)$

Question 32

Pentagon $	ext P$ and pentagon $	ext Q,$ shown below, are congruent.

Which sequence could be used to transform pentagon $	ext P$ to pentagon $	ext Q?$

Accepted Answer

a reflection over the $y	ext{-axis}$ and then a translation seven units down

Answer

a translation seve n unit s down and then a $90^\circ$clockwise rotation about the origin

Answer

a translation four units left and then a reflection over the $x	ext{-axis}$

Answer

a $180^\circ$ clockwise rotation about the origin

Question 33

A cylinder and a cone have congruent heights and radii. What is the ratio of the volume of the cone to the volume of the cylinder?

Accepted Answer

$1:3$

Answer

$1:6$

Answer

$1:1$

Answer

$1:9$

Question 34

A series of transformations on quadrilateral $	ext S$ resulted in quadrilateral $	ext T.$

$\quad\bullet\,$  The angle measures of quadrilateral $	ext T$ are congruent to those of quadrilateral $	ext S.$
$\quad\bullet\,$  The side lengths of quadrilateral $	ext T$ are twice as long as those of quadrilateral $	ext S.$

Which transformation on quadrilateral $	ext S$ MUST be included to result in quadrilateral $	ext T?$

Accepted Answer

dilation

Answer

rotation

Answer

reflection

Answer

translation

Question 35

Rectangle $	ext{FGHJ,}$ shown below, is translated $6$ units right and $1$ unit up to produce rectangle $	ext{F'G'H'J'}.$

Which statement about the side lengths of rectangle $	ext{F'G'H'J'}$ is true?

Accepted Answer

$	ext{F'G'} = 3$ and $	ext{G'H'} = 5$

Answer

$	ext{F'G'} = 9$ and $	ext{G'H'} = 6$

Answer

$	ext{F'G'} = 9$ and $	ext{G'H'} = 5$

Answer

$	ext{F'G'} = 3$ and $	ext{G'H'} = 6$

Question 36

Mia enlarged a plan for an outdoor stage. The original plan is shown below.

She dilated the outdoor stage by a scale factor of four with the center of dilation at the origin.
Which ordered pair will be the coordinates of one of the new vertices?

Accepted Answer

$ (32, 16)$

Answer

$(2, 1)$

Answer

$(8, 16)$

Answer

$(32, 4)$

Question 37

A cylinder has a radius of $3$ inches and a height of $4\frac{3}{4}$ inches. A sphere has a radius of $3$ inches. What is the difference between the volumes, to the nearest tenth of a cubic inch, of the cylinder and the sphere?

Accepted Answer

$22.2$

Answer

$96.6$

Answer

$51.8$

Answer

$68.3$

Question 38

In the diagram below, lines $	ext {MN}$ and $	ext {JK}$ are parallel and are intersected by line $	ext {QT}.$

Which transformation could be used to show that $\angle 	ext {MRS}$ is congruent to  $\angle 	ext {JST}?$

Accepted Answer

translate $\angle 	ext {MRS}$ down and to the right

Answer

rotate $\angle 	ext {MRS}$ about the origin

Answer

reflect $\angle 	ext {MRS}$ over the $x 	ext{-axis}$

Answer

dilate  $\angle 	ext {MRS}$ by a scale factor of two with the center at point $	ext R$

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