Question 1

A student has a rectangular postcard that he folds in half lengthwise.
Next, he rotates it continuously about the folded edge. Which three-dimensional
object is generated by this rotation?

Accepted Answer

3

Answer

1

Answer

4

Answer

2

Question 2

A three-inch line segment is dilated by a scale factor of 6 and
centered at its midpoint. What is the length of its image?

Accepted Answer

18 inches

Answer

15 inches

Answer

2 inches

Answer

9 inches

Question 3

Kevin’s work for deriving the equation of a circle is shown below. In which step did he make his error in his work?

Accepted Answer

Step 2

Answer

Step 3

Answer

Step 4

Answer

Step 1

Question 4

Which transformation of $\overline{OA}$ would result in an image parallel to $\overline{OA}$?

Accepted Answer

a translation of two units down

Answer

a clockwise rotation of 90° about the origin

Answer

a reflection over the y-axis

Answer

a reflection over the x-axis

Question 5

Using the information given below, which set of triangles can $not$ be proven similar?

Accepted Answer

3

Answer

4

Answer

1

Answer

2

Question 6

A company is creating an object from a wooden cube with an edge
length of 8.5 cm. A right circular cone with a diameter of 8 cm and
an altitude of 8 cm will be cut out of the cube. Which expression
represents the volume of the remaining wood?

Accepted Answer

$(8.5)^3-\frac{1}{3}\pi(4)^2(8)$

Answer

$(8.5)^3-\frac{1}{3}\pi(8)^2(8)$

Answer

$(8.5)^3-\pi(8)^2(8)$

Answer

$(8.5)^3-\pi(4)^2(8)$

Question 7

Two right triangles must be congruent if

Accepted Answer

the corresponding legs are congruent

Answer

an acute angle in each triangle is congruent

Answer

the lengths of the hypotenuses are equal

Answer

the areas are equal

Question 8

Which sequence of transformations will map $	riangle$ABC onto $	riangle$A'B'C'?

Accepted Answer

dilation and rotation

Answer

rotation and reflection

Answer

translation and dilation

Answer

reflection and translation

Question 9

In parallelogram $ABCD$, diagonals $\overline{AC}$ and $\overline{BD}$ intersect at $E$. Which statement does $not$ prove parallelogram $ABCD$ is a rhombus?

Accepted Answer

$\overline{AC} \cong \overline{DB}$

Answer

$\overline{AB} \cong \overline{BC}$

Answer

$\overline{AC} 	ext{ bisects } \angle{DCB}$

Answer

$\overline{AC} \perp \overline{DB}$

Question 10

In the diagram below of circle $O$, $\overline{OB}$ and $\overline{OC}$ are radii, and chords $\overline{AB}$, $\overline{BC}$, and $\overline{AC}$ are drawn. What statement must always be true?

Accepted Answer

$	ext{m}\angle{BAC} = \frac{1}{2}	ext{m}\angle{BOC}$

Answer

$	riangle{BAC}$ and $	riangle{BOC}$ are isosceles

Answer

The area of $	riangle{BAC}$ is twice the area of $	riangle{BOC}$.

Answer

$\angle{BAC} \cong \angle{BOC}$

Question 11

A 20-foot support post leans against a wall, making a 70° angle with
the ground. To the nearest ${tenth\ of \ a \ foot}$, how far up the wall will
the support post reach?

Accepted Answer

18.8

Answer

18.7

Answer

6.9

Answer

6.8

Question 12

Line segment $NY$ has endpoints N(-11,5) and Y(5,-7). What is the
equation of the perpendicular bisector of $\overline{NY}$ ?

Accepted Answer

$y+1 = \frac{4}{3}(x + 3)$

Answer

$y-6 = -\frac{3}{4}(x - 8)$

Answer

$y+1 = -\frac{3}{4}(x + 3)$

Answer

$y-6 = \frac{4}{3}(x - 8)$

Question 13

In $	riangle{RST}$ shown below, altitude $\overline{SU}$ is drawn to $\overline{RT}$ at $U$. If $SU= h$, $UT=12$, and $RT=42$, which value of $h$ will make $RST$
a right triangle with $\angle{RST}$ as  a right angle?

Accepted Answer

$6\sqrt{10}$

Answer

$6\sqrt{14}$

Answer

$6\sqrt{35}$

Answer

$6\sqrt{3}$

Question 14

In the diagram below, $	riangle{ABC}$ has vertices $A(4,5)$, $B(2,1)$, and $C(7,3)$. What is the slope of the altitude drawn from $A$ to $\overline{BC}$?

Accepted Answer

$-\frac{5}{2}$

Answer

$\frac{2}{5}$

Answer

$-\frac{1}{2}$

Answer

$\frac{3}{2}$

Question 15

In the diagram below, $	riangle{ERM} \sim 	riangle{JTM}$. Which statement is always true?

Accepted Answer

$	an(E) = \frac{TM}{JM}$

Answer

$	an(T) = \frac{RM}{EM}$

Answer

$\cos(R) = \frac{JM}{JT}$

Answer

$\cos(J) = \frac{RM}{RE}$

Question 16

On the set of axes below, rectangle $ABCD$ can be proven congruent
to rectangle $KLMN$ using which transformation?

Accepted Answer

reflection over the $x$-axis

Answer

reflection over the $y$-axis

Answer

rotation

Answer

translation

Question 17

In the diagram below, $\overline{DB}$ and $\overline{AF}$ intersect at point $C$, and $\overline{AD}$ and $\overline{FBE}$ are drawn. If $AC=6, DC=4, FC=15, m∠D=65°, and m∠CBE=115°$,
what is the length of $\overline{CB}$?

Accepted Answer

10

Answer

12

Answer

17

Answer

22,5

Question 18

Seawater contains approximately 1.2 ounces of salt per liter on average.
How many gallons of seawater, to the nearest tenth of a gallon, would
contain 1 pound of salt?

Accepted Answer

3.5

Answer

4.7

Answer

3.3

Answer

13.3

Question 19

Line segment $EA$ is the perpendicular bisector of $\overline{ZT}$, and $\overline{ZE}$ and $\overline{TE}$ are drawn.
Which conclusion can $not$ be proven?

Accepted Answer

Triangle $EZT$ is equilateral.

Answer

$\overline{EA}$ bisects angle $ZET$

Answer

$\overline{EA}$ is a median of triangle $EZT$

Answer

Angle $Z$ is congruent to angle $T$.

Question 20

A hemispherical water tank has an inside diameter of 10 feet. If water has a density of 62.4 pounds per cubic foot, what is the weight of the water in a full tank, to the nearest pound?

Accepted Answer

16,336

Answer

130,690

Answer

32,673

Answer

261,381

Question 21

In the diagram of $	riangle{ABC}$, points $D$ and $E$ are on $\overline{AB}$ and $\overline{CB}$, respectively, such that $\overline{AC} \parallel \overline{DE}$.
If $AD=24$, $DB=12$, and $DE=4$, what is the length of $\overline{AC}$ ?

Accepted Answer

12

Answer

16

Answer

72

Answer

8

Question 22

Triangle $RST$ is graphed on the set of axes below.
How many square units are in the area of $RST$?

Accepted Answer

45

Answer

$9\sqrt{5} + 15$

Answer

$9\sqrt{3} + 15$

Answer

90

Question 23

The graph below shows computations. $\overline{AB}$, which is a chord of circle $O$. The
coordinates of the endpoints of $\overline{AB}$ are $A(3,3)$ and $B(3,-7)$. The
distance from the midpoint of $\overline{AB}$ to the center of circle O is 2 units.
What could be a correct equation for circle $O$?

Accepted Answer

$\left(x-1\right)^2 + \left(y+2\right)^2 = 29$

Answer

$\left(x-1\right)^2 + \left(y-2\right)^2 = 25$

Answer

$\left(x+5\right)^2 + \left(y-2\right)^2 = 29$

Answer

$\left(x-5\right)^2 + \left(y+2\right)^2 = 25$

Question 24

What is the area of a sector of a circle with a radius of 8 inches and
formed by a central angle that measures 60°?

Accepted Answer

$\frac{32\pi}{3}$

Answer

$\frac{16\pi}{3}$

Answer

$\frac{64\pi}{3}$

Answer

$\frac{8\pi}{3}$

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