Question 1

In the coordinate plane, line $p$ has slope 8 and $y$-intercept (0, 5). Line $r$ is the result of dilating line $p$ by a factor of 3 with center (0, 3). What is the slope and $y$-intercept of line $r$?

(*NO CALCULATOR*)

Accepted Answer

Line $r$ has slope 8 and $y$-intercept (0, 9).

Answer

Line $r$ has slope 5 and $y$-intercept (0, 2).

Answer

Line $r$ has slope 8 and $y$-intercept (0, 5).

Answer

Line $r$ has slope 11 and $y$-intercept (0, 8).

Question 2

The equation $x^2 + y^2 - 4x + 2y = b$ describes a circle.

Determine the $y$-coordinate of the center of the circle.
Enter your answer in the box.

(*NO CALCULATOR*)

Accepted Answer

-1

Question 3

The equation $x^2 + y^2 - 4x + 2y = b$ describes a circle.

The radius of the circle is 7 units. What is the value of $b$ in the equation?
Enter your answer in the box.

(*NO CALCULATOR*)

Accepted Answer

44

Question 4

In the coordinate plane shown, point $C$ (not shown) lies on $\overline {AB}$. 
If the ratio of the length of $\overline{AC}$ to the length of $\overline {CB}$ is 3: 1, what is the $y$-coordinate of point $C$?
Enter your answer in the box.

(*NO CALCULATOR*)

Accepted Answer

8.5

Question 5

The figure shows $ \Delta ABC \sim \Delta DEF$ with side lengths as indicated. 
What is the value of $x$?
Enter your answer in the box.

(*NO CALCULATOR*)

Accepted Answer

15

Question 6

In this figure, triangle $GHJ$ is similar to triangle $PQR$.
Based on this information, which ratio represents $tanH$?

(*NO CALCULATOR*)

Accepted Answer

$\frac{8}{15}$

Answer

$\frac{8}{17}$

Answer

$\frac{17}{8}$

Answer

$\frac{15}{8}$

Question 7

The circle with center $F$ is divided into sectors. In circle $F$, $\overline {EB}$ is a diameter.
The length of $\overline {FB}$ is 3 units. 
Select the correct expression that represents the arc length of $\stackrel \frown {AED}$.

(*NO CALCULATOR*)

Accepted Answer

$\frac {11\pi}{4}$

Answer

$\frac {13\pi}{4}$

Answer

$\pi$

Answer

$\frac {7\pi}{4}$

Question 8

The figure shows line $r$, points $P$ and $T$ on line $r$, and point $Q$ not on line $r$. Also shown is ray $PQ$. 
Consider the partial construction of a line parallel to $r$ through point $Q$. What would be the final step in the construction?

Accepted Answer

draw a line through $Q$ and $S$

Answer

draw a line through $P$ and $S$

Answer

draw a line through $T$ and $S$

Answer

draw a line through $W$ and $S$

Question 9

The figure shows line $r$, points $P$ and $T$ on line $r$, and point $Q$ not on line $r$. Also shown is ray $PQ$.
Once the construction is complete, which of the reasons listed contribute to proving the validity of the construction?

Accepted Answer

When two lines are cut by a transversal and the corresponding angles are congruent, the lines are parallel.

Answer

definition of an angle bisector

Answer

definition of segment bisector

Answer

When two lines are cut by a transversal and the vertical angles are congruent, the lines are parallel.

Question 10

Luke purchased a warehouse on a plot of land for his business. The figure represents a plan of the land showing the location of the warehouse and parking area. The coordinates represent points on a rectangular grid with units in feet.
What is the perimeter of the plot of land?
Express your answer to the nearest tenth of a foot.
Enter your answer in the box.

Accepted Answer

243.2

Question 11

Luke purchased a warehouse on a plot of land for his business. The figure represents a plan of the land showing the location of the warehouse and parking area. The coordinates represent points on a rectangular grid with units in feet.
What is the area, in square feet, of the plot of land that does $not$ include the warehouse and the parking area?
Enter your answer in the box.

Accepted Answer

freetextm://1740:1,740

Question 12

Luke purchased a warehouse on a plot of land for his business. The figure represents a plan of the land showing the location of the warehouse and parking area. The coordinates represent points on a rectangular grid with units in feet.
Luke is planning to put a fence along two interior sides of the parking area.
The sides are represented in the plan by the legs of the trapezoid. What is the total length of fence needed?
Express your answer to the nearest tenth of a foot.
Enter your answer in the box.

Accepted Answer

42.8

Question 13

A spring is attached at one end to support $B$ and at the other end to collar $A$, as represented in the figure. Collar $A$ slides along the vertical bar between points $C$ and $D$. In the figure, the angle $	heta$ is the angle created as the collar moves between points $C$ and $D$.

When $	heta = 28 \degree$, what is the distance from point $A$ to point $B$ to the nearest tenth of a foot?
Enter your answer in the box.

Accepted Answer

3.4

Question 14

A spring is attached at one end to support $B$ and at the other end to collar $A$, as represented in the figure. Collar $A$ slides along the vertical bar between points $C$ and $D$. In the figure, the angle $	heta$ is the angle created as the collar moves between points $C$ and $D$.

When the spring is stretched and the distance from point $A$ to point $B$ is 5.2 feet, what is the value of $	heta$ to the nearest tenth of a degree?

Accepted Answer

$54.8 \degree$

Answer

$60.0 \degree$

Answer

$35.2 \degree$

Answer

$45.1 \degree$

Question 15

A rectangle will be rotated $360 \degree$ about a line that contains the point of intersection of its diagonals and is parallel to a side. What three-dimensional shape will be created as a result of the rotation?

Accepted Answer

a cylinder

Answer

a rectangular prism

Answer

a sphere

Answer

a cube

Question 16

The figure shows two semicircles with centers $P$ and $M$. The semicircles are tangent to each other at point $B$, and $\stackrel \longrightarrow {DE}$ is tangent to both semicircles at $F$ and $E$.

If $PB = BC = 6$, what is $ED$?

Accepted Answer

$\sqrt{72}$

Answer

$\sqrt{48}$

Answer

8

Answer

6

Question 17

The figure shows line $AC$ and line $PQ$ intersecting at point $B$. Lines $A'C'$ and $P'Q'$ will be the images of lines $AC$ and $PQ$, respectively, under a dilation with center $P$ and scale factor 2.

Which statement about the image of lines $AC$ and $PQ$ would be true under the dilation?

Accepted Answer

Line $A'C'$ will be parallel to line $AC$, and line $P'Q'$ will be the same line as line $PQ$.

Answer

Line $A'C'$ will be perpendicular to line $AC$, and line $P'Q'$ will be parallel to line $PQ$.

Answer

Line $A'C'$ will be parallel to line $AC$, and line $P'Q'$ will be parallel to line $PQ$.

Answer

Line $A'C'$ will be perpendicular to line $AC$, and line $P'Q'$ will be the same line as line $PQ$.

Question 18

Quadrilaterals $ABCD$ and $EFGH$ are shown in the coordinate plane. 
Quadrilateral $ABCD$ will be reflected across the $x$-axis and then rotated $90 \degree$ clockwise about the origin to create quadrilateral $A'B'C'D'$. What will be the $y$-coordinate of $B'$?
Enter your answer in the box.

Accepted Answer

3

Question 19

The equation $x^2 - 8x + y^2 = 9$ defines a circle in the $xy$-coordinate plane.
What is the radius of the circle?
Enter your answer in the box.

Accepted Answer

5

Question 20

In the $xy$-coordinate plane, $\Delta ABC$ has vertices $A(-4, 6), 8(2, 6)$, and $C(2, 2)$. $\Delta DEF$ is shown in the plane. 
What is the scale factor and the center of dilation that maps $\Delta ABC$ to $\Delta DEF$?

Accepted Answer

The scale factor is $\frac{1}{2}$, and the center of dilation is the origin.

Answer

The scale factor is $\frac{1}{2}$, and the center of dilation is point $B$.

Answer

The scale factor is 2, and the center of dilation is the origin.

Answer

The scale factor is 2, and the center of dilation is point $B$.

Question 21

Mariela is standing in a building and looking out of a window at a tree. The tree is 20 feet away from Mariela. Mariela's line of sight to the top of the tree creates a $42 \degree$ angle of elevation, and her line of sight to the base of the tree creates a $31\degree$  angle of depression. 
What is the height, in feet, of the tree?
Enter your answer in the box.

Accepted Answer

freetextm://30:30.03

Question 22

The table shows the approximate measurements of the Great Pyramid of Giza in Egypt and the Pyramid of Kukulcan in Mexico.
Approximately what is the difference between the volume of the Great Pyramid of Giza and the volume of the Pyramid of Kukulcan?

Accepted Answer

2,562,000 cubic meters

Answer

7,686,000 cubic meters

Answer

1,945,000 cubic meters

Answer

5,835,000 cubic meters

Question 23

In right triangle $ABC$, $m\angle B 
eq m\angle C$. Let $sinB = r$ and $cosB = s$. What is $sinC - cosC$?

Accepted Answer

$s-r$

Answer

$\frac{r}{s}$

Answer

$r-s$

Answer

$r+s$

Question 24

The figure shows the result of a geometric construction. 
The first step of the construction is to draw an arc centered at point $A$ that passes through point $B$ and point $C$. What is established by the first step?

Accepted Answer

$\overline{AB} \cong \overline{AC}$

Answer

$\overline{AD} \cong \overline{AC}$

Answer

$\overline{BD} \cong \overline{CD}$

Answer

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

Question 25

The construction creates congruent triangles. $\Delta ABD \cong \Delta ACD$ (not shown). Which statement provides evidence that $\stackrel \longrightarrow{AD}$  is the angle bisector of $\angle BAC$?

Accepted Answer

$\angle BAD \cong \angle CAD$

Answer

$\angle BAD \cong \angle ABD$

Answer

$\angle BAC \cong \angle BDC$

Answer

$\angle ACD \cong \angle ABD$

Question 26

The figure shows $\Delta ABC$ inscribed in circle $D$. 
If $m\angle CBD=44 \degree$, find $m\angle BAC$, in degrees.
Enter your answer in the box.

Accepted Answer

46

Question 27

One method that can be used to prove that the diagonals of a parallelogram bisect each other is shown in the given partial proof.
Which reason justifies the statement for step 3 in the proof?

Accepted Answer

When two parallel lines are intersected by a transversal, alternate interior angles are congruent.

Answer

When two parallel lines are intersected by a transversal, same side interior angles are supplementary.

Answer

When two parallel lines are intersected by a transversal, same side interior angles are congruent.

Answer

When two parallel lines are intersected by a transversal, alternate interior angles are supplementary.

Question 28

Which statement is justified by the reason for step 4 in the proof?

Accepted Answer

$\overline{PQ} \cong \overline{RS}$

Answer

$\overline{SQ} \cong \overline{PR}$

Answer

$\overline{PQ} \cong \overline{SP}$

Answer

$\overline{PT} \cong \overline{TR}$

Question 29

Which reason justifies the statement for step 5 in the proof?

Accepted Answer

angle-side-angle triangle congruence

Answer

angle-angle-side triangle congruence

Answer

side-angle-side triangle congruence

Answer

side-side-side triangle congruence

Question 30

Another method of proving diagonals of a parallelogram bisect each other uses a coordinate grid.
What could be shown about the diagonals of parallelogram $PQRS$ to complete the proof?

Accepted Answer

$\overline{PR}$ and $\overline{SQ}$ have the same midpoint.

Answer

$\overline{PR}$ and $\overline{SQ}$ have the same length.

Answer

$\overline{PR}$ is a perpendicular bisector of $\overline{SQ}$.

Answer

Angles formed by the intersection of $\overline{PR}$ and $\overline{SQ}$ each measure $90 \degree$.

Question 31

Line segment $AB$ with endpoints $A(4, 16)$ and $8(20, 4)$ lies in the coordinate plane. The segment will be dilated with a scale factor of $\frac{3}{4}$ and a center at the origin to create $\overline{A'B'}$. What will be the length of $\overline{A'B'}$?

Accepted Answer

15

Answer

12

Answer

4

Answer

5

Question 32

Triangle $ABC$ has vertices at $A(1, 2), B(4, 6)$, and $C(4, 2)$ in the coordinate plane. The triangle will be reflected over the $x$-axis and then rotated $180 \degree$ about the origin to form $\Delta A'B'C'$. What are the vertices of $\Delta A'B'C'$?

Accepted Answer

$A'(-1, 2), B'( -4, 6), C'( -4, 2) $

Answer

$A'(-1, -2), B'( -4, -6), C'( -4, -2) $

Answer

$A'(1, 2), B'( 4, 6), C'( 4, 2) $

Answer

$A'(1, -2), B'( 4, -6), C'( 4, -2) $

Question 33

The figure shows rectangle $ABCD$ in the coordinate plane with point $A$ at $(0, 2.76), B$ at $(3.87, 2.76), C$ at $(3.87, 0)$, and $D$ at the origin. Rectangle $ABCD$ can be used to approximate the size of the state of Colorado with the $x$ and $y$ scales representing hundreds of miles.
Based on the information given, how many miles is the perimeter of Colorado?
Enter your answer in the box.

Accepted Answer

freetextm://1326:1,326

Question 34

The figure shows rectangle $ABCD$ in the coordinate plane with point $A$ at $(0, 2.76), B$ at $(3.87, 2.76), C$ at $(3.87, 0)$, and $D$ at the origin. Rectangle $ABCD$ can be used to approximate the size of the state of Colorado with the $x$ and $y$ scales representing hundreds of miles.

At the end of 2010, the population of Colorado was 5,029,196 people. Based on the information given, what was the population density at the end of 2010?

Accepted Answer

47 people per square mile

Answer

2,269 people per square mile

Answer

25 people per square mile

Answer

7,586 people per square mile

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