Question 1

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

Determine the $	ext{y-coordinate}$ of the center of the circle.

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Accepted Answer

-1

Question 2

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?

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Accepted Answer

44

Question 3

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 $	ext{y-coordinate}$ of point $C$ ?

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Accepted Answer

8.5

Question 4

In this figure, triangle $GHJ$ is similar to triangle $PQR$.

Based on this information, which ratio represents $	ext{tan}H$?

Accepted Answer

$\frac{8}{15}$

Answer

$\frac{8}{17}$

Answer

$\frac{17}{8}$

Answer

$\frac{15}{8}$

Question 5

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 $\widehat{AED}$.

Accepted Answer

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

Answer

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

Answer

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

Answer

$\pi$

Question 6

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 $T$ and $S$

Answer

draw a line through $W$ and $S$

Answer

draw a line through $P$ and $S$

Question 7

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 segment bisector

Answer

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

Answer

definition of an angle bisector

Question 8

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 $\Theta$is the angle created as the collar moves between points $C$ and $D$.

When $\Theta=28^\circ$, what is the distance from point $A$ to point $B$ to the nearest tenth of a foot?

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Accepted Answer

3.4

Question 9

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 $\Theta$ 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 $\Theta$ to the nearest tenth of a degree?

Accepted Answer

$54.8^\circ$

Answer

$35.2^\circ$

Answer

$45.1^\circ$

Answer

$60.0^\circ$

Question 10

A rectangle will be rotated $360^\circ$ 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 cube

Answer

a sphere

Answer

a rectangular prism

Question 11

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?

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Accepted Answer

freetextm://1326: 1,326

Question 12

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

$25$ people per square mile

Answer

$2,269$ people per square mile

Answer

$7,586$ people per square mile

Question 13

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 14

In the $xy	ext{-coordinate}$ plane, $\vartriangle ABC$ had vertices $A(-4,6), B(2,6),$ and $C(2,2)$.
$\vartriangle DEF$ is shown in the plane.

What is the scale factor and the center of dilation that maps $\vartriangle ABC$ to $\vartriangle DEF$?

Accepted Answer

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

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 $B$.

Answer

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

Question 15

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

$2,562,000 \,	ext{cubic meters}$

Answer

$7,686,000 \,	ext{cubic meters}$

Answer

$1,945,000\,	ext{cubic meters}$

Answer

$5,835,000 \,	ext{cubic meters}$

Question 16

In right triangle $ABC, m\angle B  
eq m\angle C$. Let $\sin B=r$ and $\cos B$. What is $\sin C - \cos C$?

Accepted Answer

$s-r$

Answer

$\frac{r}{s}$

Answer

$r-s$

Answer

$r+s$

Question 17

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 $x	ext{-axis}$ and then rotated $180^\circ$ about the origin to form $\vartriangle A'B'C'$. What are the vertices of $\vartriangle A'B'C'$?

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 18

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

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

Accepted Answer

$\sqrt{72}$

Answer

$8$

Answer

$\sqrt{48}$

Answer

$6$

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