Question 1

Yolanda is making a springboard to use for gymnastics. She has 8-inch-tall springs and wants to form a $16.5 \degree$ angle with the base, as modeled in the diagram below.

To the $nearest tenth of an inch$, what will be the length of the springboard, $x$?

Accepted Answer

28.2

Answer

8.3

Answer

27.0

Answer

2.3

Question 2

In the diagram below of right triangle $ABC$, altitude $\overline {BD}$ is drawn to hypotenuse $\overline {AC}$.
If $BD=4, AD=x-6$, and $CD=x$, what is the length of $\overline {CD}$?

Accepted Answer

8

Answer

11

Answer

2

Answer

5

Question 3

In the diagram below of $\Delta HAR$ and $\Delta NTY$, angles $H$ and $N$ are right angles, and $\Delta HAR \sim \Delta NTY$.

If $AR=13$ and $HR=12$, what is the measure of angle $Y$, to the $nearest degree$?

Accepted Answer

$23\degree$

Answer

$65\degree$

Answer

$25\degree$

Answer

$67\degree$

Question 4

In the diagram of $\Delta ABC$ below, points $D$ and $E$ are on sides $\overline {AB}$ and $\overline {CB}$ respectively, such that $\overline {DE} \parallel \overline{AC}$.

If $EB$ is 3 more than $DB, AB=14$, and $CB=21$, what is the length of $\overline {AD}?$

Accepted Answer

8

Answer

9

Answer

6

Answer

12

Question 5

In triangle $ABC$, points $D$ and $E$ are on sides $\overline{AB}$ and $\overline {BC}$, respectively, such that $\overline {DE} \parallel \overline {AC}$, and $AD:DB=3:5$.

If $DB=6.3$ and $AC=9.4$, what is the length of $\overline {DE}$, to the $nearest tenth?$

Accepted Answer

5.9

Answer

5.6

Answer

15.7

Answer

3.8

Question 6

In the accompanying diagram of right triangle $ABC$, altitude $\overline {BD}$ is drawn to hypotenuse $\overline{AC}$.

Which statement must always be true?

Accepted Answer

$\frac{AD}{AB}=\frac{AB}{AC}$

Answer

$\frac{AD}{AB}=\frac{BC}{AC}$

Answer

$\frac{AB}{BC}=\frac{BD}{AC}$

Answer

$\frac{BD}{BC}=\frac{AB}{AD}$

Question 7

Triangle $RJM$ has an area of 6 and a perimeter of 12. If the triangle is dilated by a scale factor of 3 centered at the origin, what are the area and perimeter of its image, triangle $R'J'M'?$

Accepted Answer

area of 54 and perimeter of 36

Answer

area of 18 and perimeter of 36

Answer

area of 9 and perimeter of 15

Answer

area of 54 and perimeter of 108

Question 8

If $sin(2x+7)^\degree=cos(4x-7)^\degree$, what is the value of $x$?

Accepted Answer

15

Answer

7

Answer

30

Answer

21

Question 9

After a dilation with center (0,0), the image of $\overline{DB}$ is $\overline{D'B'}$. If $DB=4.5$ and  $D'B'=18$, the scale factor of this dilation is

Accepted Answer

4

Answer

5

Answer

$\frac1{4}$

Answer

$\frac1{5}$

Question 10

On the set of axes below, $\Delta ABC$ has vertices at $A(-2,0), B(2,-4), C(4,2)$, and $\Delta DEF$ has vertices at $D(4,0), E(-4,8), F(-8,-4)$.
Which sequence of transformations will map $\Delta ABC$  onto $\Delta DEF$?

Accepted Answer

a dilation of  $\Delta ABC$  by a scale factor of 2 centered at the origin, followed by a rotation of $180\degree$ about the origin

Answer

a dilation of  $\Delta ABC$  by a scale factor of 2 centered at point $A$

Answer

a dilation of  $\Delta ABC$  by a scale factor of $\frac1{2}$ centered at point $A$

Answer

a dilation of  $\Delta ABC$  by a scale factor of $\frac1{2}$ centered at the origin, followed by a rotation of $180\degree$ about the origin

Question 11

In the diagram below of circle $O$, points $K,A,T,I$ and $E$ are on the circle, $\Delta KAE$ and $\Delta ITE$ are drawn, $\stackrel \frown{KE} 
 \cong \stackrel \frown{EI}$, and $\angle EKA \cong \angle EIT$.

Accepted Answer

They are congruent.

Answer

They are similar but not congruent.

Answer

They are neither congruent nor similar

Answer

They are right triangles.

Question 12

In right triangle $ABC$ shown below, point $D$ is on $\overline {AB}$ and point $E$ is on $CB$ such that $\overline {AB} \parallel \overline {DE}$.
If $AB=15,BC=12$, and $EC=7$, what is the length of $\overline{BD}$

Accepted Answer

6.25

Answer

8.75

Answer

4

Answer

5

Question 13

Given right triangle $ABC$ with a right angle at $C$, $m\angle B=61\degree$. Given right triangle $RST$ with a right angle at $T$, $m\angle R=29\degree $.

Which proportion in relation to $\Delta ABC$ and $\Delta RST$ is $not$ correct?

Accepted Answer

$\frac {AB}{RS}= \frac {RT}{AC}$

Answer

$\frac {AB}{AC}= \frac {RS}{RT}$

Answer

$\frac {BC}{ST}= \frac {AC}{RT}$

Answer

$\frac {BC}{ST}= \frac {AB}{RS}$

Question 14

In the diagram below of right triangle $KMI$,  altitude $\overline {IG}$ is drawn to hypotenuse $\overline {KM}$.

If $KG=9$ and $IG=12$, the length of $\overline {IM}$ is

Accepted Answer

20

Answer

16

Answer

15

Answer

25

Question 15

From a point on the ground one-half mile from the base of a monument, the angle of elevation to its top is $$11.87\degree $. To the $nearest foot$, what is the height of the monument?

Accepted Answer

555

Answer

1110

Answer

543

Answer

1086

Question 16

In the diagram below of right triangle $ABC,AC=8$, and $AB=17$.
Which equation would determine the value of angle $A$?

Accepted Answer

$tan A=\frac{15}{8}$

Answer

$sin A=\frac{8}{17}$

Answer

$cos A=\frac{15}{17}$

Answer

$tan A=\frac{8}{15}$

Question 17

In right triangle $ABC, m\angle C=90\degree$ and $AC 
eq BC$. Which trigonometric ratio is equivalent to $sin B$?

Accepted Answer

$cos A$

Answer

$tan B$

Answer

$cos B$

Answer

$tan A$

Question 18

What is an equation of the image of the line $y=\frac{3}{2}x-4$ after a dilation of a scale factor of $\frac{3}{4}$ centered at the origin?

Accepted Answer

$y=\frac{3}{2}x-3$

Answer

$y=\frac{9}{8}x-4$

Answer

$y=\frac{3}{2}x-4$

Answer

$y=\frac{9}{8}x-3$

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