Free Printable Math 2 Ultimate Midterm

1.

are two angles that share a common vertex and share a common side.

a)

Adjacent Angles

b)

Linear Pair

c)

Supplementary Angles

d)

Supplementary Angles

2.

angles are two adjacent angles where the non-shared sides forms a line

a)

Adjacent Angles

b)

Linear Pair

c)

Supplementary Angles

d)

Supplementary Angles

3.

Supplementary Angles

a)

Supplementary Angles are two angles that add to 180°.

b)

Supplementary Angles are two angles that add to 80°.

c)

Supplementary Angles are two angles that add to 190°.

d)

Supplementary Angles are two angles that add to 10°.

4.

Complementary Angles

a)

are two angles that add to 180°.

b)

are two angles that add to 0

c)

are two angles that add to 90°.

d)

are two angles that add to 80°.

5.

Vertical Angles

a)

Vertical angles are two angles that do not share a side and are formed by 2 intersecting lines. (not next to each other)

b)

Also, vertical angles are congruent, meaning their measures are equal.

c)

Also, vertical angles are congruent, meaning their measures are equal.

d)

lol

6.

Transversal

a)

is a line that intersects one coplanar lines at two different points

b)

is a line that intersects two coplanar lines at two different points

c)

is a line that intersects three coplanar lines at two different points

d)

is a line that intersects four coplanar lines at two different points

7.

Angles in the same position at each intersection, like both the top right angles or both the bottom right angles, etc.

a)

Corresponding Angles Postulate

b)

Corresponding Angles

c)

Alternate Interior Angles

d)

Alternate Interior Angles Theorem

8.

Corresponding Angles Postulate

a)

If the two lines are parallel,

then Corresponding Angles are Congruent.

b)

Angles in the same position at each intersection, like both the top right angles or both the bottom right angles, etc.

9.

Alternate Interior Angles

a)

Angles that are in the interior (between the two lines) and are on opposite sides of the transversal, but are not adjacent.

b)

If the two lines are parallel,

then Corresponding Angles are Congruent.

10.

If the two lines are parallel,

then Alternate Interior Angles are .

(a)

11.

Angles that lie on the same side of the transversal between the two lines

a)

Same-Side Interior Angles

b)

Alternate Interior Angles Theorem

12.

If the two lines are --- ,

then Same-Side Interior Angles are Supplementary.

(a)

13.

Alternate Exterior Angles

a)

Angles outside the two lines and

on opposite sides of the transversal.

b)

If the two lines are parallel,

then Alternate Exterior Angles are Congruent.

14.

If the two lines are parallel,

then Alternate Exterior Angles are .

(a)

15.

Triangle Sum Theorem

a)

The sum of the measures of the interior angles of a triangle is equal to 180°.

b)

The sum of the measures of the interior angles of a triangle is equal to 80°.

c)

The sum of the measures of the interior angles of a triangle is equal to 70°.

d)

The sum of the measures of the interior angles of a triangle is equal to 170°.

16.

The measure of an ------ of a triangle is equal to the sum of the measures of the two remote interior angles.

a)

exterior angle

b)

interior angle

17.

Name the angle pair.

a)

Complementary

b)

Supplementary

c)

Adjacent

d)

Vertical

18.

Name the angle pair.

a)

Complementary

b)

Supplementary

c)

Adjacent

d)

Vertical

19.

Angles 4 and 1 are what angle pair?

a)

Complementary

b)

Linear Pair

c)

Acute

d)

Vertical

20.

Angles 1 and 3 are what angle pair?

a)

Complementary

b)

Supplementary

c)

Adjacent

d)

Vertical

21.

What are vertical angles?

a)

Angles that are adjacent to each other

b)

Angles that add up to 180°

c)

Angles that are opposite of each other when lines intersect

d)

Angles that add up to 90°

22.

If m∠1 = 30°, then m∠3 =

a)

30°

b)

60°

c)

150°

d)

undetermined

23.

Find x

a)

74

b)

148

c)

37

d)

90

24.

$\angle QRT$ and $\angle TRS$ are supplementary. Solve for x.

a)

12

b)

15

c)

9

d)

3

25.

Solve for x.

a)

27

b)

23

c)

47

d)

113

26.

Solve for x.

a)

6

b)

23.6

c)

8.6

d)

36

27.

Solve for x.

a)

10.5

b)

11.5

c)

34

d)

34.5

28.

Solve for x.

a)

17

b)

2

c)

28

d)

13

29.

Angle 3 and Angle 6 are examples of which type of angle pair?

a)

Alternate exterior angles

b)

Alternate interior angles

c)

Vertical angles

d)

Corresponding angles

30.

Angle 1 and Angle 5 are examples of which type of angle pair?

a)

Alternate exterior angles

b)

Alternate interior angles

c)

Vertical angles

d)

Corresponding angles

31.

Angle 6 and Angle 7 are examples of which type of angle pair?

a)

Alternate exterior angles

b)

Alternate interior angles

c)

Vertical angles

d)

Corresponding angles

32.

Which of the following angles would NOT be congruent to the measure of $\angle7$ ?

a)

$\angle2$

b)

$\angle3$

c)

$\angle6$

d)

$\angle8$

33.

Which of the following is an example of corresponding angles?

a)

$\angle8\ and\ \angle4$

b)

$\angle5\ and\ \angle7$

c)

$\angle1\ and\ \angle7$

d)

$\angle3\ and\ \angle5$

34.

Which of the following is NOT an example of supplementary angles?

a)

$\angle7\ and\ \angle8$

b)

$\angle2\ and\ \angle3$

c)

$\angle1\ and\ \angle7$

d)

$\angle6\ and\ \angle4$

35.

If the $m\angle7\ =\ 115\degree,$ find the measure of $\angle2.$

a)

$115\degree$

b)

$65\degree$

c)

$180\degree$

d)

Cannot be determined

36.

If the $m\angle5\ =\ 63\degree,$ find the measure of $\angle3.$

a)

$63\degree$

b)

$117\degree$

c)

$180\degree$

d)

Cannot be determined

37.

Which of these angles is NOT congruent to angle 5?

a)

Angle 6

b)

Angle 8

c)

Angle 1

d)

Angle 4

38.

Angles 4 and 6 are...

a)

supplementary

b)

congruent

39.

The Triangle Sum Theorem states that...

a)

90

b)

180

c)

4

d)

congruent angles

40.

The Exterior Angle Theorem states that...

a)

< 4

b)

90

c)

< 3

d)

180

41.

a)

95

b)

85

c)

35

d)

45

42.

a)

26

b)

36

c)

85

d)

144

43.

a)

145

b)

113

c)

102

d)

78

44.

a)

89

b)

211

c)

81

d)

119

45.

Find the measurement of the unknown angle, x.

a)

142

b)

38

c)

180

d)

90

46.

Find the value of x.

a)

A

b)

B

c)

C

d)

D

47.

Find the measure of the missing angle.

a)

90^o

b)

10⁰

c)

130^o

d)

50^o

48.

Find <S

a)

A

b)

B

c)

C

d)

D

49.

Which of the following terms best describes Angle d?

a)

Remote interior angle

b)

Corresponding angle

c)

Exterior angle

d)

Interior angle

50.

Which two angles are the remote interior angles to Angle W?

a)

Angle X and Angle Y

b)

Angle X and Angle Z

c)

Angle Y and Angle Z

d)

Angle Z and Angle W

51.

What is the measure of x?

a)

101°

b)

111°

c)

121°

d)

131°

52.

Set up an equation to find x.

a)

52 + 5x + 16 + 10x + 8 = 180

b)

52 - 5x + 16

c)

52 + 5x + 16 = 10x + 8

d)

52 + 10x + 8 = 5x +16

53.

Solve for x.

a)

5

b)

12

c)

-7

d)

-6

54.

What is a right triangle?

a)

A triangle where all sides equal 90 degrees

b)

A triangle where every angle is 90 degrees

c)

A triangle where all three sides are equal

d)

A triangle where there is a 90 degree angle

55.

What letter represents the hypotenuse?

a)

a

b)

b

c)

a and b

d)

c

56.

Hypotenuse

a)

Vertical side in a right triangle

b)

Longest side in a right triangle

c)

Horizontal side in a right triangle

d)

a²+ b²= c²

57.

Which choice represents the legs?

a)

a and b

b)

a

c)

b

d)

c

58.

Define the term 'right angle'

a)

Three angles in a right triangle

b)

When two angles in a triangle are 90 degrees

c)

Any angle less than 90 degrees

d)

A 90 degree angle

59.

The Pythagorean Theorem is _________

a)

a + b = c

b)

a² + b² = c²

c)

a² + b² + c²

d)

A = LW

60.

Which equation can be used to solve for "x"?

a)

15² – x² = 21²

b)

x² – 15² = 21²

c)

15² + 21² = x²

d)

21² – 15² = x²

61.

Determine the length of the missing side.

a)

7

b)

8

c)

17

d)

23

62.

Do the segment lengths 15, 12, and 9 form a right triangle?

a)

Yes

b)

No

c)

Maybe

d)

Pythagoras

63.

Does the set of numbers represent a right triangle?

20, 25, 15

a)

Yes

b)

No

64.

How is the distance formula correctly written:

a)

$d\ =\ \sqrt{\left(y_{1\ }-\ y_2\right)^2\ -\left(x_{2\ }-\ x_1\right)^2}\$

b)

$d\ =\ \sqrt{\left(x_{2\ }-\ x_1\right)^2\ +\ \left(y_{2_{\ }}-\ y_1\ \right)2}$

c)

$d\ =\ \sqrt{\left(y_{1\ }-\ y\ _2\right)^2\ +\ \left(x_{2\ }-\ x_1\right)}^2$

d)

d = $\sqrt{\left(x\right)^2-\ \left(y\right)^2}$

65.

A(3,1) B(-2,-1) written correctly is:

a)

$\sqrt{\left(-2-3\right)^2\ +\ \left(-1-1\right)^2}$

b)

$\sqrt{\left(1-3\right)^2\ +\ \left(-1-2\right)^2}$

c)

$\sqrt{\left(-2-3\right)^2\ -\ \left(-1-1\right)^2}$

d)

$\sqrt{\left(-2-3\right)^2\ -\ \left(-1-1\right)^2}$

66.

A(2,0) B(-2,4) is written as

a)

$d\ =\ \sqrt{\left(4-2\right)^2\ -\ \left(0-2\right)^2}$

b)

$d\ =\ \sqrt{\left(4-0\right)^2\ -\ \left(-2-2\right)^2}$

c)

$d\ =\ \sqrt{\left(-2\ +0\right)^2\ +\ \left(4+2\right)^2}$

d)

$d\ =\ \sqrt{\left(-2-2\right)^2\ +\ \left(4-0\right)^2}$

67.

What is the slope of the following graph?

a)

$m\ =\ 4$

b)

$m\ =\ 3$

c)

$m\ =\ \frac{1}{3}$

d)

$m\ =\ -3$

68.

What is the slope of the following graph?

a)

$m\ =-\frac{1}{4}$

b)

$m\ =\ 4$

c)

$m\ =\ -4$

d)

$m\ =\ -\frac{1}{3}$

69.

What is the distance between AB

a)

0

b)

8

c)

9

d)

7

70.

What is the slope between AB?

a)

0

b)

8

c)

undefined

d)

$\frac{1}{8}$

71.

What is the distance between AB?

a)

0

b)

undefined

c)

5

d)

4

72.

What is the slope between AB

a)

0

b)

5

c)

undefined

d)

-5

73.

How is AB written in the distance formula?

a)

$d\ =\ \sqrt{\left(5-3\right)^2\ +\ \left(0--2\right)^2}$

b)

$d\ =\ \sqrt{\left(2-5\right)^2\ +\ \left(3\ -0\right)^2}$

c)

$d\ =\ \sqrt{\left(5-3\right)^2\ -\ \left(0--2\right)^2}$

d)

$d\ =\ \sqrt{\left(4-3\right)^2\ -\ \left(2-4\right)^2}$

74.

Angle-Angle Similarity Theorem

If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.

(a)

75.

Side-Side-Side Similarity Theorem

If all three corresponding sides of two triangles are proportional, then the triangles are similar.

(a)

76.

Side-Angle-Side Similarity Theorem

If two of the corresponding sides of two triangles are proportional and the included angles are congruent, then the triangles are similar.

(a)

77.

Which property states that $\angle R\cong\angle R$ ?

a)

Triangle Sum Theorem

b)

Corresponding Angle Postulate

c)

Reflexive Property

d)

Embedded Triangles Property

78.

Which statement shows these triangles are similar by AA~?

a)

$\Delta TRS\sim\Delta QPR$

b)

$\Delta RST\sim\Delta RPQ$

c)

$\angle STR\cong\angle PQR$

79.

Are these triangles similar?

a)

No, they are not similar

b)

Not Enough Information

c)

Yes, similar by AA~

80.

Are these triangles similar?

a)

No, they are not similar

b)

Not Enough Information

c)

Yes, similar by AA~

81.

Are these triangles similar?

a)

No, they are not similar

b)

Not Enough Information

c)

Yes, similar by AA~

82.

Are these triangles similar?

a)

No, they are not similar

b)

Not Enough Information

c)

Yes, similar by AA~

83.

Are these triangles similar?

a)

No, they are not similar

b)

Not Enough Information

c)

Yes, similar by AA~

84.

Are these triangles similar?

a)

No, they are not similar

b)

Not Enough Information

c)

Yes, similar by AA~

85.

Determine if the two triangles are similar by the side-side-side similarity theorem. If they are similar, complete the similarity statement.

a)

similar, $\Delta FTU$

b)

similar, $\Delta UFT$

c)

similar, $\Delta TUF$

d)

Not similar

86.

Determine if the two triangles are similar by the side-side-side similarity theorem. If they are similar, complete the similarity statement.

a)

similar, $\Delta GMN$

b)

similar, $\Delta MNG$

c)

similar, $\Delta NGM$

d)

not similar

87.

Determine if the two triangles are similar by the side-side-side similarity theorem. If they are similar, complete the similarity statement.

a)

similar, $\Delta BCU$

b)

similar, $\Delta CUB$

c)

similar, $\Delta UBC$

d)

not similar

88.

Determine if the two triangles are similar by the side-side-side similarity theorem. If they are similar, complete the similarity statement.

a)

similar, $\Delta HUT$

b)

similar, $\Delta TUH$

c)

similar, $\Delta UTH$

d)

not similar

89.

Determine if the two triangles are similar by the side-side-side similarity theorem. If they are similar, complete the similarity statement.

a)

similar, $\Delta KLM$

b)

similar, $\Delta MLK$

c)

similar, $\Delta LKM$

d)

not similar

90.

Determine if the two triangles are similar by the side-side-side similarity theorem. If they are similar, complete the similarity statement.

a)

similar, $\Delta RSC$

b)

similar, $\Delta SCR$

c)

similar, $\Delta CRS$

d)

not similar

91.

Determine if the two triangles are similar by the side-side-side similarity theorem. If they are similar, complete the similarity statement.

a)

similar, $\Delta AMN$

b)

similar, $\Delta MNA$

c)

similar, $\Delta ANM$

d)

not similar

92.

Determine if the two triangles are similar by the side-side-side similarity theorem. If they are similar, complete the similarity statement.

a)

similar, $\Delta CTD$

b)

similar, $\Delta TDC$

c)

similar, $\Delta TCD$

d)

not similar

93.

Determine if the two triangles are similar by the side-side-side similarity theorem. If they are similar, complete the similarity statement.

a)

similar, $\Delta EST$

b)

similar, $\Delta ETS$

c)

similar, $\Delta TSE$

d)

not similar

94.

Determine if the two triangles are similar by the side-side-side similarity theorem. If they are similar, complete the similarity statement.

a)

similar, $\Delta STU$

b)

similar, $\Delta UTS$

c)

similar, $\Delta TSU$

d)

not similar

95.

Which triangle congruence theorem can be used to prove the triangles are congruent?

a)

SSS

b)

ASA

c)

AAS

d)

SAS

96.

Which triangle congruence theorem can be used to prove the triangles are congruent?

a)

AAS

b)

SSS

c)

SAS

d)

SSA

97.

What additional information is required to prove the 2 triangles are congruent by SAS

a)

A)

b)

B)

c)

C)

d)

D)

98.

In this picture,

a)

<BCA=<DCE because they are vertical angles and vertical angles are always congruent to each other

b)

<C=<C because they are vertical angles and vertical angles are always congruent to each other

c)

<EDC=<ACB because they are vertical angles and vertical angles are always congruent to each other

d)

None of the above; we don't actually have vertical angles

99.

Name the postulate, if possible, that makes the triangles congruent.

a)

SAS

b)

ASA

c)

AAS

d)

Not Possible

100.

a)

SSS

b)

SAS

c)

ASA

d)

NONE

101.

Which Angle is included between AB and AC?

a)

Angle A

b)

Angle B

c)

Angle C

102.

Which angle is included between sides BC and AC

a)

Angle A

b)

Angle B

c)

Angle C

103.

Which two sides include angle B (choose both)

a)

Side AC

b)

Side AB

c)

Side BC

104.

True or False: Angle A is included between sides BC and CA

a)

True

b)

False

c)

Side AB

d)

Angle C

105.

If two figures are similar, the corresponding sides are ______________.

a)

equal

b)

congruent

c)

proportional

d)

none of these

106.

If two figures are similar their angles are______.

a)

proportional

b)

congruent

c)

supplementary

d)

complementary

107.

Calculate the value of the scale factor between the 2 triangles

a)

2.5

b)

3

c)

3.5

d)

4

108.

The pair of figures is similar. Find the missing side.

a)

x = 12

b)

x = 3

c)

x = 40

d)

x = 4

109.

How does a dilation change the angles of a polygon?

a)

It changes by the scale factor.

b)

Dilations do not change the angles.

c)

It is impossible to answer this question. The angles change unpredictably.

d)

The angles all change to larger angles.

110.

What is the value of X?

a)

X=4

b)

X=6

c)

X=3

d)

X=2

111.

Solve for X.

a)

2 ft

b)

3 ft

c)

4 ft

d)

6 ft

112.

Are the triangles similar?

a)

Yes

b)

No

113.

Are the triangles similar?

a)

Yes

b)

No

114.

When you dilate a figure you...

a)

slide it.

b)

turn it.

c)

flip it.

d)

make it larger or smaller.

115.

Tell whether the two figures are congruent.

a)

Yes, same size and same shape

b)

No, same shape but different sizes

c)

No, different size and different shapes

116.

Tell whether the two figures are congruent.

a)

Yes, same size and same shape

b)

No, same shape but different sizes

c)

No, different size and different shapes

117.

What is ratio of any two corresponding sides?

a)

Scale Factor

b)

Corresponding Sides

c)

Similar Figures

118.

If the scale factor is less than one, the new figure will be

a)

an enlargement

b)

a reduction

c)

a scale factor

119.

If the scale factor is greater than one, the new figure will be

a)

a reduction

b)

an enlargement

c)

a scale

d)

not proportional

120.

What is the scale factor from MNOP to ABCD?

a)

2/3

b)

3/2

c)

2

d)

3

121.

What is the scale factor from ΔDEF to ΔABC?

a)

1/2

b)

7/3

c)

2

d)

10/3

122.

The two rectangles are scale drawings. What is the measurement of x?

a)

21

b)

1.25

c)

20

d)

4

123.

What is the scale factor?

a)

1/2

b)

7/3

c)

2

d)

10/3

124.

Are the following similar? Why or why not?

a)

Yes, because the corresponding angles are congruent.

b)

No, the numbers are even

c)

No, the sides are 2 times larger, but the width is the same.

125.

a)

A

b)

B

c)

C

d)

D

126.

a)

A

b)

B

c)

C

d)

D

127.

a)

A

b)

B

c)

C

d)

D

128.

a)

A

b)

B

c)

C

d)

D

129.

Which number best represents a central angle?

a)

1

b)

2

c)

5

d)

9

130.

Which number best represents an intercepted arc?

a)

1

b)

2

c)

6

d)

9

131.

central angle: an angle with its vertex _____________ the circle

a)

at the center of

b)

on

132.

Find the angle for Porter.

a)

144 degress

b)

111 degrees

c)

40 degrees

d)

72 degrees

133.

9.

a)

90

b)

30

c)

150

d)

120

134.

The team scored 50 points. How many points did Kendrick score?

a)

12 points

b)

20 points

c)

10 points

d)

72 points

135.

a)

44°

b)

88°

c)

132°

d)

176°

136.

a)

32.5°

b)

65°

c)

130°

d)

145°

137.

(a)

138.

(a)

139.

a)

30°

b)

60°

c)

90°

d)

120°

140.

a)

35°

b)

70°

c)

140°

d)

270°

141.

(a)

142.

a)

Acute

b)

Right

c)

Obtuse

d)

Straight

143.

a)

Minor Arc

b)

Semi-Circle

c)

Major Arc

144.

a)

Minor Arc

b)

Semi-Circle

c)

Major Arc

145.

a)

Minor Arc

b)

Semi-Circle

c)

Major Arc

146.

a)

Minor Arc

b)

Semi-Circle

c)

Major Arc

147.

a)

Acute

b)

Right

c)

Obtuse

d)

Straight

148.

a)

Acute

b)

Right

c)

Obtuse

d)

Straight

149.

Which side is the long leg in this 30-60-90 triangle? (not the hypotenuse)

a)

4

b)

u

c)

v

150.

Which side is the short leg of this 30-60-90 triangle?

a)

6

b)

m

c)

n

151.

What is the length of u and v in this 30-60-90 triangle?

a)

u = 8 v = 4√3

b)

u = 4√2 v = 8

c)

u = 16 v = 8

d)

u = 4√3 v = 8

152.

What are x and y in this 30-60-90 triangle?

a)

x = 6 y = 3√3

b)

x = 1.5√3 y =1.5

c)

x = 3√3 y = 6

d)

x = √3 y = 2√3

153.

a)

x=10√3 y=30

b)

x=30√3 y=10

c)

x=10, y=30√3

d)

x=30 y=10√3

154.

a)

a=√6 b=√2

b)

a=4 b=2

c)

a=√6 b=2

d)

a=2 b4

155.

Find x.

a)

10

b)

10√3

c)

10√2

d)

20

156.

Find y.

a)

6

b)

24

c)

12√3

d)

6√3

157.

Find x.

a)

2√3

b)

3√3

c)

6√3

d)

12

158.

a)

x=5√3 y=5

b)

x=5 y=5√3

c)

x=5 y=10√3

d)

x=5√3 y=10√3

159.

Which side is the long leg in this 30-60-90 triangle? (not the hypotenuse)

a)

4

b)

u

c)

v

160.

Which side is the short leg of this 30-60-90 triangle?

a)

6

b)

m

c)

n

161.

What is the length of u and v in this 30-60-90 triangle?

a)

u = 8 v = 4√3

b)

u = 4√2 v = 8

c)

u = 16 v = 8

d)

u = 4√3 v = 8

162.

What are x and y in this 30-60-90 triangle?

a)

x = 6 y = 3√3

b)

x = 1.5√3 y =1.5

c)

x = 3√3 y = 6

d)

x = √3 y = 2√3

163.

a)

x=10√3 y=30

b)

x=30√3 y=10

c)

x=10, y=30√3

d)

x=30 y=10√3

164.

a)

a=√6 b=√2

b)

a=4 b=2

c)

a=√6 b=2

d)

a=2 b4

165.

Find x.

a)

10

b)

10√3

c)

10√2

d)

20

166.

Find y.

a)

6

b)

24

c)

12√3

d)

6√3

167.

Find x.

a)

2√3

b)

3√3

c)

6√3

d)

12

168.

What type of special triangle is this?

a)

45°-45°-90°

b)

30°-60°-90°

c)

Equiangular

d)

Equilateral

169.

What is the length of y in this picture?

a)

45

b)

5√2

c)

90

d)

5

170.

Use the 45-45-90 theorem to solve for the hypotenuse.

a)

16

b)

8

c)

8√2

d)

√16

171.

a)

A

b)

B

c)

C

d)

D

172.

What is the length of y in this picture?

a)

45

b)

5√2

c)

90

d)

5

173.

In this isosceles triangle, what is the length of x?

a)

8√2

b)

$\frac{8}{\sqrt{2}}$

c)

16

d)

8

174.

What type of special right triangle is this?

a)

Isoceles right

b)

30-60-90

c)

not a special right triangle

175.

Find x - the length of the hypotenuse of the triangle.

a)

5

b)

5√2

c)

10

d)

5√3

176.

Find a.

a)

5

b)

√2

c)

5√2

d)

2

177.

Find a.

a)

4

b)

2

c)

4√2

d)

2√4

178.

Find x.

a)

4√3

b)

4√6

c)

4

d)

4√8

179.

If the leg of a 45-45-90 triangle is 7 cm long, then its hypotenuse is _____ cm.

a)

7√2

b)

49√2

c)

7

d)

7√7

180.

Find y.

a)

11√2

b)

11

c)

22

d)

(11√2)/2

181.

Find x.

a)

2

b)

18

c)

2√9

d)

9√2

182.

Find y.

a)

8√2

b)

4√2

c)

4

d)

8

183.

Find the missing side lengths.

a)

a = 4, b = 4

b)

a = 4, b = 2√2

c)

a = 2√2, b = 4

d)

a = 4, b = 4

184.

Find the lengths of the other two sides of a right triangle if the length of the hypotenuse is 4√2 inches and one of the angles is 45∘.

a)

4 inches

b)

2 inches

c)

8 inches

d)

10 inches

185.

Find the value of x and y.

a)

$x\ =\ 6,\ y\ =\ 12\sqrt{3}$

b)

$x\ =\ 3\sqrt{2},\ y\ =\ 6\sqrt{2}$

c)

$x\ =\ 6\sqrt{3},\ y\ =\ 12$

d)

$x\ =\ 3\sqrt{2},\ y\ =\ 3\sqrt{2}$

e)

$x\ =\ 3\sqrt{2},\ y\ =\ 6$

186.

A square has side length 95. What is the length of the diagonal of the square? Express your answer in simplest radical form.

a)

$\frac{95\sqrt[]{2}}{2}$

b)

$\frac{95}{\sqrt[]{2}}$

c)

95√2

d)

190 $\sqrt[]{2}$

187.

A square has diagonal length 13 m. What is the side length of the square?

a)

$\frac{13\sqrt[]{2}}{2}$

b)

$13\sqrt[]{2}$

c)

$\frac{13}{\sqrt[]{2}}$

d)

13

188.

In relation to the angle θ, label the side marked a in this right-angled triangle.

a)

Hypotenuse

b)

Adjacent

c)

Opposite

189.

In relation to the angle θ, label the side marked b in this right-angled triangle.

a)

Hypotenuse

b)

Adjacent

c)

Opposite

190.

In relation to the angle θ, label the side marked c in this right-angled triangle.

a)

Hypotenuse

b)

Adjacent

c)

Opposite

191.

In relation to the angle θ, label the side marked c in this right-angled triangle.

a)

Hypotenuse

b)

Adjacent

c)

Opposite

192.

In relation to the angle θ, label the side marked b in this right-angled triangle.

a)

Hypotenuse

b)

Adjacent

c)

Opposite

193.

In relation to the angle θ, label the side marked a in this right-angled triangle.

a)

Hypotenuse

b)

Adjacent

c)

Opposite

194.

Which side of the triangle is opposite of angle R?

a)

QP

b)

QR

c)

RP

195.

Which side of the triangle is the hypotenuse?

a)

QP

b)

QR

c)

RP

196.

Which side of the triangle is adjacent to angle R?

a)

QP

b)

QR

c)

RP

197.

Which side of the triangle is adjacent to angle R?

a)

QP

b)

QR

c)

RP

198.

Which is the correct ratio for the sine ratio?

a)

$\frac{adjacent\ }{hypotenuse}$

b)

$\frac{opposite\ }{hypotenuse}$

c)

$\frac{adjacent\ }{opposite\ }$

d)

$\frac{opposite\ }{adjacent\ }$

199.

Which is the correct ratio for the cosine ratio?

a)

$\frac{adjacent\ }{hypotenuse}$

b)

$\frac{opposite\ }{hypotenuse}$

c)

$\frac{adjacent\ }{opposite\ }$

d)

$\frac{opposite\ }{adjacent\ }$

200.

Which is the correct ratio for the tangent ratio?

a)

$\frac{adjacent\ }{hypotenuse}$

b)

$\frac{opposite\ }{hypotenuse}$

c)

$\frac{adjacent\ }{opposite\ }$

d)

$\frac{opposite\ }{adjacent\ }$

201.

What is a common way to remember the definitions of the trig ratios?

a)

SAH COH TOA

b)

SOA COH TOA

c)

SOH CAH TOA

d)

ADJ OPP HYP

202.

What is the ratio for Cosine?

a)

Opposite Leg / Adjacent Leg

b)

Opposite Leg / Hypotenuse

c)

Adjacent Leg / Hypotenuse

d)

Hypotenuse / Adjacent Leg

203.

From the top of a vertical cliff 40 m high, the angle of depression of an object that is level with the base of the cliff is 34º. How far is the object from the base of the cliff?

a)

about 27 miles

b)

about 59 miles

c)

about 72 miles

d)

about 22 miles

204.

From the top of a vertical cliff 40 m high, the angle of depression of an object that is level with the base of the cliff is 34º. How far is the object from the base of the cliff?

a)

about 27 miles

b)

about 59 miles

c)

about 72 miles

d)

about 22 miles

205.

From a point 340 meters from the base of the Hoover Dam, the angle of elevation to the top of the dam is 33°. Find the height of the dam to the nearest meter.

a)

185.18 meters

b)

523.55 meters

c)

220.80 meters

d)

624.27 meters

206.

Susan is flying a kite, which gets caught in the top of a tree. Use the diagram to estimate the height of the tree.

a)

63 ft

b)

65 ft

c)

74 ft

d)

87 ft

207.

A yacht is anchored 90 feet offshore from the base of a lighthouse. The angle of elevation from the boat to the top of the lighthouse is 26 degrees. The distance between the yacht and the top of the lighthouse is about 100 feet. Which of these is nearest to the height of the lighthouse?

a)

25 feet

b)

45 feet

c)

110 feet

d)

135 feet

208.

After traveling 400m from a runway, a plane is 300m above the ground. Calculate its angle of elevation.

a)

50

b)

0.053

c)

36.9

d)

95

209.

A ramp is being built next to a 4-inch high sidewalk. The ramps angle of elevation is 10 degrees. Estimate the length of the ramp to the nearest tenth of an inch.

a)

4.1 inches

b)

3.9 inches

c)

23.0 inches

d)

0.7 inches

210.

When the angle of elevation of the sun is 78 degrees, an statue casts a shadow that is 6m long. How far is the top of the statue to the end of its shadow?

a)

1.2 m

b)

28.9 m

c)

6.1 m

d)

28.2 m

211.

Jake built a skateboard ramp that covers a horizontal distance of 10 ft. The ramp rises a total of 3.5 ft. What angle does the ramp make with the ground? Round to the nearest degree.

a)

19 degrees

b)

20 degrees

c)

28 degrees

d)

35 degrees

212.

The pilot of a traffic helicopter sights an accident at an angle of depression of 18 degrees. The helicopter’s altitude is 1560 ft. What is the horizontal distance from the helicopter to the accident? Round to the nearest foot.

a)

543 ft

b)

1756 ft

c)

4801 ft

d)

5404 ft

213.

A building 62 feet tall casts a shadow 21 meters long. At what angle is the sun shining on the building?
HINT: Assume this is a right triangle.

a)

19.80

b)

18.71

c)

70.20

d)

71.29

214.

A vertical tower is 20 m high from the horizontal ground. The angle of depression of a ball from the top of the tower is 42°. Calculate the distance, in m, of the ball from the base of the tower

a)

18.01 m

b)

29.89 m

c)

13.38 m

d)

22.21 m

215.

Solve for the missing angle.

a)

50

b)

0.053

c)

36.9

d)

95

216.

A vertical tower is 20 m high from the horizontal ground. The angle of depression of a ball from the top of the tower is 42°. Calculate the distance, in m, of the ball from the base of the tower

a)

18.01 m

b)

29.89 m

c)

13.38 m

d)

22.21 m

217.

Choose the correct ratio.

a)

sin(37)=x/14

b)

cos(37)=x/14

c)

tan(37)=x/14

d)

sin(37)=14/x

218.

A 40 foot ladder which is leaning against a wall reaches the wall at a point 36 feet above the ground. Find the measure of the angle created between the ladder and the ground. Round to the nearest degree

a)

64 degrees

b)

26 degrees

c)

42 degrees

d)

I love Math!

219.

From a hot air balloon 2,500ft above the ground, you see a clearing whose angle of DEPRESSION is 25 degrees. to the nearest foot, what is your horizontal distance from the clearing?

a)

1166 feet

b)

5361 feet

c)

5916 feet

d)

2758 feet

220.

Find the measure of the angle of elevation of the sun when a vertical post 15 feet tall casts a shadow 20 feet long.

a)

about 37 degrees

b)

about 49 degrees

c)

I love Math!

d)

about 41 degrees

221.

From the top of a vertical cliff 40 m high, the angle of depression of an object that is level with the base of the cliff is 34º. How far is the object from the base of the cliff?

a)

about 27 miles

b)

about 59 miles

c)

about 72 miles

d)

about 22 miles

222.

A 9.0 m ladder rests against the side of a wall. The top of the ladder is 7.5 m from the base of the wall. Determine the measure of the angle between the ladder and the wall, to the nearest degree.

a)

34 degrees

b)

56 degrees

c)

40 degrees

d)

50 degrees

223.

Determine the measure of the indicated angle (?) to the nearest tenth.

a)

9.4

b)

55.2

c)

20.15

d)

19.4

224.

What is the length of side x?

a)

6.57 cm

b)

7 cm

c)

7.44 cm

d)

26.33 cm

225.

Solve for x. Round to the nearest tenth.

a)

103.5

b)

4.7

c)

55.0

d)

23.4

226.

Solve for x. Round to the nearest tenth.

a)

44.0

b)

41.4

c)

1.2

d)

1.0

227.

Solve for x. Round to the nearest tenth.

a)

9.8

b)

0.1

c)

0.038

d)

9.9

228.

What would you use to solve for a?

a)

sin

b)

cos

c)

tan

d)

Pythagorean theorem

229.

In a 30°-60°-90° triangle:

Long leg is across from the 60⁰

Short Leg is across from the 30⁰

Hypotenuse = 2 (short leg)

Long leg = (short leg) square root 3

a)

30°-60°-90° Triangle Theorem

b)

40 - 60 - 90 triangle theorem

230.

In a 45°-45°-90° triangle:

Hypotenuse is across from the 90⁰

Legs are across from each 45⁰

Both legs are congruent.

Hypotenuse = (leg)

a)

45°-45°-90° Triangle Theorem

b)

30-60-90 Triangles

231.

The reference angle is the angle that we will use in the problem.

In Math 2, we won’t be using the 90 right angle as our reference angle.

a)

Reference Angle

b)

Sine Ratio

232.

a)

Sine Ratio

b)

Line Ratio

233.

a)

Cosine Ratio

b)

Sine Ratio

234.

a)

Tangent Ratio

b)

Sine Ratio

235.

a)

inverse tangent or arctangent

b)

oh, I won a dog fight!

236.

Inverse Sine

a)

sin-1

b)

cos-1

237.

Angle of Elevation

a)

the angle above a horizontal line

b)

the angle below a horizontal line

238.

Angle of Depression

a)

the angle below a horizontal line

b)

the angle above a horizontal line

Math 2 Ultimate Midterm

Total questions: 238

Worksheet time: 10hrs 28mins

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