Question 1

In the figure below, $a = 10$ , $b = 5$ , $c = 8$ , and $d = 43$ . Find x .

Accepted Answer

A)  25 
B)  20 
C)  19 
D)  24 
E)  18 
A)  25 
B)  20 
C)  19 
D)  24 
E)  18

Question 2

A horse trots in a perfect circle around its trainer at the end of a 18-foot-long rope. How far does the horse travel as it circles the trainer once?

Accepted Answer

A)  324 ft 
B)  57 ft 
C)  1,342 ft 
D)  113 ft 
E)  1,018 ft 
A)  324 ft 
B)  57 ft 
C)  1,342 ft 
D)  113 ft 
E)  1,018 ft

Question 3

Which expression(s) is(are) true?
1. A plane as a geometric figure that has position but no length, width, or depth.
2. Points are labeled with capital letters.
3. A line extends infinitely far in both directions, but has no width or depth.
4. Planes are made up of points.
5. A line is a flat surface, extending infinitely far in every direction, that has length and width but no depth.

Accepted Answer

A)  1, 2, 3, 4 
B)  2, 3, 4 
C)  1, 2, 4, 5 
D)  1, 2 
A)  1, 2, 3, 4 
B)  2, 3, 4 
C)  1, 2, 4, 5 
D)  1, 2

Question 4

Refer the trapezoid KLMN below, with $\overline { K L } \| \overline { N M}$ . Find   x and y .

Accepted Answer

A)  $x = 83 ^ { \circ }$ , $y = 57 ^ { \circ }$ 
B)  $x = 53 ^ { \circ }$ , $y = 87 ^ { \circ }$ 
C)  $x = 57 ^ { \circ }$ , $y = 83 ^ { \circ }$ 
D)  $x = 87 ^ { \circ }$ , $y = 53 ^ { \circ }$ 
A)  $x = 83 ^ { \circ }$ , $y = 57 ^ { \circ }$ 
B)  $x = 53 ^ { \circ }$ , $y = 87 ^ { \circ }$ 
C)  $x = 57 ^ { \circ }$ , $y = 83 ^ { \circ }$ 
D)  $x = 87 ^ { \circ }$ , $y = 53 ^ { \circ }$

Question 5

Look at the illustration and match each angle with its type. $$\angle 1 = 54 ^ { \circ }$$   and $\angle 2 = 36 ^ { \circ }$ .  
-obtuse

Accepted Answer

A)  AGC 
B)  FGD 
C)  BGE 
D)  BGA 
A)  AGC 
B)  FGD 
C)  BGE 
D)  BGA

Question 6

To the nearest tenth of square inch, find the area of the regular pentagon whose apothem  measures 4.2 inches and whose sides measure 6.2 inches.

Accepted Answer

A)  $64.2 \mathrm { in } ^ { 2 }$ 
B)  $65.1 \mathrm { in } ^ { 2 }$ 
C)  $97.6 \mathrm { in } ^ { 2 }$ 
D)  $130.2 \mathrm { in } ^ { 2 }$ 
A)  $64.2 \mathrm { in } ^ { 2 }$ 
B)  $65.1 \mathrm { in } ^ { 2 }$ 
C)  $97.6 \mathrm { in } ^ { 2 }$ 
D)  $130.2 \mathrm { in } ^ { 2 }$

Question 7

Look at the illustration and match each angle with its type. $$\angle 1 = 54 ^ { \circ }$$   and $\angle 2 = 36 ^ { \circ }$ .  
-straight

Accepted Answer

A)  AGC 
B)  FGD 
C)  BGE 
D)  BGA 
A)  AGC 
B)  FGD 
C)  BGE 
D)  BGA

Question 8

What is a proper name for an angle?

Accepted Answer

A)  BC 
B)  A 
C)  PQ 
A)  BC 
B)  A 
C)  PQ

Question 9

In the figure below, angle $$a = 51 ^ { \circ }$$ . Find $X$ .

Accepted Answer

A)  166 
B)  39 
C)  129 
D)  78 
E)  64 
A)  166 
B)  39 
C)  129 
D)  78 
E)  64

Question 10

Look at the illustration and match each angle with its type. $$\angle 1 = 54 ^ { \circ }$$   and $\angle 2 = 36 ^ { \circ }$ .  
-right

Accepted Answer

A)  AGC 
B)  FGD 
C)  BGE 
D)  BGA 
A)  AGC 
B)  FGD 
C)  BGE 
D)  BGA

Question 11

Find the perimeter and the area of the quadrilateral.

Accepted Answer

A)  A = 36.0 cm 2 
B)  P = 34.0 cm 
C)  P = 17.0 cm 
D)  A = 71.0 cm 2 
E)  A = 72.0 cm 2
F) P = 68.0 cm 
A)  A = 36.0 cm 2 
B)  P = 34.0 cm 
C)  P = 17.0 cm 
D)  A = 71.0 cm 2 
E)  A = 72.0 cm 2
F) P = 68.0 cm

Question 12

Refer the trapezoid shown below. Find x .

Accepted Answer

A)  42° 
B)  138° 
C)  142° 
D)  125° 
A)  42° 
B)  138° 
C)  142° 
D)  125°

Question 13

The measures of two angles of ABC (shown in the illustration) are given. Find the measure of the third angle, if $m ( \angle A ) = 113 ^ { \circ }$  and $m ( \angle B ) = 33 ^ { \circ }$ .

Accepted Answer

A)  $34 ^ { \circ }$ 
B)  $44 ^ { \circ }$ 
C)  $33 ^ { \circ }$ 
D)  $214 ^ { \circ }$ 
E)  none of these 
A)  $34 ^ { \circ }$ 
B)  $44 ^ { \circ }$ 
C)  $33 ^ { \circ }$ 
D)  $214 ^ { \circ }$ 
E)  none of these

Question 14

The area of a rectangle is $250 \mathrm {~cm} ^ { 2 }$ . Its width is $11 \mathrm {~cm}$  Find its length.

Accepted Answer

A)  $\text { length } = 110 \mathrm {~cm}$ 
B)  $\text { length } = 23 \mathrm {~cm}$ 
C)  $\text { length } = 27 \mathrm {~cm}$ 
D)  $\text { length } = 23.5 \mathrm {~cm}$ 
E)  $\text { length } = 20 \mathrm {~cm}$ 
A)  $\text { length } = 110 \mathrm {~cm}$ 
B)  $\text { length } = 23 \mathrm {~cm}$ 
C)  $\text { length } = 27 \mathrm {~cm}$ 
D)  $\text { length } = 23.5 \mathrm {~cm}$ 
E)  $\text { length } = 20 \mathrm {~cm}$

Question 15

Name the vertex and the sides of ∠ ABC .

Accepted Answer

A)  B ; AB and BC 
B)  C ; AB and BC 
C)  B ;  AB and AC 
D)  C ; AC and BC 
A)  B ; AB and BC 
B)  C ; AB and BC 
C)  B ;  AB and AC 
D)  C ; AC and BC

Question 16

Refer to the figure above. Name the midpoint of the segment $\overline { G C}$ . Find a segment, congruent to $\overline { G C}$ .

Accepted Answer

A)  $E$ ; $\overline { A E }$ 
B)  $E$ ; $\overline { B D}$ 
C)  $C$ ; $\overline { A E }$ 
D)  $C$ ; $\overline { B D}$ 
A)  $E$ ; $\overline { A E }$ 
B)  $E$ ; $\overline { B D}$ 
C)  $C$ ; $\overline { A E }$ 
D)  $C$ ; $\overline { B D}$

Question 17

In the figure below, $l _ { 1 }$  is parallel with  $l _ { 2 }$ .
Find x , if $a = 6$ , $b = 10$ , $c = 4$  and $$d = - 10$$ .

Accepted Answer

A)  $162 ^ { \circ }$ 
B)  $342 ^ { \circ }$ 
C)  $252 ^ { \circ }$ 
D)  $18 ^ { \circ }$ 
E)  none of these 
A)  $162 ^ { \circ }$ 
B)  $342 ^ { \circ }$ 
C)  $252 ^ { \circ }$ 
D)  $18 ^ { \circ }$ 
E)  none of these

Question 18

Find the volume of the figure if a = 17 cm, b = 6 cm.   
Use 3.14 for your estimation of pi, and round your answer to the nearest hundredth. 
__________ cm $3$

Accepted Answer

The answer of Find the volume of the figure if...

Question 19

Match between columns
                        Premises: chord
radius
circumference

Accepted Answer

The Answer of A segment drawn from the center of is...

Question 20

Find the volume of a pyramid with a square base of 9 meters on each side and a height of 12 meters.

Accepted Answer

A)  $324 \mathrm {~m} ^ { 3 }$ 
B)  $108 \mathrm {~m} ^ { 3 }$ 
C)  $973 \mathrm {~m} ^ { 3 }$ 
D)  $1,296 \mathrm {~m} ^ { 3 }$ 
E)  none of these 
A)  $324 \mathrm {~m} ^ { 3 }$ 
B)  $108 \mathrm {~m} ^ { 3 }$ 
C)  $973 \mathrm {~m} ^ { 3 }$ 
D)  $1,296 \mathrm {~m} ^ { 3 }$ 
E)  none of these

In the figure below, $a = 10$ , $b = 5$ , $c = 8$ , and $d = 43$ . Find x .

A horse trots in a perfect circle around its trainer at the end of a 18-foot-long rope. How far does the horse travel as it circles the trainer once?

Refer the trapezoid KLMN below, with $\overline { K L } \| \overline { N M}$ . Find x and y . $Refer the trapezoid KLMN below, with \overline { K L } \| \overline { N M} . Find x and y .$

Look at the illustration and match each angle with its type. $\angle 1 = 54 ^ { \circ }$ and $\angle 2 = 36 ^ { \circ }$ . $Look at the illustration and match each angle with its type. \angle 1 = 54 ^ { \circ } and \angle 2 = 36 ^ { \circ } . -obtuse$ -obtuse

To the nearest tenth of square inch, find the area of the regular pentagon whose apothem measures 4.2 inches and whose sides measure 6.2 inches.

Look at the illustration and match each angle with its type. $\angle 1 = 54 ^ { \circ }$ and $\angle 2 = 36 ^ { \circ }$ . $Look at the illustration and match each angle with its type. \angle 1 = 54 ^ { \circ } and \angle 2 = 36 ^ { \circ } . -straight$ -straight

What is a proper name for an angle?

In the figure below, angle $a = 51 ^ { \circ }$ . Find $X$ . $In the figure below, angle a = 51 ^ { \circ } . Find X .$

Look at the illustration and match each angle with its type. $\angle 1 = 54 ^ { \circ }$ and $\angle 2 = 36 ^ { \circ }$ . $Look at the illustration and match each angle with its type. \angle 1 = 54 ^ { \circ } and \angle 2 = 36 ^ { \circ } . -right$ -right

Find the perimeter and the area of the quadrilateral.

Refer the trapezoid shown below. Find x .

The area of a rectangle is $250 \mathrm {~cm} ^ { 2 }$ . Its width is $11 \mathrm {~cm}$ Find its length.

Name the vertex and the sides of ∠ ABC .

$Refer to the figure above. Name the midpoint of the segment \overline { G C} . Find a segment, congruent to \overline { G C} .$ Refer to the figure above. Name the midpoint of the segment $\overline { G C}$ . Find a segment, congruent to $\overline { G C}$ .

In the figure below, $l _ { 1 }$ is parallel with $l _ { 2 }$ . Find x , if $a = 6$ , $b = 10$ , $c = 4$ and $d = - 10$ . $In the figure below, l _ { 1 } is parallel with l _ { 2 } . Find x , if a = 6 , b = 10 , c = 4 and d = - 10 .$

Find the volume of the figure if a = 17 cm, b = 6 cm. Use 3.14 for your estimation of pi, and round your answer to the nearest hundredth. __________ cm $3$

Find the volume of a pyramid with a square base of 9 meters on each side and a height of 12 meters.

Whole Numbers

The Integers

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An Introduction to Algebra

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Exam 9: An Introduction to Geometry

In the figure below, a=10a = 10a=10 , b=5b = 5b=5 , c=8c = 8c=8 , and d=43d = 43d=43 . Find x .

A horse trots in a perfect circle around its trainer at the end of a 18-foot-long rope. How far does the horse travel as it circles the trainer once?

Refer the trapezoid KLMN below, with KL‾∥NM‾\overline { K L } \| \overline { N M}KL∥NM . Find x and y .

Look at the illustration and match each angle with its type. ∠1=54∘\angle 1 = 54 ^ { \circ }∠1=54∘ and ∠2=36∘\angle 2 = 36 ^ { \circ }∠2=36∘ . -obtuse

To the nearest tenth of square inch, find the area of the regular pentagon whose apothem measures 4.2 inches and whose sides measure 6.2 inches.

Look at the illustration and match each angle with its type. ∠1=54∘\angle 1 = 54 ^ { \circ }∠1=54∘ and ∠2=36∘\angle 2 = 36 ^ { \circ }∠2=36∘ . -straight

What is a proper name for an angle?

In the figure below, angle a=51∘a = 51 ^ { \circ }a=51∘ . Find XXX .

Look at the illustration and match each angle with its type. ∠1=54∘\angle 1 = 54 ^ { \circ }∠1=54∘ and ∠2=36∘\angle 2 = 36 ^ { \circ }∠2=36∘ . -right

Find the perimeter and the area of the quadrilateral.

Refer the trapezoid shown below. Find x .

The measures of two angles of ABC (shown in the illustration) are given. Find the measure of the third angle, if m(∠A)=113∘m ( \angle A ) = 113 ^ { \circ }m(∠A)=113∘ and m(∠B)=33∘m ( \angle B ) = 33 ^ { \circ }m(∠B)=33∘ .

The area of a rectangle is 250 cm2250 \mathrm {~cm} ^ { 2 }250 cm2 . Its width is 11 cm11 \mathrm {~cm}11 cm Find its length.

Name the vertex and the sides of ∠ ABC .

Refer to the figure above. Name the midpoint of the segment GC‾\overline { G C}GC . Find a segment, congruent to GC‾\overline { G C}GC .

In the figure below, l1l _ { 1 }l1​ is parallel with l2l _ { 2 }l2​ . Find x , if a=6a = 6a=6 , b=10b = 10b=10 , c=4c = 4c=4 and d=−10d = - 10d=−10 .

Find the volume of the figure if a = 17 cm, b = 6 cm. Use 3.14 for your estimation of pi, and round your answer to the nearest hundredth. __________ cm 333

Find the volume of a pyramid with a square base of 9 meters on each side and a height of 12 meters.

Whole Numbers

The Integers

Fractions and Mixed Numbers

Decimals

Ratio, Proportion, and Measurement

Percent

Graphs, Statistics, and Probability

An Introduction to Algebra

Filters

In the figure below, $a = 10$ , $b = 5$ , $c = 8$ , and $d = 43$ . Find x .

Refer the trapezoid KLMN below, with $\overline { K L } \| \overline { N M}$ . Find x and y . $Refer the trapezoid KLMN below, with \overline { K L } \| \overline { N M} . Find x and y .$

Look at the illustration and match each angle with its type. $\angle 1 = 54 ^ { \circ }$ and $\angle 2 = 36 ^ { \circ }$ . $Look at the illustration and match each angle with its type. \angle 1 = 54 ^ { \circ } and \angle 2 = 36 ^ { \circ } . -obtuse$ -obtuse

Look at the illustration and match each angle with its type. $\angle 1 = 54 ^ { \circ }$ and $\angle 2 = 36 ^ { \circ }$ . $Look at the illustration and match each angle with its type. \angle 1 = 54 ^ { \circ } and \angle 2 = 36 ^ { \circ } . -straight$ -straight

In the figure below, angle $a = 51 ^ { \circ }$ . Find $X$ . $In the figure below, angle a = 51 ^ { \circ } . Find X .$

Look at the illustration and match each angle with its type. $\angle 1 = 54 ^ { \circ }$ and $\angle 2 = 36 ^ { \circ }$ . $Look at the illustration and match each angle with its type. \angle 1 = 54 ^ { \circ } and \angle 2 = 36 ^ { \circ } . -right$ -right

The area of a rectangle is $250 \mathrm {~cm} ^ { 2 }$ . Its width is $11 \mathrm {~cm}$ Find its length.

$Refer to the figure above. Name the midpoint of the segment \overline { G C} . Find a segment, congruent to \overline { G C} .$ Refer to the figure above. Name the midpoint of the segment $\overline { G C}$ . Find a segment, congruent to $\overline { G C}$ .

In the figure below, $l _ { 1 }$ is parallel with $l _ { 2 }$ . Find x , if $a = 6$ , $b = 10$ , $c = 4$ and $d = - 10$ . $In the figure below, l _ { 1 } is parallel with l _ { 2 } . Find x , if a = 6 , b = 10 , c = 4 and d = - 10 .$

Find the volume of the figure if a = 17 cm, b = 6 cm. Use 3.14 for your estimation of pi, and round your answer to the nearest hundredth. __________ cm $3$