Unit 1: Transformations and Angle Relationships Final Exam Review Unit 1: Transformations and Angle Relationships

Identify the transformation: 1

Identify the transformation: 2

Identify the transformation: 3

Identify the transformation: 4

A triangle with points A(-3, 4), B(-7, 6) and C(-1, 9) is rotated 90˚counter-clockwise. Which quadrant contains the rotated figure? 5

Point W(-3, 8) is dilated using a scale factor of 3 Point W(-3, 8) is dilated using a scale factor of 3. What is the dilated point’s coordinates? 6

Given points A(22, -7) and A’(11, -3.5), determine the scale factor.

A triangle with points A(5, 9), B(2, 7), and C(1, 11) is reflected over the x-axis. What are the coordinates of the reflection? 8

Describe the movement of a figure if it is translated using the following rule: (x + 2, y – 5). 9

Name a pair of vertical angles: 10

alternate interior angles: Name a pair of alternate interior angles: 11

Name a pair of corresponding angles: 12

Find the missing angle measure: 13

Find x: 14

Find x: 15

Reflection Dilation Rotation Translation Q𝐼𝐼𝐼 (3) W’(-9, 24) 1 2 A’(5, -9), B’(2, -7), C’(1, -11) Right 2, down 5 1, 4; 2, 3; 6, 7; 5, 8 3, 6; 4, 5 1, 5; 3, 7; 2, 6; 4, 8 23˚ x = 13 x = 3

Unit 2: Exponents and Scientific Notation

Simplify and Evaluate: 𝟏𝟒 𝒂 𝟓 𝒃 𝟗 𝒄 −𝟒 𝟐𝟖𝒂 𝒃 𝟔 𝒄 𝟐 1 16

What two integers is the number between? 𝟐𝟖 2 17

Evaluate and write in scientific notation: 𝟖.𝟒𝟐 𝒙 𝟏𝟎 𝟑 𝟓 𝒙 𝟏𝟎 𝟐 3 18

Which graph represents 𝟗𝟏 ? 4 19

Students at Kennesaw State pay 𝟏. 𝟓𝟖𝟓 𝒙 𝟏𝟎 𝟒 for tuition Students at Kennesaw State pay 𝟏.𝟓𝟖𝟓 𝒙 𝟏𝟎 𝟒 for tuition. Students at UGA pay 𝟒.𝟓𝟕𝟑 𝒙 𝟏𝟎 𝟓 . About how many times greater is the tuition at UGA? 5 20

Write in scientific notation: 𝟎.𝟎𝟎𝟎𝟖𝟐𝟓 6 21

Simplify and Evaluate: (𝟐 𝒂 𝟑 𝒃 𝟔 𝒄) 𝟒 7 22

Simplify: 𝟏𝟗𝟔 8 23

Evaluate and write in scientific notation: 𝟑.𝟒 𝒙 𝟏𝟎 𝟐 +(𝟒.𝟓𝟕 𝒙 𝟏𝟎 𝟑 ) 9 24

Give an example of a rational number. 10 25

Estimate to the nearest tenth: 𝟕𝟔 11 26

New York City has a population of 𝟖𝟒 𝒙 𝟏𝟎 𝟓 and Los Angeles has a population of 𝟑.𝟖𝟖𝟒 𝒙 𝟏𝟎 𝟔 . Which city is more populated? 12 27

Estimate to the nearest tenth: 𝟒𝟓 13 28

Determine the length of the square: Area = 256 in2 14 29

Simplify and Evaluate: 𝒚 𝟑 · 𝒚 𝟐 · 𝒚 −𝟔 · 𝒚 𝟎 15 30

The Jones family wants to build a square deck with an area of 100 square feet. What will be the length of one side of the deck? 16 31

Give an example of an irrational number. 17 32

Simplify and Evaluate: (𝟏𝟐 𝒙 𝟐 𝒚 𝟓 ) 𝟎 𝟒𝒙 18 33

(Write in scientific notation) If light travels at 𝟏.𝟏𝟖𝟑 𝒙 𝟏𝟎 𝟕 miles in one minute, how many miles will it travel in one hour? (Write in scientific notation) 19 34

Write in standard notation: 𝟒.𝟖 𝒙 𝟏𝟎 −𝟒 20 35

Write in standard notation: 𝟏.𝟒𝟑 𝒙 𝟏𝟎 𝟓 21 36

Evaluate and write in scientific notation: (𝟕.𝟏 𝒙 𝟏𝟎 −𝟓 )(𝟔.𝟕 𝒙 𝟏𝟎 −𝟔 ) 22 37

Simplify and Evaluate: 𝟓 𝒄 −𝟔 𝒅 𝟐 23 38

Evaluate and write in scientific notation: 𝟖.𝟒𝟏 𝒙 𝟏𝟎 −𝟓 −(𝟕.𝟗 𝒙 𝟏𝟎 −𝟔 ) 24 39

16) 1 a 4 b 3 2 c 6 5 and 6 1.684 x 10 C About 30 8.25 x 10 −4 16 a 12 b 24 c 4 14 4.91 x 10 3 Answers vary (Any whole number, fraction, or decimal that repeats/terminates) 8.7 New York City 28) 6.7 29) 16 30) 1 y 10 feet Answers vary (Any decimal number that goes on forever without repeating or terminating) 1 4x 7.098 x 10 8 0.00048 143000 4.757 x 10 −10 5 d 2 c 6 7.62 x 10 −5

Unit 3: Pythagorean Theorem and Volume

Find the volume: Remember: 𝑽= 𝟏 𝟑 𝝅 𝒓 𝟐 𝒉 24 m 40

Find the volume: Remember: 𝑽=𝝅 𝒓 𝟐 𝒉 41

Find the volume: Remember: 𝑽= 𝟒 𝟑 𝝅 𝒓 𝟑 42

Which equation would you use to determine if a triangle with side lengths 5, 7, 8 is a right triangle? 𝟏𝟎+𝟏𝟒=𝟏𝟔 𝟖 𝟐 − 𝟕 𝟐 = 𝟔 𝟐 𝟖 𝟐 + 𝟔 𝟐 = 𝟕 𝟐 𝟓 𝟐 + 𝟕 𝟐 =𝟔𝟒 43

Daniel lost the key to his house Daniel lost the key to his house. There is a window 20 feet above the ground that he can climb through to get into the house. He has a 32 foot ladder. How far can he place the ladder from the house and still be able to reach the window? (Round to the nearest whole number) **Strategy – Draw a picture! 44

Find the length of the missing side. (Estimate to the nearest tenth.) 45

Find the length of the missing side. 46

Solve: 𝟓 𝒙 𝟐 =𝟕𝟐𝟎 47

Solve: 8 𝒙 𝟑 =𝟐𝟏𝟔 48

The volume of a cylinder is 𝟑𝟐𝟒𝝅 𝒇𝒕 𝟑 The volume of a cylinder is 𝟑𝟐𝟒𝝅 𝒇𝒕 𝟑 . If the height of the cylinder is 9 feet, what is its radius? Remember: 𝑽=𝝅 𝒓 𝟐 𝒉 49

How is the volume of a cone related to the volume of a cylinder with the same height and diameter? 50

Determine the length of the line segment Determine the length of the line segment. Round your answer to the nearest tenth. 51

The vertices of 3 squares are joined to form a right triangle The vertices of 3 squares are joined to form a right triangle. What is the area of the largest square? 52

The volume of a cylinder is 𝟗𝟑 𝒊𝒏 𝟑 The volume of a cylinder is 𝟗𝟑 𝒊𝒏 𝟑 . What is the volume of a cone with the same height and radius? 53

40. V = 1230.88 𝑚 3 41. V = 1177.5 𝑓𝑡 3 42. V = 57876.48 𝑐𝑚 3 43. D 44. b = 25 45. c = 5.4 46. x = 16 cm 47. x = 12 48. x = 3 49. r = 6 ft. 50. The volume of the cone is 1 3 the volume of the cylinder. 51. c = 5.8 52. A = 121 𝑐𝑚 2 53. V = 31 𝑖𝑛 3