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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. What is the dilated point’s coordinates?

6

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

scale factor.

7

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

Name a pair ofalternate interior angles:

11

Name a pair of corresponding angles:

12

Find the missing angle measure:

13

Find x:

14

Find x:

15

1. Reflection2. Dilation3. Rotation4. Translation5. Q𝐼𝐼𝐼 (3)6. W’(-9, 24)

7.1

2

8. A’(5, -9), B’(2, -7), C’(1, -11)9. Right 2, down 510.1, 4; 2, 3; 6, 7; 5, 811.3, 6; 4, 512.1, 5; 3, 7; 2, 6; 4, 813.23˚14.x = 1315.x = 3

Unit 2: Exponents and Scientific Notation

Simplify and Evaluate:

𝟏𝟒𝒂𝟓𝒃𝟗𝒄−𝟒

𝟐𝟖𝒂𝒃𝟔𝒄𝟐

116

What two integers is the number between?

𝟐𝟖

217

Evaluate and write in scientific notation:

𝟖. 𝟒𝟐 𝒙 𝟏𝟎𝟑

𝟓 𝒙 𝟏𝟎𝟐

318

Which graph represents 𝟗𝟏 ?

419

Students at Kennesaw State pay 𝟏. 𝟓𝟖𝟓 𝒙 𝟏𝟎𝟒 for tuition.

Students at UGA pay

𝟒. 𝟓𝟕𝟑 𝒙 𝟏𝟎𝟓. About how many times greater is the

tuition at UGA?5

20

Write in scientific notation:

𝟎. 𝟎𝟎𝟎𝟖𝟐𝟓

621

Simplify and Evaluate:

(𝟐𝒂𝟑𝒃𝟔𝒄)𝟒

722

Simplify:

𝟏𝟗𝟔

823

Evaluate and write in scientific notation:

𝟑. 𝟒 𝒙 𝟏𝟎𝟐 + (𝟒. 𝟓𝟕 𝒙 𝟏𝟎𝟑)

924

Give an example of a rational number.

1025

Estimate to the nearest tenth:

𝟕𝟔

1126

New York City has a

population of 𝟖𝟒 𝒙 𝟏𝟎𝟓 and Los Angeles has a

population of 𝟑. 𝟖𝟖𝟒 𝒙 𝟏𝟎𝟔. Which city is more

populated?12

27

Estimate to the nearest tenth:

𝟒𝟓

1328

Determine the length of the square:

Area = 256 in2

1429

Simplify and Evaluate:

𝒚𝟑 · 𝒚𝟐 · 𝒚−𝟔 · 𝒚𝟎

1530

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?

1631

Give an example of an irrational number.

1732

Simplify and Evaluate:

(𝟏𝟐𝒙𝟐𝒚𝟓)𝟎

𝟒𝒙18

33

If light travels at 𝟏. 𝟏𝟖𝟑 𝒙 𝟏𝟎𝟕 miles in one minute, how many miles will it travel in one hour?(Write in scientific notation)

1934

Write in standard notation:

𝟒. 𝟖 𝒙 𝟏𝟎−𝟒

2035

Write in standard notation:

𝟏. 𝟒𝟑 𝒙 𝟏𝟎𝟓

2136

Evaluate and write in scientific notation:

(𝟕. 𝟏 𝒙 𝟏𝟎−𝟓)(𝟔. 𝟕 𝒙 𝟏𝟎−𝟔)

2237

Simplify and Evaluate:

𝟓𝒄−𝟔𝒅𝟐

2338

Evaluate and write in scientific notation:

𝟖. 𝟒𝟏 𝒙 𝟏𝟎−𝟓 − (𝟕. 𝟗 𝒙 𝟏𝟎−𝟔)

2439

16) 1a4b3

2c6

17) 5 and 618) 1.684 x 1019) C20) About 3021) 8.25 x 10−4

22) 16a12b24c4

23) 1424) 4.91 x 103

25) Answers vary (Any whole number, fraction, or decimal that repeats/terminates)

26) 8.727) New York City

28) 6.729) 16

30) 1

y

31) 10 feet32) Answers vary (Any decimal number

that goes on forever without repeating or terminating)

33)1

4x

34) 7.098 x 108

35) 0.0004836) 14300037) 4.757 x 10−10

38)5d2

c6

39) 7.62 x 10−5

Unit 3: Pythagorean Theorem and Volume

Find the volume:

Remember:

𝑽 =𝟏

𝟑𝝅𝒓𝟐𝒉

24 m

40

Find the volume:

Remember:

𝑽 = 𝝅𝒓𝟐𝒉

41

Find the volume:

Remember:

𝑽 =𝟒

𝟑𝝅𝒓𝟑

42

Which equation would you use to determine if a triangle with side lengths 5, 7, 8 is a right triangle?

A. 𝟏𝟎 + 𝟏𝟒 = 𝟏𝟔

B. 𝟖𝟐 − 𝟕𝟐 = 𝟔𝟐

C. 𝟖𝟐 + 𝟔𝟐 = 𝟕𝟐

D. 𝟓𝟐 + 𝟕𝟐 = 𝟔𝟒43

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:

𝟓𝒙𝟐 = 𝟕𝟐𝟎

47

Solve:

8𝒙𝟑 = 𝟐𝟏𝟔

48

The volume of a cylinder is 𝟑𝟐𝟒𝝅 𝒇𝒕𝟑. If the height of the cylinder is 9 feet, what is its radius?

Remember:

𝑽 = 𝝅𝒓𝟐𝒉

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. Round your answer to the nearest tenth.

51

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 𝒊𝒏𝟑. What is the volume of a cone with the same height and

radius?

53

40. V = 1230.88 𝑚3

41. V = 1177.5 𝑓𝑡3

42. V = 57876.48 𝑐𝑚3

43. D44. b = 2545. c = 5.446. x = 16 cm47. x = 1248. x = 349. r = 6 ft.

50. The volume of the cone is 1

3the

volume of the cylinder.51. c = 5.852. A = 121 𝑐𝑚2

53. V = 31 𝑖𝑛3