Final Exam Review - Ace Soccermahermath.weebly.com/.../final_exam_review_-_units_1-3.pdf ·...
Transcript of Final Exam Review - Ace Soccermahermath.weebly.com/.../final_exam_review_-_units_1-3.pdf ·...
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