Final Exam Review

1. Find the midpoint, the distance and the slope between (4,-2) and (-5, 3)

2. Jacinta hangs a picture 15 inches from the left side of a wall. How far from the edge of the wall should she mark the location

to nail the picture so that the right side of the picture is 37.5 inches from the wall’s left side?

3. Point P is located on the segment between point point A (1,4) and point D (7,13). The distance from A to P is twice the

distance from P to D. What are the coordinates of point P?

4. Parallel lines have ____________________________ slopes.

5. Perpendicular lines have _____________________________ slopes.

6. Determine whether the lines are parallel, perpendicular or neither.

a. 2x + 3y = 4 b. y = -4x + 1 c. 2y = x – 1

3x - 2y = 3 4x + y = 8 y = -2 x + 4

___________ ____________ _____________

7. Maggie and Mike want to go to the music store near Maggie’s house after school. They can walk 3.5 miles per hour and ride

their bikes 10 miles per hour.

a. Create a table to show how far Maggie and Mike can travel walking and riding their bikes.

b. Create a graph to show how far Maggie and Mike can travel based on the chart above.

c. What does the slope represent in the graph?

d. Maggie’s mom said that they can only go if they can make it to the music store and back in less than two hours. If

they want to spend at least 30 minutes in the music store and it is four miles away, can they make it?

line a // line b

8. Given : m 1 = 3x + 1

m 6 = 5x + 3

m 8 = y

x=______ y=______

9. Given : m 2 = 13x + 4

m 3 = 4z + 21

m 5 = 7y + 2

m 6 = 6x + 25

x=______ y=_______ z=________

10. Name the types of angle pairs that are congruent with respect to parallel lines.

11. Name the types of angle pairs that are supplementary with respect to parallel lines.

Questions 12 – 14: Are these lines parallel, perpendicular or neither

12. Given: y = 3x + 7

y = 1

3x + 7

13. Given: y =2

3

x – 5

-10x – 15 y = 40

14. Given : 3x = 6y – 15

2y = -4x + 7

15 – 16. Find the area and perimeter of the following regular polygons.

15. 16.

Area = ____________________ Area = ____________________

17. 18.

Area = ____________________ Area = ____________________

Perimeter = ______________________ Perimeter = ______________________

19. 20.

Area = ____________________ Area = ____________________

Perimeter = ______________________ Circumference = ______________________

Find the area of the shaded part.

21. 22.

Area = ____________________ Area = ____________________

45

55

65

85

65

88

140

32.4 .in

28.2 .in

23. 24.

Area = ____________________ Area = ____________________

Angle of Elevation/Depression

25.) A sonar operator on a cruiser detects a submarine at a distance of 500m and an angle of depression of 37°. How deep is the sub?

26.) The top of a signal tower is 120m above sea level. The angle of depression from the top of the tower to a passing ship is 25m.

How many meters from the base of the tower is the ship?

27.) Antonio is flying a kite. He lets out 500ft of kite string. The kite is flying so that Antonio’s angle of elevation is 36° How high

above the ground is the kite?

Special Right Triangles

28.) 29.)

16

45°

y

x

x y

21

30°

30.) A ladder leaning against a wall makes a 60° angle with the ground. The base of the ladder is 3m from the building. How high

above the ground is the top of the ladder?

31.) What is the perimeter of an isosceles right triangle whose hypotenuse is ?

Pythagorean Theorem

Determine whether each set of numbers can be represent side lengths of a right triangle.

32.) 15, 36, 39 33.) 2, 3, 2 34.) 5, 7, 12

35.) List 4 Pythagorean Triples. For each, show that a2 + b

2 = c

2.

a.) _____, _____, _____ b.) _____, _____, _____ c.) _____, _____, _____ d.) _____, _____, _____

36.)

AC = __________ AB = __________ BC = __________

3

5

2

B

A

C

Right Triangle Trigonometry

37.) The sinA =

. Find cosA and tanA. 38.) The cosA =

. Find sinA and tanA.

cosA = __________ tanA = __________ sinA = __________ tanA = __________

39) The acute angles of a right triangle are ________ and add up to _______º

40) 2 angles of a triangles are 45º and 72º, what is the measure of the last angle?________

41) 3 angles of a quadrilateral are 100º, 120º, and 40º, find the measure of the 4th

angle.____

42) In a right triangle, the hypotenuse is 10 ft and a leg is 19 , find the length of the other leg.

43) If one acute angle in a right triangle is 57º, find the measure of the other angle is _______

44) Supplementary angles add up to ____________

45) A 12 ft tree casts a 48 ft shadow at the same time a girl casts a 20 ft shadow. Find the height of the girl.

46) What parallelogram has congruent diagonals? ____________ and _________

47) Which parallelogram has congruent sides? _____________ and ______________

A B

C

A B

C

48) Which parallelogram has perpendicular diagonals? ___________and ____________

49) In a triangle, an exterior angle is equal to the sum of the other 2 ____________***

50) An altitude in a triangle is a segment from a vertex to the opposite side and is ____________ to the opposite side

51) A median in a triangle is a segment from a vertex to the opposite and ________ the opposite side.

52) Given parallelogram ABCD, write a similarity statement for the 2 triangles

A B

D C

53) Name the longest side of 63, 70 47ABCif A B and C

A

B C

54) Find the area of the figure below

10

3

8 6

1

55) A circle has a radius of 5, find the area and circumference

A = ________ C = _________

15

56) In a parallelogram, the sum of a pair of opposite angles is 200º. Find the measure of the other angles.

Consecutive angles of a parallelogram add up to _________

57) Name the figures:

____________ ___________ _______________ ______________

58) A side of a regular octagon is 3, find the perimeter

59) 20 X =

60) Find the missing angle measure

25

61) Find the missing angle measure

In Circle D, 37BAC B

A

x

X

D

10 + x

______BDC C

62) Find the area of the sector, Find the arc length

Diameter = 10

63) The set of points in a plane equidistant to the center is called a ________________

64) Find the area of a square with a diagonal of 20.

65) Find the altitude of an equilateral triangle with sides of length 10. Find the area.

66) Find the missing side length

15 5

Proportions

68. m m + 7

=8 9

69.

6 4=

9 5b b 70.

8 6=

5x - 4 x + 5

Similarity

71. What proportions could be used to find x?

X

45

6 12

15

x

9

D

A B

C

L

O

MP

N

72. The scale factor of ∆RST to ∆XYZ is 3:4. Find the perimeter of ∆XYZ.

73. T is the centroid of ∆GHI and GOIH .

Find the area of ∆OTH

In the figures below, the triangles are congruent by which theorem/postulate: SSS, SAS, ASA, AAS, or HL.

74.;BC BD AC AD

75.

and N are right angles;

MO OP

L

76.

77.

BDCBAB ,

bisects AC

6

G

O

N M

I H

X

R

S Y

T

Z 4

15

10

10

T

A C

B

D

78.

79. 80.

81.

:

8

34

26

Given

Diameter in

m EAD

mCD

82). Arc angle measurement of AE

83). Minor Arc angle measurement of DE

84). Minor Arc angle measurement of AC

85). Area and Circumference of the circle.

86). Sector area ofCD .

Find the angle measurement of x.

6

x

8

3

x

4

8

6

4

5

x

E

B

A

C

D

x

87) 88)

89) A thin wire is formed into a rectangle with an area of 236cm . If it is reshaped so that the 9cm side is decreased by 3cm, will the

area of the new rectangle that is formed be increased or decreased? (and by how much).

90) Guiseppe’s always made personal sized pizzas with a 6 inch radius. He decided to start making larger pizzas that had a 12 inch

radius. He figured that if he kept the thickness of the crust, sauce, and cheese the same as his personal sized pizzas, he would just

need to double the ingredients to make the larger pizzas.

a) Determine how many pizzas Guiseppe will be able to make by doubling the ingredients.

b) Explain why or why not Guiseppe’s is correct.

91) The formula for the volume of a cylinder is 2V r h . If the radius of a cylinder is doubled, how does the change affect

the volume?

92) Cylinder A has a height of 12ft and a radius of 4 ft. Cylinder B has a height of 24 ft and a radius of 8 feet. How many times

greater is the volume of Cylinder B?

93) How many times greater is the volume of a cube with 6 inch edges than that of a cube with 2 inch edges?

Answer below if E is the centroid of ABC and BG=9.

60 x

94 146

A

B

C

F D

G

E 6

4

7

94. EC =

95. EF =

96. AC =

97. IF BG=9, then BE =

98. IF BG=9, then GE =

99.

100.

101.

102.

103.

104.

105. Find the value of x , m D and m F

129

2x-3

144

5x+12 108

141

131

C

B

A

G

F

E

D

106.

107.

108.

109.

110.

111) Two cubes are shown. Use the figures to answers each question below.

A. Find the volume of figure A. Show all your work here.

B. Find the volume of figure B. Show all your work here.

C. Multiple Choice: Which of the following statements is true?

A. When the length of a cube doubles, the volume also doubles.

B. When the length of a cube doubles, the volume triples.

C. When the length of a cube doubles, the volume is four times bigger.

D. When the length of a cube doubles, the volume is eight times bigger.

5 .ft 10 .ft

D. If figure B was filled with water, which weighs 8 pounds per cubic foot, how many

pounds of water would the cube hold?

112.) Two cylinders are shown. Use the figures to answers each question below.

A. Find the volume of figure A. Show all your work here.

B. Find the volume of figure B. Show all your work here.

C. Multiple Choice: Which of the following statements is true?

A. When the radius of a cylinder tripled the volume stay the same.

B. When the radius of a cylinder tripled the volume also triples.

C. When the radius of a cylinder tripled the volume is eight times bigger.

D. When the radius of a cylinder tripled the volume is nine times bigger.

10m 30m

20m20m