Math 8 - Review for Final Exam#1 2014macomb.k12.mi.us/utica/Eppler/media/13-14 Final Exam Review...

Math 8ID: 1

Name___________________________________

Period____Date________________Review for Final Exam #1 - 2014

Solve each system by graphing.

1)

y

x

y

x

2)

y

x

y

x

3)

y

x

y

x

4)

y

x

y

x

-1-

5)

y

x

y

6)

y

x

y

x

Solve each system by substitution.

7)

y

x

x

y

8)

x

y

y

x

9)

x

y

y

x

10)

y

x

x

y

11)

y

x

x

y

12)

x

y

y

x

13) Solve by Elimination:x + y = 10x - y = 2

14) Solve by Elimination:7x + 2y = 10-7x + y = -16

-2-

15) Solve by Elimination:4x + y = 8-3x - y = 0

16) Solve by Elimination:2x - 3y = 5x + 2y = -1

17) Solve by Elimination:3x + 2y = -19x - 12y = 19

18) Solve by Elimination:x + y = -32x + 2y = -6

Graph the image of the figure using the transformation given.

19) translation:

x

,

y

x

,

y

x

y

D

20) translation:

x

,

y

x

,

y

x

y

Y

A

H

Write a rule to describe each transformation.

21)

x

y

G

N W

P

G'

N' W'

P'

22)

x

y

S

R

H

S'

R'

H'

-3-


23) reflection across the x-axis

x

y

Z

N

M

K

24) reflection across the y-axis

x

y

D

R

J


25)

x

y

V

U

Y

U'

Y'

V'

26)

x

y

Z

A

D

A'

D'

Z'

-4-


27) rotation 180° about the origin

x

y

H

Z K

E


x

y

X

M

Z

29) rotation 90° counterclockwise about theorigin

x

y

A

M S

V


x

y

I

R

M

Find the measure of all missing angles.

31)

141°

b

32)

98°

b

-5-

33)

48°

b

34)

138°

b

Find the value of x AND the angle measurement of that angle.

35)

39°

(6x + 3)°

36)

34°

(4x + 2)°

37)

39°

3x°

38)

(4x + 1)°

(2x + 5)°

-6-

Find the measure of angle b.

39)

111°

36°

b

40)

107°

40°

b

41)

124°

25°

b

42)

26°

65°b

Find the value of x AND the measurement of the missing angle.

43)

73° 74°

(10x + 3)°

44)

28°

121°

(5x + 6)°

-7-

45)

76°

63°

(13x + 2)°

46) 61°

(15x - 1)°

Use the Pythagorean Theorem to find each missing length to the nearest tenth.

47)

3.66.3

48)

7.9

4.1

49)

5.5

3.1

50)

79.1

51)

3

4.4

52)

5.9

9.5

-8-

Do the following lengths form a right triangle?

53)

5.6 9

10.6

54)

6 6.3

7.7

55)

3.9

8

8.9

56)

6

9.1

10.1

57)

3.6 7.7

8.2

58)

3.6

7.7 8.1

Find the distance between each pair of points.

59)

,

,

,

60)

,

,

,

61)

,

,

,

62)

,

,

,

-9-

63)

x

y64)

x

y

65)

x

y66)

x

y

Find the volume of each figure. Round to the nearest tenth.

67)

9 mi

14 mi

68)

12 km

69) 12 ft

6 ft

70)

16 cm

16 cm

71)

5 m

72)

5 m

6 m

-10-

73)

11 km

8 km74)

9.6 mi

75) 14 in

7 in

-11-

Math 8ID: 1

Name___________________________________

Period____Date________________Review for Final Exam #1 - 2014

Solve each system by graphing.

1)

y

x

y

x

,

2)

y

x

y

x

No solution

3)

y

x

y

x

,

4)

y

x

y

x

,

-1-

5)

y

x

y

,

6)

y

x

y

x

No solution

Solve each system by substitution.

7)

y

x

x

y

Infinite number of solutions

8)

x

y

y

x

,

9)

x

y

y

x

,

10)

y

x

x

y

,

11)

y

x

x

y

,

12)

x

y

y

x

,

13) Solve by Elimination:x + y = 10x - y = 2

(6, 4)

14) Solve by Elimination:7x + 2y = 10-7x + y = -16

(2, -2)

-2-

15) Solve by Elimination:4x + y = 8-3x - y = 0

(8, -24)

16) Solve by Elimination:2x - 3y = 5x + 2y = -1

(1, -1)

17) Solve by Elimination:3x + 2y = -19x - 12y = 19

(-5, -2)

18) Solve by Elimination:x + y = -32x + 2y = -6

infinite number of solutions


19) translation:

x

,

y

x

,

y

x

y

D

D'

20) translation:

x

,

y

x

,

y

x

y

Y

A

H

Y'

A'

H'


21)

x

y

G

N W

P

G'

N' W'

P'

translation:

x

,

y

x

,

y

22)

x

y

S

R

H

S'

R'

H'

translation:

x

,

y

x

,

y

-3-


23) reflection across the x-axis

x

y

Z

N

M

K

N'

M'

K'

Z'

24) reflection across the y-axis

x

y

D

R

J

R'

J' D'


25)

x

y

V

U

Y

U'

Y'

V'

reflection across the x-axis

26)

x

y

Z

A

D

A'

D'

Z'

reflection across the y-axis

-4-



x

y

H

Z K

E

H'

Z'K'

E'


x

y

X

M

ZX'

M'

Z'


x

y

A

M S

V

A'

M'

S' V'


x

y

I

R

M

I'

R' M'

Find the measure of all missing angles.

31)

141°

b

141°

32)

98°

b

98°

-5-

33)

48°

b

48°

34)

138°

b

138°

Find the value of x AND the angle measurement of that angle.

35)

39°

(6x + 3)°

6

36)

34°

(4x + 2)°

8

37)

39°

3x°

13

38)

(4x + 1)°

(2x + 5)°

29

-6-

Find the measure of angle b.

39)

111°

36°

b

33°

40)

107°

40°

b

33°

41)

124°

25°

b

31°

42)

26°

65°b

89°

Find the value of x AND the measurement of the missing angle.

43)

73° 74°

(10x + 3)°

3

44)

28°

121°

(5x + 6)°

5

-7-

45)

76°

63°

(13x + 2)°

3

46) 61°

(15x - 1)°

2

Use the Pythagorean Theorem to find each missing length to the nearest tenth.

47)

3.66.3

5.2

48)

7.9

4.1

8.9

49)

5.5

3.1

6.3

50)

79.1

5.8

51)

3

4.43.2

52)

5.9

9.5

11.2

-8-

Do the following lengths form a right triangle?

53)

5.6 9

10.6

Yes

54)

6 6.3

7.7

No

55)

3.9

8

8.9

Yes

56)

6

9.1

10.1

No

57)

3.6 7.7

8.2

No

58)

3.6

7.7 8.1

No

Find the distance between each pair of points.

59)

,

,

,

60)

,

,

,

61)

,

,

,

62)

,

,

,

-9-

63)

x

y

64)

x

y

65)

x

y

66)

x

y

Find the volume of each figure. Round to the nearest tenth.

67)

9 mi

14 mi

1385.4 mi³

68)

12 km

904.8 km³

69) 12 ft

6 ft

452.4 ft³

70)

16 cm

16 cm

1072.3 cm³

71)

5 m

523.6 m³

72)

5 m

6 m

565.5 m³

-10-

73)

11 km

8 km

2211.7 km³

74)

9.6 mi

463.2 mi³

75) 14 in

7 in

718.4 in³

-11-

Math 8 Final Exam

The final exam covers the following concepts:

Bivariate Data – Scatter Plots and Two-Way Tables

Systems of Equations

Transformations

Parallel Lines cut by a Transversal

Triangles

Pythagorean Theorem

Volume of Cylinders, Cones, Spheres

Remember, not everything that we did is in our textbook. Your notes, quizzes, and tests are

great places to look at the content that will be on the exam.

Math 8 Name ___________________________________ Review for Final Exam #2 Date ____________________________ HR _____

Bivariate Data

1.

Based on the data in this graph, what is the expected mass of an animal that is 180 cm long?

A 54 kg B 67 kg C 78 kg D 89 kg

2. Julie drew a scatter plot comparing the number of hours students watched TV and

their grade in their math class. She graphed the ordered pairs (hours watching tv, math grade) for each student in the class. Which of the three scatter plots below most likely represent the data?

https://www98.achievedata.com/imagebank/12087470.jpg

Tell whether a scatter plot made for each set of data would describe

a positive trend, a negative trend, or no trend.

3. amount of education and annual salary

4. weight and speed in foot race

5. test score and shoe size 160

155 158 160 162 164 166 168 170 172 174

6. The members of Rick’s intramural team recorded their heights and their weights in the table below. Rick wanted to determine the relationship between the heights and the weights of theses team members, so he drew a scatter plot and a line of best fit. Which graph shows the most appropriate line of best fit?

A

C

B

D

7.

Given the following scatter plot, use the given equation for the line of best fit to make predictions using the following information.

a) If someone’s arm span is 50 inches, what is their predicted height?

b) If someone’s height is 48 inches, to the nearest inch, about how long is their arm span?

8.

Given the following scatter plot, use the given equation for the line of best fit to make predictions using the following information.

a) If the afternoon temperature is 55 degrees, to the nearest degree, what was the morning temperature?

b) If the morning temperature is 20 degrees, predict what the afternoon temperature will be.

9. Mackenzie surveyed the students in her cafeteria and found that 38 males agree with the new cafeteria rules while 70 do not. There were 92 females surveyed and 41 of them agree with the new cafeteria rules.

Agree Disagree TOTAL

Male

Female

TOTAL

a) What is the percentage of students who agree with the rules?

b) What is the percentage of males who disagree with the rules?

10. In a restaurant, customers were asked whether they liked chicken or beef, and whether they

liked rice or pasta. 30% of the customers liked rice, while 70% liked pasta. 20% liked chicken and

rice. 60% of the customers liked chicken.

Construct a two-way relative frequency table summarizing the data for this situation.

a) What is the percentage of customers that like rice?

b) What is the relative frequency of those that chose beef and rice?

Chicken

Beef

TOTAL

Rice

Pasta

TOTAL


1. The sum of two numbers is 61. Their difference is 13. Write a system of equations that

describes this situation. Solve to find the two numbers.

2. The sum of two numbers is 17. Their difference is 27. Write a system of equations that

describes this situation. Solve to find the two numbers.

3. Uncle Billy Bob is raising goats and chickens. There are a total of 44 goats and chickens

being raised. Between them, they have 134 legs. How many goats are there total? How many

chickens are total?

4. Two different families go out to eat. One family buys three pizzas and six sodas. Their bill

is $33. The other family buys six pizzas and four sodas. Their bill is $50. How much does a

pizza cost? How much does a soda cost?

5. I went to Target and I bought some books and video games. I bought a total of 8 items. The

books cost $10 and the video games cost $40. My total bill (without tax) was $170. How many

books did I buy? How many video games did I buy?

Transformations

1. At the half-time show, a marching band marched in formation. The lead drummer started at

a point with coordinates (3, 4) and moved 3 steps down and 4 steps left.

a. Write a rule to describe the translation.

b. What were the coordinates of the drummer’s final position?

a. c.

b. d.

2. What series of transformations can be used to describe the movement from the pre-image

(shaded figure) to the image?

3. Find the image of after a dilation with the given center and scale factor.

center A, scale factor

a.

c.

b.

d.

4. Enlargements have a scale factor _____________ than 1. Reductions have a scale factor

between ________________ and ____________________.

5. Name the transformations that produce figures that have congruent side lengths and angle

measures.

6. Dilations result in ___________________ images.

7. In the box below, draw a right triangle that has legs that are 3cm and 4 cm. Draw a

reduction with a scale factor of 0.5. Draw an enlargement that has a scale factor of 2.

8. What is the scale factor of the following dilations (drawings are not drawn to scale)?

A A’

C

2cm 4cm

4cm D C’

B 3cm

B’ D’

9. Quadrilateral QUAD was rotated 180o about the origin to create quadrilateral Q’U’A’D’ as

shown in the graph below.

What was Dm in the original quadrilateral?

Parallel Lines Cut by a Transversal and Triangles

1. Use the following diagram to answer each of the following.

a. Corresponding angle to 6 __________

b. Vertical angle with 1 __________

c. Alternate exterior angle with 4 __________

d. Same-Side interior angle with 3 __________

e. Alternate interior angle with 3 __________

f. Supplementary angle with 8 __________

g. Corresponding angle to 1 __________

h. Same-Side exterior angle with 8 __________

2. Classify how the angles 3 and 6 are related. Find the value of the variable if m ll n, 2943 xm , and 6786 xm . Find the degree measure of both angles. Show your work for

full credit. The diagram is not to scale.

3 and 6 _______________________________

x = ____________

3m __________ 6m __________

3. Classify how the angles 1 and 7 are related. Find the value of the variable if m ll n, 4491 xm , and 55187 xm . Find the degree measure for ALL of the angles. Show your

work for full credit. The diagram is not to scale.

1 and 7 _______________________________

x = ____________

1m __________ 2m __________

3m __________ 4m __________

5m __________ 6m __________ 7m __________ 8m __________

1

2

3

n

m 4 5

6

7

8

7 8

6 5

3 4

2 1 m

n

7 8

6 5

3 4

2 1 m

n

4. Solve for x. Find the measure of all the missing angles. The diagram is not to scale.

x = ____________

5. Find the measures of all the missing angles. The diagrams are not to scale. .

6. . Find the measures of all the missing angles. The diagrams are not to scale.

(4x + 3)⁰

(7x – 21)⁰

39⁰

56⁰

Pythagorean Theorem

Draw a diagram for each picture and round your answers to the nearest tenth when necessary.

1. A baseball player throws a ball from second base to home plate. How far does the player

throw the ball?

2. The distance from the pitcher’s mound to home plate is 60.5 feet. The distance from the

pitcher’s mound to 1st base is 63.7 feet? Does this form a right triangle? Explain your

reasoning.

3. The recommended angle for a firefighting ladder is 75°. When a 100-foot ladder is put up

against a building at this angle, the base of the ladder is about 30 feet from the building. How

high on the building will the ladder reach?

4. The post office is 5 miles west of your home. Your school is 4 miles north of the post office.

To the nearest tenth, how many more miles do you walk to school when you have to stop at the

post office first?

5. Two cars are traveling from Florida. One family is driving north 70 mi/hr and the other is

heading west at 60 mi/hr. To the nearest tenth, how far apart are they after an hour of traveling?

6. A firework is being shot into the air 400 m away from where you are sitting. The distance

from your eyesight to the firework is 535m. Find the height of the firework from the ground to

the nearest tenth.

7. Find the perimeter of the triangle. Round answer to the nearest tenth.

535 m

400 m

10 ft

Volume

1. Use the diagram below. Which has the greater volume? Use 3.14 for

2. Find the height (h) of the cylinder below. Use 3.14 for Round to the nearest tenth.

4. Racquet balls are usually sold in pairs. They are packaged in a cylindrical container as

shown below. The balls just touch the top, bottom, and sides of the cylinder. The diameter of

each ball is 10 cm.

6. Carla cut a spherical orange into four congruent wedges to share with her friends. The edge

where the four pieces met measured 3 inches. What is the volume of fruit each person

received? Use 3.14 for

r = 2.4 cm

h

Volume = 27.14 cm3

What is the volume of the cylinder? Use 3.14 for

Show your work.

What is the total volume of the racquet balls? Use 3.14 for

Show your work.

Answer Key

Bivariate Data

1. C

2. I

3. positive

4. negative

5. no trend

6. A

7. A) 70 in B) 26 in

8. A) 42 degrees B) 35 degrees

9.

a) What is the percentage of students who agree with the rules? 79/200

b) What is the percentage of males who disagree with the rules? 70/121 = 57.9% or

10.

a) 30%

b) 10%


1. 37 and 24

2. 22 and -5

3. 23 goats and 21 chickens

4. Pizza $7, Soda $2

5. 5 books and 3 video games

Transformations

1. A

2. Rotation (or rotations and translation) Reflection

Dilation (reduction) Reflection and Translation

3. B

4. Greater; Zero; One

5. Translations, Reflections, Rotations

6. Similar

7. Check students drawings…

a. Original – legs of 3 cm and 4cm

b. Reduction – legs of 1.5cm and 2 cm

c. Enlargement – legs of 6 cm and 8 cm

8. Scale factor 2; scale factor ¾

9. 90 degrees

Parallel Lines cut by a Transversal

1a. 8 b. 7 c. 8 d. 2

e. 7 f. 7 or 1 (or 3 or 5) g. 3 h. 5

2. alternate interior and equal; x = 24; 125 degrees; 125 degrees

3. same side exterior and supplementary; x = 3; angles 1, 4, 5, 8 = 71 degrees;

angles 2, 3, 6, 7, = 109 degrees

4. x = 8; the acute angles are 35 degrees and the obtuse angles are 145 degrees

5. The top angles are 46 degrees and 116 degrees.

The bottom angles are 46 degrees, 18 degrees, and 162 degrees.

6. First drawing: left side from top to bottom 104 degrees, 76 degrees, 81 degrees, 99

degrees; right side 23 degrees

Second drawing: on top 39degrees and 141 degrees; triangle 85 degrees; next to triangle

95 degrees

Pythagorean Theorem

1. 127.3 ft

2. No, 7717.94 does not equal 8100. It is not a right triangle. It is an obtuse triangle.

3. 95.4 feet

4. 2.6 miles

5. 92.2 miles

6. 356.8 m (leg is 355.3 + person’s height of 1.5)

7. 23.2 feet (leg is 9.2 feet)

Volume

1. Same volume: 301.44 cm2

2. Cylinder is 1.5cm tall.

4. Cylinder height is 1570 cm3 { };

Balls are 1046.7 cm3 { (

)

6. Each orange wedge is 3.53 in3 {

}

4 cm

6 cm

6 cm

8 cm

Math 8 - Review for Final Exam#1 2014macomb.k12.mi.us/utica/Eppler/media/13-14 Final Exam Review...

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Transcript of Math 8 - Review for Final Exam#1 2014macomb.k12.mi.us/utica/Eppler/media/13-14 Final Exam Review...