June 12, 2014 Dear Families, A math packet has been provided on the Goodman website for students to familiarize themselves with the content that is taught in the Grade 8 Math Course that your student will be skipping. If you do not have access to a computer/printer, which would allow you to print the packet, please contact the office. We are requiring students to complete the packet to ensure that critical concepts are mastered for success in Algebra 1. Please make sure that your student shows all their work and attaches any additional pages used. The packet is due the first day of school, September 3, 2014. This will be recorded as a homework completion grade during the first marking period. Attached is a chart that shows a summary of the lessons that are covered with corresponding page numbers from the grade 8 textbook. To assist your student’s progress through the packet, we have provided access to the Grade 8 online textbook that will be of assistance: Access Holt Grade 8 Math Textbook/Resources Online:

Go to: my.hrw.com

• Enter the user name: sgrade155 • Enter the password: peninsula • Click on: Go to Online Textbook

o Access book pages from the student textbook by entering the page number then click Go!

o On the book pages you will find examples with lesson tutorial videos, interactivities, and interactive quizzes on the right

o On the Student Resources tab under lesson resources you will find Homework Help

If you have any questions, please feel to contact your student’s school or Bridgit Reichel at

reichelb@psd401.net.

Sincerely,

Bridgit Reichel

K-12 Math Specialist

2

8th Grade Standards on the 8th Grade EOC

Page # Lesson Page Concept

2

3.3 100 Scientific Notation

3 3.4 105 Operations with Sci Not

4 3.5 112 Squares and Square Roots

5 3.8 132 Pythagorean Theorem

6 3.9 138 Applying PT

7 5.1 196 Angle Relationships

8 5.2 202 Parallel and Perpendicular Lines

9 5.4 213 Coordinate Geometry

10 5.6 226 Transformations

11 6.1 262 Circles

12 6.2 267 Volume of Prisms and Cylinders

13 6.3 276 Volume of Pyramids and Cones

14 6.4 282 Spheres

15 7.2 304 Solving Multi-Step Equations

16 7.3 309 Solve Equations with Variables on Both sides

17 8.2 345 Slope

18 8.3 350 Slopes and Intercepts

19 8.5 362 Direct Variation

20 8.6 368 Solving Systems via Graphing

21 9.1 386 Scatter Plot

22 9.3 400 Linear Functions

3

Exponents and Roots Ch 3.3 Practice B: Scientific Notation

Write each number in standard notation.

1. 2.54 × 102 2. 6.7 × 10−2 3. 1.14 × 103 4. 3.8 × 10−1

_______________ _______________ _______________ ________________

5. 7.53 × 10−3 6. 5.6 × 104 7. 9.1 × 105 8. 6.08 × 10−4

_______________ _______________ _______________ ________________

9. 8.59 × 105 10. 3.331 × 106 11. 7.21 × 10−3 12. 5.88 × 10−4

_______________ _______________ _______________ ________________

Write each number in scientific notation.

13. 75,000,000 14. 208 15. 907,100

_______________________ ________________________ ________________________

16. 56 17. 0.093 18. 0.00006

_______________________ ________________________ ________________________

19. 0.00852 20. 0.0505 21. 0.003007

_______________________ ________________________ ________________________

22. 5226 23. 0.04 24. 98,856

_______________________ ________________________ ________________________

25. Jupiter is about 778,120,000 kilometers from the Sun. Write this number in scientific notation.

________________________________________________________________________________________

26. The E. coli bacterium is about 5 × 10−7 meters wide. A hair is about 1.7 × 10−5 meters wide. Which is wider, the bacterium or the hair?

4

Exponents and Roots Ch 3.4 Practice B: Operating with Scientific Notation

Write your answer in scientific notation.

1. Rhode Island is the smallest state. It has an area of approximately 1.55 × 103 square miles. Alaska is the largest state. The area of Alaska is 4.28 × 102 times greater than the area of Rhode Island.

What is the approximate area of Alaska in square miles? _________________

2. In 2008, the total trade between the United States and Japan was $2.04 × 1011. The total trade between the U.S. and Australia was $3.28 × 1010.

How many times greater was the trade with Japan than the trade with Australia? _________________

3. Between 2008 and 2009, Americans spent $8.48 × 108 on baby food. During the same period, Americans spent $4.52 × 109 on ice cream.

How much did Americans spend altogether on ice cream and baby food between 2008 and 2009? _________________

4. Wrangell-St. Elias National Park in Alaska is the largest national

park. It includes approximately 1.32 × 107 acres. Thaddeus Kosciuszcko National Memorial in Pennsylvania is the smallest national park. It is located on approximately 2.0 × 10–2 acres.

How many times greater is the area of Wrangell-St. Alias National Park than Thaddeus Kosciuszcko National Memorial? _________________

5. Approximately 3.25 × 106 cubic yards of material were used to build Boulder Dam on the Arizona-Nevada border. The New Cornelia Tailings Dam in Arizona used 2.74 ×108 cubic yards of material.

How many more cubic yards of material were used to build the Cornelia Tailings Dam than Boulder Dam? _________________

5

Exponents and Roots Ch 3.5 Practice B: Squares and Square Roots

Find the two square roots of each number.

1. 36 2. 81 3. 49 4. 100

_______________ _______________ _______________ ________________

5. 64 6. 121 7. 25 8. 144

_______________ _______________ _______________ ________________

Simplify each expression.

9. 32+17 10. 100 −19 11. 64 + 36 12. 73 − 48

_______________ _______________ _______________ ________________

13. 2 64 +10 14. 36 − 36 15. 100 − 25 16. 121+16

_______________ _______________ _______________ ________________

17.

254

+ 12

18.

10025

19.

19649

20. 3( 144 − 6 )

_______________ _______________ _______________ ________________

The Pyramids of Egypt are often called the first wonder of the world. This group of pyramids consists of Menkaura, Khufu, and Khafra. The largest of these is Khufu, sometimes called Cheops. During this time in history, each monarch had his own pyramid built to bury his mummified body. Cheops was a king of Egypt in the early 26th century B.C. His pyramid’s original height is estimated to have been 482 ft. It is now approximately 450 ft. The estimated completion date of this structure was 2660 B.C.

21. If the area of the base of Cheops’ pyramid is 570,025 ft2, what is the length of one of the sides of the ancient structure?

(Hint: s = A )

________________________________________________________________________________________

6

Exponents and Roots Ch 3.8 Practice B: The Pythagorean Theorem

Find the length of the hypotenuse to the nearest te nth.

1. 2. 3.

_______________________ ________________________ ________________________

Solve for the unknown side in each right triangle t o the nearest tenth.

4. 5. 6.

_______________________ ________________________ ________________________

7. 8. 9.

_______________________ ________________________ ________________________

10. A glider flies 8 miles south from the airport and then 15 miles east. Then it flies in a straight line back to the airport. What was the distance of the glider’s last leg back to the airport?

_______________________

8.4 c

6.3

7

Exponents and Roots Ch 3.9 Practice B: Applying the Pythagorean Theorem and its Converse

1. The length of a rectangular swimming pool is 50 feet. The width of the pool is 20 feet. What is the length of the diagonal of the pool? Round your answer to the nearest tenth.

_______________________________________

2. A map is placed on a coordinate grid. Cincinnati located at (5, 4) and San Diego is located at (–10, –3). How far apart is Cincinnati from San Diego on the map? Round your answer to the nearest tenth.

_______________________________________

3. Katie, Ralph, and Juan are tossing a football. Katie is 22.5 feet away from Ralph. Ralph is 58.5 feet away from Juan. Juan is 54 feet away from Katie. Do the distances between Katie, Ralph, and Juan form a right triangle? Explain.

_______________________________________

4. A rectangular picture from has a length of 7 inches and a width of 5 inches. What is the length of the diagonal of the picture frame? Round your answer to the nearest tenth.

_______________________________________

Find the distance between the two points to the nea rest tenth.

5. (0, 5) and (–4, 2) 6. (1, 9) and (6, 3) 7. (–6, 4) and (2, –6)

_______________________ ________________________ ________________________

8. (–1, –7) and (–3, –5) 9. (4, 0) and (–9, 7) 10. (0, –8) and (4, 0)

_______________________ ________________________ ________________________

Tell whether the given side lengths form a right tr iangle.

11. 7, 24, 25 12. 30, 40, 45 13. 21.6, 28.8, 36

_______________________ ________________________ ________________________

14. 10, 15, 18 15. 10.5, 36, 50 16. 2.5, 6, 6.5

_______________________ ________________________ ________________________

8

Geometric Relationships Ch 5.1 Practice B: Angle Relationships

Use the diagram to name each figure.

1. a right angle

_______________________________________

2. two acute angles

_______________________________________

3. two obtuse angles

_______________________________________

4. a pair of complementary angles

_______________________________________

_______________________________________

_______________________________________

5. three pairs of supplementary angles

_______________________________________

_______________________________________

_______________________________________

Use the diagram to find each angle measure.

6. If m∠2 = 110º, find m∠4. 7. If m∠1 = nº, find m∠3.

_______________________________________ ________________________________________

8. The diagram shows the intersection of three roadways on a map. Based on the diagram, what should be the measure of ∠ECD?

9

Geometric Relationships Ch 5.2 Practice B: Parallel and Perpendicular Lines

1. Measure the angles formed by the transversal and the parallel lines. Which angles seem to be congruent?

_______________________________________

_______________________________________

In the figure, line m || line n. Find the measure of each angle. Justify your answer.

2. ∠1 3. ∠2

_______________________ ________________________

4. ∠5 5. ∠6

_______________________ ________________________

6. ∠8 7. ∠7

_______________________ ________________________

In the figure, line a || line b. Find the measure of each angle. Justify your answer.

8. ∠2 9. ∠5

_______________________ ________________________

10. ∠6 11. ∠7

_______________________ ________________________

12. ∠4 13. ∠3

_______________________ ________________________

In the figure, line r || line s.

14. Name all angles congruent to ∠2.

_______________________________________

15. Which line is the transversal?

________________________________________________________________________________________

10

Geometric Relationships Ch 5.4 Practice B: Coordinate Geometry

Graph the polygons with the given vertices. Give th e most specific name for each polygon.

1. S(−3, −3), T(−3, 4), U(4, −3) 2. M(−1, 2), N(2, 0), Q(2, −4), P(−1, −2)

_______________________________________ ________________________________________

Find the coordinates of each missing vertex.

3. Triangle WUV has a right angle at W 4. Quadrilateral JKLM is a square. and WU = 5.

_______________________________________ ________________________________________

Find the coordinates of the midpoint of each segmen t.

5. XY with endpoints X(1, 2) and Y(4, 5) _______________________________________________

6. ST with endpoints S(−8, 6) and T(2, 4) ______________________________________________

7. FG with endpoints F(3, 9) and G(−5, 6) ______________________________________________

8. LP with endpoints L(6, 0) and P(−3, −4) _____________________________________________

9. EC with endpoints E(−2, −8) and C(−1, −7) __________________________________________

11

Geometric Relationships Ch 5.6 Practice B: Transformations

Graph each translation.

1. 3 units left and 9 units down 2. 3 units right and 6 units up

Graph each reflection. 3. across the x-axis 4. across the y-axis

Graph each rotation around the origin. 5. 90° clockwise 6. 180°

7. A parallelogram has vertices A(−1, 3), B(4, 3), C(6, −1), and D(1, −1). After a transformation, the coordinates of the image are A ' (1, 3), B ' (−4, 3), C ' (−6, −1), and D ' (−1, −1). Describe the transformation. _____________________________________

12

Measurement and Geometry Ch 6.1 Practice B: Circles

Find the circumference of each circle, both in term s of ππππ and to the nearest tenth. Use 3.14 for ππππ.

1. circle with radius 10 in.

_______________________________________

3. circle with diameter 18 m

_______________________________________

5. circle with radius 11.5 in.

_______________________________________

2. circle with diameter 13 cm

________________________________________

4. circle with radius 15 ft

________________________________________

6. circle with diameter 16.4 cm

________________________________________

Find the area of each circle, both in terms of ππππ and to the nearest tenth. Use 3.14 for ππππ.

7. circle with radius 9 in.

_______________________________________

9. circle with radius 20 ft

_______________________________________

11. circle with diameter 15.4 m

_______________________________________

13. Graph a circle with center (0, 0) that passes through (0, −3). Find the area and circumference, both in terms of π and to the nearest tenth. Use 3.14 for π.

_______________________________________

_______________________________________

14. A Wheel has a radius o of 213

feet.

About how far does it travel if it makes 60

complete revolutions? Use

227

for π.

8. circle with diameter 14 cm

________________________________________

10. circle with diameter 17 m

________________________________________

12. circle with radius 22 yd

________________________________________

13

Measurement and Geometry Ch 6.2 Practice B: Volume of Prisms and Cylinders

Find the volume of each figure to the nearest tenth . Use 3.14 ππππ.

1. 2. 3.

_______________________ ________________________ ________________________

4. 5. 6.

_______________________ ________________________ ________________________

7. 8. 9.

_______________________ ________________________ ________________________

10. A cylinder has a radius of 6 ft and a height of 25 ft. Explain whether tripling the height will triple the volume of the cylinder.

________________________________________________________________________________________

________________________________________________________________________________________

11. Contemporary American building bricks are rectangular blocks with the standard dimensions of about 5.7 cm by 9.5 cm by 20.3 cm. What is the volume of a brick to the nearest tenth of a unit?

________________________________________________________________________________________

12. Find the volume of the figure.

14

Measurement and Geometry Ch 6.3 Practice B: Volume of Pyramids and Cones

Find the volume of each figure to the nearest tenth . Use 3.14 for ππππ.

1. 2. 3.

_______________________ ________________________ ________________________

4. 5. 6.

_______________________ ________________________ ________________________

7. The base of a regular pyramid has an area of 28 in2. The height of the pyramid is 15 in. Find the volume. _______________________

8. The radius of a cone is 19.4 cm and its height is 24 cm. Find the volume of the cone to the nearest tenth. _______________________

9. Find the volume of a rectangular pyramid if the height is 13 m and the base sides are 12 m and 15 m. _______________________

10. A funnel has a diameter of 9 in. and is 16 in. deep. Use a calculator to find the volume of the funnel to the _______________________ nearest hundredth.

11. A square pyramid has a height 18 cm and a base that measures 12 cm on each side. Explain whether tripling the height would triple the volume of the pyramid.

________________________________________________________________________________________

________________________________________________________________________________________

________________________________________________________________________________________

15

Measurement and Geometry Ch 6.4 Practice B: Spheres

Find the volume of each sphere, both in terms of ππππ and to the nearest tenth. Use 3.14 for ππππ.

1. r = 9 ft 2. r = 21 m 3. d = 30 cm

_______________________ ________________________ ________________________

_______________________ ________________________ ________________________

4. d = 24 cm 5. r = 15.4 in. 6. r = 16.01 ft

_______________________ ________________________ ________________________

_______________________ ________________________ ________________________

Find the surface area of each sphere, both in terms of ππππ and to the nearest tenth. Use 3.14 for ππππ.

7. 8. 9.

_______________________ ________________________ ________________________

_______________________ ________________________ ________________________

10. 11. 12.

_______________________ ________________________ ________________________

_______________________ ________________________ ________________________

13. Compare the volume and surface area of a sphere with diameter 3 m with that of a cylinder with height 1.5 m and a base with radius 1 ft.

________________________________________________________________________________________

________________________________________________________________________________________

16

Multi-Step Equations Ch 7.2 Practice B: Solving Multi-Step Equations

Solve.

1. 2x + 5x + 4 = 25 2. 9 + 3y − 2y = 14 3. 16 = 2(2w + w − 1)

_______________________ ________________________ ________________________

4. 26 = 3b − 2 − 7b 5. 31 + 4t − t = 40 6. 2(7 − x) + 4x = 20

_______________________ ________________________ ________________________

7.

5m8

−

68

+

3m8

=

28

8. −4

23

=

2n3

+

13

+

n3

9. 7a + 16 − 3a = −4

_______________________ ________________________ ________________________

10.

x2

+ 1 +

3x4

= −9 11. 7m + 3 − 4m = −9 12.

2x5

+ 3 −

4x5

=

15

_______________________ ________________________ ________________________

13.

7k8

−

34

−

5k16

=

38

14. 3(2y + 3) − 4y = −3 15.

5a6

−

712

+

3a4

= −2

16

_______________________ ________________________ ________________________

16. The measure of an angle is 28° greater than its complement. Find the measure of each angle.

________________________________________________________________________________________

17. The measure of an angle is 21° more than twice its supplement. Find the measure of each angle.

________________________________________________________________________________________

18. The perimeter of the triangle is 126 units. Find the measure of each side.

_______________________________________

_______________________________________

19. The base angles of an isosceles triangle are congruent. If the measure of each of the base angles is twice the measure of the third angle, find the measure of all three angles.

17

Multi-Step Equations Ch 7.3 Practice B: Solving Equations with Variables on Both Sides

Solve.

1. 7x − 11 = −19 + 3x 2. 11a + 9 = 4a + 30 3. 4t + 14 =

6t5

+ 7

_______________________ ________________________ ________________________

4.

3y8

− 9 = 13 +

y8

5.

3k5

+ 44 =

12k25

+ 8 6. 15 − x = 2(x + 3)

_______________________ ________________________ ________________________

7. 15y + 14 = 2(5y + 6) 8. 14 −

w8

=

3w4

− 21 9.

12

(6x − 4) = 4x − 9

_______________________ ________________________ ________________________

10. 4(3d − 2) = 8d − 5 11.

y3

+ 11 =

y2

− 3 12.

2x − 93

= 8 − 3x

_______________________ ________________________ ________________________

13. Forty-eight decreased by a number is the same as the difference of four times the number and seven. Find the number. _________________________

14. The square and the equilateral triangle at the right have the same perimeter. Find the length of the sides of the triangle.

_______________________________________

15. The equation V =

13

Bh gives the volume V of a pyramid,

where B is the area of the base and h is the height. Solve this equation for B.

18

Graphing Lines Ch 8.2 Practice B: Slope of a Line

Find the slope of each line.

1. 2.

_______________________________________ ________________________________________

Find the slope of the line that passes through each pair of points.

3. (−2, −8), (1, 4) 4. (−2, 0), (0, 4), 5. (0, 4), (4, 4) 6. (3, −6), (2, −4)

_______________ _______________ _______________ ________________

7. (−3, 4), (3, −4) 8. (3, 0), (0, −6), 9. (3, 2), (3, −2) 10. (−4, 4), (3, −1)

_______________ _______________ _______________ ________________

11. The table shows the distance Ms. Long had traveled as she went to the beach. Use the data to make a graph. Find the slope of the line and explain what it shows.

_______________________________________

_______________________________________

_______________________________________

_______________________________________

Time (min) Distance (mi)

8 6

12 9

16 12

20 15

Graphing Lines Ch 8.3 Practice B: Using Slopes and Intercepts

Find the x-intercept and y-intercept of each line. Use the intercepts to graph the equation.

1. x − y = −3 2. 2x + 3y = 12

_______________________________________ ________________________________________

_______________________________________ ________________________________________

Write each equation in slope-intercept form, and th en find the slope and y-intercept.

3. 3x + y = 0 4. 2x − y = −15 5. x − 5y = 10

_______________________ ________________________ ________________________

_______________________ ________________________ ________________________

Write the equation of the line that passes through each pair of points in slope-intercept form.

6. (3, 4), (4, 6) 7. (−1, −1), (2, −10) 8. (6, 5), (−9, −20)

_______________________ ________________________ ________________________

9. A pizzeria charges $8 for a large cheese pizza, plus $2 for each topping. The total cost for a large pizza is given by the equation C = 2t + 8, where t is the number of toppings. Graph the equation for t between 0 and 5 toppings, and explain the meaning of the slope and y-intercept.

_______________________________________

_______________________________________

_______________________________________ 18

Graphing Lines Ch 8.5 Practice B: Direct Variation

Determine whether the data sets show direct variation.

1. x y

6 9

4 6

0 0

−2 −3

−8 −12

________________________________________________________________________________________

2. Write the equation of direct variation for Exercise 1.

________________________________________________________________________________________

Find each equation of direct variation, given that y varies with x.

3. y is 32 when x is 4 4. y is −10 when x is −20

_______________________________________ ________________________________________

5. y is 63 when x is −7 6. y is 40 when x is 50

_______________________________________ ________________________________________

7. y is 87.5 when x is 25 8. y is 90 when x is 270

_______________________________________ ________________________________________

9. The table shows the length and width of various U.S. flags. Determine whether there is direct variation between the two data sets. If so, find the equation of direct variation.

Length (ft) 2.85 5.7 7.6 9.88 11.4

Width (ft) 1.5 3 4 5.2 6

________________________________________________________________________________________

________________________________________________________________________________________

________________________________________________________________________________________ 19

Graphing Lines Ch 8.6 Practice B: Solving Systems of Linear Equati ons by Graphing

Solve each linear system by graphing. Check your an swer.

1. y = −1 2. x − y = 6 y = 2x − 7 2x = 12 + 2y

_______________________________________ ________________________________________

3. 12

x − y = 4 4. y = 4x − 3

2y = x + 6 2y − 3x = −4

_______________________________________ ________________________________________

5. Two skaters are racing toward the finish line of a race. The first skater has a 40 meter lead and is traveling at a rate of 12 meters per second. The second skater is traveling at a rate of 14 meters per second. How long will it take for the second skater to pass the first skater?

_______________________________________

Data, Prediction, and Linear Functions Ch 9.1 Practice B: Scatter Plots

1. Use the given data to make a scatter plot, and describe the correlation.

Tall Buildings in U.S. Cities

Building City Stories Height (meters)

Sears Tower Chicago 110 442

Empire State Building New York 102 381

Bank of America Plaza Atlanta 55 312

Library Tower Los Angeles 75 310

Key Tower Cleveland 57 290

Columbia Seafirst Center Seattle 76 287

NationsBank Plaza Dallas 72 281

NationsBank Corporate Center Charlotte 60 265

_______________________________________

2. Make a scatter plot of the data, and draw a line of best fit. Then use the data to predict the percentage of American homeowners in 1955.

Percent of Americans Owning Homes

Year 1950 1960 1970 1980 1990

Percent 55.0% 61.9% 62.9% 64.4% 64.2%

21

Data, Prediction, and Linear Functions Ch 9.3 Practice B: Linear Functions

Determine whether each function is linear. If so, g ive the slope and y-intercept of the function’s graph.

1. f(x) = −3x + 2 2. f(x) = x2 − 1

_______________________________________ ________________________________________

Write a rule for each linear function.

3. 4. x y

−3 16

−1 12

3 4

7 −4

_______________________________________ ________________________________________

5. At the Sweater Store, the price of a sweater is 20% more than the wholesale cost, plus a markup of $8. Find a rule for a linear function that describes the price of sweaters at the Sweater Store. Use it to determine the price of a sweater with a wholesale cost of $24.50.

________________________________________________________________________________________

________________________________________________________________________________________

22