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Mourning Sr. High Geometry Summer Assignment Parts A-E are required for all students. Parts F-H are required for Geometry Honors students only. Directions: 1. Show all of your work. 2. Write your final answers on the answer sheet provided at the end of the assignment. 3. If you need help, there are links provided on the last page with extra help resources. This assignment will be collected for a grade the first week of school.

Geometry Summer Assignment - Miami-Dade County …teachers.dadeschools.net/sdaniel/Geometry Summer... · Geometry Summer Assignment ... Geometry 2017 – Summer Assignment

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Page 1: Geometry Summer Assignment - Miami-Dade County …teachers.dadeschools.net/sdaniel/Geometry Summer... · Geometry Summer Assignment ... Geometry 2017 – Summer Assignment

Mourning Sr. High

Geometry Summer Assignment

Parts A-E are required for all students. Parts F-H are required for Geometry Honors students only.

Directions:

1. Show all of your work.

2. Write your final answers on the answer sheet provided at the end of the assignment.

3. If you need help, there are links provided on the last page with extra help resources.

This assignment will be collected for a grade the first week of school.

Page 2: Geometry Summer Assignment - Miami-Dade County …teachers.dadeschools.net/sdaniel/Geometry Summer... · Geometry Summer Assignment ... Geometry 2017 – Summer Assignment

Geometry 2017 – Summer Assignment – Alonzo & Tracy Mourning Senior High

A. The Coordinate Plane

Use this graph to answer the following questions.

Name the coordinates of each point.

1. M 6. T

2. N 7. U

3. K 8. V

4. R 9. W

5. S 10. Q

11. Name all the points shown that lie on the x-axis.

12. Name all the points shown that lie on the y-axis.

13. What is the x-coordinate of every point that lies on a vertical line through P?

14. Identify which of the following point(s) lie on a horizontal line through W.

(-2, 1), (2, 3), (1, -3), (-2, 0), (0, -3), (2, 0)

15. Name the two points that both have a y-coordinate value of 3.

B. Solving Equations and Inequalities

Solve each equation or inequality. Show all steps. Simplify and leave answers as fractions.

1. 2𝑝 + 5 = 13 2. 12 + 2𝑏 = 2 + 5𝑏 3. 4𝑥 + 5 + 5𝑥 + 40 = 180

4. 2(4𝑥 + 4) = 𝑥 + 1 5. 2(𝑥 + 5) = 3(𝑥 − 2) 6. 180 − 𝑥 ≤ 3(90 − 𝑥)

Page 3: Geometry Summer Assignment - Miami-Dade County …teachers.dadeschools.net/sdaniel/Geometry Summer... · Geometry Summer Assignment ... Geometry 2017 – Summer Assignment

Geometry 2017 – Summer Assignment – Alonzo & Tracy Mourning Senior High

7. 180 − 𝑦 > 2(90 − 𝑦) 8. 6𝑥 − 3(6 − 5𝑥) ≥ −4(2 − 𝑥)

9. 10 −1

4(8𝑥 − 12) <

1

2(2𝑥 − 4) 10. – (3𝑥 − 1) + 7 > 3(𝑥 − 5) + 4

C. Solving Literal Equations

Solve each equation for the given variable.

1. Perimeter of rectangle: 𝑃 = 2𝑤 + 2𝑙. Solve for l.

2. Volume of a Prism: 𝑉 = 𝑙𝑤ℎ. Solve for w.

3. Surface Area of a Sphere: 𝑆 = 4𝜋𝑟2. Solve for r.

4. Lateral Area of a Cylinder: 𝐴 = 2𝜋𝑟ℎ. Solve for h.

5. Area of a Regular Polygon: 𝐴 =1

2𝑎𝑃. Solve for a.

6. Volume of a Cylinder: 𝑉 = 𝜋𝑟2ℎ. Solve for h.

Page 4: Geometry Summer Assignment - Miami-Dade County …teachers.dadeschools.net/sdaniel/Geometry Summer... · Geometry Summer Assignment ... Geometry 2017 – Summer Assignment

Geometry 2017 – Summer Assignment – Alonzo & Tracy Mourning Senior High

7. Area of a Triangle: 𝐴 =1

2𝑏ℎ. Solve for h.

8. Circumference of a Circle: 𝐶 = 2𝜋𝑟. Solve for r.

9. Volume of a Cone: 𝑉 =1

3𝜋𝑟2ℎ. Solve for r.

10. Area of a trapezoid: 𝐴 =1

2ℎ(𝑏1 + 𝑏2). Solve for 𝑏2.

D. The Distance Formula and Slope

In order to be successful in Geometry class next year, it is crucial that you understand how to use both the distance and slope formulas. Memorizing these formulas is a MUST!

The Distance Formula: 𝑑 = √(𝑥2 − 𝑥1)2 + (𝑦2 − 𝑦1)2

Formula for Slope: 𝑚 =𝑦2−𝑦1

𝑥2−𝑥1

Find the distance between each pair of points. Round your answer to the nearest tenth, if necessary.

1. (-2, 3), (-7, -7) 2. (2, -9), (-1, 4) 3. (5, 9), (-7, -7)

4. (8, 5), (-1, 3) 5. (-10, -7), (-8, 1)

Page 5: Geometry Summer Assignment - Miami-Dade County …teachers.dadeschools.net/sdaniel/Geometry Summer... · Geometry Summer Assignment ... Geometry 2017 – Summer Assignment

Geometry 2017 – Summer Assignment – Alonzo & Tracy Mourning Senior High

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

6. (-2, 3), (-7, -7) 7. (2, -9), (-1, 4) 8. (5, 9), (-7, -7)

9. (8, 5), (-1, 3) 10. (-10, -7), (-8, 1)

E. Graphing.

Slope-Intercept Form: 𝑦 = 𝑚𝑥 + 𝑏

Point-Slope Form: 𝑦 − 𝑦1 = 𝑚(𝑥 − 𝑥1)

Use the slope formula to find the slope of the line containing each set of points. Write the equation of each line in both slope-intercept and point-slope form.

1. (3, 6), (-6, 0) 2. (-7, 2), (-1, -4) 3. (5, 1), (5, 4)

Graph each of the equations on the graph provided.

4. −10𝑥 + 2𝑦 = 6 5. 𝑦 = 5𝑥 − 4

Page 6: Geometry Summer Assignment - Miami-Dade County …teachers.dadeschools.net/sdaniel/Geometry Summer... · Geometry Summer Assignment ... Geometry 2017 – Summer Assignment

Geometry 2017 – Summer Assignment – Alonzo & Tracy Mourning Senior High

Graph each system of linear equations on the graph provided.

6. 𝑦 = 1 − 2𝑥 7. 𝑦 = 2𝑥 + 7

𝑦 = −5 + 4𝑥 𝑥 = −3

F. Simplifying Radical Expressions

Radicals are in the simplest form when there are no perfect square factors inside the radical.

Simplify the following problems completely using perfect squares or factor trees. Do NOT use a calculator to find the decimal approximations for these square roots. Show ALL work.

1. √36 2. √27 3. √400 4. √80

5. −√9 6. √64

25 7. 2√72 8. (√5)2

Page 7: Geometry Summer Assignment - Miami-Dade County …teachers.dadeschools.net/sdaniel/Geometry Summer... · Geometry Summer Assignment ... Geometry 2017 – Summer Assignment

Geometry 2017 – Summer Assignment – Alonzo & Tracy Mourning Senior High

G. The Pythagorean Theorem.

The Pythagorean Theorem: 𝑎2 + 𝑏2 = 𝑐2.

Use the Pythagorean theorem to find the missing side. Leave your answers in simplest radical form.

1. 2.

3. 4.

5. 6.

Page 8: Geometry Summer Assignment - Miami-Dade County …teachers.dadeschools.net/sdaniel/Geometry Summer... · Geometry Summer Assignment ... Geometry 2017 – Summer Assignment

Geometry 2017 – Summer Assignment – Alonzo & Tracy Mourning Senior High

H. Basic Figures.

For each geometric solid below, identify the following: name of solid, number of vertices, number of edges, number of faces, number of bases, and the shape of the base.

1. 2.

3. 4.

5. 6.

7. 8.

Page 9: Geometry Summer Assignment - Miami-Dade County …teachers.dadeschools.net/sdaniel/Geometry Summer... · Geometry Summer Assignment ... Geometry 2017 – Summer Assignment

Geometry 2017 – Summer Assignment – Alonzo & Tracy Mourning Senior High

Name: _____________________________________ Answer Sheet

Part A

1. 2. 3.

4. 5. 6.

7. 8. 9.

10. 11. 12.

13. 14. 15.

Part B

1. 2. 3. 4. 5.

6. 7. 8. 9. 10.

Part C

1. 2.

3. 4.

5. 6.

7. 8.

9. 10.

Part D

1. 2. 3. 4. 5.

6. 7. 8. 9. 10.

Page 10: Geometry Summer Assignment - Miami-Dade County …teachers.dadeschools.net/sdaniel/Geometry Summer... · Geometry Summer Assignment ... Geometry 2017 – Summer Assignment

Geometry 2017 – Summer Assignment – Alonzo & Tracy Mourning Senior High

Part E

1. 2. 3.

4. 5.

6. 7.

Page 11: Geometry Summer Assignment - Miami-Dade County …teachers.dadeschools.net/sdaniel/Geometry Summer... · Geometry Summer Assignment ... Geometry 2017 – Summer Assignment

Geometry 2017 – Summer Assignment – Alonzo & Tracy Mourning Senior High

Part F

1. 2. 3. 4.

5. 6. 7. 8.

Part G

1. 2. 3.

4. 5. 6.

Part H

1. Name of solid:

Number of vertices:

Number of edges:

Number of faces:

Number of bases:

Shape of base:

2. Name of solid:

Number of vertices:

Number of edges:

Number of faces:

Number of bases:

Shape of base:

3. Name of solid:

Number of vertices:

Number of edges:

Number of faces:

Number of bases:

Shape of base:

4. Name of solid:

Number of vertices:

Number of edges:

Number of faces:

Number of bases:

Shape of base:

5. Name of solid:

Number of vertices:

Number of edges:

Number of faces:

Number of bases:

Shape of base:

6. Name of solid:

Number of vertices:

Number of edges:

Number of faces:

Number of bases:

Shape of base:

7. Name of solid:

Number of vertices:

Number of edges:

Number of faces:

Number of bases:

Shape of base:

8. Name of solid:

Number of vertices:

Number of edges:

Number of faces:

Number of bases:

Shape of base:

Page 12: Geometry Summer Assignment - Miami-Dade County …teachers.dadeschools.net/sdaniel/Geometry Summer... · Geometry Summer Assignment ... Geometry 2017 – Summer Assignment

Geometry 2017 – Summer Assignment – Alonzo & Tracy Mourning Senior High

Resources:

The Coordinate Plane –

https://www.khanacademy.org/math/basic-geo/basic-geo-coordinate-plane

http://www.mathopenref.com/coordplane.html

Solving Linear Equations and Inequalities -

https://www.khanacademy.org/math/algebra/solving-linear-equations-and-inequalities

Solving Literal Equations -

http://www.purplemath.com/modules/solvelit.htm

The Distance Formula/Pythagorean Theorem -

https://www.khanacademy.org/math/basic-geo/basic-geo-pythagorean-topic

Graphing Lines and Slope –

https://www.khanacademy.org/math/algebra-basics/core-algebra-graphing-lines-slope

Simplifying Radical Expressions -

https://www.khanacademy.org/math/pre-algebra/exponents-radicals/radical-radicals

Basic Figures –

http://www.mathopenref.com/tocs/solidtoc.html