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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 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)
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.
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)
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
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
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.
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.
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.
Geometry 2017 – Summer Assignment – Alonzo & Tracy Mourning Senior High
Part E
1. 2. 3.
4. 5.
6. 7.
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:
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