Name Date Period

DUE First Friday of the Semester

ALL problems are to be worked out by hand on the pages provided. If you do your work on another sheet of paper, please keep the

problems in order of the packet, writing down the page numbers and problem numbers. When working the problems, students should

may use a calculator, and must show math work in detail in order to receive credit.

Some of these problems are a preview of content in Geometry; therefore, if you experience difficulty working through this packet, we

recommend you utilize the following free websites:

1. www.khanacademy.org

2. www.coolmath-games.com/

3. www.teachertube.com/videos/

4. www.purplemath.com/modules/index.htm

Geometry Summer Packet

Review prerequisite skills: combining like terms, solving linear equations, finding slope, midpoint, distance, plotting points on a coordinate plane, perimeter, circumference,

area, volume, systems of equations, and simplifying radicals

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Geometry Prerequisite Skills

Directions: Solve each problem in each section. Show all work.

Part I. Combining Like Terms.

Simplify.

1. 5x + 2y – 3x + 8y + 6 2. 7x + 8x2 − 5x + x2

+ 8x 3. 6ab – 4ab + ab

Part II. Solving equations.

Directions: Solve for the variable. Show all work! 4. 5x + 3x = 80 5. 3x + 16 + 5x = 180 6. 180(n – 2) = 1080

7. 1 – x = 4x + 21 8. 7n + 9 + 3n – 3 = 6n 9. −5𝑦 − 11

4= 9

10.

2

3𝑥 = 5

1

3 11. 2(12b + 7) + 9b + 1 = 180 12. ½(4x – 8 ) - 3x - 6 = 90

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Part III. Graphing in coordinate Plane

13. Plot the following points on the coordinate plane. Then connect the points and name the shape that is formed. A (5, 2), B (3, -5), and C (-6, 4)

Part IV. Slope

2 4 6–2–4–6 x

2

4

6

–2

–4

–6

y

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Directions: Plot the points on the coordinate plane and connect them with a line. Then find the slope of the line connecting the two points by doing rise over run and then confirm your answer by using the slope formula. Show ALL work. 14. (1, 2) and (6, 6) 15. (5, 6) and (5, -4)

16. (-3, 6) and (5, -4) 17. (6, -3) and (-2, -3)

1 2 3 4 5 6 7–1–2–3–4–5–6–7 x

1

2

3

4

5

6

7

–1

–2

–3

–4

–5

–6

–7

y

1 2 3 4 5 6 7–1–2–3–4–5–6–7 x

1

2

3

4

5

6

7

–1

–2

–3

–4

–5

–6

–7

y

1 2 3 4 5 6 7–1–2–3–4–5–6–7 x

1

2

3

4

5

6

7

–1

–2

–3

–4

–5

–6

–7

y

1 2 3 4 5 6 7–1–2–3–4–5–6–7 x

1

2

3

4

5

6

7

–1

–2

–3

–4

–5

–6

–7

y

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Part V. Perimeter, Area and Circumference

Directions: For each problem, draw the figure and calculate the perimeter or circumference and area of each figure. Remember to include the UNITS for each answer. 18. A rectangle has a length of 10 inches and 19. A square has a side length of 6.25 centimeters a width of 4 inches 20. A right triangle has a base of 16 meters and a 21. A circle with a radius of 4.5 feet. height of 12 meters (hint: you will need to use the pythagorean theorem to find the third side.) 22. A circle with a diameter of 15 inches. 23. The area of a 10 cm wide rectangle is 176 cm. Find the length. 24. Find the area of the triangle below. 25. If the area of a circle is 100π cm2, find the diameter.

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Part VI. Volume.

Volume is the measure of space occupied by a solid. Volume is measured in cubic units.

Find the volume of each figure. If necessary, round to the nearest tenth. Use the π key on the calculator.

26. 27. 28.

29. 30. 31.

Part VII. Midpoint and Distance Formula in Coordinate Plane

Directions: Find the midpoint of line segment AB. 32. a) A(-4, 5) and B(0, 8).

b) A(2, 7) and B(-4, -6).

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Directions: Find the perimeter of pentagon ABCDE with A(0, 4), B(4, 0),

C(3, -4), D(-3, -4) and E(-3, 1).

33. Plot the points on the coordinate plane below and connect the points in alphabetical order.

34. a. Use the distance formula to find the length of segment AB.

b. Use the distance formula to find the length of segment BC.

c. Use the distance formula to find the length of segment CD.

d. Use the distance formula to find the length of segment DE

e. Use the distance formula to find the length of segment AE

35. Find the Perimeter of ABCDE.

1 2 3 4 5 6 7–1–2–3–4–5–6–7 x

1

2

3

4

5

6

7

–1

–2

–3

–4

–5

–6

–7

y

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Part VIII. Names of Polygons

36. Write the name of

each polygon

based on its

number of sides.

Part IX. Systems of Equations

Solve each equation by substitution. Answers should be written as an ordered pair.

37. 2x + 2y = 38 38. y – 2x = 3

y = x + 3 3x – 2y = 5

Solve by elimination. Answers should be written as an ordered pair.

39. 2x + 3y = 9 40. 6x – 3y = 15

x + 5y = 8 7x + 4y = 10

Name of Polygon Number of Sides

Name of Polygon Number of Sides

Triangle 3 8

4 9

5 10

6 12

7

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Part X. Simplifying Radicals.

Write answers in simplest radical form.

41. a) √80 b) 2√75

42. a) √36 ∙ √81 b) √12 ∙ √20

43. a) √81

64

44. a) √7

3 b)

4√5

√2

45. a) 2√3 + 5√3 b) 3√2 + 4√3 + 5√2 − 6√3

46. a) (2 + 4√2)(2 − 4√2)

Part XI. Quadratic Equations Solve each equation by factoring.

47. x2 + 4x – 32 = 0

48. p2 – 4 p = 21

Solve each equation by using the quadratic formula. Round answers to the nearest tenth if necessary.

49. 2x2 – 3x – 5 = 0

50. - 3x2 – 11x + 4 = 0