Geometry Summer Packet 2011

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Geometry Summer Packet - 2011

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Name: _________________IA Regents Grade: _______ Class Grade: ____

Geometry and Honors GeometrySummer Review Packet

DUE ON SEPTEMBER 9, 2011NO EXCEPTIONS

The problems in this packet are designed to help you review topics fromprevious mathematics courses that are important to your success in

Geometry or Honors Geometry. You must complete all work in thispacket. Show all of your work. Do not use a calculator and use aPENCIL to complete this packet. Bring the packet with you to yourGeometry or Honors Geometry class on the first week of school.Additional copies of this summer packet can be printed from the KIPPHigh School website (in pdf) at: www.kippnyc.org in the “Family and

Student Documents” section.

All work should be completed and ready to turn in on September 9,

2011. This packet WILL count as part of your first quarter Geometry

or Honors Geometry grade.

Enjoy your summer! We are looking forward to seeing you in the fall.

http://www.kippnyc.org/







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Name: __________________________________________

Be sure to show all your work for the problems. All work MUST be completed in

PENCIL!!!!!!

Integers

Integers are the set of whole numbers and their opposites. Every positive integer has a negative integer. Thenumber line is used to represent integers. This is shown below.

Integers can be added or subtracted. There are rules for adding and subtracting integers.

In 1-9, add the following integers. Do not use a calculator. Answer the question that follows. BOX YOUR ANSWER.

1. -1 + (-3) = 2. -2 + (+4) = 3. +1 + (+5) = 4. -17 + (-2) =

5. +23 + (-5) = 6. -8 + (+8) = 7. +7 + (-3) = 8. -10 + (+6) =

9. What is the rule for ADDING positive and negative integers?




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In 10-18, perform each indicated subtraction. Do not use a calculator and BOX YOUR ANSWER. Answer the question

that follows.

10. 9 - (-3) = 11. 5 - 7 = 12. (+8) - (-4) = 13. -23 - (-5) =

14. -8 - (+8) = 15. +10 - (+6) = 16. 6 - 8 = 17. -4 - (-6) =

18. What is the rule for SUBTRACTING positive and negative integers?

Integers can also be multiplied or divided. There are rules for multiplying and dividing integers.

Rules for Multiplying/Dividing:

Multiplying ...

The product of two numbers with the same signs is positive. The product of two numbers with different signs is negative.

Dividing ...

The quotient of two numbers with the same sign is positive. The quotient of two numbers with different signs is negative.




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In 19-33, find the product (×) or quotient (÷) of each pair of numbers withoutusing a calculator.

19. +9 × +3 = 20. -17(-6) = 21. -8 ÷ -2 =

22. +27(-6) = 23. -18 ÷ -9 = 24. -96 ÷ 12 =

25. (-4)(-9) = 26. 63 ÷ 9 = 27. -48 × 6 =

28. 150/-15 = 29. (15)(-15) = 30. (-9)(-3) =

31. +56 ÷ 8 = 32. (-11)(-5) = 33. 99 ÷ -11 =

Radicals

Simplifying Radical Expressions:

25 , read “the square root of 25,” means one of the two positive equal factors of 25.

55525 ; 66636 ; 10101002 ; 7749

2

aaaa 2

;3336

aaaa ;88816

mmmm ;510

y y

a is called a radical, a is called the radicand.




4

Simplify (Simplifying Perfect Squares):

In 34- 45, simplify each expression.

34. 4

35. 16

36. 100

37. 8a

38. 12w 39. 106

ba 40. 29a 41. 64

81m

42. 12449 ba 43. 614

121 y x 44. 81 45. 144

Simplify (Simplifying Radicals that are not Perfect Squares):

52220 3222248 aaaaaa 5

= 52 = 322 = aaa

= 34 = aa2




5

In 46- 57, simplify each expression.

46. 18

47. 125

48. 72

49. 180

50. 3a 51. 7

b 52. 9m 53. 57

75 y x

54. 71127 ba 55. 47

32 ba 56. 89a 57. 7

45a




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Angles

Types of Angles:

An acute angle is an angle that measures less than 90o.

An obtuse angle is an angle that measures more than 90o.

A straight angle is a straight line that measures 180o.

Complementary angles are two angles that sum to 90o.

Supplementary angles are two angles that sum to 180o.

In 58-63, find the measure of the missing angle. Identify the missing angle as acute, obtuse or straight. Additionally,

identify the pair of angles as complementary or supplementary.

Missing Angle Measure: __________Type of Angle: _________________Pair of Angles: _________________



15

o

150o

180o

50o

40o

60o

120o

A

CB

136o

?26

o

?

58. 59. 60.

? 39o




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Angle Relationships:

In 64-74, complete each of the following.

64.

Name a pair of adjacent angles.

_________________________

65.

Name a pair of vertical angles.

________________________

66.

Name a pair of supplementaryangles.________________________

67.

Name a pair of complementaryangles.

________________________

68.


__________________________

69.

Name a pair of adjacent angles.

___________________________

165o

?

22o 158

o

?

?

? 39o

?

61. 62. 63.




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70.

Name a pair of supplementaryangles.

________________________

71.


_________________________

72.


_________________________

73.


_________________________

74.

Name a pair of complementaryangles.

________________________

Notes:

Triangles

Right Triangles:

All right triangles have a 90o angle. To determine the length of the sides of a right triangle when we know the length of

the other two sides, we use the Pythagorean Theorem.

For example, a2 + b2 = c2

(4)2 + (4)2 = c2

16 + 16 = c2

32 = c2

32 = c

4 2 = c

?

4

4

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In 75-80, use the Pythagorean Theorem, to find the 3rd side in each of these triangles. Show your work and leave all

answers in simplest radical form.

Missing Side: __________ Missing Side: __________ Missing Side: __________

Missing Side: __________ Missing Side: __________ Missing Side: __________

?

3

4

25

7

?

8 15

?

78. 80.

10

10

?9

18

?

75. 76. 77.

79.

20

12

?




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All Triangles:

The sum of the degree measures of the angles in any triangle equals 180o.

In 81-83, determine the measure of the missing angle in triangle ABC.

Missing Angle: __________ Missing Angle: __________ Missing Angle: __________

AlgebraAlgebraic Expressions and Equations:

In 84-87, simplify each algebraic expression.

84. 7( y + 2) – 5( y + 8)

Answer: __________

85. 3(m + 9) + 2m

Answer: __________

86. 4(n-8) – 6(n -10)

Answer: __________

87. (2 x – 3 y + 4 z) + (9 x – 8 y + 7 z)

Answer: __________

A

C

B60

o

?

60o

B

C23

o

A

?

47o

CB

A

50o

35o

?

81. 83.82.




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In 88-97, solve each algebraic equation.

88. x + 2 = 10 89. 26 = 8 + v

90. 8 - p = 3 91. p - 6 = -5

92. 14b = -56 93. 12 z – 3 = 8 z+13

94. 6v + v + 9 = 4 - 3v 95. 2(3m - 1) = 2m + 2

96. 12 = -4(-6 x – 3) 97. 2g + g – 7 = 1 + 3g




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In 98-103, solve each rational equation.

98. 16

2

4

1

aa

99. bb

b

2

6

5

11

100. 9

4

3

1

cc

101. bb

b

2

6

5

11

102. 30

10

12

x

x

103. 5

17

3

33

x x

Solving Quadratic Equations:

In 104-111, determine the roots of the quadratic equation.

104. What are the roots of the equation

x2 − 10 x+21=0?

105. What are the roots of the equation

( x 4)( x 3) 0?




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106. Solve for x: x2 3 x 40 0 107. Solve for x: x2

3 x 28 0

108. One of the roots of the equation x2

3 x 18 0is 3. What is the other root?

109. What is the solution set of the equation

x2 4 x 12 0?

110. What is the solution set of m2

3m10 0? 111. What is the solution set for the equation

x2

5 x 6 0?




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Graphing

In 112-114, graph the following lines on the coordinate plane.

112. y = 3 x + 2

113. 2 y = 8 x -6




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114. y = x -5

In 115 – 118, use graph paper to complete the following exercises.

115. Perform the following.A. Graph the line x =3.B. On the same coordinate plane, graph the line 2 units to the right of the line x = 3. Label the line

with the correct equation.C. Now, graph the line 2 units to the left of the line x = 3. Label the line with the correct equation.




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116. A. On the same coordinate plane, graph the equation y = x and y = x2 – 2.

B. What are the coordinates of the points where the two functions intersect?

117. A. Graph the quadratic equation y = x2

+ 3 x + 2.B. On the same coordinate plane, graph the line y = -x + 2.C. Circle the points on the graph where the two functions intersect.D. Name the coordinates of the points of intersection. These two points are the solution to the system

of equations.




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118. On the coordinate plane, perform the following steps.Step 1: Graph the points A(-5,4), B(6,4), C(6,1) and D(-5,1).Step 2: Label each point with its corresponding letter.Step 3: Connect each point using a straight edge.

What polygon is this?

Step 5: Use slope formula to determine the slope of AB.Step 6: Use slope formula to determine the slope of AD.

What do you notice about the two slopes?

Step 7: Using the coordinate plane, determine the length of AD.Step 8: Using the coordinate plane, determine the length of BC.

What do you notice about the two lengths?




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Lines

In 119-122, determine the slope of the line through each pair of points using the slope formula.

119. (5, 1) and (2, 7) 120.

(5, 3) and (-2, 3)

121. (-1/2, -2) and (-3/2, 1) 122. (2, -4) and (2, 6)

In 123-125, answer the following questions.

123. What is the equation of the line that passes through the points (−3,7) and (3,3)?

124. What do we know about the slope of two parallel lines?

125. What do we know about the slope of perpendicular lines?




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Use this information to answer question 126.

126. What is the equation of a line that passes through the point (-3,-11) and is parallel to the line whoseequation is 2 x - y = 4? Determine the answer algebraically and graphically.Graphically:

Step #1: Graph the line 2x – y = 4Step #2: Plot the point (-3,-11).Step #3: Determine the equation of the line that answers the question.

Algebraically:Hint: Consider the standard equation of a line. How can you find the two critical pieces of information?

Graphically:




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Algebraically:

FiguresIn 127-132, identify each figure by name.

129.

128.

130.

127.

132.131.




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Word Problems

133. Square Deal Pizza offers square pizza that is 15 inches long on each side. A cheese pizza costs $9.00.Roundoff Pizza offers circular pizza that is 16 inches in diameter. A cheese pizza at Roundoff costs $8.75

- Which restaurant’s pizza is bigger? Justify your answer using words, symbols, or both. - Which restaurant’s pizza is a better buy? Justify your answer using words, symbols, or both.

134. A juice pitcher holds 1.5 gallons of liquid. How many 8 -ounce glasses of juice can be poured from a fullpitcher? (1 gallon = 128 ounces) Explain your answer by writing or describing the steps you used tosolve the problem.

Contact Information:

Ms. Abrams [email protected] Ms. Nelson [email protected] Cell 917- 939 - 0700

mailto:[email protected]






Geometry Summer Packet 2011

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