Name ________________________________________________________

1

Pre-IB Geometry Summer Assignment This summer assignment is for all incoming freshman in the IB program, whom will begin their math course of study with Pre-IB Geometry. All work must be completed in pencil, neatly and completely. Your solution will be worked in the boxes provided. Problems will be discussed during the first week of class. This assignment is due the first full day of school in August to the Pre-IB Math teacher, as this is a summer assignment. Answers should be simplest form – no decimals. Calculator: A scientific calculator (such as the TI 30XIIs, but not limited to this model) is required the first day of school. A graphing scientific calculator, rather than a basic scientific calculator, is strongly recommended (such as the TI –NSPIRE CX). The models suggested are acceptable for use on the ACT and SAT college entrance exams. These calculators are tools that would be necessary in all four high school math courses, physics, chemistry, and exams such as International Baccalaureate Math, ACT and SAT. The graphing calculators can be priced to be around $100 and oftentimes are on sale during the summer. Your student will become more and more proficient at using their calculators over the course of their lower level math classes, so as to be prepared for when these tools are essential in upper level math classes.

Name ________________________________________________________

2

Part 1: Properties of Numbers Define each property and provide a mathematical example of each.

A. Commutative Property of Addition

B. Commutative Property of Multiplication

C. Associative Property

D. Additive Inverse

E. Multiplicative Inverse

F. Additive Identity

G. Multiplicative Identity

H. Multiplicative Property of Zero

I. Reflexive Property

J. Symmetric Property

K. Transitive Property

L. Substitution Property

Name ________________________________________________________

3

Part 2 :

Find the value of each expression: (remember to use order of operations)

1) 8 + 5 - 3 2) 9(42 + 6) 3) 11 - (5 - 2)2

4) 14 + (9 3) 5) [18 - (6 + 4)] 2 6) (9 - 2) (3 + 4)

7) 7 + 24 - 18 6 8) 7 · 6 + 3 3 - 5 9) 3 + (5 - 3)2 - 6

Name ________________________________________________________

4

Evaluate each expression if a = 15,b = 5,c = 4,x=1/2, and y = 2.

Simplify each equation

16)

17) 2a + 7b + 8a - 3b + 4a

18) 10(3x - 2y) + 4(4x + 3y)

19)

10) y a b 11) cb xb 12) 8y + b2(ay)

13) 26 4

1

2

abc x b 14)

21

3y x 15)

2

a bx

b

99 3 12

10x y y x

4 1

9 3 3 83 2

a b a b

Name ________________________________________________________

5

20) 2x(3y - 4) + 5y(2x + 1) 20) 3x(x + y) - 2y(2x - 5y)

Name ________________________________________________________

6

Solve each equation

21) 4x = 16 22) 15 = 8 - x 23) 6x - 1 = 7x - 3

24)

25) 26) -2 = -(x + 8)

27)

28)

29) Solve for w, given : P = 2l + 2w

30) 3 - 5x = -25 31) 4(2x - 3) = 3x - 7 32) Solve for w, given A = l w

3 718

2 2x

2 7

3 9x

113 7

2x

10 2 4

3 5 3x

Name ________________________________________________________

7

Solve each problem 33) A number is increased by 11 is 56. Find the number.

34) The sum of four times a number and 5 is 41. Find the number.

35) The sum of two consecutive integers plus 7 is 148. What are the integers?

36) Sherry is 25 years younger than her dad. The sum of their ages is 59. How old is Sherry?

37) Mrs. Chin bought some $0.20 stamps and an equal number of $0.29 stamps. She paid a total of $4.90 for all the stamps. How many of each type stamp did she buy?

38) Enrique Romero bought a refrigerator for $50 more than half its original price. He paid $375 for the refrigerator. What was the original price of the refrigerator?

Name ________________________________________________________

8

Solve each absolute value equation

39) |x + 2| = 6 40) |x - 4| -5 = 2 41) |3x - 7| - 10 = -2

42) |x - 7| = -13 43) |3x - 4| + 15 = 41 44) 2|3x - 7| = 10

45)

46)

47)

13 11

2x 2 10

43 3

x 2 4

23 9

x

Name ________________________________________________________

9

Solve each inequality

48) 2x - 4 > 18 49) 7x + 2 16

50) 3(4x - 3) 15 51) 4 - 5x > -11

52) 2 + 3(x + 4) 2(x - 3) 53) 4x + 5 < 6x - 1

1 1 54) x <

2 4 x - 5

55)

56)

57) 2 1 1 1

3 2 5 2x

23 5

3x

4 2 2 4

3 5 3 5x x

Name ________________________________________________________

10

Write each linear function in standard form Ax + By = C Remember: A, B, or C may not be a fraction and A should be a positive number

58) y = -2x + 7 59) -3x + 2y = -14 2

60) y = x - 4 3

3 61) x = y + 3

2

62) 63) 2x + 3y = 6

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

64) (-4,0), (2,3) 65) (0,3), (-2,0)

66) (2,1/2 ) , (-3,1)

67) (5,2), (5, -3)

43

5y x

Name ________________________________________________________

11

Solve each system using the substitution method 70)

71)

72) 3 7

4 2 16

x y

x y

73)

4

2 3 19

x

x y

Solve each system using the elimination method.

74) 5 2 8

2 3 2

x y

x y

75)

4 12

4 2 6

x y

x y

2 2 4

2 0

x y

x y

2 5

3 3 3

x y

x y

Name ________________________________________________________

12

76) 5 4 12

7 6 40

x y

x y

77)

5 2 12

6 2 14

x y

x y

Simplify

78) 2x(3x + 1) + 3(2x - 3) 79) 3x(2x - 4) - 3(x + 5)

80) 3xy(2x2 - 3x + 2y - y2) 81) 2x2y3(2x - 3xy + y)

82) (x - 3)(x - 4) 83) (x + 2)(x + 6)

84) (2x + 5)(x - 3) 85) (3x - 2)(2x + 1)

Name ________________________________________________________

13

86) 3(x - 4)(x + 2) 87) x(5x - 1)(3x + 2)

88) (x + 2)2 89) (x + 1)(x2 - 2x + 5)

Factor

90) x2 + 5x + 6 91) x2 - 6x + 8

92) x2 + 3x - 10 93) x2 - 3x - 18

94) 2x2 - 5x - 3 95) 2x2 - 5x - 12

96) 6x2 - 13x - 5 97) 8x2 - 6x - 5

Name ________________________________________________________

14

98) x3 + x2 - 6x 99) 2x3 + 5x2 + 2x

100) x2 - 16 101) x2 + 6x + 9

102) 2x3 - 2x2 - 24x

103) 2 1 3

2 2x x

Solve each quadratic by either factoring or using the quadratic formula

2 4

2

b b acx

a

104) x2 - 12x + 27 = 0 105) x2 - 7x - 44 = 0

106) 16x2 = 49 107) 3x2 - 13x = -10

Name ________________________________________________________

15

108) 4x2 - 35x - 9 = 0 109) -2x2 - 5x + 12 = 0

110) x2 - 2x - 5 = 0 111) – x2 + 4x = -2

112) 2x2 - x = 2 113) -3x2 + 2x + 6 = 0

114) Simplify 4√10 ⋅ 3√6 exactly (no decimals) 115) Simplify √98𝑥4𝑦6𝑧2 exactly, (no decimals)

116) Simplify √2

5 ⋅ √

6

5 , radical form (no

decimals)

117) Simplify, radical form (no decimals) √8/(2 + √3)

Name ________________________________________________________

16

118) Simplify, radical form (no decimals) 2√5 + 4√5

119) Simplify, radical form (no decimals)

3√6 + 3√2 – √50 + √24

120) On graph paper, graph the line 2x + 5y = 5

121)On graph paper, graph the line y = -(2/5)x + 1

122) Write the equation of a line, in standard form, of a line parallel to y = -(2/5)x + 1. Graph the line on graph paper.

123) Write the equation of a line, in slope-intercept form, of a line perpendicular to y = -(2/5)x + 1. Graph the line on graph paper.

123) Create a table of values that make Y = -(2/5)x + 1 true. Graph the coordinates.

124) Graph the inequality x > 3 or x ≤-2.

125) Write an expression for the area of a square with a side length of 2x.

126) Write an expression for the perimeter of a rectangle with a length and width of (2x +1) and (3x-1), respectively