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Name _____________________________ Period ____ Algebra1 – SEM1 Final Review (Fall)

Chapters 1 & 2

Less Than < Greater Than > Examples: Insert the proper symbol, < or >, to get a true statement.

1) 8 128 2) 13 713

3) -5 7 – 5 4) 14 -814 Addition 1. If the signs are the same, find the sum (ADD) and keep the sign the same.

2. If the signs are different, find the difference (SUBTRACT) and the big guy wins! Examples: 5) 9 8 6) 10 7 7) 3 3 8) 18 8 9) 10 7 10) 6 6 11) 0 8 12) 55 55 13) 27 20Subtraction Subtracting is the same as ADDING THE OPPOSITE.

14) 10 15 15) 3 816) 11 5 17) 11 2018) 10 15 19) 3 820) 11 5 21) 11 20 Multiplication& Division

positive positive positive positive negative negative

negative negative positive negative positive negative

positive

positivepositive

negative

negativepositive

positive

negativenegative

negative

positivenegative

Try these: 22) 8 2 23) 8 2

24)

8

2 25) 8

2

26) 3 2 4 27) 5 1 3 28) 24 6

2

Exponents 29) 3

2b g 30) 33b g 31) 1

3b g

32) 14b g 33) 2

2b g 34) 25b g

Simplify.

35) 4 • 3 + 12 ÷ 2 36) 16 8 4 2 1 b g 37) 4 14 7 1 22 3b g

Evaluate each expression.

38) z4 – 1 for z = -1 39) 4x2 for x = -2 40) (4x)2 for x = -2

Examples: Use the distributive property to write an equivalent expression.

41) 6(x + y) 42) 2(x + y + z) 43) 7(a – 2)

44) 1 2 (r + s – t) 45) (6x + 7 + 5p)3 46) −6(2e – 3f – g)

Examples: Factor.

48) 3a + 3b 49) 6x + 12y 50) 3z – 3y 51) ua – ub – uc 52) 5x – 35y – 10 53) −6u + 4v – 8w

Examples: Collect like terms.

54) y + y 55) 3c + 2c 56) −7x + 2x – 3x 57) −6a + 5b + 4a – b 58) 4(x + 3) + 5(x + 3) 59) 7(m2 + 2) + 7(m2 + 2)

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Distribute the negative. 60) −(2y + 3) 61) −(a – 2) 62) −(5y – 3z + 4w)

63) 3 – (x + 1) 64) x – (2x – 3y) 65) 3z – 2y – (4z + 5y)

66) 9x – (4x+3) 67) 3a + 2a – (4a + 7) 68) (3x + 2y) – (5x -4y)

Examples: Write as an algebraic expression. 69) the sum of x and 2 70) the sum of a number and 3

71) six more than a number 72) nine less than a number

73) twice a number 74) half of a number

75) the product of u and v 76) 6 less than h

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Chapter 3 Notes Examples – Solve each equation. Show your work!

77) 7 7b 78) 23 18m

79)

910

m

80) x4 + 5 = 11

81) 2 3 7 11( )x 82) 5 3 4 2 8x x ( )

83) 5x = 8 + x 84) 8a + 1 = 3a + 7 85) 8w + 4 – 2w = w + 1

86) 3(7 + 2x) = 30 + 7(x – 1)

87) 4(3 + 5y) – 4 = 3 + 2(y – 2)

88) 13 p +

16 =

32 89)

32 x +

34 x +

38 x = 21

90) 26.45 = 4.2x + 1.25

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91) | y | = 3 92) -3| x | = -27 93) | x | = -16

94) | a + 3 | = 7 95) | 4 + w | = 63

96) 3 | x +2 | = 12 97) 2| x – 3 | − 5 = 7

98) 52

1 x

99) 6

7

4

m

100) x

24

7

4

101) If a car moving at a constant speed travels 55 miles in 2 hours, how many miles will it travel in 7 hours?

102) Sally can bake 20 cookies in 30 minutes. How many minutes will it take her to bake 125 cookies?

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Change the decimal to a fraction. Change the fraction to a decimal.

103) 0.34 104) 0.8 105)

3

5 106)

3

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Change the decimal to a percent. Change the percent to a decimal.

107) 0.08 108) 1.25 109) 56% 110) 4%

Changing the fraction to a percent.

111) 3

5 112)

3

10 113)

7

6

Solve. 114) What is 25% of 48? 115) 45 is 60% of what? 116) What percent of 24 is 12?

117) the sum of two consecutive integers is 85. Find the numbers.

118) The sum of two consecutive odd integers is 144. Find the integers.

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0 5 10 x-12-11-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 x

-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 x-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 x

-1 0 1 2 3 4 5 6 7 8 9 10 x -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 x

Chapter 4 Notes Write an inequality for the following number line graphs. 119) 120) 121) 122)

Examples: Solve and graph your solution. 123) 5x + 2 < 22 124) 7 – 4x < −1 125) 4(a – 2) – 5 ≤ 7 126) −2(u + 7) + 4 > −10

127) x + 8 < 10 or x – 5 > 2

128) 5 ≤ 2x – 1 < 7

Write the compound inequality that matches each graph.

129) 130)

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Chapter 7 Notes

SLOPE between two points (x1, y1) and (x2, y2)

Slope (m) = values-in x change

values-y in change

run

rise

12

12

xx

yym

INTERCEPTS x – intercept is when y = 0 y – intercept is when x = 0

Example: y = 2x + 8 x –intercept

0 = 2x+8 -8=2x -4 =x (-4, 0)

y –intercept y= 2(0)+8 y = 0 + 8

y = 8 (0, 8)

Write an equation of a line in Slope-Intercept Form Given the slope and the y-intercept

Ex. 1

5,3 bm

53 xy

Ex. 2

9,3

1 bm

93

1 xy

Given two points Example: (-4, 5) (2, 2) Step 1: Find the slope

2

1

6

3

42

52

m

Step 2: Put in slope-intercept form

bxy 2

1 Step 3: Plug in one point to solve for b

325

)4(2

15

bb

b

Step 4: Plug in the value for b

32

1 xy

Given a point and the slope

Ex. (2, 3) 6m

Step 1: Put in slope-intercept form

bxy 6 Step 2: Plug in the point to solve for b

b

b

b

15

123

)2(63

Step 3: Plug in the value for b

156 xy

Parallel Lines have the same slope

53

2 xy and 7

3

2 xy are parallel

xy 3 and 93 xy are parallel

Perpendicular-have Opposite-Reciprocal Slopes

53

2 xy and 7

2

3 xy are perpendicular

xy 3 and 93

1 xy are perpendicular

m is the slope b is the y-intercept

Slope-Intercept Form

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The x – intercept of a line is the point where the line crosses the x – axis. The y– intercept of a line is the point where the line crosses the y – axis.

Find the x and y intercepts for the following lines 132) x – intercept:

y – intercept:

133) x – intercept:

y – intercept:

134) x – intercept:

y – intercept:

Find the intercepts. 135) 6x – 3y = 6 136) 4x + 3y =12 137) 2y = 3x – 6

Find the slope of the lines containing these points. 138) (-2, 3), (3, 5)

139) (0, -3), (-3, 2)

140) (3, 8), (3, 5)

141) (0, -2), (3, -2)

131) Plot these points on the coordinate plane above.

a) A (3, 4) b) B (3, -4) c) C (-3, 4) d) D (-3, -4) e) E (5, 0) f) F (0, -6) g) G (-2, 0) h) H (0, 7)

Origin is at the point (0, 0)

(x, y)

Right (+) Left (-)

Up(+) Down (-)

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Graph.

142) y x 12 5 143) y x

144) x = 3

145) 2 3 6x y 146) 3 5x y 147) y = -5

Write the equation of the line described in slope - intercept form.

148) m 23 , b 5 149) (2, 5), m 5 150) (-3, 5), (-1, -3)

151) (2, 4), m 34 152) (3, 2), (1, 5) 153) m 1, b 0

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154) Parallel lines have the _______________ slope.

155) Perpendicular lines have ________________________________ slopes.

Write the equation of the line that passes through the given point and is parallel to the given line.

156) 53 xy ; (2, 3) 157) 132 xy ; (-6, 5)

Write the equation of the line that passes through the given point and is perpendicular to the given line. 158) xy 5

1 ; (8, -3) 159) 3 xy ; (-2, -3)

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Chapter 8 Notes Example 2: Solve each system by graphing.

160) y x

y x

4 7

8

161)

y x

y x

2

Solve using the substitution method.

162) y xx y 3

2 4 28 163)

a bb a

42 5

Examples: Solve using the addition method. 164) 4x + 3y = 5 5x 3y = 4 165) 83

1424

yx

yx

166) 2a + 5b = 9 3a – 2b = 4

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Example : Graph the following inequalities. 167) y < 2x – 3 168) y ≥ – 2

3 x + 1

169) y – 3x < 0

170) y ≤ 2

171) y > 4x – 1 y < –2x + 3

172) y ≤ 23 x

y ≥ –x + 1

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For each of the following, write two equations, then solve. 173) The sum of two numbers is 82. One number is twelve more than the other. Find both numbers. Let x = y = Equation #1 Equation #2

174) Ronald has nickels and quarters totaling $2.65. He has 17 coins in all. How many quarters does he have? How many nickels? Let x = y =

Eq #1

Eq #2

175) The length of a rectangle is 5 more than the width. If the perimeter is 38, what are the dimensions? Let x = y =

Equation #1

Equation #2

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Final Exam Review-Packet_Sem1_KEY 1  < 51 u(a –b – c) 2  < 52 5(x – 7y – 2) 3  < 53 2(-3y + 2v – 4w) 4  > 54 2y 5  -17 55 5c 6  17 56 -8x 7  -6 57 -2a +4b 8  10 58 9x + 27 9  -3 59 14m2 + 28 10  0 60 -2y – 3 11  -8 61 -a + 2 12  0 62 -5y + 3z – 4w 13  -7 63 2 – x 14  -5 64 -x + 3y 15  -11 65 -z – 7y 16  -16 66 5x – 3 17  -9 67 a – 7 18  25 68 -2x + 6 y 19  5 69 x + 2 20  -6 70 x + 3 21  31 71 x + 6 22  -16 72 x – 9 23  16 73 2x 24  4 74 x/2 25  -4 75 u • v 26  24 76 h – 6 27  -15 77 0 28  -4 78 27 29  9 79 90 30  -27 80 24 31  -1 81 6 32  1 82 -2 33  4 83 2 34  -32 84 6/5 35  18 85 -3/5 36  21 86 -2 37  26 87 -3 38  0 88 4 39  16 89 8 40  64 90 6 41  6x + 6y 91 3,-3 42  2x + 2y +22 92 9,-9 43  7a – 14 93 No solution 44  r/2 + 5/2 – t/2 94 -11, 4 45  18x + 21 + 15p 95 59, -67 46  -12e + 18f + 6g 96 2, -6 47  97 9, -3 48  3(a + b) 98 5/2 49  6(x + 2y) 99 14/3 50  3(z – y) 100 42

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101  192.5 miles 123 x < 4

102  187.5 minutes 124 x > 2

103  17/50 125 a ≤ 5

104  4/5 126 u < 0

105  .6 127 x < 2 or x > 7

106  .3 128 3 ≤ x< 4

107  8% 129 3 < x ≤ 8 108  125% 130 -2 ≥ x > 5

109  .56 131 

110  .04 132 x-int:(-2,0) y-int: (0,-5)

111  60% 133 x-int: none y-int: 3

112  30% 134 x-int: -5 y-int: none

113  116.66% 135 x = (1,0) y = (0,-2)

114  12 136 x = (3,0) y = (0,4)

115  75 137 x = (2,0) y = (0,-3)

116  50% 138 2/5 117  42, 43 139 -5/3 118  71,73 140 No slope 119  x ≥ 5 141 0

120  x < -2 142 

121  x > 0 143 

122  X ≤ 8

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144 

156  y= 3x −3

145 

157  y= −⅔x +1

146 

158  y= −5x +37

147 

159  y= −1x −5

148  y= −⅔x −5 160 

149  y= 5x −5 161 

150  y= −8/3x −3 162 (2,6)

151  y= ¾x −5/2 163  (1, -3)

152  y= −3/2x +6.5 or y= −3/2x +13/2 164 (-1, 3) 153  y=-1x 165 (3, 1) 154  Same slope 166 (2, 1)

155  Opposite-Reciprocal slopes 167 

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168 

 

169 

 

170 

 

171 

 

172 

 

173 

Let x = fist number ; Let y = second number Equation #1: x + y = 82 Equation #2: x + 12 = y x = 35 ; y = 47  

174 

Let x = nickels ; Let y = quarters Equation #1: x + y = 17 Equation #2: 5x + 25y = 265 x = 8 nickels ; y = 9 quarters  

175 

Let x = L ; Let y = W Equation #1: L = W + 5 Equation #2: 2L + 2W = P (perimeter) L = 12 ; W = 7