Algebra 1 FINAL EXAM REVIEW Spring Semester Material (by ...gvmath.weebly.com/uploads/5/6/5/3/56539921/gv.alg_i.worksheet... · FINAL EXAM REVIEW . Spring Semester Material (by chapter)

Algebra 1 – Final Review Packet

1

Name: _________________________ Per.: _____ Date: _______________

Algebra 1 FINAL EXAM REVIEW

Spring Semester Material (by chapter)

Your Algebra 1 Final will be on _________________________ at ________. You will need to bring your textbook and number 2 pencils with you to the final exam. The final exam will cover the entire year. Re-review the material from the fall semester as well.

Do not lose this packet. Replacement packets will cost $$$.


2

What You Must Memorize For Final

1) Quadratic Formula: x = –b ± b2 – 4ac

2a

2) Standard Form: ax2 + bx + c = 0

3) Perfect Squares from 0 to 169: √0 , √1 , √4 , √16 … ,

4) Discriminant: b2 - 4ac

5) Complete the Square: x2 + __ 5x _

5

2

2

25

4

6) Direct Variation: y=kx

7) Inverse Variation:

8) Vertex:

9) Pythagorean Theorem: a2 + b2 = c2

10) X and Y Intercepts: To find y-intercept, set x’s equal to zero. To find, x-intercepts, set y equal to zero and solve for x.


3

*** show your work wherever applicable for full credit *** Chapter 5 Match each of the following polynomials with its special term name. 1. 4x2 + 27x – 8 _____

2. 5x3y10 _____

3. 3x + 5x3 _____

a) trinomial

b) binomial

c) monomial

Add or subtract the following polynomials. 4. (8t2 – 10t + 2) + (8t + 13) _________________________

5. (x2 + 5x – 1) – (7x2 + 2) _________________________

6. (x4 + 7x3 + 7) – (2x4 – 4x3 + 1) _________________________

7. (3n3 + n2 – n – 4) + (5n3 – 4n2 + 11) _________________________ Write in decimal form (standard notation). 8. 8 × 104

9. 9.82 × 105

10. 9 × 10-3

11. 7.24 × 10-6 Write in scientific notation. 12. 400,000

13. 5412

14. 0.00056

15. 0.0000814


4

Simplify the following. Leave all answers with positive exponents. 16. x2 • x7 17. (a4)12 18. (3b)3 19. 9770

20. 3−51

21. –6x8y–8

22. (2w2x4)3

23. 9

2

y28x

−

24. 6

14

xx

25. 8

yx⎟⎟⎠

⎞⎜⎜⎝

⎛

26. 5

6

5

4

fd

df7d

•

27. 3t4 v3

21t2 v6

Multiply or Divide. Express your answers in scientific notation. 28. (2.3 × 102)(4.5 × 10–7)

29. 4.8 × 102

1.2 × 105


5

Multiply. 30. 3x(4x – 9) _________________________

31. 4x2(x + 6) _________________________

32. 2x2(15x3 – 10) _________________________ Multiply the following. Use your choice of methods, but show your work!! 33. (x + 9)(x – 6) 34. (x + 3)(4x + 5) 35. (3x – 1)(8x + 1)

36. (x – 6)(x – 8) 37. (7x + 3)(7x – 2) 38. (3x3 – 2x2 + 6)(x + 5)


6

Chapter 6 Factor out the largest possible monomial. 39. 5x2 – 15 40. 8a + 10b – 16 41. 3c4 – 6c2 – 15c

Factor completely (remember – they are not always “ready” to go…). 42. x2 + 9x + 14 43. y2 – 15y + 54 44. t2 + 8t + 15

45. m2 + 23m – 24 46. x2 – x – 12 47. x2 + xy – 42y2

Factor the following differences of squares completely. 48. x2 – 121 49. 100a2 – 144 50. 5m2 – 20


7

Factor the following perfect square trinomials completely. 51. x2 + 18x + 81 52. 25m2 + 30m + 9 53. 4y3 – 16y2 + 16y

Factor completely (remember – they are not always “ready” to go…). 54. 3y2 – 20y + 12 55. 2x2 – 13x – 45 56. 18n3 + 33n2 – 6n

Solve for the given variable. 57. (a – 5)(a + 2) = 0 58. x(x – 3) = 0 59. y2 + 23y – 24 = 0


8

Chapter 10 Multiply or Divide.

60. 23 •

316 61.

34 ÷

78

62. 5x2 •

x15 63.

5x2 ÷

x15

Add or Subtract.

64. 34 +

74 65.

13 –

57

66. (5x – 7) – (8x – 12) 67.

(12x + 4)5 –

(4x + 3)5

Simplify Completely.

68. 12x4y6

8x7y2 69. 3x + 9

3x


9

70. 3a + 9b

12a2 71. 6y2 + 3y3y2 + 6y

72. 14a2 − 14b2

21a − 21b 73. b2 − 10b + 21b2 − 11b + 28

Multiply.

74. 52x •

4x17 75.

2x2

x • 52x

76. 4x

2x + 2 • 4x + 4

8x 77. m2 − 4

5m • 4m2

m + 2


10

Divide.

78. 2x7 ÷

12x21 79.

10x3

5x ÷ 2x3y6x2

80. 7

x + 4 ÷ 26

x + 4 81. 4x − 6

5 ÷ 6x − 9

25

Add or Subtract.

82. 4x7 +

6x7 83.

5x + 3x + 3 +

3x + 7x + 3

84. 2w2 + w

w3 – 9w3 85.

(4x + 2)(3x + 1) −

(7x − 6)(3x + 1)


11

86. 3x2 + 2x − 5

5x + 1 + 2x2 − x + 6

5x + 1 87. 13x –

5x

88. 5m

m − 1 − 3

m(m − 1) 89. 2uuv3 −

vu2 v2

90. 3a

a + 2 + −1

a 91. 1

x − 4 − x + 4

x2 − x – 12

92. 3

x – 2 + 3

x2 + 4x – 12 93. 15

b2 − 9 − 7

2b − 6


12

Chapter 11 94. Estimate which two integers each square root is between:

a) 73 is between ____ and ____ b) 13 is between ____ and ____

95. Simplify (show work):

a) 180 b) 252 c) x2y3 d) 196b5

96. Simplify to find (show work):

a) 81 • 25 b) 700

7

c) 3 7 + 8 7 d) 5 24 − 4 6

e) 5

3 f) 5 ( )5 + 5

97. Find the missing side length for each triangle (show your steps):

a) b)

u 13 12

2 v 5


13

98. Solve (show work):

a) 4x + 7 = 15 b) x + 5 + 8 = 19 99. To hang a math poster in his office, Mr. Zito leaned a 10 foot ladder against the wall, placing

the bottom of the ladder on the floor 3 feet away from the wall. How high up on the wall was the ladder? (Show work. A labeled picture is also required)

Chapter 13 100. Write the quadratic formula.

Solve the following using the QUADRATIC FORMULA. Complete all blanks.

101. 3x2 + 4 = 8x

_____________________ (standard form)

a = _____ substitution

b = _____

c = _____

solution(s) for x:


14

102. 6x + 5 = -2x2

_____________________ (standard form)

a = _____ substitution

b = _____

c = _____

solution(s) for x:

103. Write the formula for the discriminant

For questions 5 – 7, the blanks provided are for the following information:

a) Substitute values for a, b, & c into the discriminant formula. b) Find the discriminant. c) Tell how many solutions the quadratic has.

104. 3x2 + 4 = 3x a) d = __________________ (substitution)

b) d = __________________ (simplified)

c) _____________________ (# of solutions)

105. 4x + 2 = 3x2 a) d = __________________ (substitution)

b) d = __________________ (simplified)

c) _____________________ (# of solutions)

106. x2 = 8x – 16 a) d = __________________ (substitution)

b) d = __________________ (simplified)

c) _____________________ (# of solutions)


15

107. Solve each of the following using the zero-product property. SHOW WORK.

a) (x + 10)(x + 24) = 0 b) (2x – 6)(5x + 2) = 0 c) x(x + 158) = 0 d) 5x(4x – 16)(x + 9) = 0

108. Solve each of the following equations by factoring: SHOW WORK.

a) x2 – 8x + 16 = 0 b) x2 + 4x – 21 = 0

109. Complete the square for the following: a) x2 + 20x __________ b) u2 – 26u __________

110. Solve using any method you want… show work!!

a) x2 – 49 = 0 b) x2 + 10x = –4


16

Chapter 12 Identify the domain and range for each. Tell if the relation is a function. 111. h: {(3, 1), (2, 4), (3, 5), (4, 8)} 112. j: {(2, 7), (3, 6), (4, 5), (5, 4), (6, 3)}

a) domain: ____________________ a) domain: ____________________

b) range: ____________________ b) range: ____________________

c) function / not a function c) function / not a function 113. k: {(1, 2), (2, 3), (3, 2), (4, 1)} 114. m: {(4, 5), (4, 2), (4, 1), (4, 3), (1, 6)}

a) domain: ____________________ a) domain: ____________________

b) range: ____________________ b) range: ____________________

c) function / not a function c) function / not a function Find the indicated outputs for the following functions.

115. f(x) = –4x2 – 2 116. g(x) = –| x – 3 | + 6

f(1) = g(–2) =

f(–3) = g(–1) =

f(0) = g(4) =


17

Determine which of the following graphs represent functions. 117. 118. 119. y y y

x x x

function / not a function function / not a function function / not a function State the domain and range for the following graphs. 120. 121. 122. y Domain: _________ Domain: _________ Domain: _________

Range: __________ Range: __________ Range: __________ Graph the following functions.

123. f(x) = | x | 124. g(x) = | x – 3 | – 4 125. h(x) = – 23 x + 2

x

y

x

y

x

y

x x

y y

x


18

Graph each of the following quadratic functions, finding all indicated information. 126. f(x) = x2

– b 2a

Vertex

y-intercept x-intercept(s)

127. f(x) = x2 – 5

– b 2a

Vertex


128. f(x) = x2 – 4x – 12

– b 2a

Vertex



19

129. Find an equation of variation where y varies directly as x for each pair of values given.

a) y = 3 when x = 24 b) y = 50 when x = 25 130. Find an equation of variation where y varies inversely as x for each pair of values given.

a) y = 23 when x = 27 b) y = 4 when x = 8


20

131. Find the Vertex: f(x) = 4x2 + 8x + 1

132. Write the equation in Standard Form and then identify a, b, and c. 3x2 = -2x + 1

133. Solve using the quadratic formula: 3x2 -7x +4 = 0

134. Find the x and y intercepts: f(x) = x2 – 3x – 10

135. Function? Yes or No Domain: ________________ Range: _________________

136. What is the Domain and the Range of a relation defined by: {(5,2), (5,3), (6,2), (3,1)} Domain: _________________ Range: __________________

137. Find the indicated outputs for the function: f(x) = 3x2 – 1 for f(-2)

138. Find the equation of variation where y varies directly as x, and y = 14 and x = 2.

y

x


21

139. Find the equation of variation where y varies inversely with x, and y = 14 and x = 2.

140. 41 =−x

141. 16)3( 2 =+x 142. What number should be added to complete the square? X2 + 6x + __

143. 254

144. 325

145. =− 212

146. 2)52(

147. Find the length of side a.

9

a

3


22

ANSWER KEY

17 a48

18 27b3

19 1

20 5 5 3 or 12

21 6

22 8w6x12

23 28x2y9 or 28y9x2

24 X8

25

26 7

27 7

28 1.035x10‐4

29 4.4x10‐3

30 12x2‐27x

31 4x3+24x2

32 30x5‐20x2

33 x2+3x‐54

Page 3‐21 34 4x2+17+15

1 a 35 24x2+5x‐1

2 c 36 X2‐14x=48

3 b 37 45x2+7x‐6

4 8t2‐2t+15 38 3x4+13x3‐10x2+6x+30

5 ‐6x2+5x‐3 39 5(x2‐3)

6 ‐x4+11x3+6 40 2(4a+5b‐8)

7 8n3‐3n2‐n+7 41 3c(c3‐2c‐5)

8 80,000 42 (x+2)(x+7)

9 982,000 43 (y‐6)(8‐9)

10 .009 44 (t+3)(t+5)

11 .00000724 45 (m‐1)(m+24)

12 4 x 105 46 (x+3)(x‐4)

13 5.412 x 103 47 (x‐6y)(x+7y)

14 5.6 x 10‐4 48 (x‐11)(x+11)

15 8.14 x 10‐5 49 (10a‐12)(10a+12)

16 X9 50 5(m‐2)(m+2)


23

ANSWER KEY

51 (x+9)2 81 103

52 (5m+3)2 82 10

7

53 4y(y‐2)2 83 8 10

3

54 (3y‐2)(y‐6) 84 2 9

55 (2x+5)(x‐9) 85 3 8

3 1

56 3n(6n‐1)(n+2) 86 5 1

5 1

57 a=5 ; a=‐2 87 14

3

58 X=0 ; x=+3 88 5 3

1

59 Y=1 ; =‐24 y 89 2

60 18 90

3 22

61 67 91

134

62 6 92

3 2126

63 752 93

7 72 3 3

64 52 94

a) 8 and 9b) an 3 d 4

65 8

21 95 a) 6√5 ; b) 6√7 ; c) xy ; d) 14 √

66 ‐3x+5 96 a) 45 ; b) 10 ; c) 11√7 ; d) 6√6 ; e) √

67 8 1

5 97 a) 5 b) √29 or 5.4

68 32

98 a) 16 b) 116

69 3 99 √91 or 9.5

70 3

4 100 √ 4

2

71 2 1

2 101 x = 2 & x =

72 2

3 102 NO SOLUTION; can’t have a negative

in l side radica

73 34

103 4

74 1017

104 b) ‐39 ; c) zero solutions

75 5 105 b) 40 ; c) 2 solutions

76 1 106 b) 0 ; c) 1 solution

77 4 2

5 107 a) ‐10 & ‐24 ; b) 3 & ; c) 0 & ‐158

d) 0 & 4 & ‐9

78 12

108 a) 4 ; b) ‐7 & 3

79 6

109 a) +100 ; b) +169

80 7

26 110 a) 7 & ‐7 ; b) 5 √21


24

ANSWER KEY

111 a) {2,3,4} ; b) {1,4,5,8} ; c) not a function

112 a) {2,3,4,5,6} ; b) {3,4,5,6,7} ; c) function

113 a) {1,2,3,4} ; b) {1,2,3} ; c) function

114 a) {1,4} ; b) {1,2,3,5,6} ; c) not a function

115 ‐6 ; ‐38 ; ‐2

116 1 ; 2 ; 5

117 Not a function

118 Not a function

119 function

120 Domain: {x|x≤2} ; Range: {y|all real numbers}

121 Domain: {x|1≤x≤5} ; Range: {y|1≤y≤4}

122 Domain: all real numbers ; Range: all real numbers

123 Graph should form a v:

124 Graph should form a v:

125 Graph should be a negative sloped line:

126 0 ; vertex (0,0) ; y‐intercept (0,0) ; x‐intercepts (0,0)

127

0 ; vertex (0,‐5) ; y‐intercept (0,‐5) ; x‐intercepts = √5 √5 , 0 & √5 , 0

128 2 ; x (2,‐16) ; y‐intercept (0,‐12) ; x‐intercepts = 6 & ‐2 or (6,0) & (‐2,0) verte

129 a) x ; b) y=2

130 a) ; b)

131 (‐1, ‐3)

132

3x2 + 2x 1 = 0 =3 ; b=2 ; c= 1 a

133 & 1

134 ‐2 & 5 ; or (‐2, 0) & (5,0)

135 Yes ; all real numbers; {y|y 4

136 {3,5,6} ; {1,2,3}

137 11

138 y=7x

139

28

140 17

141 1 & 7


25

142 9

143

25

144

5√33

145 2√3 √2

146 20

147 √78

Documents

Algebra 1 FINAL EXAM REVIEW Spring Semester Material (by ...gvmath.weebly.com/uploads/5/6/5/3/56539921/gv.alg_i.worksheet... · FINAL EXAM REVIEW . Spring Semester Material (by chapter)