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Name: _____________________________ Mod: _________
Algebra 1 Advanced
Mrs. Crocker
Final Exam Review Spring 2014
The exam will cover Chapters 6 – 10 You must bring a pencil,
calculator, eraser, and exam review “flip book” to your exam.
You may bring the following:
1. A 3x5 handwritten notecard (both sides may be used)
2. Your finished exam review (this will earn you extra credit on
the exam) The exam will consist of three parts: Multiple Choice,
Written Free Response, and Mental Math.
Mod 3-4: Tuesday 6/3 from 7:25 – 9:25
Mod 10-11: Wednesday 6/3 from 7:25 – 9:25
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Chapter 6 – Systems of Equations and Inequalities In your flip
book complete the following topics. Write necessary formulas,
information, and draw diagrams:
A. Solve Systems Graphically B. Solve Systems using Substitution
C. Solve Systems using Elimination D. Applications of Systems E.
Graphing Linear Inequalities F. Solving Systems of Linear
Inequalities
Solve the following problems to practice these above concepts.
Use a pencil and show work. For #1 & 2, solve the system
graphically:
1. ! = 2! − 1 2. −! + 2! = −2 ! = 2 2! + ! = 4 3. Describe the
three different types of systems: a). Consistent and Independent:
b). Consistent and Dependent: c). Inconsistent for #4 & 5,
solve the system using substitution:
4. ! − ! = −2 5. ! = 2! −5! + 5! = 10 2! + 6! = 15
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For #6 & 7, solve the system using elimination:
6. 4! + 3! = −19 7. −2! + 5! = 7 3! − 2! = −10 −2! + 5! = 12 For
#8 – 10, solve using any algebraic method. Write a system and
define your variables.
8. A corner store sells two kinds of baked goods: cakes and
pies. A cake costs $15 and a pie costs $6. In one day, the store
sold 12 baked goods for a total of $108. How many cakes id they
sell? 9. Sharon has some one-dollar bills and some five-dollar
bills. She has 14 bills. The value of the bills is $30. Solve a
system of equations to find how many of each kind of bill she has.
10. At the local ballpark, the team charges $8 for each ticket and
expects to make $1,100 in concessions. The team must pay its
players $2,100 and pay all other workers $1,200. Each fan gets a
free bat that costs the team $4 per bat. How many tickets must be
sold to break even? For #11 & 12, graph the solution to the
system of linear inequalities:
11. ! ≥ −! + 1 12. 2! − !!! < 1
! < 3! − 2 4! + 8! > −24
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Chapter 7 – Exponents & Exponential Functions In your flip
book complete the following topics. Write necessary formulas,
information, and draw diagrams:
G. Laws of Exponents H. Scientific Notation I. Exponential
Functions J. Exponential Growth / Compound Interest K. Exponential
Decay
Solve the following problems to practice these above concepts.
Use a pencil and show work. For #13 – 16, simplify each
expression:
13. !"
!!!!! 14. !! !
15. !! !!!!!
16. −6!! 3!! (6!!)
17. !!!!!
!!!
!! 18. 4!
!!!!! !
19. Last year, a large trucking company delivered 6.0×10! tons
of goods with an average value of $20,000 per ton. What was the
total value of the goods delivered? Write the answer in scientific
notation. 20. Suppose a population of 200 crickets doubles in size
every month. The function ! ! = 200 ∙ 2! gives the population after
! months. How many crickets will there be after 3 years?
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For #21 & 22, provide a table and graph the exponential
function:
21. ! = 4 ∙ 5! 22. ! = − !!
!
23. Suppose the population of a town is 19,000 and is growing 2%
each year. Write an exponential growth function and predict he
population after 11 years. 24. A tractor costs $15,100 and
depreciates in value by 9% per year. Write an exponential decay
function and predict how much it will be worth after 9 years. 25.
Suppose that the amount of algae in a pond doubles every 3 hours.
If the pond initially contains 50 pounds of algae, how much algae
will be in the pond after 8 hours? 26. Steve invests $4000 in a
money market account that pays 1.25% interest compounded monthly.
Use the compound interest formula to find how much will be in the
account after 4 years. 27. Shelly invests $10,000 in a money market
account that pays 2.5% interest compounded annually. Use the
compound interest formula to find how much will be in the account
after 12 years.
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Chapter 8 – Polynomials & Factoring In your flip book
complete the following topics. Write necessary formulas,
information, and draw diagrams:
L. Polynomials M. Factoring (!! + !" + ! !"# !!! +
!" + !) N. Factoring Special Patterns O. Factoring by Grouping
Solve the following problems to practice these above concepts.
Use a pencil and show work. For #28 & 29, what is the degree of
the monomial?
28. 7!!! 29. 6 For #30 & 31, what is the degree of the
polynomial?
30. 2!! − 5! 31. 6!! − 7! + 1 For #32 – 33, simplify, write in
standard form and name the polynomial based on its degree and
number of terms. 32. 4!! − 6! − 4 − (5!! + 2! − 2) 33. 10! − 8!! +
6!! − 9 For #34 – 37, multiply the polynomials:
34. 3!(2!! − 4! + 1) 35 (3! − 1)(4! + 2) 36. 2! − 5! ! 37. (2! +
3)(2! − 3)
For #38 – 47, factor each of the following. Be sure to look for
a GCF first.
38. !! + 5! − 24 39. 2!! + 9! − 5 40. 4!! + 2! − 6 41. 8!! −
18
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42. 4!! − 81!! 43. 9!! + 57! + 60 44. 4!! + 4! + 1 45. 18!! − 32
46. 3!! + 16! + 20 47. 4!! + 28! + 40 For #48 – 51, factor by
grouping.
48. 3!! + 2!! − 9! − 6 49. 6!! + 2!! − 24! − 8 50. 4!! + 16!! −
20! − 80 51. 3!! + 2!! − 3!! − 2! 52. The volume of a box (!
= !"#) is given by the trinomial !! + 2!! − 63!. What are the
dimensions of the box? Factor.
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Chapter 9 – Quadratic Functions & Equations In your flip
book complete the following topics. Write necessary formulas,
information, and draw diagrams:
P. Graphing Quadratics Q. Solving Quadratics using Square Roots
R. Solving Quadratics by Factoring S. Solving Quadratics by
Completing the Square T. Solving Quadratics by the Quadratic
Formula U. The Discriminant
Solve the following problems to practice these above concepts.
Use a pencil and show work. For #53 – 56, graph the quadratic.
Identify the Axis of Symmetry, Vertex, Domain, and Range.
53. ! = −2!! 54. ! = 3!! − 5 55. ! = 2!! − 2! + 1 56. ! = −!! +
6! − 3
For #57 & 58, solve the quadratics using square roots:
57. 3!! + 11 = 86 58. 3!! + 12 = 0
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For #59 – 62, solve the quadratics by factoring:
59. !! − 8! + 15 = 0 60. 2!! − 3! − 9 = 0 61. 8!! − 32! = 0 62.
25!! − 20! = −4 For #63 – 66, solve the quadratics by completing
the square:
63. !! − 2! = 9 64. 2!! + 12! = −4 65. !! + 3! = −1 66. 3!! + 2!
− 9 = 0
67. Order the group of quadratic functions from widest to
narrowest graph. ! = −2!!; ! = −4!!; ! = −3!! 68. Does the table
represent a linear or an exponential function? ! 1 2 3 4 ! 1 3 5
7
69. How is the graph of ! = −4!! + 2 different from the graph of
! = 4!!? Name two differences.
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Chapter 10 - Radicals In your flip book complete the following
topics. Write necessary formulas, information, and draw
diagrams:
V. Simplifying Radicals W. Rationalizing the Denominator X.
Solving Radical Equations
Solve the following problems to practice these above concepts.
Use a pencil and show work. For #70 – 77, simplify the radical.
70. !!72 71. 5 12! ∙ 4 28!
72.
!!48!! ∙ 5 73. −4 2!! ∙ 3 6! ∙ 5
For #78 – 83, simplify the radicals and rationalize the
denominator.
78. !"!
79. !!
!"!"
80. !!!
!! 81.
!!!"#!!!!
82. !!!∙ !"!
!
! 83.
!!
!"!!∙ !!!
For #84 – 91, add, subtract or multiply the radicals and
simplify.
84. − 45 + 2 125 85. 3 3 + 5 3 − 6 5
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86. 3 2 2 − 3 87. 10 + 3 10 − 3
88. 6 2 + 2! 89. 2 2 − 5 2 2 + 5
For #92 & 93, simplify using conjugates: 92.
!!!!!
93. !
!! !
For #94 & 95, solve the proportion:
94. !
!! != !! !
! 95.
!! !!! !
= !! !!
For #96 – 101, solve the radical equation:
96. ! − 6 = 2 97. 2! − 5 = ! + 4 98. 5! + 4 − ! = 0 99.
−! + 6 = !
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100. 4! − 8 = ! − 2 101. 3! + 7 = ! + 1
Mental Math Practice Complete the following questions without
using a calculator.
102. 2 !!− !
!! − 1 = !
!+ !
!! 103. !
!2 !!÷ !
!
104.
!!6 − 9 ! − (−2)(5) 105. 3! 4! + 1 − 2!(! − 3)
106. !! !!! !!!(!)
! !! 107. 144!!!!
For #108 & 109, solve:
108. !!!!!!
= − !! 109. 3 − 2! ≤ 15
For #110 & 110, write in slope intercept form:
110. 2! − 6! = 18 111. !!! + 4! = 12