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

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

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

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?

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.

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

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.

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

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.

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

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 = !

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