semester 2 final exam review packet name -...
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Semester 2 Final Exam Review Packet Name
Algebra 1 – _____ Hour Final Exam Review Days
Assigned
on
Assignment
Complete and On Time
5 points
Complete and Late 4 points
At Least 50%
Complete
2.5 points
Less Than 50%
Complete
1 point
6/6 Final Exam Review Chapters 11 and 12
Problems 54 – 73
6/7 Final Exam Review Chapters 10
Problems 44 – 53
6/8 Final Exam Review Chapters 8
and 9 Problems 1 – 43
6/9 Final Exam Review – Practice Exam Problems 74 – 98
Category Totals
Homework Grade ________ / 20 Points This sheet is due Monday, June 12th
Other Things You Need to Know:
There are 31 Multiple Choice and 6 Free Response questions on the exam.
The Multiple Choice portion is an Illuminate bubble sheet
You will be provided with a note sheet and you will use one of my calculators.
You may use a calculator on the entire exam.
If you would like to estimate your semester grade, use the formula below. Semester Grade = 0.8(S2 percentage) + 0.2(Exam percentage take a guess)
Your exam is on ___________________
Algebra 1 – Chapters 8-12 Exam – Note Sheet Chapter 8 – Exponents and Exponential Functions
Exponent Properties
nmnm aaa
nmnm aa )( mmm baab )( n
n
a
a 1
1
nm
n
m
aa
a m
mm
b
a
b
a
1
1 n
n
a
a
10 a
Scientific Notation
Exponential Growth and Decay
a = Initial Amount r = Rate t = Time
Chapter 11: Square Root Functions
Product Property: Quotient Property of Radicals:
baba b
a
b
a
4 2 9 3 16 4 25 5
36 6 49 7 64 8 81 9
100 10 121 11 144 12 169 13
Chapter 12: Rational Functions
Inverse Variation
x
ay
Chapter 10 – Quadratics
Standard Form of a Quadratic
cbxaxy 2 Axis of Symmetry:
a
bx
2
Vertex Form of a Quadratic
khxy 2
Vertex: kh , Axis of Symmetry: hx
Quadratic Formula
a
acbbx
2
42
Discriminant
SolutionNoacb
SolutionOneacb
SolutionsTwoacb
04
04
04
2
2
2
Function Models
Linear
bmxy
Exponential xbay
Quadratic
cbxaxy 2
Square Root
xy
Rational
xy
1
Chapter 8: Exponents and Exponential Functions In #1-4 simplify the expression. Write your answer using exponents.
1) 52 )2)(2()2( 2) 53 )6(
3) 7
11
4
4 4)
8
127
6
66
In #5-7 simplify the expression
5) 85
1
6) 22 )4( nm 7)
33
r
In #8-11, Simplify the expression. Write your answer using only positive exponents.
8)
2
3
22
yz
x 9)
2
23
2
1
c
ab
a
10) 432 )2()6( mm 11) 4
32 )2(
4
)3(
n
m
m
mn
12) In the following, use the function y = 3x
a) Complete the table for the function b) Graph the function c) Identify the domain and range. Domain: Range:
13) Write 0.00384 in scientific notation 14) Write 1,308,000 in scientific notation 15) A company is offering its employees a retirement benefit of $24,000 per year and guarantees an annual cost of living increase of 2% of the benefit.
a) Write a function that models the retirement benefit over time. Assume that the retirement benefit only increases by the cost of living increase.
tray 1
b) Use the function to find the amount of the retirement benefit after 6 years. 16) You buy a new car for $32,000. It depreciates at the rate of 12% per year.
a) Write a function that models the value of your car over time.
tray 1
b) Use the function to find the amount the car is wroth after 5 years. In 17 and 18, Tell whether the graph represents exponential growth or exponential decay. Then write a rule for the function. 17) 18)
In 19 and 20, simplify the expression.
19) 22 2x when x = 5 20) 32 12 x when x = 3
Chapter 9: Polynomials and Factoring In 21 and 22, find the sum of the polynomials.
21) )3()3573( 323 xxxxx 22) )119()1437( 22 aaaa
In 23 and 24, find the difference of the polynomials.
23) )8211()5617( 22 yyyy 24) )113()162( 323 bbbbb
In #25-28, find the product of the polynomials. (double-distribute/FOIL)
25) )12)(39( rr 26) )35)(27( 22 ttt
27) 2)53( ba 28) )29)(29( zz
In #29- 34, factor the polynomial.
29) 21102 xx 30) 6234 2 yy
31) 20205 2 xx 32) 1212 x
33) 3072 2 xx 34) 121669 2 yy
In #35-36, what are the x-intercepts? (Also called Zeros/Roots/Solutions) 35) ( 7)( 3)x x y 36) (5 2)( 11)x x y
In #37-42, solve the equation.
37) 0562 xx 38) zz 261692
39) 01512 2 x 40) 453114 2 xxx
41) 5523 xxx 42) 1226 23 mmm
x
y
43) A rectangle has the length of (3x+2) inches, a width of (x+4) inches, and an area of 153 square inches. Find the value of x. (hint: draw a picture!) Chapter 10: Quadratic Equations and Functions Find the vertex of the following quadratics:
44) 2 4 1x x 45) 22 8 5x x 46) Given the following information about the parabola, answer the questions.
382 2 xxy
a) a = b = c = b) Does the parabola open up or down? c) Does the parabola have a maximum or minimum? d) Find and draw the axis of symmetry ( Also known as the x coordinate of the vertex) e) Find a plot the vertex. Find more points on the graph and graph the parabola Vertex
x
y
47) Given the following information about the parabola, answer the questions.
342 xxy
a) a = b = c = b) Does the parabola open up or down? c) Does the parabola have a maximum or minimum? d) Find and draw the axis of symmetry ( Also known as the x coordinate of the vertex) e) Find a plot the vertex. Find more points on the graph and graph the parabola Vertex
In 48-49 solve the equation. Round to the nearest hundredth, if necessary
48) 02252 x 49) 71881 2 x
50) Use the Quadratic Formula to solve. 527 2 xx
Use the discriminant to tell whether the equation has two, one, or zero solutions.
51) 09124 2 xx 52) 4292 2 www
53) The discriminant of 2 5x x c is -7. What is the value of c?
Chapter 11: Radicals and Geometry Connections In # 54-61, simplify the expression
54) 24
108
x 55) 3218 xx 56) 5232
57) 4275 npm 58) 5
108 59)
6
5
49
81
d
k
60) 2723515 61) 500253
x
y
Und.
In #62-64, solve for x.
62) 2463 x 63) 124 xx 64) 034 xx
Chapter 12: Rational Equations and Functions 65) Given that y varies inversely with x, use the specified values to write an inverse variation equation that relates x and y. Then find y when x = 6.
x = 4, y = 3 66) Given that y varies inversely with x, use the specified values to write an inverse variation equation that relates x and y. Then find y when x = 18.
x = 6, y = 9 Graph the function.
67) x
y2
Simplify the expressions.
68) 152
5
42
1032
2
xx
x
x
xx 69)
62
672
2
1232
22
xx
xx
x
x
70)
2 12 35
7
x x
x
71)
3
2(2 )
5 14
xx
x x
72)
8
5 5
6 8
2 14
x x
x x 73)
2
2
3 3 2
2 3 1
n n
n n
Name: ____________________________ Date: _____________ Hour:___________
Algebra Practice Exam – Chapters 8-12 – Multiple Choice
Please select the choice that best answers the question and mark your answer on the provided Scantron
sheet.
_____ 74. What is the equation of the graph?
a.) y = 2x
b.) y = 3x
c.)
y 1
3
x
d.)
y 1
2
x
_____ 75. Simplify
5a5b2
3a3b
6a2b5
15a5b2.
a.)
2a5b4
3
b.)
15a5
6b2
c.)
2a5
3b2
d.)
15a5b4
6
_____ 76. Rewrite 6.5 x 106 in standard form.
a.) 0.0000065
b.) 0.00000065
c.) 65,000,000
d.) 6,500,000
_____ 77. Which of the models below are exponential decay models?
I. y = 1.19x II. y = 0.12x
III.
y 5
3
x
IV.
y 2
3
x
a.) I and II
b.) II and III
c.) I and III
d.) II and IV
_____ 78. You buy a used tractor for $55,120. It depreciates at the rate of 8.8% per year.
What is the value of the tractor after 6 years?
tr-1y a
a.) $16,458.74
b.) $91,428.71
c.) $31,715.99
d.) $2,433,639.82
_____ 79. You deposit $2700 in an account that pays 8% interest compounded yearly. How
much money is in the account after 10 years?
tr1y a
a.) $13,000
b.) $5829.10
c.) $1172.84
d.) $964,026.15
_____ 80. Simplify 242 44 ?
a.) 4
8
b.) 416
c.) 410
d.) 412
_____ 81. Which number represents 65,006,000 in scientific notation?
a.) 6.5006 x 10
-7
b.) 6.5006 x 107
c.) 65.006 x 10-6
d.) 65.006 x 106
_____ 82. Which of the following is equal to
8x3 12x2 25x 13 4x2 14x 40 ?
a.)
7x3 2x2 3x 8
b.)
8x3 16x2 11x 53
c.)
8x3 16x2 39x 27
d.)
12x3 2x2 3x 8
_____ 83. Which of the following is equal to (6a – 4b)2 ?
a.)
36a2 48ab16b2
b.)
36b2 48ab16a2
c.)
36a2 16b2
d.)
16b2 49a 36
_____ 84. Which of the following is equal to the expression 25x4 + 30x3 – 35x – 42 ?
a.) (3x – 7)(6x + 5)
b.) (5x3 + 6)(x
2 – 7)
c.) (6x2 + 7)(x + 5)
d.) (5x3 – 7)(5x + 6)
_____ 85. Which of the following is a solution of the equation 7x2 –11 = 4x2 +97 ?
a.) 0
b.) -5
c.) -6
d.) -3
_____ 86. What is the x-coordinate of the vertex of the graph of the equation
y = -2x2 + 12x – 7 ?
a.) 2
b.) -2
c.) 3
d.) 12
_____ 87. What are the zeros of the function
y 3x2 24x 36 ?
a.) -2 and 3
b.)
3 and2
3
c.) -2 and 6
d.) 6 and 2
_____ 88. What is the discriminant of the equation y = 2x2 – x – 1 ?
a.) 0
b.) 9
c.) -7
d.) -8
_____ 89. Name the type of model that the graph suggests.
a.) Quadratic
b.) Exponential Decay
c.) Exponential Growth
d.) Linear
_____ 90. What is the correct factorization of -3x2 +16x + 35 ? (Factor the expression)
a.) (3x + 5)(x – 7)
b.) -(3x + 5)(x – 7)
c.) -(3x – 5)(x + 7)
d.) (3x – 5)(x – 7)
_____ 91. What is the simplest form of (5x + 2)(5x – 2)?
a.) 25x
2 -4
b.) 10x2
c.) 25x2 + 10x - 4
d.) 25x2 + 20x – 4
_____ 92. What are the x-intercepts for the graph of y = (x – 3)(x + 2)
a.) 2 and 3
b.) -2 and 3
c.) -3 and 2
d.) -3 and -2
_____ 93. Which of the following is
7 6 2 12 24 , in simplified form?
a.) 95
b.) 3469
c.) 186
d.) 6233
_____ 94. Solve
8 x - 5 34= 58.
a.) 710x
b.) 4x
c.) 14x
d.)
x 77
_____ 95. Which function is graphed?
a.) 2xy = 0
b.) 2
xy
c.) 22
1
xx
d.) xy = 2