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

6/1 Unit 5 and Unit 6, 1-39

6/4 Unit 7 and Unit 8, 40-60

6/5 Practice Test, 61-81

Category Totals

Homework Grade ________ / 15 Points This sheet is due Thursday, June 7th

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 – Units 5-8 Exam – Note Sheet

• 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

• Exponential Growth and Decay

a = Initial Amount r = Rate t = Time

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

= = = =

= = = =

= = = =

• Function Models

Linear

bmxy +=

Exponential xbay =

Quadratic

cbxaxy ++= 2

Square Root

xy =

• 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

−

=−

−

× 1 2 3 4 5 6 7 8 9 10 11 12

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

2 2 4 6 8 10 12 14 16 18 20 22 24

3 3 6 9 12 15 18 21 24 27 30 33 36

4 4 8 12 16 20 24 28 32 36 40 44 48

5 5 10 15 20 25 30 35 40 45 50 55 60

6 6 12 18 24 30 36 42 48 54 60 66 72

7 7 14 21 28 35 42 49 56 63 70 77 84

8 8 16 24 32 40 48 56 64 72 80 88 96

9 9 18 27 36 45 54 63 72 81 90 99 108

10 10 20 30 40 50 60 70 80 90 100 110 120

11 11 22 33 44 55 66 77 88 99 110 121 132

12 12 24 36 48 60 72 84 96 108 120 132 144

Unit 5: 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) 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. 14) 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 15 and 16, Tell whether the graph represents exponential growth or exponential decay. Then write a rule for the function. 15) 16)

Unit 6: Polynomials and Factoring In 17 and 18, find the sum of the polynomials.

17) )3()3573( 323 xxxxx −++−+ 18) )119()1437( 22 aaaa +++−

In 19 and 20, find the difference of the polynomials.

19) )8211()5617( 22 +−−+− yyyy 20) )113()162( 323 bbbbb +−−+−

In #21-24, find the product of the polynomials.

21) )12)(39( −+ rr 22) )35)(27( 22 −−+ ttt

23) 2)53( ba − 24) )29)(29( −+ zz

In #25- 32, factor the polynomial.

25) 21102 ++ xx 26) 6234 2 −+ yy

27) 20205 2 ++ xx 28) 1212 −x

29) 3072 2 −+ xx 30) 121669 2 ++ yy

31) 5523 +++ xxx 32) 1226 23 −+− mmm

In #33-34, what are the x-intercepts? (Also called Zeros/Roots/Solutions) 33) ( 7)( 3)x x y+ − = 34) (5 2)( 11)x x y+ − =

In #35-38, solve the equation.

35) 0562 =−+ xx 36) zz 261692 =+

37) 01512 2 =−x 38) 453114 2 +=+− xxx

39) 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!) Unit 7: Quadratic Equations and Functions Find the vertex of the following quadratics:

40) 2 4 1x x+ + 41) 22 8 5x x− + +

x

y

x

y

42) 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 more points on the graph and graph the parabola Vertex

43) 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 more points on the graph and graph the parabola Vertex

In 44-45 solve the equation. Round to the nearest hundredth, if necessary

44) 02252 =−x 45) 71881 2 =−x

46) Use the Quadratic Formula to solve. 527 2 += xx

Use the discriminant to tell whether the equation has two, one, or zero solutions.

47) 09124 2 =−+− xx 48) 4292 2 −=+ www

49) The discriminant of 2 5x x c+ + is -7. What is the value of c?

Unit 8: Radicals and Geometry Connections In # 50-57, simplify the expression

50) 24

108

x 51) 3218 xx 52) ( )( )5232 −+

53) 4275 npm 54) 5

108 55)

6

5

49

81

d

k

56) 2723515 −+ 57) 500253 +

In #58-60, solve for x.

58) 2463 =−−x 59) 124 −=+ xx 60) 034 =−− xx

Name: ____________________________ Date: _____________ Hour:___________

Algebra Practice Exam – Unit 5-8 – Multiple Choice

Please select the choice that best answers the question and mark your answer on the provided Scantron

sheet.

_____ 61. What is the equation of the graph?

a.) y = 2x

b.) y = 3x

c.)

d.)

_____ 62. Simplify

 

5a5b2

3a3b×

6a-2b5

15a-5b2.

a.)

b.)

c.)

d.)

_____ 63. Which of the models below are exponential decay models?

I. y = 1.19x II. y = 0.12x

III. IV.

a.) I and II

b.) II and III

c.) I and III

d.) II and IV

_____ 64. 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

_____ 65. 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

_____ 66. Simplify ( )242 44 ?

a.) 48

b.) 416

c.) 410

d.) 412

_____ 67. Which of the following is equal to ?

a.)

b.)

c.)

d.)

_____ 68. Which of the following is equal to (6a – 4b)2 ?

a.)

b.)

c.)

d.)

_____ 69. Which of the following is equal to the expression 25x4 + 30x3 – 35x – 42 ?

a.) (3x – 7)(6x + 5)

b.) (5x3 + 6)(x2 – 7)

c.) (6x2 + 7)(x + 5)

d.) (5x3 – 7)(5x + 6)

_____ 70. Which of the following is a solution of the equation 7x2 –11 = 4x2 +97 ?

a.) 0

b.) -5

c.) -6

d.) -3

_____ 71. 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

_____ 72. What are the zeros of the function

 

y = 3x2 - 24x + 36 ?

a.) -2 and 3

b.)

c.) -2 and 6

d.) 6 and 2

_____ 73. What is the discriminant of the equation y = 2x2 – x – 1 ?

a.) 0

b.) 9

c.) -7

d.) -8

_____ 74. Name the type of model that the graph suggests.

a.) Quadratic

b.) Exponential Decay

c.) Exponential Growth

d.) Linear

_____ 75. 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)

_____ 76. What is the simplest form of (5x + 2)(5x – 2)?

a.) 25x2 -4

b.) 10x2

c.) 25x2 + 10x - 4

d.) 25x2 + 20x – 4

_____ 77. 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

_____ 78. Which of the following is

 

7 6 - 2 12 + 24 , in simplified form?

a.) 95

b.) 3469 −

c.) 186

d.) 6233 +

_____ 79. Solve

 

8 x - 5 + 34 = 58.

a.) 710=x

b.) 4=x

c.) 14=x

d.) 7

_____ 80. Which expression is equivalent to 72 ?

a.) 270 +

b.) 36

c.) 26

d.)

_____ 81. Find the area of the rectangle. (A = l * w)

a.) 34

b.) 316

c.) 122

d.) 212

34

2 34

24