2nd Semester Algebra I

Exam Study Guide

Name__________________________________________

Exam Date______________________________________

2012-2013

Chapter 7 Solve each system of linear equations using any method. 1.

4x ! 2y = 24y = x ! 5

2.

3x + 51 = 8yy + 6x = 0

3.

!4x + y = !23x + 2y = !4

4.

12x ! 9y = 11412x + 7y = 82

5.

5x ! 2y = 832x + 7y = 2

6.

7x + 3y = !122x + 5y = 38

7.

3x + 2y = 106x + 4y = 4

8.

x ! 2y = !4

y =12

x + 2 9.

6x + 3y = 92x + 9y = 27

10. You have decided to solve #3 using substitution. You solved the first equation for y. What expression do you substitute into the 2nd equation for y?

11. If you were to graph the equations in problem # 8, would the graphs be parallel lines, intersecting lines, or the same line?

For problems 12-14 match each linear system to the graph that represents its solution.

12.

4x + 3y = 52x ! y = 5

13.

!x + 3y = 94x ! y = 8

14.

5x ! y = !4!2x + y = 1

A) B) C)

15. A library is having a book sale. Hardcover books cost $4 each and paperback books cost $2 each. Jane buys 8 books and spends $26. How many hard cover books did she buy?

16. A website allows users to download individual songs or an entire CD. All individual songs cost the same to download and all CDs cost the same to download. Ryan pays $14.94 to download 5 individual songs and 1 CD. Seth pays $22.95 to download 3 individual songs and 2 CDs. How much does the website charge to download an individual song?

Chapter 8 Simplify each of the following expressions. (Remember no negative or 0 exponents)!!

1. 2x 4( )3 2.

!2x 4( )3 3.

2x2y( ) !3xy( )3

4. 2x2y( ) !3xy( )!3

5.

4a5b2

3c

!

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3

•9ca15

!

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$

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5x !3y 0

3

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#$

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2

•259x 7

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#$

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!1

7. 4( )3 • !2( )4 • 50 • 16( )!1

8. !4( )2 • !2( )3 • 50 • !4( )!2

9. !5x 3y !4( )!2

10.

5x2yz( )325xy3

11. !c2 • 3c 4 •2c6 12.

2b( )5

13. Write 12,566, 000 in scientific notation.

14, Write 7.43 ! 10"3 in standard form.

15. Simplify and rewrite in scientific notation.

2.5 ! 106( ) 6 ! 10"3( )

16. Write 0.0000345 in scientific notation.

17, Write 2.41 ! 105 in standard form.

18. Simplify and rewrite in scientific notation.

5.26 ! 104( ).2 ! 10"5( )

Chapter 9

Simplify the following problems using addition, subtraction or multiplication. 1.

4n2 + 7n ! 5( ) + 3n2 ! 7n ! 8( ) 2.

4n2 + 7n ! 5( ) ! 3n2 ! 7n ! 8( ) 3.

4n ! 5( ) 3n2 ! 7n ! 8( )

4. 2 6g + 4( ) + 7 3g ! 9( ) 5.

2x + 7( )2 6.

9a ! 3( ) ! 6a ! 2( )

7. 2 3x ! 5( ) ! 3 4x ! 6( ) 8.

!3x2 x 3 + 2x ! 8( ) 9.

6a ! 2( ) 7a + 1( )

10. 3y + 4( ) 3y ! 4( ) 11.

3y ! 4( ) 3y ! 4( ) 12.

3y ! 4( )2

13. 2b2 + 5c( ) 3b2 ! 8c( ) 14.

6a + 7( ) 2a ! 5( ) 15.

2n2 + 5( ) 7n2 + 2n + 3( )

Find the GCF of the following sets of numbers. 16. 16 and 96 17. 42x2y and 24xy 18. 36xy and 48x2y2

Factor the following COMPLETELY. 19. x2 ! 8x + 12 20. 2x2 + 14x ! 36 21. 3x2 ! 27

22. x2 ! 8x 23. 36x 6 + 18x 3 24. 49x2 ! 100

25. 4x2 ! 12x + 9 26. x 3 ! x2 ! 4x + 4 27. 12x2 ! x ! 6

Find the roots of the following equations. (Solve for x). 28. x2 ! 81 = 0 29. 42x2 ! 8x = 2 30. 4x2 = 24x

31. A picture has a width of w ! 4( ) feet and a length of

w + 2( ) feet.

a) Draw a picture to represent this scenario. b) Write an expression to represent the perimeter of the picture. c) Write an expression to represent the area of the picture. d) If the area of the picture is 7 square feet find the dimensions of the picture.

Chapter 10 Quadratic Equation: ax2 + bx + c = 0 Quadratic Function: y = ax2 + bx + c or

f x( ) = ax2 + bx + c

The solutions to a quadratic EQUATION are called______________________________. These roots are related to the quadratic FUNCTION. They are the _________________ of the graph of the related parabola. The x values of the x-intercepts are called the ______________________of the function.

Solve each QUADRATIC equation (find the roots). 1.

5x x + 3( ) = 0 2. 5x2 ! 73x + 156 = 0 3. 4x2 = 12x

Use the graph to find the zeros of the given function.

4. y = !x2 + 4 5. f x( ) = x2 + 2x ! 8

For #6-9 match each function with its graph. 6.

f x( ) = x2 ! 3 7.

g x( ) = !x2 + 3 8.

m x( ) = !4x2 + 4 9.

p x( ) = 4x2 + 3

a)

b)

c)

d)

10. Consider the function y = !2x2 + 12x ! 7 .

a) Does the parabola open up or down?

b) What is the axis of symmetry for this function?

c) What is the vertex of this parabola?

11. Consider the function y = 3x2 ! 6x + 2 .

a) Does the parabola open up or down?

b) What is the axis of symmetry for this function?

c) What is the vertex of this parabola?

12. The height h in meters of a model rocket t seconds after it is launched is modeled by the equation:

h = 64t ! 2t 2 . a) How high is the rocket 4 seconds after it is launched?

b) After how many seconds will the rocket land on the ground again?

13. The height h in meters of a model rocket t seconds after it is launched is modeled by the equation:

h = 3t 16 ! t( ) . a) How high is the rocket 10 seconds after it is launched?

b) After how many seconds will the rocket land on the ground again?

Use the parent graph y = x2 to describe the changes in the graph of the following functions:

14. y = 2x2 15. y = x2 ! 6

16. y =

12

x2 17. y = x2 + 10

Use the quadratic formula x =

!b ± b2 ! 4ac2a

to solve these equations. List your final

answers as both exact values and estimated values rounded to the nearest 100th.

18. x2 + 10x + 1 = 0

19. 2x2 ! 8x + 3 = 0

20. 3x2 + 5x ! 2 = 0

Chapter 11 For each of the following sets of ordered pairs: a) find the coordinates of the MIDPOINT given the two endpoints.

b) find the distance between the two points. (List your final answers as both exact values and estimated values rounded to the nearest 100th).

1.

8,14( ) 2,6( ) 2.

7,2( ) !5,7( ) 3.

!3,!8( ) !7,2( )

Midpoint Formula:

x1+ x

2

2,

y1+ y

2

2

!

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Distance Formula: d = x

2! x

1( )2 + y2! y

1( )2

Simplify the following radical expressions. 4. 32 5. 125b 6. 81m3

7.

a3

121 8. 2 2 + 6 2 9. 12 + 6 3 + 2 6

10. 75m2np4 11.

4

3 12. 3 7 ! 5 14 + 2 28

13.

2x2

5 14. 48 15.

6

2

Solve the following radical equations. 16. 4 ! 3x = 7 17. x + 7 + 5 = 11

18. 7x ! 7 ! 5 = 2 19. 2 4 ! x ! 3 = 1

20. 24 + 5x = x 21. 2 x ! 8 = 0

Chapter 13

Data Analysis

Find the least value, greatest value, mean, median, mode, and range of the data sets. Round to the nearest tenth. 1.) Stem Leaves 2 2 4 8 8 8 3 0 4 6 4 1 1 4 key 2/4 = 24 Least Value _________ Greatest Value __________ Mean _____________ Median _________________ Mode _____________ Range _________________

2. ) 3, 16, 22, 25, 24, 23, 16, 16 Least Value _________ Greatest Value __________ Mean _____________ Median _________________ Mode _____________ Range _________________

3. Use the box plot to answer the following questions.

Greatest value___________ Least value_________ Range____________________

Q1(lower quartile)_________ Q2(median)_________ Q3(upper quartile)___________

What percent of the data falls above 23? ____________________________________

What percent of the data falls below 21? ____________________________________

What percent of the data falls between 15 and 23? _____________________________

What is the interquartile range ?___________________________________________

4.) Given data set: 5, 4, 16, 21, 10, 6, 15 find the following information: Minimum Value _________________ Maximum Value ______________________ Median ______________________ Lower Quartile (

!

Q1) ___________________ Upper Quartile (

!

Q3) _____________ Inner Quartile Range __________________ Which of the following box and whiskers graphs match this data set?

a.)

b.)

c.)

d.)

5. Use the frequency table to make a histogram.

Number of Sit-ups Students Can Do in 1 Minute Number 0-9 10-19 20-29 30-39 40+ Frequency 10 8 9 6 2

Freq

uenc

y

2

4

6

8

10

12

0-9 10-19 20-29 30-39 40+

Number of Sit-ups

Probability/Odds

I have a jar of money. The jar contains 100 quarters, 75 dimes, 200 nickels, and 125 pennies. 6. If one coin is chosen, what is the probability that a quarter will be chosen? 7. What would be the odds in favor of choosing a quarter if all the dimes were removed first? 8. What are the odds in favor of choosing a penny? A card is selected at random from a standard deck of 52 cards. A standard deck of cards consists of 4 suits with 13 cards in each suit. 9. What is the probability of selecting a black card? 10. What is the probability of selecting a jack and then another jack if the 1st jack was not replaced? 11. What are the odds in favor of selecting a heart? 12. What are the odds in favor of NOT selecting a red 9? 13. How many possible outcomes are there when you toss three coins? 14. How many possible outcomes are there when you toss 1 coin and roll 2 number cubes? 15. You toss two coins and roll 1 number cube. What is the probability that one coin shows heads, one coin shows tails, and the number cube shows a 6?

Division Review: Simplify the following expressions.

16.

18x 5 • 4x 3

2x 17.

18x 5 + 4x 3

2x 18.

12x 3 + 21x2( ) 3x( )!1