Welcome, You have received this summer packet because you are enrolled in Honors Algebra II for the 2012 – 2013 School year. The material in this packet has been covered in both Algebra I and Geometry. You are expected to complete this packet over the summer. For each section, show all of your work and solutions on a separate piece of paper or graph paper. No Calculators. The completed packet will be due on the first day of school. This packet will be graded and is worth several assignments. You may visit the school website at www.ketteringschools.org and access the teacher website of Janet Johnson or John Harvey (or access the math department web sight and select us) to view extra examples of each topic worked out. Solutions to the packet will be posted in early August. If you do not have access to a computer at home, ask a friend or go to your local library. Please make sure that you check the answers to verify whether or not you understand the material. Should you need additional help on any of the material, teachers will be available at school on August 8th and August 9th for drop in help from 10:00 a.m. to 12:00 p.m. You may also email either of us and we can try to help. The material in the packet serves as a foundation to Algebra 2. It is very important that you, the students, possess these skills. As such, upon return to school, students will be given quizzes on the material found in the packet. Students will be expected to earn a minimum of an 80% on each quiz. A score of zero will be given until the student reaches the minimum required percentage. Students will be encouraged to come in before and after school to get help on the trouble areas. Up to three attempts may be made on each quiz. The quizzes will need to be completed by midterm of the first quarter. We encourage you to take the packet seriously. Again, if we can be of any help, please email us throughout the summer. We look forward to seeing you next year. Math Department Fairmont High school

Number Systems Identify all of the sets of numbers to which each number listed belongs. 1) 5

2) 2/3 3) -7 4)

!

3 5)

!

16 6)

!

"16

7)

!

"15 8) 44 9) π 10) 1.765

11) -10,000 12)

13)

!

" 6 14) 0 15) 1

16) 17) 8 18)

19) -2.6 20) 21) 10 22)

!

10 23) 5.11 24)

!

"123

25) -1

Give an example of: 26) a rational number that is not an integer.

27) an irrational number that is not positive.

28) an imaginary number.

29) a negative even number.

30) a natural number. 31) a real number that is not natural.

32) a real number that is neither positive or negative. 33) an irrational number that is not a real number. Numerical Properties Identify the properties: 1) 0 + 21 = 21

2) ( 8 + 4 ) + 2 = 8 + ( 4 + 2 ) 3) 23 ( 1 ) = 23

4) 5 ( ab ) = ( 5a ) b 5) 3abc * 0 = 0

6) 3 ( a + 2b ) = ( a + 2b ) 3

7) ( a + b ) c = ac + bc

8) 5x + ( 4y + 3x ) = 5x + ( 3x + 4y ) 9) 3 = 3 + 0

10) 5a + 2b = 2b + 5a 11) 10 + 5x = ( 2 + 8 ) + 5x

12) 4m - 4n = 4 ( m - n )

13) ( 0 ) ( 15 ) = 0

14) ax + 2b = xa + 2b 15) (14 - 6 ) + 3 = 8 + 3

16) 3 + ( -3 ) = 0 17) 5a + 7a = ( 5 + 7 ) a

18) 3x * 2y = 3 * 2 * x * y

19) abc = 1abc 20)

!

313

"

# $ %

& ' = 1

21) 5 ( 4x - 9 ) = 20x - 45

22) ( a + b ) + [ - ( a + b ) ] = 0 23) v ( 4t ) = ( 4t ) v

24) -a2b + a2b = 0

25) 7 * π is a real #

26) -6r + 0 = -6r 27) ( 8 + n ) + ( -n ) = 8 + [ n + ( -n ) ]

28) m - n = 1 ( m - n ) 29) 8 +

!

2 is a real #

30) mn + 2 = nm + 2

31) -5 ( 3t ) = ( -5 * 3 ) t 32) 5 +

!

3 is a real # 33) m ( n2 + n ) = mn2 + mn

34)

!

w4"

4w

= 1 35) 2c + 3c2 = 3c2 + 2c 36) 2c is a real #

Combining Like Terms Name the terms, variables, coefficients, and constants of the expressions. 1) 3a + 5b + 2 2) 5x - 2 + 3y Combine like terms. 3) -5q - 2 + 2q -8

4) 4a + 2b - 3 - 6a - 5b

5) 7c - 2 ( 3c - 5 ) + 4

6) -3 ( 8 - 7z ) + 6z - 9 ( 4 - 3z )

7)

!

56"24a + 36b( )+ " 13( ) 60a " 42b( )

8)

!

15

10a " 4( )+ 12 8 + 4a( )

9) 5 - [ 7 - ( 4 - 2m ) - ( 3 - m ) ] + 2m 10) 8 - 2 [ 7 - ( 4 - y ) - ( y - 6 ) ] - ( 8 - y )

11) 3 ( 6x - 5 ( x - 1 )) 12) 7 - 2 [ 3 - 2 ( x + 4 )]

13) 8 + 4 [ 5 - 6 ( x - 2 )]

14) 3x - [ 2x + ( x - 5 )]

15) 4x - [ 3x - ( 2x - x )] 16) 6 - 2 [ x - 3 - ( x + 4 ) + 3 ( x - 2 )]

17) 7 [ 2 - 3 ( x - 4 ) + 4 ( x - 6 )]

18) x2 + y2 - [ x ( x + y ) - y ( y - x )]

19) 4x2 - 2x ( x - 2y ) + 2y ( 2y + x ) - 2x2 Simplify and Evaluate. 20) -6r + 5 - 3 ( 2r - 1 ) for r = -7

21) -2 ( 3 - n ) - ( 5n + 4 ) - 7n for n = -2

22) 6b - 3 ( b + 7 ) - ( 5 - 4b ) for b = 2

Simplify, then Evaluate for x = -2, y = -3, and z = -4. 23) 7x + 2 [ 6 + 5 ( 3y + 4 ) ]

24) 2 ( 5z + 4 ) + 3 [ 4 + 2 ( 3x + 4y ) ]

25) [ 8x + ( y + 3 ) 2 ] 3 + ( 7z - 4 ) 2

Equations Solve the following equations. Answers should be simplified. 1) -3x – 12 = -5x - 24

2) 5x + 6 – 7x = 2x - 10

3) 4x + 4 – x = -2x - 6

4) 5n + 4 = 7 ( n + 1 ) – 2n

5) 6 ( x – 3 ) – 4 = 2 ( 2x + 7 )

6) 3 ( 2x + 3 ) – 4 ( 5x – 1 ) = -5 ( 3x – 2 ) + 4

7) 5x – 4 + 3x = 2 ( x – 4 ) – 2x

8) 4 ( x + 2 ) + 2 ( x + 1 ) = 3 ( 1 – x )

9) 7y – ( 4 – 2y ) = 3 ( y + 5 )

10) 2 ( x – 8 ) + 7 = 5 ( x + 2 )5 - 5x – 19

11) 5 ( 2 – 3x ) = 4 – 3 ( 4x + 7 )

12) 2 [ x + 3 ( x – 1 )] = 5 ( x – 6 ) + 9

13) 4 [ 6 – 4 ( x – 2) ] = 2 ( x + 4 )

14) 6t – 2 [ 7 ( t + 1 ) + 4 ] = 10t - 5 15) 7x – 2 [ 4 – ( 5 – x ) ] = 3x – ( 6 – 2x )

16)

!

25

m = 6

17)

!

32

y = 74

18)

!

2x = 53

44)

!

34

n + 5 = 11 6)

!

x4

+16 = 18

7)

!

34

x " 23

=58

x "2

18)

!

25

x "1= 34

x + 5x

23)

!

23

x " 35

x = 25

x + 34

24)

!

34

x " 12

=14

x + 5

25)

!

23

y + 52

=45

y + 76

26)

!

34m " 1

2=56m

27)

!

12

30"12x( ) = "3 2x "5( ) 28)

!

89

4x +1( ) = 23 5x " 4( )"2

29)

!

34

8x "12( )"2 = 45 10x "15( )

30)

!

x2

=94

31)

!

2x + 77

="35

32)

!

3x + 3

= "6

33)

!

2x + 54

=4x "3

6

34)

!

8x "36x + 9

="23

35) 5 - 0.03w = 0.7w – 0.11

36) 0.12x – 4 = 0.112x + 1

37) 4.8 – 0.02x = 6x – 12.7

38) -2.5x – 4 ( -0.5x + 1 ) = 6.5

39) 0.01 ( 5 – 0.2x ) = 0.75 + 0.198x

40) 0.2 ( 5 – 0.3x ) = 0.16x + 0.208

41) | x | = 9

42) | x + 6 | = 19

43) | 4x - 3 | = -27

44) 3 | x + 6 | = 36 45) 8 | 4x - 3 | = 64

46) -6 | 2x - 14 | = -42

47) | 7 + 3a | = 11 - a 48) | 2a + 7 | = a – 4 49) 3 | x + 6 | = 9x – 6

50) 2 + 3 | x + 6 | = 35 51) -4 - 2 | 3x + 1 | = -12 52) -1 + 5 | 2x - 3 | = -6

53) t – 2k = m; solve for k 54)

!

t = dr

; solve for d

55)

!

k = 34

m t + q( ) ; solve for t 56)

!

V = 43"r2h ; solve for h

57) V = lwh; solve for w 58)

!

A = 12

bh; solve for b

59)

!

F = wd

; solve for d

60) Ax + By = C; solve for y

61) 5 – 3bx = -2b + 2bx; solve for x 62) ay + z = am – ny; solve for y

63)

!

PD

= Q + RD

; solve for D

64) 4r ( x + t ) = 3rx + n; solve for x

65)

!

IT

=E

A+ B; solve for B

66)

!

m = a2

j + t( ); solve for t

67) yx - a = cx; solve for x. 68)

!

x + yc

= d ; solve for x.

69)

!

p =ab" ca "b

; solve for b. 70)

!

A = 12h b1 + b2( ) ; solve for b1.

Inequalities. Solve each inequality. Write the solution in set notation form, and graph the solution on a number line. 1) x + 3 < 6

2) 6 – 2x < -4 3) 4x + 8 ≥ -8

4) –7 – 4x < 13

5) 2x + 3 < 6x - 1 6) 3x – 2 ≥ 7x – 10 – 4x

7) 2x – 14 > 4x + 4

8) 6x + 3 ≤ 3 ( x + 2 ) 9) –2 ( x + 4 ) > 6x - 4

10) 2 ( 3x – 4 ) ≥ 6 ( x + 5 ) 11) 5p - ( 7p + 2 ) < 29 + 3 ( 2p - 5 )

12)

!

56a " 3

8a # 1

2a "2

13)

!

56(18"12t)" 2

3(12t +15) #14

14)

!

2x + 73

"x + 4

3 15)

!

2y + 3"5

> 3" y

Formulas. Find the distance between each pair of points whose coordinates are given. 1) ( 1, 5 ), ( 3, 1 ) 2) ( -2, -8 ), ( 7, -3 )

3) ( 3, -4 ), ( -4, -4 )

4) ( -3, -1 ), ( -11, 3 )

5) (

!

"2 7 , 10 ) (

!

4 7 , 8 ) 6) (

!

2 3 ,

!

4 3 ) (

!

2 3 ,

!

" 3 )

Find the coordinates of the midpoint of the line segment whose endpoints are given. 7) ( 5, 7 ), ( 3, 9 ) 8) ( 10, -8 ), ( 4, -3 )

9) ( 2, 7 ), ( 8, 4 )

10) ( -3, 2 ), ( -3, -4 )

11) ( -4, -7 ), ( 2, 1 ) 12) ( 8, -3 ), ( 5, 4 )

If M is the midpoint of line segment AB, find the coordinates of the missing point A, B, or P. 13) A( 1, 5 ), M( 3, 7 ) 14) M( -2, -1 ), A( -3, -5 )

15) B( -14, 24 ), M( -2, 7 )

16) A( 11, 12 ), M( 2, 17 )

17) B( 0, 12 ), M( -5, -1 ) 18) A( 4, -11 ), M( 5, -9 )

Find the missing variable, given the midpoint M.

19) M(2, -5), A(3, 4), B(1, y) 20) M(5,

!

32

), A(2, -1), B(x, 4) 21) M(

!

"52

, 3), A(4, y), B(x, -6)

Determine the slope of the line passing through each pair of points. Indicate the type of slope you have found and the function’s movement. 22) ( 2, 1 ), ( 8, 9 )

23) ( -10, 7 ), ( -20, 8 ) 24) ( 4, 1 ), ( -4, 1 ) 25) ( 3, 2 ), ( 3, -2 )

26) ( 7, 5 ), ( 3, 1 ) 27) ( 4, 9 ), ( 4, 6 ) 28) ( -4, -1 ), ( -2, -5 ) 29) ( 3, 18 ), ( -12, 18 ) Determine the value of r so the line passing through each pair of points has the given slope.

30) ( 10, r ), ( 3, 4 ),

!

m = "27

31) ( -1, -3 ), ( 7, r ),

!

m =34

32) ( 12, r ), ( r, 6 ), m = 2

33) ( 6, 8 ), ( r, -2 ), m = -3 34) ( 6, 3 ), ( r, 2 ),

!

m =12

35) ( r, 3 ), ( -4, 5 ),

!

m = "25

Determine if the three points listed below are collinear. 36) A( 2, 2), B( -2, -6 ) C( 6, 10 ) 37) A( 2, 5), B( 0, 7 ), C( 3, 2 ) 38) A( 4, -1 ), B( 0, -5 ), C( 2, -1 )

Writing Equations of Lines. Write an equation of a line in slope intercept form given the following: 1) ( -5, 2 ) and m = -4

2) ( 3, 6 ) and m =

!

25

3) ( -6, 6 ) and m =

!

23

4) ( -2, 4 ) ( 7,4 )

5) ( -6, 2 ) ( 3, -5 )

6) ( 4, 5 ) ( 2, 9 )

7) ( -3, 1 ) ( -1, -3 )

8) ( 2, -4 ) ( 2, -1 ) 9) ( 6, 0 ) ( 0, 4 )

10) Vertical thru (6, -2) 11) Horizontal thru ( 8, 4 ) Write an equation of a line in point slope form given the following:

12) (-4 2) m =

!

34

13) (9, 7) m = -6 14) (-8, 3) m =

!

12

15) (-1,0) m = 3 16) (-2, -6) m =

!

"52

17) ( 0, 4 ) m = -1 Write an equation of a line in standard form given the following: 18) (6, 3 ) m = -5 19) (5, -2) m =

!

14

20) (6, 1) m = 0

21) (-3, -5) m = undefined

22) y = 6 – 2x 23)

!

x =35

+14y

24) What is the slope perpendicular to

!

y = 23

x "3.

25) What is the slope parallel to y = 5x – 4. 26) What is the slope parallel to 3x – 4y = 8. 27) What is the slope perpendicular to 5x + 2y = 14. Determine if each set of equations is parallel, perpendicular, or neither. 28) 2x + y = 3 4x + 2y = 5 29)

!

y = 43

x " 5

!

y = 34

x + 2

30) 2y + x = 4 y = 2x - 5

31) y = -4x – 3 y = 4x - 3

32) Write an equation of a line in slope intercept form that is parallel to 3x – 5y = 10 and contains

the point (10, 7). 33) Write an equation of a line in slope intercept form that is parallel to 2x + y = 12 and contains

the point (-4, 5).

34) Write an equation of a line in standard form that is parallel to 6x – 2y =2 and contains the

point (-2,-8). 35) Write an equation of a line in standard form that is parallel to 4x + 3y = 12 and contains the

point (5, 1). 36) Write an equation of a line in slope intercept form that is perpendicular to 2x – 3y =12 and

contains the point (4, 5). 37) Write an equation of a line in slope intercept form that is perpendicular to x + 5y = 20 and

contains the point (-2, 4). 38) Write an equation of a line in standard form that is perpendicular to 3x – 6y = 6 and contains

the point (4, 1). 39) Write an equation of a line in standard form that is perpendicular to 4x + 2y = 10 and

contains the point (-6, -2). 40) Write an equation of a line that is perpendicular to y = 4 and contains ( 5, 7 ). 41) Write an equation of a line that is parallel to y = -3 and contains ( -8, 3 ). 42) Write an equation of a line that is parallel to x = 9 and contains ( 5, 2 ). 43) Write an equation of a line that is perpendicular to x = 4 and contains ( -5, 3 ). 44) Write an equation of a line that is parallel to the x-axis thru ( 4, 7 ). 45) Write an equation of a line that is parallel to the y-axis thru ( -3, -2 ) 46) Write an equation of a line that is perpendicular to x-axis thru ( -3, 9 ) 47) Write an equation of a line that is perpendicular to y-axis thru ( -6, -1 ) Determine if the following tables are linear, if you say yes, write the equation in slope intercept form 48. 49. 50. 51. 52.

x y -4 -7 -2 -4 0 -1 2 2

x y 0 8 2 7 4 6 6 5

x -1 -2 -3 -4 y 5 11 21 35

x y 6 115 9 100 12 85 15 75

x 8 6 4 2 y 28 22 16 10

53) Write the equation of the lines in slope intercept form (if possible)

a

b

c

d

e f

g h

Determine if the given points lie on the given line. 54) 3x + y = 8 A ( 2, 2 ) B(3, 1)

55) 2x – 5y = 1 A( 2, 1 ) B( -7, -3 )

56) 3x = 8y – 4 A( 2, 1 )

B(

!

23

,

!

34

)

Graphing Equations of Lines Find the x and y intercept of each line. 1) 2x + 3y = 6

2) 4x – 5y = 30 3) 5x – 7y = 28

4)

!

12

x +

!

34

y = 6 5) 3y = 6 6) 2x = 7

Graph the following equations:

7) y = 2x – 3

8)

!

y = "23

x + 2

9) y = -4x - 3

10) y = -3

10) x = 4

11) y = x + 2

12) y =

!

"53

x + 2

13) y = -x 14) y =

!

23

x –

!

52

15) 4y = 12

16) 4x – 2y = 4

17) 2x + 3y = 9

18) 2x = -6

19) 2x + y = 5

20) 4x – 5y = 14

21) x – y = 6

22) 2x + 6y = 12

23) 4x – 2y = 7

Inequalities. Graph the following inequalities. 1) 3x > 6

2) 3x – 2y ≤ 6

3) 2x + 4y ≤ 8

4) 4y – 1 < -9

5) x – 3y ≥ -12

6) 3x – y < 2

7) x – 3y > -6

8) -2y ≤ 4

9) 3x + y ≤ 3

10) -4x + 1 < 5

11) 3x – 2y > 8

12) 6x – 9y ≤ -9

13) 4x + 2y > -6

14) x – y ≤ 4

15) 5y ≥ -2x

Write an inequality for each graph 16)

17)

18)

19)

20)

21)

22)

23)