Download Packet Summer 2013

Welcome,
You have received this letter because you are enrolled in Honors Algebra II for the
2013 – 2014 School year.
At the end of July, you will find your summer math packet on the teacher website of
Janet Johnson under a folder called summer packet. The school website is located at
www.ketteringschools.org. If you do not have access to a computer at home, ask a
friend or go to your local library. 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.
While you are working on your packet, you may find a topic you are unfamiliar
with. If you need to view extra examples of each topic worked out, access the
teacher website of Janet Johnson or John Harvey. Solutions to the packet will be
posted in early August. 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 7th and August 8th 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)
7)
13)
! 19)
5
"15
" 6
-2.6
2)
2/3
3)
-7
4)
3
5)
16
6)
8)
44
9)
π
10)
1.765
11)
-10,000
12)
14)
0
15)
1
! 16)
20)
21)
"7
2
10
10
22)
! 17)
1
9
23)
5.11
8
24)
!
!
Give an example of:
!
"16
! 18)
"12!
3!
"1 12
4
5
25)
!
26)
a rational number that is not an integer.
27)
! that is not positive.
an irrational number
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
20)
" 1%
3$ ' = 1
# 3&
21)
5 ( 4x - 9 ) = 20x - 45
19)
abc = 1abc
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
36)
2c is a real #
34)
w 4
" =1
4 w
!
!35)
!
!
-1
2c + 3c2 = 3c2 + 2c
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 )
8)
1
1
10a " 4 + 8 + 4a
5
2
7)
9)
!
5
6
(
) ( )(
)
"24a + 36b + " 13 60a " 42b
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
21)
-2 ( 3 - n ) - ( 5n + 4 ) - 7n for n = -2
Simplify and Evaluate.
20)
-6r + 5 - 3 ( 2r - 1 ) for r = -7
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 ) ]
25)
[ 8x + ( y + 3 ) 2 ] 3 + ( 7z - 4 ) 2
24)
2 ( 5z + 4 ) + 3 [ 4 + 2 ( 3x + 4y ) ]
Equations
Solve the following equations. Answers should be simplified.
1)
-3x – 12 = -5x - 24
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)
2
m=6
5
44)
3
n + 5 = 11
4
!
18)
!
25)
!
27)
!
!30)
33)
!
2)
17)
6)
!
2
3
x "1= x + 5x
5
4
23)
!
2
5 4
7
y+ = y+
3
2 5
6
)
x 9
=
2 4
2x + 5 4x " 3
=
4
6
)
28)
2x =
x
+16 = 18
4
7)
3
2 5
x " = x "2
4
3 8
24)
3
1 1
x " = x +5
4
2 4
!
2
3
2
3
x" x= x+
3
5
5
4
(
) (
)
2x + 7 "3
=
7
5
3
4
8x "12 " 2 = 10x "15
4
5
3
32)
= "6
x +3
)
34)
!
8x " 3 "2
=
6x + 9 !3
0.12x – 4 = 0.112x + 1
5 - 0.03w = 0.7w – 0.11
36)
! 37)
4.8 – 0.02x = 6x – 12.7
! 38)
0.01 ( 5 – 0.2x ) = 0.75 + 0.198x
29)
(
!
40)
5
3
3
1 5
m" = m
4
2! 6
8
2
4x +1 = 5x " 4 " 2
9
3
35)
39)
!
!
! 31)
4x + 4 – x = -2x - 6
18)
!
(
3)
3
7
y=
2
4
26)
1
30 "12x = "3 2x " 5
2
(
5x + 6 – 7x = 2x - 10
(
)
-2.5x – 4 ( -0.5x + 1 ) = 6.5
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)
49) 3 | x + 6 | = 9x – 6
| 2a + 7 | = a – 4
50)
2 + 3 | x + 6 | = 35
51)
-4 - 2 | 3x + 1 | = -12
53) t – 2k = m; solve for k
55)
57)
k=
3
m t + q ; solve for t
4
(
)
!
59)
61)
56)
V=
58)
1
A = bh ; solve for b
2
60)
w
; solve for d
d
4 2
"r h ; solve for h
3
Ax + By = C; solve for y
!
5 – 3bx = -2b + 2bx; solve for x
62) ay + z = am – ny; solve for y
63)
P
R
= Q + ; solve for D
D
D
64) 4r ( x + t ) = 3rx + n; solve for x
65)
I
E
; solve for B
=
T A+ B
!
!
67)
66)
yx - a = cx; solve for x.
!
69)
!
d
; solve for d
r
t=
!
F=
-1 + 5 | 2x - 3 | = -6
54)
!
V = lwh; solve for w
52)
!
p=
ab " c
; solve for b.
a "b
m=
a
j + t ; solve for t
2
( )
68)
x+ y
= d ; solve for x.
c
70)
A = 21 h 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 )
13)
5
(18 "12t) " 23 (12t +15) # 14
6
14)
2x + 7 x + 4
"
3
3
!
!
!
!
a " 38 a # 21 a " 2
12)
5
6
15)
2y + 3
> 3" y
"5
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,
3
), A(2, -1), B(x, 4)
2
21)
M( "
5
, 3), A(4, y), B(x, -6)
2
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 = "
2
7
33) ( 6, 8 ), ( r, -2 ), m = -3
!
31) ( -1, -3 ), ( 7, r ), m =
34) ( 6, 3 ), ( r, 2 ), m =
!
3
4
1
2
32) ( 12, r ), ( r, 6 ), m = 2
35) ( r, 3 ), ( -4, 5 ), m = "
2
5
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
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)
( 3, 6 ) and m =
2
5
2)
3)
( -6, 6 ) and m =
2
3
11) Horizontal thru ( 8, 4 )
Write an equation of a line in point slope form given the following:
12) (-4 2) m =
13) (9, 7) m = -6
3
4
15) (-1,0) m = 3
16) (-2, -6) m =
!
14) (-8, 3) m =
1
2
17) ( 0, 4 ) m = -1
"5
2
!
Write an equation of a line in standard form given the following:
18)
(6, 3 ) m = -5
21)
(-3, -5) m = undefined
19)
!
1
(5, -2) m =
4
22)
y = 6 – 2x
20)
(6, 1) m = 0
23)
x=
!2
24) What is the slope perpendicular to y = x " 3.
3 1
+ y
5 4
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)
4
x "5
3
3
y = x+2
4
y=
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. x
y
x -1 -2
-3 -4
x
y
-4 -7
y 5
11 21 35
0
8
-2 -4
2
7
0 -1
4
6
2
2
6
5
51.
52. x
y
6
115
x 8
6
4
2
9
100
y 28 22 16 10
12 85
15 75
53)
Write the equation of the lines in slope intercept form (if possible)
a
c
d
b
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(
! !
2 3
, )
3 4
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)
1
3
x+ y=6
2
4
5)
3y = 6
6)
2x = 7
Graph the following equations:
!
!
7) y = 2x – 3
8) y =
10) y = -3
10) x = 4
5
12) y = " x + 2
3
15) 4y = 12
! 18) 2x = -6
21) x – y = 6
!
"2
x+2
3
13) y = -x
9) y = -4x - 3
11) y = x + 2
14) y =
2
5
x–
3
2
16) 4x – 2y = 4
17) 2x + 3y = 9
19) 2x + y = 5
!20) !
4x – 5y = 14
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)
Systems of Equations and Inequalities.
Solve each system of equations using the method indicated below.
Solve by Graphing.
1)
y=x+4
y = -x + 2
2)
y = 2x - 4
y = 2x + 5
3)
y = 2x
y = -2x + 4
4)
2y - 8 = x
1
y = x+4
2
5)
-2x + 5y = -14
x-y=1
6)
x+1=y
2x - 2y = 8
7)
1
1
x+ y =2
2
3
x - y = -1
8)
2x + 3y = 5
-6x - 9y = -15
9)
3x + 6 = 7y
x + 2y = 11
!
!
Solve by Substitution.
10)
y = 2x
x+y=9
11)
x = 4y
2x + 3y = 22
12)
15x + 4y = 23
10x - y = -3
13)
2x + y = 4
3x + 2y = 1
14)
4x - 2y = 5
2x = y - 1
15)
2x - 3y = 6
1
1
3
x + y = and
2
4
4
18)
16)
2x 3y
"
= "2
5
4
x y
+ =7
2 4
!
Solve by Elimination.
!
17)
0.5x - 0.2y = 0
2
" x + y = "2
3
3x - y + 2 = 0
5x - 3y + 4 = 0
!
!
19)
5x - 2y = 30
x + 2y = 6
20)
5x + 3y = 4
4x - 3y = 14
21)
6x - y = 5
8x + 2y = 10
22)
3x + 2y = 12
2x + 5y = 8
23)
3x + 2y = 5
4x = 22 + 5y
24)
3x + 2y = 5
-6x - 4y = -10
25)
2x - 4y = 5
-x + 2y = 8
26)
x " 2y 1
=
8
2
27)
3x + 2y = 4
!
!
!
x y+4
=
2
3
x"y 1
=
6
2
Identify the type of solution that is displayed below.
[ Both names that identify type and the number of solutions.]
28)
29)
30)
Solve the following quadratic inequalities by graphing.
31)
34)
!
37)
y " 2x # 3
y"
#1x
2
32)
y + 1 < -x
y≥1
33)
x≥5
x+y≤3
35)
5x – 2y < 10
x+y<4
36)
3x + 4y ≤ 24
x–y>5
38)
2≤x≤6
y > -1
x – 2y ≥ -6
1
y"5#" x "4
2
39)
x+y≥3
3x – 2y > 6
y ≥ 4x + 1
+2
y≤3
0≤x≤5
x > -y
3x + 2y ≤ 12
-2x + 5y > -10
x – y ≥ -1
(
!
)
Factoring.
Factor using GCF techniques.
1)
75b2c3 + 60bc6
2)
82e3 - 122ef
3)
6r2f - 3rf2
4)
20p2 - 16p2q2
5)
9c4d3 - 6c2d4
6)
20r3s2 + 25rs3
Factor using grouping techniques.
7)
6xy2 - 3xy + 8y - 4
8)
8x2 + 2xy + 12x + 3y
9)
6mn - 9m - 4n + 6
10)
2e2f - 12ef + 3e - 18
11)
2ac + ad + 6bc + 3bd
12)
x3 + xy2 - x2y - y3
Factor using difference of squares - special product rules
13)
36n2 - 25
14)
4c2 - 25
15)
25x2 – 9
16)
49 – 9x2
17)
16y2 - 9z2
18)
100x4 – 169
19)
9t2 - 16z4
20)
x4-y4
21)
16x6 – 81y4
Factor using Trinomial Techniques.
22)
x2 - 4x - 12
23)
x2 + x - 12
24)
x2 - 9x + 18
25)
x2 + 12x + 20
26)
x2 + 5x - 14
27)
x2 - 9x + 20
28)
x2 – 5xy + 4y2
29)
x2 + 6xy - 72y2
30)
-x2 + 8x - 1
31)
8r2 - 46r + 45
32)
15q2 - 19q + 6
33)
18a2 - 9a – 35
34)
3b2 + 10b - 48
35)
2x2 - 11x - 40
36)
6a2 + 5a - 1
37)
2y2 - y – 10
38)
3y2 - 14y - 24
39)
4x2 - 12xy + 9y2
40)
4y2 + 7y - 2
41)
10x2 - 3xy - y2
42)
3m2 + 19mn - 14n2
43)
16x2 - 35x + 6
44)
15x2 + 8x - 12
45)
6x2 + 19x – 20
46)
6x2 + 7x – 20
47)
10x2 - 29x + 21
48)
25x2 + 40x + 16
49)
3x2 + xy - 10y2
50)
6x2 - 11xy - 10y2
51)
4x2 - 12xy + 9y2
Factor completely using a combination of all methods.
52) 3x3 + 15x2 + 12x
53) 4a2 - 24a + 20
54) 6g3 - 28g2 - 10g
55) 30e3 + 22e2 - 28e
56) 3ar - 6yr + 9am - 18ym
57) 3x3 - 3x
58) 5n2 - 10n
59) 10b3 + 34b2 - 24b
60) 6m3n + 38m2n2 – 28mn3
61) 36a3b2 + 66a2b3 - 210ab4
62) 4x6 – 4x2
63) 81x4 – 16
64) 18p3 - 51p2 - 135p
65) 5x3 + 6x2 – 45x – 54
66) x4 - 26x2 + 25