Download 1 SUMMER STUDY PACKET ALGEBRA II Dear prospective

SUMMER STUDY PACKET
ALGEBRA II
Dear prospective Algebra II student,
This summer packet is designed to help you practice the concepts you learned in Algebra
I and Geometry so that you are prepared to study Algebra II this fall. The content and philosophy
of this summer packet is consistent with the math department goals and will enable you to:
(1) value mathematics,
(2) become confident in your ability to do mathematics,
(3) become mathematical problem solvers,
(4) communicate mathematically, and
(5) reason mathematically.
You are responsible for knowing how to do all the exercises noted before the first day of
classes. If you do not know how to solve a problem you are expected to use the sources available
to you (notes, handouts, books, Internet, etc.) to figure it out independently. The best study
routine during the summer months is to constantly review topics and do a few problems each
day, not attempt to do the entire packet the day before school starts. For your convenience, the
answers to all of the exercises are included at the end of the document.
Unless specifically stated or unless you are to give a decimal approximation to a square
root, you should not use a calculator to do these exercises. You may, however, use your
calculator to check your answers. Use separate sheets as necessary to show your work in a neat
and organized way. Do not try to show all work on these worksheets; there isn’t enough room!
The topics covered in this packet are:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
Connections to algebra
Properties of real numbers
Order of operations
Solving linear equations
Graphing linear equations and functions
Writing linear equations
Solving and graphing linear inequalities
Systems of linear equations
Exponents and exponential functions
Quadratic equations and functions
Polynomials and factoring
Rational equations and functions
Radicals and trigonometry
1
This summer assignment will not be collected. You are responsible for knowing how to
solve every single problem. Motivated students can work additional problems to gain confidence
and familiarity with the more difficult topics at the following websites:
1. http://www.khanacademy.org/4
4
2. http://www.algebralab.org/lessons/lesson.aspx4
4
3. http://www.purplemath.com/modules/index.htm4
4
4. http://www.classzone.com/books/algebra_1/index.cfm?state=VA 4
4
Important: You will have a test on this summer packet study material during your second math
class of the year. The test will consist of approximately twenty free response questions. You will
not be able to use your calculator on the test. This exam will not count towards your math grade;
however, those students who fail the exam will be obliged to attend remedial sessions during
lunch or after school until they pass a similar exam.4
4
If you have any questions, please email [email protected] or
[email protected].
Enjoy your summer and do your best!
Sincerely,
The ASFG Math Department
2
Solve each equation.
1) x
2) k
3)
k
4) n
State the quadrant in which the terminal side of each angle lies.
5)
°
7)
°
Simplify each expression.
6)
8)
( r )
( b )
x)
n)
n
9)
r
11)
b
13) (
(
15)
Divide.
°
°
(
10)
12)
14)
16)
(n
(k
17) ( k
k
k )
k
19) ( b b
b )
b
Solve each equation.
18)
20)
( x
( n
( m )
21)
m
(n )
23) n
Solve each equation with the quadratic formula.
22)
24)
p
a
n)
)
) k
(a )
x)
x
(
p)
31)
(y )
x y
30)
x y
(
y
)
32)
x y
yx
Evaluate each function.
33) h(n)
35) h( x)
n
x
; Find h(
x; Find h(
)
)
©Y LKOuctGaA uStopfOtawSaYrdem vL0LQCe.p n jAElKlT drMi2gOhgtwsY XrXe8sEeurIvfetdl.U H AM5aZdNeh UwoivtehZ kIknAfhixnSiUtDeR ZA3lngqe0bvrpa1 Y2t.J
(
(
x
m n
m n
y
x y
34) f (a)
36) w(n)
-1-
n
nm
x
n
p
x)
25) r r
26) b
b
27) x
28) n
Simplify. Your answer should contain only positive exponents.
29)
n)
n
(
x
a
n
)
)
; Find f (
; Find w(
)
)
Worksheet by Kuta Software LLC
Sketch the graph of each line.
37) x-intercept = , y-intercept =
38) x-intercept =
39) x
y
40)
41) y
x
42) y
©I RKDuxt9aU aSvojfitlwDaxrxeE 2L4LCCM.P A rAOlrlj PrdiLg5h2tasc nrOecsreprAvAeBdp.F L nMUaTdjea 1wzictWhR bICnYfIiLnniPtleL BA6lagre8bRrmaf u2w.9
-2-
x
, y-intercept =
y
x
Worksheet by Kuta Software LLC
Sketch the graph of each linear inequality.
43) y
x
45) y
44) y
x
46) y
x
Solve each system by graphing.
47) y
x
48) y
y
x
y
49)
x
y
50) x
x
y
x
Solve each compound inequality and graph its solution.
51)
53)
52)
p
x
or
x
©S JKCuktVaT iSGo2fTttwUaIrper pLfLlCH.3 Z SAmlRls wraiSgkhdtSs4 vrFecsXeircvEend4.K K PMqaudpeF XwDiStjh7 0IwnSfiiCnGictfe5 MAKlTgdejbMr8aZ E22.u
54)
-3-
x
x
y
y
m
n
or n
Worksheet by Kuta Software LLC
Write the slope-intercept form of the equation of each line.
55)
56)
Find each product.
)
57) ( n
)( v )
59) ( v
Evaluate each expression.
58)
60)
61)
62)
(
))
63) (
Solve each system by substitution.
64)
65) x
66)
y
( x
( a
)
)( a
)
(
)
x y
x
y
x y
67) The senior classes at High School A and High School B planned separate trips to the indoor climbing
gym. The senior class at High School A rented and filled 6 vans and 7 buses with 438 students. High
School B rented and filled 6 vans and 6 buses with 384 students. Each van and each bus carried the
same number of students. Find the number of students in each van and in each bus.
68) The senior classes at High School A and High School B planned separate trips to Yellowstone National
Park. The senior class at High School A rented and filled 7 vans and 6 buses with 375 students. High
School B rented and filled 12 vans and 6 buses with 450 students. Every van had the same number of
students in it as did the buses. Find the number of students in each van and in each bus.
69) Mike and Nicole are selling wrapping paper for a school fundraiser. Customers can buy rolls of plain
wrapping paper and rolls of holiday wrapping paper. Mike sold 1 roll of plain wrapping paper and 12
rolls of holiday wrapping paper for a total of $218. Nicole sold 3 rolls of plain wrapping paper and 6
rolls of holiday wrapping paper for a total of $144. Find the cost each of one roll of plain wrapping
paper and one roll of holiday wrapping paper.
70) Jimmy's school is selling tickets to a fall musical. On the first day of ticket sales the school sold 11
adult tickets and 3 child tickets for a total of $75. The school took in $207 on the second day by selling
13 adult tickets and 12 child tickets. What is the price each of one adult ticket and one child ticket?
Find the measure of each angle indicated. Round to the nearest tenth.
71)
72)
A
C
7.4
8
3.7
B
A
B
73)
3.5
C
B
A
74)
C
10
4
7
C
©V 1KsuftGaa USTowfNt0w1aYrQeF bLVL5Cq.r R zARl8lK zrCixgVhktHsV frUexsaeHrBv4efdV.J n 6MFaEdhe6 5wXiStphL JIGnzfhiWnaiItbeS pAJlJgXeEb9rLaH I2v.u
B
-4-
16
A
Worksheet by Kuta Software LLC
Answers to
1) ,
5) II
9)
r
13)
k
17)
21)
25)
29)
33)
37)
x
k
,
y
x
k
2) ,
6) IV
10)
14) k
x
18)
22)
26)
30)
3) ,
7) III
11)
b
15)
n
b
b
19)
n
x
,
n
m
34)
23)
27)
,
31)
x y
4) ,
8) II
12) n
16)
a
b
20) n
24)
28)
35)
40)
41)
42)
43)
44)
45)
46)
47)
©R 2KLuttsal iS2oKfjtDw0ajrxek zLOLSCP.m A RAxlDl5 Drbi1gahstss3 hrlersIeor5vgemdR.L A FM5akdPez uwyixtuhq hIenofzienhiAtjew CAdlWgye5bHrgaL j2O.0
48)
-5-
,
i
36)
39)
)
i
32)
38)
( ,
n
( ,
)
Worksheet by Kuta Software LLC
49)
51)
(, )
50)
p
:
52)
m
:
53) x
or x
:
54) n
or n
:
55) y
x
59)
63)
67)
69)
70)
73)
(,
56) y
)
x
57)
v
n
n
60) a
61)
64)
65) ( , )
Van: 10, Bus: 54
68) Van: 15, Bus: 45
roll of plain wrapping paper: $14, roll of holiday wrapping paper: $17
adult ticket: $3, child ticket: $14
71) 46.6°
60.3°
74) 51.3°
©z MKmuVt2aF pSAomf4t5w0a1rte9 DLrLWC1.y D gAIlHlb brDiZgfhXtUsQ ZrMeCsPeLrlvteFdg.a C 5MqaGdeem 9wfijtvhc sIYnOfCiGnJiBtse1 QAqlvg6eqbtr7aZ k2I.y
-6-
58)
x
62)
66)
( , )
x
72) 42.8°
Worksheet by Kuta Software LLC