Download Honors Algebra I - The Steward School

Honors Algebra I
Summer Work 2016
•
•
due date:
estimated time:
third day of class
10 hours (for planning purposes only; work until you finish)
Dear Honors Algebra I Students,
This assignment is designed for you to review all of your algebra skills and make sure you are well
prepared for the start of Honors Algebra I in the fall. The assignment is in two parts: written problems in
this packet, and problems on iXL.com. See the next page for detailed instructions. We anticipate that the
work will take about 10 hours to complete.
Both the written work and the online work are due on the third day of class. At that time you will have a
short quiz with problems taken directly from both this packet and the iXL sections listed on the next
page. A portion of the quiz grade will be based on the completeness of your summer work.
We are really looking forward to the upcoming school year and hope you are, too! Please email any of
us if you have questions.
[email protected]
[email protected]
[email protected]
[email protected]
[email protected]
Page 1 of 14
Assessment of Summer Work
1. On the third day of class, you will submit your written work, and your teacher will check
your online work.
2. You will have a quiz made up of problems taken directly from the on-line and written work.
3. Your written and online work will be evaluated for completeness; that grade will form part
of the quiz grade.
On-Line Work
1. Log in to iXL.com with the username and password you were given in your math class.
 Students new to Steward: your parents will receive an email with your username
and password.
2. Work the problems listed below, until you earn a score of at least 60% for each section.
 If you find that the name of the section does not match the numbers below, go by the
section name.
3. If you are having difficulty of any sort with iXL, reach out to a teacher at one of the email
addresses above.
1. click this tab
8 (8th grade)
2. find this section
3. work these problem sets
A.1 - Factors
A.2 - Divisibility rules
A.3 - Prime or composite
A.4 - Prime factorization
A.5 - Greatest common factor
A.6 - Least common multiple
A.7 - GCF and LCM: word problems
A.8 - Classify numbers
Number Theory
Written Work
1. Complete each problem on the following pages.
2. Do the problems on separate paper. Do the problems in order and number them clearly.
o Exception: print the graphing problems (pages 12-13) rather than drawing your
own graphs.
3. Please show all of your work as was required of you throughout the entire school year.
o Remember: no work, no credit.
Page 2 of 14
I. Writing Algebraic Expressions
In algebra, we use letters such as x and y to represent a number or value. These letters are called
variables, because the number they represent can vary.
Write an algebraic expression for each phrase below. For help with these problems, use the search
term “Writing simple algebraic expressions” on Khan Academy.
1)
Seven times a number decreased by eleven
3)
The quotient of two more than a number and six
2)
4)
Five more than the product of seven and a number
Ten less than twice a number
II. Order of Operations
Evaluate each expression. For help with these problems, use the search term “Order of operations:
PEMDAS” on Khan Academy.
5)
6)
250 ÷ [5 (3 g7 + 4)]
52 g4 − 5g42
5(4)
7)
1
g26 − 32
2
8)
82 ÷ (2g8) + 2
9)
50 − (12 + 32 ) + (6 − 1) 2
10)
2g42 − 8 ÷ 2
(5 + 2)g2
Page 3 of 14
III. Evaluating Algebraic Expressions
Evaluate each expression. For help with these problems, use the search term “Evaluating
expressions in two variables” on Khan Academy.
11)
12)
13)
14)
5 x 2 y − y when x =
4 and y =
24
3 xy − 4
7x
when
=
x 2=
and y 3
( z ÷ x) 2 +
4
x when=
x 2 and=
z 4
5
y2 − 2z2
x+ y−z
when
=
x 12,
=
y 9, and
=
z 4
IV. The Real Number System
For each number, tell all the sets to which it belongs. Include real numbers, rational numbers,
integers, whole numbers, and irrational numbers.
For help with this topic, use the search term “Categorizing numbers” on Khan Academy.
15)
-4.2
16)
8
17)
25
18)
5
3
19)
-0.9
20)
−
12
4
Page 4 of 14
V. Integers
Evaluate each expressions below. For help, use the following search terms on Khan Academy:
• “Learn how to add and subtract negative numbers”
• “Multiplying positive and negative numbers”
• “Dividing positive and negative numbers”
21)
-15 + -35
22)
-13 – (-6)
23)
32 – 68
24)
45 – (-14)
25)
-143 + 31
26)
-34 + 12 – (-9) – 10
27)
(-9)(7)
28)
48 ÷ (−8)
29)
−70 ÷ −7
30)
31)
32)
−12 ⋅ 3 ÷ 4
 −14 
3

 15 
3  7
− ÷− 
4  8
Page 5 of 14
VI. Fractions
Evaluate each expression. For help, use the following search terms on Khan Academy:
• “Adding fractions: common denominator”
• “Adding fractions: different denominators”
• “Subtracting fractions: different denominators”
• “Multiplying negative and positive fractions”
• “Dividing negative fractions”
33)
34)
35)
36)
5 1
−
8 2
1
1
1 −2
2
2
3 7
+
2 9
5
1
4 −3
6
4
37)
3
2
7 +5
4
3
38)
9−2
39)
40)
41)
42)
43)
44)
3
7
3 7
g
4 9
5 1
g
6 2
7
5g
8
1 1
3 g2
2 5
6 3
÷
11 4
4 3
÷
5 8
Page 6 of 14
VII. The Distributive Property
Rewrite each expression using the distributive property. For help, use the search term
“Distributive property algebraic expressions” on Khan Academy.
45)
46)
47)
7( x − 4)
3(2 x + 5)
4(5 x − 9)
48)
1
(14 − 6 y )
2
49)
3(7 x 2 − 3 x + 2)
50)
1
(16 x − 12 y + 4 z )
4
VIII. Combining Like Terms
Simplify each expression. For help, use the search term “combining like terms” on Khan
Academy.
51)
5x − 9x + 2
53)
c 2 + 4d 2 − 7d 2
52)
54)
55)
56)
3q 2 + q − q 2
5 x 2 + 6 x −12 x 2 − 9 x + 2
2(3x − 4 y) + 5( x + 3y)
10 xy − 4( xy + 2 x 2 y)
Page 7 of 14
IX. Solving Equations
Solve each equation. For help, use the search term “Simple equations: examples solving a variety of
forms” on Khan Academy.
57)
58)
59)
98 = b + 34
−14 + y = −2
8k = −64
60)
14n − 8 = 34
61)
5 + 3n =
38
62)
3k − 7 =
16
63)
d
+ 12 =
−7
5
64)
−4m − 15 =
21
65)
10 + 5n =
85
66)
n
−8 =
12
3
67)
12 +
68)
3( x − 4) =
15
x
=
−9
−2
Page 8 of 14
X. Percent of Change
Tell whether each of the following represents an increase or a decrease. Then find the
percent of change.
For help, watch the following video on YouTube:
• “How to Find the Percent Change Increase: The Easy Way,” posted by
MathMotor
69)
original: 50
new: 80
71)
original: 27.5
new: 25
70)
72)
original: 14.5
new: 10
original: 250
new: 500
XI. Percent of Change (Continued)
Figure out the final price of each item. For numbers 77 and 78, calculate the discount price before
finding the tax.
For help, watch the following videos on YouTube:
• “Discounts and Sale Prices,” posted by whitchermath
• “Math Help: How to Calculate Sales Tax and Total Cost,” posted by Acadsoc
73)
two concert tickets: $28
student discount: 28%
75)
CD player: $142.00
sales tax: 5.5%
74)
76)
77)
78)
airline ticket: $248.00
frequent flyer discount: 33%
celebrity calendar: $10.95
sales tax: 7.5%
camera: $110.95
discount: 20%
sales tax: 5%
iPod: $89.00
discount: 17%
sales tax: 5%
Page 9 of 14
XII. Simplifying Exponents
Simplify each expression. For help, use the following search terms on Khan Academy:
• “Exponent properties involving products”
• “Exponent properties involving quotients”
79)
34 g32
80)
x3 ⋅ x5 ⋅ x 2
81)
2m3 ⋅ 4m ⋅ 3m 4
82)
5y ⋅6y
83)
84)
85)
86)
87)
88)
8m5
m3
6 xy 3
6 xy
7 x0 ⋅ 5x ⋅
1
x
(x y )
5
3 0
9 xy 4
7 x0
( 2m p )
3
5 3
Page 10 of 14
XIII. Solving Word Problems
Write an algebraic equation to model each situation. Then solve the equation and answer the
question.
For help, watch the following video on YouTube:
• “Beginning Algebra and Word Problem Steps,” posted by Bill Witte
89)
90)
91)
92)
A video game store charges a one‐time membership fee of $11.75, plus $1.50 per game
rental. How many videos did Charles rent if he spent $72.00?
Tanya is 30 years less than 3 times Helen’s age. If the sum of their ages is 74, how old is
each of the women?
Three-fourths of the student body attended the pep rally. If there were 630 students at
the pep rally, how many students are there in all?
Andrea drove 3 hours more than Cameron on their trip to Texas. If the trip took 37
hours, how long did Andrea and Cameron each drive?
Page 11 of 14
XIV. Graphing Linear Equations
Print pages 12 and 13 and graph the equations. For help, use the search term “Standard form for
linear equations” on Khan Academy.
93)
y = 3x + 4
94)
=
y
1
x−3
2
Page 12 of 14
95)
y = –2x + 5
96)
𝑦𝑦 =
−1
4
𝑥𝑥 + 2
Page 13 of 14
XV. Finding Slope
Find the slope of the line through each pair of points. For help, use the search term “Slope from two
ordered pairs example 1” on Khan Academy.
97)
(4, 17), (-2, 13)
99)
(-20, 8), (-16, 16)
98)
100)
101)
102)
(-8, 5), (-12, -4)
(-8, -12), (-7, -7)
(3, 9), (3, 12)
(10, -2), (-1, 5)
Determine the slope of the line in each graph.
103)
104)
Page 14 of 14