Name ________________________________ Date _______________________
Algebra I Beginning of the Year Packet
Chapter 1
1-1 Using Variables
Variable – a symbol, usually a letter, that represents one or more numbers.
Algebraic Expression – a mathematical phrase that can include numbers, variables, and
operation symbols (does not include an equal sign)
Writing Algebraic Expressions
Ex: Seven more than n
n+7
**Note** “more than” switch the order
Ex: The difference of n and 7
n–7
Ex: The product of seven and n
7n
Ex: The quotient of n and seven
n
7
** Other Key Words **
!
Add –
Subtract –
Multiply –
Divide –
Writing an Algebraic Expression
Ex: two times a number plus 5
2n + 5
Ex: 7 less than 3 times a number
3a – 7
** Note ** “less than” switch the order
Equation – a mathematical sentence that uses an equal sign.
Open sentence – an equation that contains one or more variables
** Note ** “is” means equals
Writing an Equation
Ex: Track One Media sells all CDs for $12 each. Write an equation that represents the
cost “c” of a given number “n” CDs.
Let n = number of CDs
c = cost of all CDs
Translate ~ the total cost is $12 times the number of CDs
c = 12n
Practice
1. Write an algebraic expression for each phrase
a. 4 more than p
b. the quotient of n and 8
c. the product of 15 and c
d. 23 less than x
e. the sum of v and 3
2. Define a variable and write an expression for each phrase
a. 2 more than twice a number
b. the product of 5 and a number
c. the sum of 13 and twice a number
d. a number minus 11
3. Define variables and write an equation to model each situation
a. The total cost is the number of cans times $.70
b. The total length of rope, in feet, used to put up tents is 60 times the number of
tents.
c. The perimeter of a square equals 4 times the length of a side
4. Write a phrase for each expression
a. q + 5
b. 9n + 1
c. 7hb
1 – 2 Exponents and Order of Operations
Exponent – tells how many times a number is multiplied by itself.
Order of Operations
PEMDAS
a x u i d u
r p l v d b
e o t i
t
n n i d
r
t e p e
a
h n l
c
e t y
t
s s
i
s
Simplifying a Numerical Expression
!
Ex: 25 " 8 # 2 + 32
= 25 – 8 · 2 + 9
= 25 – 16 + 9
=9+9
= 18
Evaluate – solve
Evaluating an Algebraic Expression
Ex: 3a " 2 ÷ b for a = 7 and b = 4
= 3(7) – 23 ÷ 4
= 3(7) – 8 ÷ 4
= 21 – 8 ÷ 4
= 21 – 2
!
= 19
!
!
Real – World Problem Solving
Ex: The equation c = p + 0.06p represents the cost c of a pair of sneakers with price p and
sales tax of 6%. Use a table to find the cost for $20, $30, $45, and $59 pairs of sneakers.
Price p
P + 0.06P
Cost c
$20
20 + 0.06(20)
$21.20
$30
30 +0.06(30)
$31.80
$45
45 + 0.06(45)
$47.70
$59
59 + 0.06(59)
$62.54
3
!
Simplifying and Evaluating Expressions With Grouping
Symbols
Simplifying an Expression With Parentheses
Ex: 15(13 – 7) ÷ (8 – 5)
= 15(6) ÷ 3
= 90 ÷ 3
= 30
Evaluating Expressions With Exponents
Ex: Evaluate each expression for c = 15 and d = 12
a. (cd)2
b. cd2
= (15 · 12)2
= 15 · 122
2
= (180)
= 15 · 144
= 32,400
= 2,160
Ex: 2[(13 – 7)2 ÷ 3]
= 2[(6)2 ÷ 3]
= 2[36 ÷ 3]
= 2[12]
= 24
Simplifying an Expression
Real World Problem Solving
Ex: A neighborhood association turned a vacant lot into a park. The park is shaped like
the trapezoid below. Use the formula
&b +b #
A = h$ 1 2 !
% 2 "
& 100 + 200 #
= 130$
!
2
%
"
& 300 #
= 130$
!
% 2 "
= 130 (150)
= 19,500
&b +b #
A = h$ 1 2 ! to find the area of the lot.
% 2 "
b1=100ft
h=130ft
b2=200ft
Practice
1. Simplify
a. 5 + 6 · 9
b. 8 + 12 ÷ 6 – 3
c. 5 · 32 – 13
2. Evaluate for a = 5, b = 12, and c = 2
a. 2b ÷ c + 3a
b. 5a + 12b
3. The equation s = p – 0.15p represents the sale price s of an item with an original price
p, after a 15% discount. Make a table to find the discount prices for items with original
prices of $12, $16, $20, and $25.
4. Simplify
a. 2(5 + 9) – 6
b. 17 – 52 ÷ (24 + 32)
5. Simplify
a. [3(7 + 4) – 2]6
b. 27[52 ÷ (42 + 32) + 2]
1.3 Exploring Real Numbers
Natural Numbers – 1, 2, 3, …
Whole Numbers – 0, 1, 2, 3, …
Integers - …-2, -1, 0, 1, 2, …
Rational Numbers – any number that can be expressed as a fraction (terminating
decimals, repeating decimals, fractions, and intergers)
Classifying Numbers
Ex: Name the set(s) of numbers to which each belong
a.
!
17
31
b. 23
c. 0
d. 4.581
Rational Number
Natural, whole, integer, rational
whole, integer, rational
rational
Real World Problem Solving
Ex: Which set of numbers is most reasonable for each situation?
a. the number of students who will go on the class trip
b. the height of the door frame in your classroom
whole
rational
Irrational Numbers – cannot be expressed as a fraction (non-terminating non-repeating
decimals, , non-perfect square roots)
Real Numbers
Rational Numbers
Irrational Numbers
Integers
Whole
Numbers
Natural
Numbers
Comparing Numbers
Inequality – a mathematical sentence that compares the value of two expressions using
an inequality symbol, such as < (less than) or > (greater than) or ≤ (less than or equal to)
or ≥ (greater than or equal to).
Ordering Fractions
Ex: Write !
3
1
5
, ! , and !
in order from least to greatest
8
2
12
3
= - 0.375
8
1
! = - 0.5
2
5
!
= - 0.416
12
!
1
5
3
! , ! , and !
2 12
8
Absolute value – the distance a number is from 0
Finding Absolute Value
Ex: Find the absolute value
a.
12
b.
!5
= 12
=5
Practice
1. Name the set(s) of numbers to which each number belongs
a. -1
b. -4.8
c. 0
d.
7
1239
2. Are whole numbers, integers, or rational numbers the most reasonable for each
situation?
a. your shoe size
b. a temperature in a news report
c. the number of quarts of paint you use when you paint a room
3. Find the absolute value
a. ! 9
b. 0.5
1.6 Mean, Median, Mode, and Range
Measures of Central Tendency – mean, median, mode, and range
Mean (average) – Sum of the data items divided by the total number of data items
Outlier – a data value that is much higher or lower than the other data values in the set
Median – the middle value (odd # of data values) or the average of the two middle
numbers (even # of data values)
**Data must be in numerical order**
Mode – the data value that occurs the most often
Real World Problem Solving
Ex: Find the mean, median, and mode of the data below. Which measure of central
tendency best describes the data?
Wages/hour
#of
employees
Mean:
Hourly Wages of Employees at a Local Restaurant
$6.25 $6.50 $6.75 $7.00 $7.25 $7.50 $7.75
5
3
0
1
0
0
0
$8.00
$8.25
0
1
5(6.25) + 3(6.50) + 7.00 + 8.25
= $6.60
10
Median: 6.25, 6.25, 6.25, 6.25, 6.25, 6.50, 6.50, 6.50, 7.00, 8.25
6.25 + 6.50
= $6.38
2
Mode: $6.25
The mean is greater than the salary of 8 workers. The mode is the salary of the 5 workers
with the lowest salary. The median best describes the data.
Solving an Equation
Ex: Suppose your grades on three history exams are 80, 93, and 91. What grade do you
need on your next exam to have a 90 average on the four exams?
80 + 93 + 91 + x
= 90
4
264 + x
= 90
4
& 264 + x #
4$
! = 4(90)
% 4 "
264 + x = 360
-264
-264
x = 96
You must get a 96 on your next test.
Range – the difference between the greatest and smallest data values
Finding the Range and Mean of Data
Ex: Find the range and mean: 25, 30, 30, 47, 28
Range: 47 – 25 = 22
Mean:
25 + 30 + 30 + 47 + 28
= 32
5
Stem-and-leaf plot – display of data made by using the digits of the values
Making a Stem and Leaf Plot
Ex: Make a stem and leaf plot
Gasoline Prices: $2.39, $2.47, $2.43, $2.21, $2.33, $2.28, $2.57, $2.26
2.2
2.3
2.4
2.5
1 6 8
3 9
3 7
7
2.5
7 means 2.57
Practice:
1. Find the mean, median, and mode. Which measure of central tendency best describes
the data?
a. weights of textbooks in ounces
12
10
9
15
16
10
b. time spent on Internet in min/day
75
38
43
120 65
48
52
2. Write and solve an equation to find the value of x
a. 100, 121, 105, 113, 108, x; mean 112
b. 3.8, 4.2, 5.3, x; mean 4.8
3. Find the range
a. 12, 15, 17, 28, 30
b. 5.3, 6.2, 3.1, 4.8, 7.3
4. Make a stem and leaf
a. 18, 35, 28, 15, 36, 10, 25, 22, 15
b. 0.8, 0.2, 1.4, 3.5, 4.3, 4.5, 2.6, 2.2