The document contains notes from Chapter 1 on algebra topics including: variables, expressions, equations, exponents, order of operations, real numbers, patterns and functions, scatter plots, and measures of central tendency. Lesson topics include using variables, exponents and order of operations, exploring real numbers, patterns and functions, scatter plots, and defining mean, median, mode, range and outliers. Examples are provided for writing expressions and equations, simplifying expressions, identifying functions, and calculating mean, median and mode.

1. Chapter 1 Notes
Lesson 1.1
Lesson 1.4
Lesson 1.2
Lesson 1.5
Lesson 1.3
Lesson 1.6

2. 1.1 Using Variables
variable
a symbol usually a letter to represent a number (s)
coefficient
the number in front of a variable
Algebraic expression
a mathematical phrase containing number(s), operation(s) and variables

3. Examples
Writing an Algebraic expression translating from verbal into math
8 more than a number
8+x
the difference of 6 and a number
6-x
the product of 5 and a number
5x
the quotient of n and 10
n
10

4. Examples
Writing an alegbraic expression
5 times a number plus 7
5x + 7
9 less than four times a number

5. Examples
Writing an Equation
Write an equation to show the total income from selling tickets to a school play for $5 each.
Let i = income
Let t = tickets
i=5t
Write an equation for the data from the table
Gallons 4 6 8 10
used
Miles 80 120 160 200
Traveled
Let g = gallons
Let M = miles traveled
m = 20g
End

6. 1.2 Exponents and Order of Operations
simplify
an expression in simplest form
Exponent
tells how many times a number is used as a factor
base
the bottom number of a power
power
has a base raised to an exponent
order of operations Pull
Parentheses
Exponents
Multiply and Divide from left to right
Add and subtract from left to right

7. Examples
48 - 8 * 2 + 42
48 - 8*2 + 16
48 - 16 + 16
32 + 16
48
Evaluate:
4n - 2m for n = 5 and m = 2
4(5) - 2(2)
20-4
16

8. Examples
Simplify 3(8 + 6) + (42 - 10)
3(14) + (16-10)
3(14) +(6)
42+6
48
Evaluate each expression for x = 11 and z = 16.
a. (xz)2 xz2
b.
(11*16)2
1 11*162
762 1
3 1*256
0,976
2,816

9. Examples
4[(2 * 9) + (15 ÷ 3)]
4[(18) + (5)]
4(23)
92
End

10. 1.3 Exploring Real numbers
Natural Numbers 1,2,3,...
Whole Numbers 0, 1, 2, 3, ...
Integers
..., -2, -1, 0, 1, 2, 3, ...
rational number
can be written as a fraction or a terminating or repeating decimal
irrational number
cannot be written as a fraction or a terminating or repeating decimal
real numbers
the set of rational and irrational numbers

11. whole numbers integers
natural numbers 0
π
2 -7
√3
0.3
2.5 Rational numbers
irrational numbers
Real Numbers

12. Examples
Ordering Fractions form least to greatest
Absolute value
distance away from zero
| -2| | 8| | x|
-2 8 x
End

13. 1.4 Patterns and Functions
Function
a relation where there is only one output for each input
dependant variable
is changing because of the independat variable
independant Variable
changes by itself
domain
the input value
range
the output value

14. 10 12
1 3
7 9 4 6
function
y=x+2
6 8 input output machine
3 5
9 11
domain range
x y

15. Example
Writing a function rule
Write a function rule
Number if 1 2 3 4
Apples
Cost $.35 $.70 $1.05 $1.40
Let A = apples
Let C = Cost
C = .35a

16. Example
Variables
Identify the independant and dependant variables
The number of minutes a call lasts then the cost of the call increases
Independent = minutes
dependant = cost
The presure increases and the as you dive deeper into the ocean
Independent = depth
dependant = pressure
End

17. 1.5 Scatter plots
Scatter plot
relates two groups of data
correlation
how one set of data effects the other

18. Positive Correlation
Negative Correlation Pull
Pull
No Correlation
Pull

19. Example
Tell if a positive, negative or no correlation
As the temperature outside drops the amount of time you spend outside in shorts
positive
the month you were born and your math average
no correlation
the number of carolies burned as the time of exercise increases
positive
the noise level in the class room and the teacher's patience level
negative correlation
End

20. 1.6 Mean, Median, Mode and Range
Mean
Median
Mode
Range
Outlier

21. Example
12, 10, 9, 1, 14, 16, 10
Mean
Median
Mode
Range
Outlier

22. Example
Find x
3.8, 4.2, 5.3, x : mean 4.8
3.8+4.2+5.3+x
4 = 4.8
13.3+x
4 = 4.8
13.3+x
= 19.2
End
x = 5.9