algebra 1 chapter 1 complete notes
DESCRIPTION
Chapter 1 for Algebra ITRANSCRIPT
Chapter 1 Notes
Lesson 1.1
Lesson 1.2
Lesson 1.3
Lesson 1.4
Lesson 1.5
Lesson 1.6
1.1 Using Variables
variable
Algebraic expression
a symbol usually a letter to represent a number (s)Pull
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a mathematical phrase containing number(s), operation(s) and variablesPull
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coefficient
the number in front of a variablePull
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Writing an Algebraic expression translating from verbal into math
8 more than a number
the difference of 6 and a number
the product of 5 and a number
the quotient of n and 10
Examples
8+x
6-x
5x
n10
Writing an alegbraic expression
5 times a number plus 7
9 less than four times a number
Examples
5x + 7
Writing an Equation
Write an equation to show the total income from selling tickets to a school play for $5 each.
Write an equation for the data from the table
Gallons used
4 6 8 10
Miles Traveled
80 120 160 200
Examples
End
Let i = incomeLet t = ticketsi=5t
Let g = gallonsLet M = miles traveledm = 20g
1.2 Exponents and Order of Operations
simplify
Exponent
base
power
order of operations
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an expression in simplest form
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the bottom number of a power
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has a base raised to an exponent
tells how many times a number is used as a factor
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ParenthesesExponentsMultiply and Divide from left to rightAdd and subtract from left to right
48 - 8 * 2 + 42
Evaluate:4n - 2m for n = 5 and m = 2
Examples
48 - 8*2 + 1648 - 16 + 1632 + 1648
4(5) - 2(2)20-416
Simplify 3(8 + 6) + (42 - 10)
Evaluate each expression for x = 11 and z = 16.
(xz)2
xz2a.b.
Examples
3(14) + (16-10)3(14) +(6)42+648
(11*16)2
1762
30,976
11*162
11*2562,816
4[(2 * 9) + (15 ÷ 3)]
Examples
End
4[(18) + (5)]4(23)92
1.3 Exploring Real numbers
Natural Numbers
Whole Numbers
Integers
1,2,3,...
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0, 1, 2, 3, ...Pull
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..., -2, -1, 0, 1, 2, 3, ...
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rational number
irrational number
can be written as a fraction or a terminating or repeating decimalPull
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cannot be written as a fraction or a terminating or repeating decimalPull
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real numbers
the set of rational and irrational numbers
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2 -7
2.5
0
whole numbers integers
natural numbers
irrational numbersRational numbers
Real Numbers
0.3
√3
π
Examples
Ordering Fractions form least to greatest
Absolute value
distance away from zeroPull
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| -2| | 8| | x|
End
-2 8 x
1.4 Patterns and Functions
Function
dependant variable
independant Variable
domain
range
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Pull a relation where there is only one output for each input
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is changing because of the independat variable
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changes by itself
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the input value
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the output value
1 3
4 67 9
10 12
3 59 11
input output6 8y = x + 2
x y
domain range
functionmachine
Example
Writing a function rule
Number if Apples
1 2 3 4
Cost $.35 $.70 $1.05 $1.40
Write a function rule
Let A = applesLet C = CostC = .35a
Example
Variables
Identify the independant and dependant variables
The number of minutes a call lasts then the cost of the call increases
The presure increases and the as you dive deeper into the ocean
End
Independent = minutesdependant = cost
Independent = depthdependant = pressure
1.5 Scatter plots
Scatter plot
relates two groups of data
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correlation
how one set of data effects the other
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Positive Correlation
Negative Correlation
No Correlation
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Example
Tell if a positive, negative or no correlation
As the temperature outside drops the amount of time you spend outside in shorts
the number of carolies burned as the time of exercise increases
the month you were born and your math average
the noise level in the class room and the teacher's patience level
End
positive
no correlation
positive
negative correlation
1.6 Mean, Median, Mode and Range
Mean
Median
Mode
Range
Outlier
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Example
12, 10, 9, 1, 14, 16, 10
Mean
Median
Mode
Range
Outlier
Example
3.8, 4.2, 5.3, x : mean 4.8
Find x
End
3.8+4.2+5.3+x 4 = 4.8
13.3+x 4 = 4.8
13.3+x
= 19.2
x = 5.9