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

Pull

a mathematical phrase containing number(s), operation(s) and variablesPull

Pull

coefficient

the number in front of a variablePull

Pull

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

Pull

Pull

an expression in simplest form

Pull

Pull

the bottom number of a power

Pull

Pull

has a base raised to an exponent

tells how many times a number is used as a factor

Pull

Pull

Pull

Pull

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,...

Pull

Pull

0, 1, 2, 3, ...Pull

Pull

..., -2, -1, 0, 1, 2, 3, ...

Pull

Pull

rational number

irrational number

can be written as a fraction or a terminating or repeating decimalPull

Pull

cannot be written as a fraction or a terminating or repeating decimalPull

Pull

real numbers

the set of rational and irrational numbers

Pull

Pull

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

Pull

| -2| | 8| | x|

End

-2 8 x

1.4 Patterns and Functions

Function

dependant variable

independant Variable

domain

range

Pull

Pull a relation where there is only one output for each input

Pull

Pull

is changing because of the independat variable

Pull

Pull

changes by itself

Pull

Pull

the input value

Pull

Pull

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

Pull

Pull

correlation

how one set of data effects the other

Pull

Pull

Positive Correlation

Negative Correlation

No Correlation

Pull

Pull

Pull

Pull

Pull

Pull

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

Pull

Pull

Pull

Pull

Pull

Pull

Pull

Pull

Pull

Pull

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