CH 1 NOTESVariables, Function Patterns, Graphs

Winter, 2010-2011

CH 1-1 Using VariablesBackground: In STEM careers, it is typical to make observations of an event and

try to explain a relationship to describe that event. Ex. a nurse monitoring a patient’s heart rate after giving that

patient some medication.

Vocabulary:STEM career: Any career involving Science, Technology, Engineering and Math.

Variable: a symbol representing any number. Ex. x, y, n Expression: a phrase, with variables and any mathematical

operators (EXCEPT the = sign!) Equation: expression written WITH the = sign

CH 1-1 Using VariablesHow To Use Them: Ex.1: State whether each one below is a variable, expression, or

equation.a) z°

variable (measured in degrees)b)z°+5s

expressionc) 2x

expressiond)2x=6

equatione) b (cm)

variable (measured in cm)

CH 1-1 Using VariablesHow To Use Them Cont.:

Ex.2 Write an expression for the following data collected by an accountant:

Answer: h = hours worked (define your variable)

$7.50∙h

Hours Worked (h) Pay ($/hr)

1 $7.50∙1

2 $7.50∙2

3 $7.50∙3

ANSWER: ______ ___________

CH 1-1 Using VariablesHow to Use It Cont.: Before we can “translate” words into algebraic expressions,

let’s review some definitions from elementary school:

Sum/More than tells us to: _________________Difference tells us to: _______________________Product tells us to: _________________________Times tells us to: ___________________________Quotient tells us to: ________________________Is tells us to: ______________________________

Can you think of any others?

CH 1-1 Using VariablesHow to Use Them Cont.: Ex.3 Write an algebraic expression for each phrase.

a)p multiplied by 3 3pb)n less 7

n-7c)3 plus m

3+m

NOTE: MAKE SURE YOU WRITE THINGS EXACTLY IN THE ORDER GIVEN!!!!!

CH 1-1 Using VariablesNOW, YOU DO ODDS,

#’s 1-9 IN 10 MINUTES!

READY…….

SET……..

GO!

CH 1-1 Using VariablesHow to Use It Cont.: Ex. 4 Define a variable and write an algebraic expression

for each phrase.

a) the sum of 4 and a numberdefine variable: n= number

write expression: 4+ n

b) 3 increased by a number define variable: x= number write expression: 3 + x

CH 1-1 Using VariablesNOW, YOU DO ODDS,

#’s 11-15 IN 10 MINUTES!

READY…….

SET……..

GO!

CH 1-1 Using VariablesHow to Use It Cont.: Ex. 5 Define a variable and write an algebraic expression to

model each situation.a) The number of gal of water used to water trees is 30 times

the number of trees.define variable: y = number of gallons of water used

x = number of trees write expression: y = 30∙xb) What is the cost of buying several pairs of jeans at $32.95

per pair? define variable: z = total cost, t = number of pairs of jeans write expression: z = 32.95∙t

CH 1-1 Using VariablesThink About It:

WOULD YOU RATHER WRITE: The number of gal of water used to water trees is 30 times the number of trees.OR:y = 30∙x????????????????

Algebra lets you take shortcuts!!!!!!

CH 1-1 Using VariablesNOW, YOU DO ODDS,

#’s 17-27 IN 10 MINUTES!

READY…….

SET……..

GO!

CH 1-2 Order of OperationsBackground: If we don’t all agree on the order of simplifying

expressions, we will all have different answers! Scientists and Mathematicians gathered and

decided on PEMDAS.

Vocabulary:PEMDAS: Please Excuse My Dear Aunt Sally

CH 1-2 Order of OperationsPlease (Parentheses first)Excuse (Exponents/Powers next)My (Multiply next)Dear(Division next)Aunt(Add next)Sally(Subtract last)

CH 1-2 Order of OperationsHow to Use It: Ex. 1 Simplify each expression.

a) (72-32)/8

P (72 - 32) /8

P&E (49-9)/8

E (40)/8

M (none in this problem)

D (40)/8 = 5

A (none in this problem)

S (none in this problem)

b) (102-4*8)/(8+9)

P (102-4*8) /(8+9)

P&E (100 – 32)/ (8+9)

E (68)/(17)

M (none in this problem)

D 68/17 = 4

A (none in this problem)

S (none in this problem)

CH 1-2 Order of OperationsNOW, YOU DO ODDS IN YOUR BOOK,

PAGE 12 ODDS #’s 1-39ANSWERS ON PAGE 836!!!!!!

READY…….

SET……..

GO!

Ch 1-3 Exploring Real NumbersBackground:

All numbers are not created equally. John Venn, this statistician dude from 1880 England, came up with a way to classify all numbers.

Vocabulary:

Natural #s: “Counting numbers” 1,2,3,…..

Whole #s: “Counting #’s plus 0” 0,1,2,3,……

Integers: All - and + whole numbers …-3,-2,-1,0,1,2,3,…

Rational #s: All fractions or decimals, but denominator ≠0. All fractions are terminating or repeating. 3.72 or ⅛

Irrational #s: All the weird stuff: √, i, non-repeating, non-terminated fractions, Π, etc.

Vocabulary Continued:

Real #s: all rational numbers and irrational numbers.

Venn Diagram: A circle diagram that shows how sets of things are related. Real Numbers

Ch 1-3 Exploring Real Numbers

Rational Numbers Irrational Numbers

0.755/8 -2/3

0.31

-3200

-2000000

Integers

Whole Numbers

540000

0

√10

√2/3

π

√1.6

0.101001000…..

i

Nat #1,2

Ch 1-3 Exploring Real NumbersHow To Use Them:

Ex.1 Name the set(s) of numbers to which each number belongs.

a. -0.002

rational number, real number

b. 8

whole number, natural number, integer, rational, & real

c. √7

irrational number, real number

d. -3.4

rational number, real number

CH 1-3 Exploring Real Numbers

NOW, YOU DO EVENS#2 - #8, and 26 & 28

READY…….

SET……..

GO!

Ch 1-3 Exploring Real NumbersVocabulary Contd:

Counterexample: An example that proves a statement false.

Ex. 2 Everyone in this room has dark hair.

Counterexample: Ron and Christen have light colored hair.

Ex.3 True or False: All negative numbers are integers.

False: -1/2 is a negative RATIONAL number

Now YOU try #’s 10 & 12!

Ch 1-3 Exploring Real NumbersVocabulary Contd:

Inequality: Statement that compares the value of two expressions using < or > symbols.

Less than is <

Greater than is >

Ex. 4 Use < = or > to compare these expressions.

a) -10.98 _____ -10.99

-10.98 > -10.99

b) 3/8 ________ 9/16

3/8 (0.375) < 9/16 (0.5625)

CH 1-3 Exploring Real Numbers

NOW, YOU DO EVENS:

#14- #24

READY…….

SET……..

GO!

Ch 1-3 Exploring Real NumbersVocabulary Contd:

Absolute Value: The absolute value of a number is the distance it is from 0. We write |-3| with absolute value bars.

Ex. 5 Find the absolute value of the following numbers.

a) |-5.44|

5.44

b) |3|

3

Now, you do #s 30 & 32