honors algebra 2 1.1 real numbers and real operations objectives: 1.know the categories of numbers...

Honors Algebra 2

1.1 Real Numbers and Real Operations Objectives:1. Know the categories of numbers2. Know where to find real numbers on the

number line3. Know the properties and operations of real

numbers 

…., -4, -3, -2, -1, 0, 1, 2, 3, 4,…

counting numbers

…., -4, -3, -2, -1, 0, 1, 2, 3, 4,…

counting numbers

whole numbers

…., -4, -3, -2, -1, 0, 1, 2, 3, 4,…

counting numbers

whole numbers

integers

rational numbers - numbers that can be written as a fraction or a decimal that repeats or terminates. Examples?

irrational numbers - numbers that can’t be written as a fraction or a decimal that repeats or terminates. Examples?

Locate these numbers on a number line:

,31

,8,5

127.2,,33.4,2,

1. Approximate to decimal2. Determine range and mark line3. Plot original values

property addition multiplication

closure a + b = real number ab = real number

property addition multiplication

closure a + b = real number ab = real number

commutative

property addition multiplication

closure a + b = real number ab = real number

commutative a + b = b + a

property addition multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

property addition multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative

property addition multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

property addition multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

property addition multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity

property addition multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a

property addition multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

property addition multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse

property addition multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0

property addition multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0 a x 1/a = 1

property addition multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0 a x 1/a = 1

distributive

property addition multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0 a x 1/a = 1

distributive a(b + c) = ab + acopposite of a = -a

Inverse of a = 1/a

property addition multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0 a x 1/a = 1

distributive a(b + c) = ab + acIdentify the property:

1. 5 + -5 = 0

2. 2(3●5) = (2●3)5

3. 4(3 + 7) = 4●3 + 4●7

4. 5 + 3 = 3 + 5

5. (x + 5) + 4 = x + (5 + 4)

6. 1x = x

7. 3●1/3 = 1

8. 2●3●4 = 3●2●4

Honors Algebra 2

1.2 Algebraic Expressions and Models

 Objectives:1. Evaluate algebraic expressions2. Simplify expressions3. Apply expressions to real world examples  

Vocabulary: power – a number and it’s exponent

Vocabulary: power

base

exponent

52

Vocabulary: power – a number and it’s exponent

Vocabulary: power

52=5∙55 to the second power5 squared

Vocabulary: power – a number and it’s exponent

Vocabulary: power

53=5∙5∙55 to the third power5 cubed

34

25

93

16

3∙3∙3∙3

2∙2∙2∙2∙2

9∙9∙9

1∙1∙1∙1∙1∙1

3 to the fourth power

2 to the fifth power

9 cubed (to the 3rd power)

1 to the sixth power

to the 4th power

4

7

Please Excuse My Dear Aunt Sally

P – parenthesisE – exponentsM – multiplicationD – divisionA – additionS – subtraction

Left to Right

1421 65

P – parentheses and other grouping symbols from left to right

E – exponents from L to R

M – multiplication/division from L to R

A – addition/subtraction from L to R

Please Excuse My Aunt

Evaluate these expressions:

25 )13 )(( 4

153)4(1 2

54 5 )( 32

2

2

2731)(4

22 22)(

Evaluate 5x2x3 2

when x = 2

when x = 2/3

11

-7/3

**Calculator Tip : Decimal Fraction

Math, >Frac

Like terms –

2x4x2x31x7x 232 2222 yx4x y2yx3x y7yx

8 )5 ( x2 )3 ( x

terms that have the same variables with the same powers

Simplify these expressions:

2 )x44 ( x2 )3 ( x 2

8 )r2 ( 3r3

Real World Applications

• See Note Sheet…

You have 122 dollars from bagging at Dominick’s and you want to buy some DVD’s. If each DVD cost $13, write an expression to represent the amount of money you have left buying in DVD’s.

You want to buy either scented lotion or bath soap for 8 people. The lotions are $6 for each and the soaps are $5 each. Write and expression for the total amount you must spend. Evaluate the expression when 5 people get the lotion.

Write an expression for the total amount of juice in 15 cans if some hold 8 oz and some hold 12 oz. What is the total if 9 of the cans hold 8 oz?

Practice…Try These on the Back

HMWK!

• Worksheet 1.1-1.3: #s 7-15, 13-24

Today’s Agenda!

• Collect Signed Syllabus

• Return Syllabus Scavenger Hunt

• HW Questions/Concerns

• Section 1.3 Notes– 1.3 Domino Worksheet

• Word Problems

• HA2 Pretest Tomorrow! (Bring #2 Pencil)

Honors Algebra 2

1.3 Solving Linear Equations 

Objectives:1. Solve simplified linear equations2. Solve linear equations that need simplifying3. Solve linear equation from real life 

Vocabulary: solution, equation, identity equation, inconsistent equation

PEMA – used to evaluate an expression

5- x w h e n3 ,2 x

4 x when,3

8-3)2(x

Rules for Solving an Equation

3

2

1. Distribute2. Combine Like Terms3. Move variable to one side4. Isolate variable using inverse

operations5. Check

Solving an equation – working backwards

2(x 3) - (3x + 2) - 4 -27

63

8-3)2(x

(4/5)(x – 2) = 16

2x + 5 = 7x – 16

3(x – 7) + 2x = -5(2x – 4)

2x + 8 = 5x – 2(x – 8)

Infinite Solutions/No Solutions

• 4x – 3 = 2(2x – 9) + 4 • 7x + 5 – 3x = -8x + 5 + 12x

Domino WKST!

Real World Applicaiton

• See Note Sheet…

Katie works at a restaurant. She earns $3 per hour base plus tips. She averages $12 in tip per hour. How many hours until she has earned $333?

3

2

22.2 hours

A car salesman base salary is $21,000 plus 5% commission on sales. How much must he sell to earn $65,000.

3

2

$880,000 of cars

The bill from your plumber is $134. The cost for labor was $32 per hour. The cost for material was $46. How many hours did the plumber work?

2.75 hours

Honors Alg 2

The perimeter of a triangle is 35 feet. If the sides are 3x – 5, 2x – 3, and 15-x, what are its dimensions?

3

2

x = 7sides of 16, 13, and 8 units

Assignment:• WS 1.1-3, #11-

23 on backside

Honors Alg 2