Algebra 1A

Unit 02 Chapter 1… sections 1-6, 8

GUIDED NOTES

NAME _________________________

Teacher _______________

Period ___________

1

Date: __________________________

Section 1 – 1: Variables and Expressions Notes – Part 1

Writing Mathematics Expressions: Variables:

Algebraic Expressions:

Factors:

Product:

Example #1: Write an algebraic expression for each verbal expression.

a.) five less than a number c

b.) 9 plus the product of 2 and the number d

c.) two thirds of the original volume v

d.) 8 more than a number n

e.) 7 less than the product of 4 and a number x

f.) one third of the size of the original area a

2

Incorporating Exponents: Power:

Base:

Exponent:

Symbol Words Meaning 13 23 33 62b

nx Example #2: Write each expression algebraically. a.) the product of

43 and a to the seventh power

b.) the sum of 11 and x to the third power c.) the product of 7 and m to the fifth power d.) the difference of 4 and x squared

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Date: __________________________

Notes – Part 2 Section 1 – 1: Variables and Expressions

Writing Mathematics Expressions: Evaluate:

Example #1: Evaluate each expression.

a.) 43

b.) 28

c.) 62

d.) 34 Writing Verbal Expressions: Example #2: Write a verbal expression for each algebraic expression. a.) 34m b.) dc 212 +

c.) 5

8 2x

d.) yy 165 −

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Date: __________________________

Notes – Part 1 Section 1 – 2: Order of Operations

Evaluating Rational Expressions: Order of Operations:

1.) 2.) 3.) 4.)

Example #1: Evaluate each expression.

a.) 5323 +•+

b.) 245315 −•÷

c.) 3246 •−+

d.) 53248 3 +•÷

2

e.) 34

118

62

+ •

f.) ( ) ( )8 3 3 3 2− • +

g.) ( )[ ]4 12 6 2 2÷ −

h.) 2 6 2

3 5 3 2

5

3

− •− • −

Example #2: Laurie and Chase are evaluating the following. Who is correct? Explain!

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Date: __________________________

Notes – Part 2 Section 1 – 2: Order of Operations

Evaluating Algebraic Expressions:

Example #1: Evaluate )4( 32 cba −− if a = 7, b = 3, and c = 5. Example #2: Evaluate 22 )(2 zyx +− if x = 4, y = 3, and z = 2. Example #3: Each of the four sides of the Great Pyramid at Giza, Egypt, is a triangle. The base of each triangle originally measured 230 meters. The height of each triangle originally measured 187 meters. The area of any triangle is one-half the product of the length of the base b and the height h. a.) Write an expression that represents the area of one side of the Great Pyramid. b.) Find the area of one side of the Great Pyramid.

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Date: __________________________

Notes – Part 1 Section 1-3: Open Sentences

Solving Equations: Open Sentence:

Equation:

Set:

Solution Set:

Example #1: Find the solution set for each equation if the replacement set is {2, 3, 4,

5, 6}.

a.) 4 a +7 = 23

b.) 3(8 – b) = 6

2

Example #2: Use the Oder of Operations to solve the following equations.

a.) k=−−+

3)35(18)28(5

b.) q=−

+)45(3)4(213

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Date: __________________________

Notes – Part 2 Section 1 – 3: Open Sentences

Solving Inequalities: Inequality:

4 Symbols:

Example #1: Find the solution set for the following inequality if the replacement set

is {20, 21, 22, 23, 24}.

3211≥+z

Example #2: Find the solution set for the following inequality if the replacement set is {7, 8, 9, 10, 11}.

1018 <− y

2

Example #3: A four wheel drive tour of Canyon de Chelly National Monument in Arizona

cost $45 for the first vehicle and $15 for each additional vehicle. How many vehicles can the

Smith family take on the tour if they want to spend no more than $100? Show all work!

1

Date: ___________________

Section 1-4: Identity and Equality Properties Notes

Additive Identity: Multiplication Properties:

Property Words Symbols Examples

Multiplicative

Identity

For any number a, the

product of a and 1 is a.

Multiplicative

Property of Zero

For any number a, the

product of a and 0 is 0.

Multiplicative

Inverse

For every number ba ,

where a and b do not

equal 0, there is

exactly one number ab

such that the product

of ba and

ab is 1.

2

Properties of Equality:

Property Words Symbols Examples

Reflexive Any quantity is equal to itself.

Symmetric

If one quantity equals a second quantity,

then the second quantity equals the

first.

Transitive

If one quantity equals a second quantity and

the second quantity equals a third

quantity, then the first quantity equals the

third quantity.

Substitution A quantity may be substituted for its

equal in any expression.

Example #1: Name the property used in each equation. Then find the value of n.

a.) 012 =•n

b.) 151=•n

c.) 0 + n = 8

Example #2: Evaluate )2515(3)812(41

−÷+− . Name the property used in each step.

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Date: ___________________

Notes –Part 1 Section 1-5: Distributive Property

Evaluating Expressions: Distributive Property:

Example #1 – Rewrite 5(7 + 2) using the Distributive Property. Then evaluate. Example #2 – Rewrite (16 – 7)3 using the Distributive Property. Then evaluate. Example #3 – Rewrite 7(10 + 5) using the Distributive Property. Then evaluate. Example #4 – Rewrite 15(6 – 5) using the Distributive Property. Then evaluate.

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Example #5 – The Avery family owns two cars. In 1990, they drove the first car 16,000 miles and the second car 18,000 miles. Use the graph to find the total cost of operating both cars. Use the Distributive Property to write and evaluate an expression! Example #6 – Use the Distributive Property to find each product. a.) 10212 ⋅

b.)

171317

c.) )99(16

d.)

32327

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Date: ___________________

Notes –Part 2 Section 1-5: Distributive Property

Evaluating Expressions: Distributive Property:

Example #1 – Rewrite each product using the Distributive Property. Then simplify. a.) )3(12 +y b.) )28(4 2 ++ yy c.) )9(5 −g d.) )142(3 2 −+ xx

2

Algebraic Expressions: Term:

Like Terms:

Coefficient:

Example #2 – Simplify each expression. a.) aa 2117 + b.) bbb 6812 22 +− c.) xx 1815 + d.) 22 9310 nnn ++

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Date: ___________________

Notes Section 1-6: Commutative and Associative Properties

Example #1: Mentally add the following numbers.

a.) 9 + 7 + 8 + 3

b.) 15 + 6 + 2 + 5 Example #2: Mentally multiply the following numbers. 5328 ⋅⋅⋅ What would make adding or multiplying the above numbers easier??? Commutative Property

–

Associative Property

–

Example #3: Simplify 3c + 5(2 + c). List the properties that you use with each step!

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Example #4: Use the expression four times the sum of a and b increased by twice the sum of a and 2b. a.) Write an algebraic expression for the verbal expression. b.) Simplify the expression and indicate the properties used. Example #5: Use the expression three times the sum of 3x and 2y added to five times the sum of x and 4y. a.) Write an algebraic expression for the verbal expression. b.) Simplify the expression and indicate the properties used.