FUNDAMENTAL CONCEPTS OF ALGEBRA Unit 1

EXPONENTS AND RADICALS Lesson 1.2

Lesson Essential Question (LEQ) How do we simplify radicals and algebraic expressions with rational exponents?

Laws of Exponents for Real Numbers

Fractional Exponents

Simplifying Expressions with Exponents Examples: Textbook Page 29 #’s 16, 22, 32, 38, 44, 46

Homework: Page 29 #’s odds only

Bell Work:

Radicals

You need to know: Squares: Cubes: Prime Factorization:

Laws of Radicals Page 24 in your textbook. These are properties and laws of radicals that you should file into your long-term memory!!!

Removing/Simplifying nth Powers

Rationalizing Denominators

Homework: Pages #’s odds only

Bell Work:

Class Examples: Textbook Pages #’s 24, 30, 44, 64, 70, 74, 76, 78, 80, 100

Homework: Review Blue Tables on Pages 32, 36, and 38.

Bell Work:

ALGEBRAIC EXPRESSIONS Lesson 1.3

Lesson Essential Question (LEQ) How do we perform operations and factor algebraic expressions?

Polynomials Adding Subtracting Multiplying Dividing

Polynomial Product Formulas

Polynomial Examples Textbook Page 43 #’s 4, 10, 14, 18, 28, 34

Homework: Pages #’s 1-21 odds, 25, 29, 33, 35, 37, 39

Bell Work:

Factoring Polynomials

Trinomials

Special Case Binomials: Difference of Two Squares Difference of Two Cubes Sum of Two Cubes **(Blue Table on Page 38)** Examples Page 44 #’s 72, 76, 78, 80

Factoring By Grouping When you have four different terms that are separated by addition or subtraction, you can group certain terms together in order to factor. Examples Page 44 #’s 86, 88

Remember:

Homework: Page 44 #’s 47, 51, 55, 57, 61, 69, 75, 81, 85, 89, 95 What you need to know for the quiz tomorrow: Powers and Radicals Add/Sub/Mult/Div Polynomials Factoring Look through the examples we did in class and the problems from previous homework assignments and you should be fine!

Bonus for the Quiz:

Bell Work:

FRACTIONAL EXPRESSIONS Lesson 1.4

Lesson Essential Question (LEQ) How do we perform operations with fractional expressions?

Things to remember: A fractional expression is a quotient of two algebraic expressions. Whenever we have a variable in the denominator, we are going to have excluded values. Why?

Examples of Multiplying/Dividing Page 54 #’s 8, 12, 14

Adding and Subtracting Fractional Expressions MUST HAVE A COMMON DENOMINATOR!!! If it does not have a common denominator, find it! Examples: Page 54 #’s 20, 22, 26

Homework: Page 54 #’s 5 – 27 odds only

Bell Work:

Complex Fractions: A complex fraction is when you have a quotient in which the numerator and/or the denominator is a fractional expression. We need to simplify the numerator and denominator as much as possible before we divide them! Examples: Page 54 #’s 34, 40, 44 Remember that division is the same as multiplying by the reciprocal!!!!!!!!!!!

Rationalizing Sometimes it is necessary to rationalize a denominator or numerator of a fractional expression. We multiply the numerator and denominator by the conjugate. Examples: Page 55 #’s 52, 56, 60

Homework: Pages #’s 33, 39, 43, 49, 51, 55

Bell Work:

Class Work: Pages 54 – 55 #’s 14, 20, 26, 28, 30, 36, 42, 44, 50, 76, 77, 78 Work on this in class today and tonight for extra practice with fractional expressions. We are going to review tomorrow, and have a small test on Monday!!!

Bell Work:

Unit 1 Test You need to know: Exponents/Radicals (1.2) Add/Sub/Mult/Div Polynomials (1.3) Factoring (1.3) Fractional Expressions (1.4)

Review Problems We have a Unit 1 test tomorrow on Lessons Pages 56-57, you should be able to do Today, work on the following in groups: 16, 20, 28, 30, 38, 40, 42, 66, 74, 76, 82, 84 For extra practice, you can try doing the odds at home to prepare!

Bonus for the Test! A 5 inch wooden cube is painted blue. The cube is then cut into smaller 1 inch cube pieces. How many of the smaller 1 inch cubes have paint on 3 sides? 2 sides? 1 side? 0 sides?