Unit 1 FUNDAMENTAL CONCEPTS OF ALGEBRA Lesson 1
Unit 1 FUNDAMENTAL CONCEPTS OF ALGEBRA
Lesson 1. 2 EXPONENTS AND RADICALS
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, 38, 44, 46
Homework: �Page 29 #’s 11 -45 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 29 -30 #’s 53 -79 odds only
Bell Work: �
Class Examples: �Textbook Pages 29 -30 #’s 24, 30, 44, 64, 70, 74, 76, 78, 80, 100
Homework: �Review Blue Tables on Pages 32, 36, and 38.
Bell Work: �
Lesson 1. 3 ALGEBRAIC EXPRESSIONS
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 43 -44 #’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: �
Lesson 1. 4 FRACTIONAL EXPRESSIONS
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 54 -55 #’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 1. 2 -1. 4. �Pages 56 -57, you should be able to do 13 -84. �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?
- Slides: 50