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1 Curriculum Catalog 2017 Glynlyon, Inc.

2 Table of Contents ALGEBRA II FUNDAMENTALS COURSE OVERVIEW... 1 UNIT 1: SET, STRUCTURE, AND FUNCTION... 1 UNIT 2: NUMBERS, SENTENCES, AND PROBLEMS... 1 UNIT 3: LINEAR EQUATIONS AND INEQUALITIES... 2 UNIT 4: POLYNOMIALS... 2 UNIT 5: ALGEBRAIC FRACTIONS... 2 UNIT 6: SEMESTER REVIEW AND EXAM... 2 UNIT 7: REAL NUMBERS... 3 UNIT 8: QUADRATIC RELATIONS AND SYSTEMS... 3 UNIT 9: EXPONENTIAL FUNCTIONS... 3 UNIT 10: COUNTING PRINCIPLES... 4 UNIT 11: REVIEW... 4 UNIT 12: SEMESTER REVIEW AND EXAM... 4 UNIT 13: FINAL EXAM Glynlyon, Inc. i

3 Course Overview Algebra II is a full-year, high school math course intended for the student who has successfully completed the prerequisite course Algebra I. This course focuses on algebraic techniques and methods in order to develop student understanding of advanced number theory, concepts involving linear, quadratic and polynomial functions, and precalculus theories. This course also integrates geometric concepts and skills throughout the units, as well as introducing students to basic trigonometric identities and problem solving. By the end of the course, students will be expected to do the following: Understand set notation and the structure of mathematical systems. Know how to use functional notation and operations on functions. Simplify and solve algebraic fractions. Perform operations on polynomials, including factoring, long division, and synthetic division. Solve algebraic word problems involving mixtures, money, integers, and work. Evaluate and solve radical expressions and equations. Solve systems of equations with graphing, substitution, and matrices. Graph and solve quadratic equations, including conic sections. Graph and solve exponential and logarithmic equations. Calculate permutations, combinations, and complex probabilities. Unit 1: Set, Structure, and Function 1. Course Overview 13. Algebraic Expressions: Exponents Part 2 2. Properties of Sets 14. Algebraic Expressions: Multiplication and Division 3. Operations of Sets Part 1 4. Quiz 1: Set Theory 15. Algebraic Expressions: Multiplication and Division 5. Structure: Axioms Part 2 6. Structure: Applications 16. Exponents of Exponential Expressions 7. Relations and Functions: Definitions 17. Algebraic Expressions: Combining Terms 8. Relations and Functions: Graphs 18. Quiz 3: Algebraic Expressions 9. Relations and Functions: Function Notation 19. Special Project* 10. Relations and Functions: Inverses 20. Test 11. Quiz 2: Relations and Functions 21. Alternate Test* 12. Algebraic Expressions: Exponents Part Glossary and Credits Unit 2: Numbers, Sentences, and Problems 1. Number Order and Absolute Value 11. Compound Sentences 2. Sums and Products 12. Quiz 2: Equalities and Inequalities 3. Quiz 1: Numbers 13. Number Problems 4. Solving Equations 14. Motion Problems 5. Multiplication Property 15. Miscellaneous Problems 6. Multi-step Equations 16. Quiz 3: Problems 7. Equations with Parentheses 17. Special Project* 8. Literal Expressions 18. Test 9. Solving Inequalities 19. Alternate Test* 10. Graphing Solution Sets for Inequalities 20. Glossary and Credits 2017 Glynlyon, Inc. 1

4 Unit 3: Linear Equations and Inequalities 1. Line Graphs 12. Solutions by Addition 2. Line Graphs by Two Points 13. Solutions by Substitution 3. Slope of Lines Part Application of Systems of Equations 4. Slope of Lines Part Quiz 2: Solutions for Systems 5. Equations: Point Slope Part Solving Inequalities 6. Equations: Point Slope Part Solving Two-order Inequalities 7. Equations: Point Slope Part Quiz 3: Solving Inequalities 8. Equations: Slope-Intercept 19. Special Project* 9. General Equation of a Line 20. Test 10. Quiz 1: Lines 21. Alternate Test* 11. Solutions for Systems of Equations 22. Glossary and Credits Unit 4: Polynomials 1. Products and Factoring 12. Quiz 2: Polynomials 2. Multiplying Polynomials by Polynomials 13. Direct Variation 3. Using Special Products Part Inverse Variation 4. Using Special Products Part Joint and Combined Variation 5. Factoring Trinomials 16. Quiz 3: Working Variations 6. Factoring Special Products Part Project: Creating an Algorithm 7. Factoring Special Products Part Special Project* 8. Quiz 1: Special Products 19. Test 9. Addition and Subtraction Operations 20. Alternate Test* 10. Division with Polynomials 21. Glossary and Credits 11. Synthetic Division Unit 5: Algebraic Fractions 1. Multiplying and Dividing with Fractions 12. Proportions 2. Reducing Rational Expressions 13. Quiz 3: Fractional Equations 3. Multiplying Algebraic Fractions 14. Applications of Fractions 4. Dividing Algebraic Fractions 15. Mixture Problems 5. Quiz 1: Algebraic Fractions 16. Work Problems 6. Adding and Subtracting Algebraic Fractions 17. Quiz 4: Problems with Fractions 7. Addition and Subtraction 18. Special Project* 8. Mixed Expressions and Complex Fractions 19. Test 9. Quiz 2: Addition and Subtraction of Fractions 20. Alternate Test* 10. Equations with Fractions 21. Glossary and Credits 11. Fractional Equations Unit 6: Semester Review and Exam A II F 1. Review 3. Alternate Exam - Form A* 2. Exam 4. Alternate Exam - Form B* 2017 Glynlyon, Inc. 2

5 Unit 7: Real Numbers 1. Real Numbers 11. Word Problems Involving Quadratic Equations 2. Law of Radicals 12. Sum and Product of Roots 3. Conjugates 13. The Discriminant 4. Radical Equations 14. Imaginary Numbers 5. Quiz 1: Real Numbers 15. Quiz 3: Quadratic Formula 6. Quadratic Equations 16. Special Project* 7. Factoring Quadratic Equations 17. Test 8. Completing the Square 18. Alternate Test* 9. Quiz 2: Quadratic Solutions 19. Glossary and Credits 10. Quadratic Formula Unit 8: Quadratic Relations and Systems 1. Distance Formula 12. Systems of Equations 2. Circle 13. Solutions of Inequalities 3. Ellipse 14. Applications of Conic Sections: Part 1 4. Ellipse Continued 15. Applications of Conic Sections: Part 2 5. Quiz 1: Conics and the Coordinate Plane 16. Applications of Conic Sections: Part 3 6. Conic Sections: Parabola 17. Constant of Proportionality 7. Conic Sections: Parabola Continued 18. Quiz 3: Applications of Conics 8. Conic Sections: Hyperbola 19. Special Project* 9. Conic Sections: Hyperbola Continued 20. Test 10. Identifying Conic Sections 21. Alternate Test* 11. Quiz 2: Conics 22. Glossary and Credits Unit 9: Exponential Functions 1. Exponential Functions 13. Graphs of Logarithmic Functions 2. Fractional Exponents 14. Solving Logarithmic Equations 3. Exponential Equations 15. Logarithmic Applications 4. Graphing Exponential Functions 16. Quiz 2: Logarithmic Functions 5. Exponential Applications 17. Matrices 6. Quiz 1: Exponential Functions 18. System Solutions with Matrices 7. Logarithmic Functions 19. Addition and Multiplication of Matrices 8. Evaluation of Logarithms 20. Quiz 3: Matrices 9. Evaluating Exponential Functions, Common 21. Special Project* Logarithms, and Natural Logarithms 22. Test 10. General Properties of Logarithms 23. Alternate Test* 11. Scientific Notation 24. Glossary and Credits 12. Calculation of Common Logarithms 2017 Glynlyon, Inc. 3

6 Unit 10: Counting Principles 1. Progressions: Sequences 11. Quiz 3: Combinations 2. Progressions: Series 12. Probability: Concepts 3. Quiz 1: Sequences and Series 13. Probability: Equally Likely Outcomes 4. Permutations: Factorials 14. Probability: Multiplication Principle 5. Permutation Formula 15. Conditional Probability 6. Permutations: Applications 16. Quiz 4: Probability 7. Quiz 2: Permutations 17. Special Project* 8. Combination Formula 18. Test 9. Combinations: Applications 19. Alternate Test* 10. Combinations: Binomial Coefficients 20. Glossary and Credits Unit 11: Review 1. Integers 14. Real Numbers Continued 2. Integers Continued 15. Quiz 2: Review 3. Open Sentences 16. Quadratic Relations and Systems 4. Open Sentences Continued 17. Quadratics Continued 5. Graphs 18. Exponential Functions 6. Graphs Continued 19. Exponential Functions Continued 7. Quiz 1: Review 20. Counting Principles 8. Polynomials 21. Counting Principles Continued 9. Polynomials Continued 22. Quiz 3: Review 10. Algebraic Fractions Part Special Project* 11. Algebraic Fractions Part Test 12. Algebraic Fractions Part Alternate Test* 13. Real Numbers 26. Glossary and Credits Unit 12: Semester Review and Exam A II F 1. Review 3. Alternate Exam - Form A* 2. Exam 4. Alternate Exam - Form B* Unit 13: Final Exam A II F 1. Exam 3. Alternate Exam - Form B* 2. Alternate Exam - Form A* (*) Indicates alternative assignment 2017 Glynlyon, Inc. 4

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