CURRICULUM CATALOG. Algebra II (3135) VA

Transcription

1 CURRICULUM CATALOG Algebra II (3135) VA

2 Table of Contents COURSE OVERVIEW... 1 UNIT 1: STRUCTURE AND FUNCTIONS... 1 UNIT 2: LINEAR FUNCTIONS... 2 UNIT 3: INEQUALITIES AND ABSOLUTE VALUE... 2 UNIT 4: POLYNOMIALS... 2 UNIT 5: ALGEBRAIC FRACTIONS... 2 UNIT 6: SEMESTER EXAM... 3 UNIT 7: REAL NUMBERS... 3 UNIT 8: FUNCTIONS... 3 UNIT 9: MORE FUNCTIONS... 3 UNIT 10: STATISTICS... 4 UNIT 11: SEMESTER EXAM... 4 UNIT 12: 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 and concepts involving linear, quadratic, exponential, rational, radical, and polynomial functions. Students also explore statistical concepts, applying their understanding of functions to solve problems. Structure and Functions: Student will review the properties of functions, determine the domain, range, and inverse of a function, and simplify expressions by combining like terms and applying rules for exponents. Linear Functions: Student will determine the slope of a line and use that information to write an equation, compare lines, and solve a system of equations using the addition property of equality, the substitution property of equality, and graphical methods. Inequalities and Absolute Value: Student will solve and graph inequalities, including absolute value inequalities in one or two variables. Polynomials: Student will factor polynomials, including applying their understanding of the difference of two squares, perfect square trinomials, and the difference of two cubes. The student will also solve problems involving direct variation, inverse variation, and joint or combination variation. Algebraic Fractions: Student will add, subtract, multiply, and divide with rational expressions, as well as solve and graph rational equations and functions that model mathematical and real-world situations. Real Numbers: Student will evaluate and simplify expressions containing radicals and fractional exponents and solve quadratic equations and systems of quadratic equations using a variety of methods. The student is also introduced to the concept of imaginary numbers and complex solutions. Functions: Student will explore a variety of functions and systems of equations, including exponential, absolute value, radical, and piece-wise defined functions. More Functions: Student will deepen the understanding of inverse functions, understanding the inverse relationship of exponential and logarithmic functions. Statistics: Student will algebraically represent sequences and series, including arithmetic and geometric, and distinguish between permutations and combinations. The student will also describe properties of normal distributions and solve statistical problems with linear, quadratic, and exponential models. Unit 1: STRUCTURE AND FUNCTIONS 1. Course Overview 10. Algebraic Expressions: Exponents Part 2 2. Relations and Functions: Definitions 11. Algebraic Expressions: Multiplication and Division Part 1 3. Relations and Functions: Graphs 12. Algebraic Expressions: Multiplication and Division Part 2 4. Relations and Functions: Domain and Range 13. Exponents of Exponential Expressions 5. Relations and Functions: Function Transformations 14. Algebraic Expressions: Combining Terms 6. Relations and Functions: Function Notation 15. Quiz 2 7. Relations and Functions: Operations 16. Special Project* 8. Quiz Test 9. Algebraic Expressions: Exponents Part Alternate Test* 2018 Glynlyon, Inc. 1

4 Unit 2: LINEAR FUNCTIONS 1. Line Graphs 11. General Equation of a Line 2. Line Graphs by Two Points 12. Quiz 3 3. Slope of Lines Part Solutions for Systems of Equations 4. Slope of Lines Part Solutions by Addition 5. Quiz Solutions by Substitution 6. Equations: Point Slope Part Application of Systems of Equations 7. Equations: Point Slope Part Quiz 4 8. Equations: Point Slope Part Special Project* 9. Equations: Slope-Intercept 19. Test 10. Quiz Alternate Test* Unit 3: INEQUALITIES AND ABSOLUTE VALUE 1. Solving Inequalities 11. Absolute Value Solution Sets 2. Graphing Solution Sets for Inequalities 12. Absolute Value Inequalities with One Variable 3. Compound Inequality Graphs 13. Absolute Value Inequalities with Two Variables 4. Solving Compound Inequalities 14. Quiz 3 5. Quiz Performance Task 6. Solving Inequalities 16. Alternate Performance Task* 7. Solving Two-order Inequalities 17. Special Project* 8. Number Order and Absolute Value 18. Test 9. Quiz Alternate Test* 10. Compound Sentences Unit 4: POLYNOMIALS 1. Products and Factoring 13. Quiz 2 2. Multiplying Polynomials by Polynomials 14. Graphing Polynomials 3. Using Special Products Part Numerical Relationships from Identities 4. Using Special Products Part Direct Variation 5. Factoring Trinomials 17. Inverse Variation 6. Quiz Joint and Combined Variation 7. Factoring Special Products Part Quiz 3 8. Factoring Special Products Part Performance Task 9. Addition and Subtraction Operations 21. Alternate Performance Task* 10. Division with Polynomials 22. Special Project* 11. Synthetic Division 23. Test 12. The Remainder Theorem 24. Alternate Test* Unit 5: ALGEBRAIC FRACTIONS 1. Multiplying and Dividing with Fractions 12. Proportions 2. Reducing Rational Expressions 13. Quiz 3 3. Multiplying Algebraic Fractions 14. Applications of Fractions 4. Dividing Algebraic Fractions 15. Mixture Problems 5. Quiz Work Problems 6. Adding and Subtracting Rational Expressions 17. Graphs of Rational Functions 7. Addition and Subtraction 18. Graphs of Rational Functions (2) 8. Mixed Expressions and Complex Fractions 19. Quiz 4 9. Quiz Special Project* 10. Equations with Fractions 21. Test 11. Fractional Equations 22. Alternate Test* 2018 Glynlyon, Inc. 2

5 Unit 6: SEMESTER EXAM 1. Exam 2. Alternate Exam* Unit 7: REAL NUMBERS 1. Real Numbers 15. Quadratic Formula 2. Law of Radicals 16. Graphs of Quadratic Functions 3. Multiplying Radicals 17. Word Problems Involving Quadratic Equations 4. Dividing Radicals 18. Sum and Product of Roots 5. Quiz Imaginary Numbers 6. Adding and Subtracting Radicals 20. Complex Solutions 7. Conjugates 21. Systems of Equations 8. Radical Equations 22. The Fundamental Theorem of Algebra 9. Quiz Quiz Standard Form of a Quadratic Function 24. Performance Task 11. Quadratic Equations 25. Alternate Performance Task* 12. Factoring Quadratic Equations 26. Special Project* 13. Completing the Square 27. Test 14. Quiz Alternate Test* Unit 8: FUNCTIONS 1. Exponential Functions 9. Radical Functions 2. Fractional Exponents 10. Graphs of Piece-Wise Defined Functions 3. Quiz Solving Equations by Graphing Functions 4. Exponential Equations 12. Quiz 3 5. Graphing Exponential Functions 13. Special Project* 6. Exponential Applications 14. Test 7. Quiz Alternate Test* 8. Absolute Value Functions Unit 9: MORE FUNCTIONS 1. Logarithmic Functions 10. Logarithmic Applications 2. Evaluation of Logarithms 11. Comparing Functions 3. Evaluating Exponential Functions, Common and Natural 12. Relations and Functions: Inverses Logarithms 13. Inverse Functions 4. General Properties of Logarithms 14. Systems of Equations 5. Calculation of Common Logarithms 15. Quiz 2 6. Graphs of Logarithmic Functions 16. Special Project 7. Quiz Test 8. Solving Logarithmic Equations 18. Alternate Test 9. Graphs of Natural Logarithms 2018 Glynlyon, Inc. 3

6 Unit 10: STATISTICS 1. Progressions: Sequences 15. Probability: Equally Likely Outcomes 2. Arithmetic and Geometric Sequences 16. Quiz 3 3. Geometric Sequences (2) 17. Normal Distributions 4. Project: Recursive Sequences 18. Z-Scores 5. Progressions: Series 19. Probability and Decisions 6. Quiz Appropriate Models 7. Permutations: Factorials 21. Regression Models 8. Permutation Formula 22. Quiz 4 9. Permutations: Applications 23. Performance Task 10. Quiz Alternate Performance Task* 11. Combination Formula 25. Special Project* 12. Combinations: Applications 26. Test 13. Combinations: Binomial Coefficients 27. Alternate Test* 14. Probability: Concepts Unit 11: SEMESTER EXAM 1. Exam 2. Alternate Exam* Unit 12: FINAL EXAM 1. Exam 2. Alternate Exam* (*) Indicates alternative assignment 2018 Glynlyon, Inc. 4