Algebra 2 Syllabus

• This course focuses on reviewing and extending the main topics of Algebra.  

• It contains an emphasis on both an algebraic and graphic approach to learning concepts. 

• It includes the following topics: systems of equations, matrices, quadratic functions, polynomials, exponents, logarithms, complex numbers, conic sections, sequences and series, right triangle trigonometry, radian and degree measure, law of sines, and law of cosines.  

• The method of presentation is designed to meet the needs of students who desire a strong four year mathematical foundation for future study of mathematics and science or preparation for post-high school entrance requirements.

1 Equations and Inequalities

  1.1 Expressions and Formulas                         

  1.2 Properties of Real Numbers                       

  1.3 Solving Equations                                

  1.4 Solving Absolute Value Equations                   

  1.5 Solving Inequalities                               

  1.6 Solving Compound and Absolute Value Inequalities    

2 Linear Relations and Functions

  2.1 Relations and Functions                              

  2.2 Linear Equations                                    

  2.3 Slope                                             

  2.4 Writing Linear Equations                             

  2.5 Statistics: Using Scatter Plots                         

  2.6 Special Functions                                   

  2.7 Graphing Inequalities                                

3 Systems of Equations and Inequalities

  3.1 Solving Systems of Equations by Graphing     

  3.2 Solving Systems of Equations Algebraically     

  3.3 Solving Systems of Inequalities by Graphing    

  3.4 Linear Programming                       

  3.5 Solving Systems of Equations in Three Variables 

4 Matrices

  4.1 Introduction to Matrices                    

  4.2 Operations with Matrices                   

  4.3 Multiplying Matrices                       

  4.4 Transformations with Matrices              

  4.5 Determinants                            

  4.6 Cramer’s Rule                            

  4.7 Identity and Inverse Matrices               

  4.8 Using Matrices to Solve Systems of Equations  

5 Quadratic Functions and Inequalities

  5.1 Graphing Quadratic Functions                      

  5.2 Solving Quadratic Equations by Graphing            

  5.3 Solving Quadratic Equations by Factoring            

  5.4 Complex Numbers                               

  5.5 Completing the Square                           

  5.6 The Quadratic Formula and the Discriminant         

  5.7 Analyzing Graphs of Quadratic Functions            

  5.8 Graphing and Solving Quadratic Inequalities          

6 Polynomial Functions

  6.1 Properties of Exponents                  

  6.2 Operations with Polynomials              

  6.3 Dividing Polynomials                    

  6.4 Polynomial Functions                    

  6.5 Analyzing Graphs of Polynomial Functions  

  6.6 Solving Polynomial Equations             

  6.7 The Remainder and Factor Theorems      

  6.8 Roots and Zeros                        

  6.9 Rational Zero Theorem                  

7 Radical Equations and Inequalities

  7.1 Operations on Functions                  

  7.2 Inverse Functions and Relations            

  7.3 Square Root Functions & Inequalities        

  7.4 nth Roots                              

  7.5 Operations with Radical Expressions        

  7.6 Rational Exponents                       

  7.7 Solving Radical Equations and Inequalities   

8 Rational Expressions and Equations

  8.1 Multiplying and Dividing Rational Expressions          

  8.2 Adding and Subtracting Rational Expressions           

  8.3 Graphing Rational Functions Rational Functions                         

  8.4 Direct, Joint, and Inverse Variation                    

  8.5 Classes of Functions                                

  8.6 Solving Rational Equations and Inequalities             

9 Exponential and Logarithmic Relations

  9.1 Exponential Functions                            

  9.2 Logarithms and Logarithmic Functions               

  9.3 Properties of Logarithms                          

  9.4 Common Logarithms                             

  9.5 Base e and Natural Logarithms                    

  9.6 Exponential Growth and Decay                     

10 Conic Sections

  10.1 Midpoint and Distance Formulas            

  10.2 Parabolas                                

  10.3 Circles                                  

  10.4 Ellipses                                  

  10.5 Hyperbolas                              

  10.6 Conic Sections                            

  10.7 Solving Quadratic Systems                  

11 Sequences and Series

  11.1 Arithmetic Sequences                     

  11.2 Arithmetic Series                         

  11.3 Geometric Sequences                     

  11.4 Geometric Series                        

  11.5 Infinite Geometric Series                  

  11.6 Recursion and Special Sequences           

  11.7 The Binomial Theorem                    

  11.8 Proof and Mathematical Induction          

12 Probability and Statistics

  12.1 The Counting Principle                          

  12.2 Permutations and Combinations                  

  12.3 Probability                                    

  12.4 Multiplying Probabilities                        

  12.5  Adding Probabilities                             

  12.6  Statistical Measures                            

  12.7 The Normal Distribution                        

  12.8 Exponential and Binomial Distribution             

  12.9 Binomial Experiments                          

  12.1 Sampling and Error                            

13 Trigonometric Functions

  13.1 Right Triangle Trigonometry                   

  13.2 Angles and Angle Measure                    

  13.3 Trigonometric Functions of General Angles       

  13.4 Law of Sines                                

  13.5 Law of Cosines                              

  13.6 Circular Functions                            

  13.7 Inverse Trigonometric Functions                

14 Trigonometric Graphs and Identities

  14.1 Graphing Trigonometric Functions        

  14.2 Translations of Trigonometric Graphs      

  14.3 Trigonometric Identities                 

  14.4 Verifying Trigonometric Identities         

  14.5 Sum and Difference of Angles Formulas   

  14.6 Double.Angle and Half.Angle Formulas    

  14.7 Solving Trigonometric Equations