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