# ALGEBRA 2, PART 2

## Price: $125 | Credits: One Semester | Dept: Math | Course ID# 222-2

This course is the second semester of Algebra 2 and builds upon the skills and knowledge gained from the first semester. The course includes the topics: Exponents, Roots, Radicals, Exponential and Logarithmic Functions, Conic Sections- Solving, Graphing, Trigonometry, Permutation & Combinations, Sequence and Series, and Complex Numbers. Algebra 2 is approved by the University of California A-G as mathematics (category C).

Upon completion of this course, the student is awarded 5 credits. Each credit corresponds to 15 hours of study. Of course, some students work more quickly than others, and some can devote more hours to study, so some students are able to complete the course in an accelerated rate.

### LEARNING OBJECTIVES

- In this module, students gain a comprehension of the following:
- To simplify and be able to analyze patterns from positive and negative powers.
- To understand the inverse relationship between roots and exponents.
- How to solve radical equations and perform operations with radical expressions.
- How to simplify radicals in fractions and how to rationalize a denominator.
- How to simplify fractions in the exponent and how to switch to root form.
- How to write repeating decimals as fractions.
- What exponential functions look like and how they behave.
- To solve exponential equations.
- To simplify exponents with base 10, and with base e.
- How to use scientific notation to represent very large or very small numbers.
- How to solve for inverse functions.
- How to solve and graph logarithmic equations, including the translation of exponential and logarithmic graphs from their parent graphs.
- The equations and graphs for circles, ellipses, hyperbolas, and parabolas.
- How to solve for and utilize the six trigonometric functions; sine, cosine, tangent, secant, cosecant, and cotangent.
- How to convert between radians and degrees.
- To use trigonometric ratios to solve special triangles.
- How to interpret and use the unit circle.
- How to use the law of sines and the law of cosines to solve triangles.
- To identify and distinguish between permutations and combinations, and when to apply which to a real life scenario.
- To solve basic probability problems.
- How to use the binomial theorem to expand polynomials raised to exponential powers.
- How to identify and distinguish between arithmetic and geometric sequences.
- To solve for the nth term of an arithmetic sequence, as well as the sum of the first n terms of that sequence.
- To solve for the nth term of an geometric sequence, as well as the sum of the first n terms of that sequence.
- How to determine if an infinite geomtric sequence is converging or diverging and to solve for the sum of that sequence if it exists.
- To perform basic operations with complex numbers, including addition, subtraction, multiplication, and division.
- How to add and subtract functions.
- How to multiply and divide functions.
- Finding compositions of functions.

### TOPICS COVERED

- This course covers the following topics:
- Positive and Negative Powers
- Roots and Exponents
- Radical Equations and Operations
- Radicals in Fractions
- Fractions in the Exponent
- Writing Repeating Decimals as Fractions
- Exponential Functions
- Exponential Equations
- Exponents with Base 10
- Base e
- Scientific Notation
- Inverse Functions
- Properties of Log Functions
- Logarithmic Equations
- Translation of Exponential and Logarithmic Graphs
- Circles: Equations & Graphs of
- Ellipses: Equations & Graphs of
- Hyperbolas: Equations & Graphs of
- Parabolas: Equations & Graphs of
- Sin, Cos, Tan, Cosec, Sec, Cot
- Converting Between Radians & Degrees
- Trig Ratios of Special Angles
- The Unit Circle
- The Law of Sines
- The Law of Cosines
- Permutations
- Combinations
- Basic Probability
- Binomial Theorem
- Arithmetic Sequence ( nth Term)
- Arithmetic Series (Sum Of)
- Geometric Sequence (nth Term)
- Geometric Series (Sum Of)
- Sum of Infinite Series
- Basic Operations With Complex Numbers
- Multiplying and Dividing Complex Numbers
- Adding & Subtracting Functions
- Multiplying & Dividing Functions
- Composition of Functions