High School

# Math Topics: Advanced Algebra and Trigonometry

.5 Credits
Open

This course provides a series of math topics for students to select from based on their needs. It can be used for math acceleration, remediation or to supplement existing curriculum. Each topic begins with a pre-assessment from which a personal learning path is developed for the student. Based on the pre-assessment, the learning path includes refreshers on concepts students may have forgotten and lessons on concepts the student has not yet mastered. The learning path does not require students to complete lessons on concepts the student has mastered.

### Competencies

##### Adv. Algebra: Exponential and Logarithmic Functions

Students will demonstrate an understanding of exponential and logarithmic functions by converting between the two forms; using properties to simplify and solve logarithmic and exponential functions; graphing and solving logarithmic and exponential equations with various bases including "e"; and solving applied problems using both types of functions.

Students will demonstrate an understanding of functions by identifying whether a relation is a function by multiple means; evaluating and graphing linear, quadratic and radical functions; identifying domain and range of functions; and performing operations with two or more functions.

Students will demonstrate understanding of radical expressions by finding and approximating square and cubic roots; simplifying expressions with odd and even roots; converting between radicals and exponential notation; simplifying radical expressions; performing operations with radical expressions; rationalizing denominators; solving radical equations; performing operations with complex numbers; solving quadratics by completing the square; and solving application problems requiring the quadratic formula and having complex solutions.

Students will demonstrate an understanding of rational expressions by simplifying and performing operations with rational expressions; solving problems involving rational expressions; simplifying complex rational expressions; identifying extraneous solutions; and solving problems involving direct, inverse and joint variations.

##### Trigonometry

Students will demonstrate an understanding of trigonometry concepts by using the six trigonometric ratios to solve problems; solving right triangle application problems using the Pythagorean Theorem and special right triangles; working with the unit circle as it relates to the six trigonometric functions; completing calculations with both radians and degrees; graphing the sine and cosine functions; and adjusting the graphs of sine and cosine by manipulating the amplitude and/or period.

### Major Topics and Concepts

• Rational Expressions
• Functions
• Exponential and Logarithmic Functions

### Course Materials

Students work with a certified VLACS math teacher throughout the course. The teacher coaches the student through the course by completing a Welcome Call at the beginning of the course, monitoring student progress, identifying areas of struggle, meeting regularly with the student, and completing monthly calls with the student and parent.

Students may work with their school to identify the set of topics that meet their needs. The groupings below are provided to aid in potential sets of topics, but students may select whatever topics meet their particular needs.

Credit for completion of topics will be determined by the student’s school of record. VLACS will not award credit but will report topics in which a student has demonstrated competency, which can be used by schools to award credit. Credit Recommendations: VLACS recommends that students be awarded 0.5 credits for each set of 4 competencies completed.