Algebra, Trigonometry, and Relations - Comprehensive Course Description

Algebra, Trigonometry, and Relations

Course Overview

This comprehensive mathematics course is designed for 11th-grade students aiming to dive deep into the realms of algebraic reasoning, trigonometric analysis, and the exploration of relations and functions. The course offers a structured curriculum that builds a strong foundation in mathematical concepts and problem-solving techniques.

Course Competencies

1. Algebra and Number

Focuses on developing algebraic reasoning and number sense.

  • Understand the absolute value of real numbers
  • Perform operations on radicals and radical expressions
  • Solve problems involving radical equations
  • Determine equivalent forms of rational expressions
  • Perform operations on rational expressions
  • Solve problems involving rational equations

2. Algebraic Reasoning

Absolute Value and Real Numbers

  • Explain the concept of absolute value through distance on a number line
  • Determine the absolute value of positive and negative numbers
  • Compare and order absolute values
  • Express numerical expressions in absolute value

Operations on Radicals

  • Compare and order radical expressions
  • Simplify and rationalize radical expressions
  • Explain properties involving radical expressions and operations

Rational Expressions and Equations

  • Simplify and perform operations on rational expressions
  • Solve rational equations
  • Identify non-permissible values

3. Trigonometric Reasoning

Develops understanding and problem-solving skills related to trigonometric functions and laws.

Angles and Trigonometric Ratios

  • Sketch angles in standard positions
  • Determine reference angles and their properties
  • Solve problems using primary trigonometric ratios

Cosine and Sine Laws

  • Solve problems involving non-right triangles using cosine and sine laws
  • Identify situations with potential multiple solutions

4. Relations and Functions

Involves studying and analyzing various types of functions and their properties.

Polynomial Functions

  • Factor different forms of polynomial expressions
  • Graph and analyze absolute value and quadratic functions
  • Solve problems involving quadratic equations

Quadratic Inequalities and Sequences

  • Solve and analyze linear and quadratic inequalities
  • Understand and solve problems involving arithmetic and geometric sequences and series

Reciprocal Functions

  • Graph and analyze reciprocal functions of linear and quadratic functions
  • Identify values and interpret vertical asymptotes

Learning Outcomes

  • Algebraic Mastery: Develop a thorough understanding of algebraic expressions, equations, and functions.
  • Trigonometric Proficiency: Master trigonometric functions, ratios, and laws to solve complex problems.
  • Function Analysis: Analyze and graph absolute value, quadratic, and reciprocal functions.
  • Problem-Solving Skills: Apply mathematical concepts to real-world problems and scenarios.

Target Audience

This course is ideal for 11th-grade students who wish to enhance their mathematical knowledge and problem-solving abilities, particularly those with an interest in mathematics, engineering, or sciences.

Prerequisites

Students should have a foundational understanding of basic algebra and geometry concepts typically covered in earlier grades.

Enrollment

Ready to strengthen your mathematics skills? Enroll today and set the stage for your academic growth and success!