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The AP Precalculus course from the College Board is designed to prepare students for college-level calculus by covering a broad range of topics essential for understanding calculus concepts. The curriculum is divided into four main units, each focusing on different mathematical concepts and skills. 

1. Unit 1: Polynomial and Rational Functions

• Standards Covered:
  • Analyzing the characteristics of polynomial and rational functions.
  • Understanding end behavior, intercepts, zeros, and asymptotes of these functions.
  • Performing operations on polynomial and rational expressions.
  • Solving polynomial and rational equations and inequalities.
  • Modeling real-world situations using polynomial and rational functions.

2. Unit 2: Exponential and Logarithmic Functions

• Standards Covered:
  • Understanding and applying the properties of exponential and logarithmic functions.
  • Solving exponential and logarithmic equations.
  • Modeling with exponential growth and decay.
  • Exploring the inverse relationship between exponential and logarithmic functions.
  • Using logarithms to solve real-world problems, including those involving compounded interest.

3. Unit 3: Trigonometric and Polar Functions

• Standards Covered:
  • Analyzing the characteristics of trigonometric functions, including amplitude, period, phase shift, and vertical shift.
  • Solving trigonometric equations and verifying identities.
  • Understanding and applying the unit circle and trigonometric functions of any angle.
  • Exploring polar coordinates and graphs of polar equations.
  • Modeling periodic phenomena using trigonometric functions.

4. Unit 4: Functions involving Parameters, Vectors, and Matrices

• Standards Covered:
  • Understanding and graphing parametric functions.
  • Converting between parametric and Cartesian forms of functions.
  • Applying parametric functions to model real-world scenarios involving motion and other dynamic systems.
  • Introduction to vectors in two dimensions.
  • Understanding vector addition, scalar multiplication, and the dot product.
  • Applying vectors to solve problems involving force, velocity, and other physical quantities.
  • Understanding matrix notation and operations, including addition, subtraction, multiplication, and finding determinants.
  • Using matrices to solve systems of linear equations.
  • Applying matrices in transformations and other applications.

Additional Skills Emphasized Throughout the Course:

• Graphical Analysis: Understanding and interpreting the graphs of various types of functions.
• Algebraic Manipulation: Strengthening skills in algebraic manipulation, including factoring, simplifying expressions, and solving complex equations.
• Modeling and Problem Solving: Applying mathematical concepts to model real-world problems and develop problem-solving strategies.
• Communication of Mathematical Ideas: Developing the ability to communicate mathematical reasoning and solutions effectively.