• AP Precalculus/MAT188

    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.
Copyright Pat Byrnes