Precalculus to AP Calculus Bridge Course

Course Description

Are you considering taking an AP Calculus class but feeling uncertain about your readiness? Or perhaps you're looking to brush up on your precalculus skills before diving into AP Calculus? Maybe you're simply curious about the fundamental concepts of calculus and advanced mathematics? If any of these scenarios resonate with you, then this comprehensive math course is tailor-made for your needs!

This course serves as an ideal bridge between precalculus and AP Calculus, offering a preview of the core concepts of calculus while reinforcing essential precalculus topics. You'll get a head start on understanding derivatives and integrals, the building blocks of calculus, while also reviewing critical precalculus subjects such as trigonometric functions, exponents and logarithms, sequences and series, and limits.

What You'll Learn

  • How to find and interpret rates of change, a fundamental concept in calculus
  • Using areas to convert rates of change into totals, introducing the concept of integration
  • A thorough review of key precalculus topics essential for success in AP Calculus
  • An introduction to the big ideas of calculus, preparing you for more advanced study
  • How to apply mathematical concepts to real-world problems and situations

Prerequisites

  • Completion of a high school precalculus class
  • Familiarity with trigonometric functions
  • Understanding of exponents and logarithms
  • Knowledge of sequences and series
  • Basic understanding of limits (helpful but not required)

Course Content

  • Introduction to calculus concepts and their real-world applications
  • Rates of change and their significance in calculus
  • Accumulation and integration of changes
  • In-depth review of exponents and logarithms
  • Comprehensive review of trigonometry
  • The concept of limits, both graphically and numerically
  • Sequences and series, including the idea of convergence
  • Preparation strategies for AP Calculus

Who This Course Is For

  • High school students planning to take AP Calculus
  • Students who want to reinforce their precalculus knowledge
  • Individuals curious about calculus and advanced mathematics
  • Anyone looking to bridge the gap between precalculus and calculus
  • Students seeking a preview of AP Calculus content

Real-World Applications

  • Understanding rates of change is crucial in fields like economics, physics, and engineering
  • Integration concepts are used in probability, statistics, and data analysis
  • Trigonometry is essential in architecture, navigation, and acoustics
  • Exponents and logarithms are fundamental in finance, computer science, and scientific research
  • Limits and series are used in advanced physics and mathematical modeling

Syllabus

1. Why Calculus?

  • Lesson #1: Introduction
  • Lesson #2: Rates of Change
  • Lesson #3: Adding up the Changes

2. Exponents & Logarithms

  • Lesson #4: Working with Exponents

3. Using Trigonometry

  • Lesson #5: Review of Trigonometry

4. The Concept of a Limit

  • Lesson #6a: Limits at Finite Values – Graphical
  • Lesson #6b: Limits at Finite Values – Numerical
  • Lesson #6c: Limits at Infinity

5. Series Basics

  • Lesson #7a: Sequences and Series
  • Lesson #7b: The Idea of Convergence

6. Get Ready for AP Calculus

  • Wrap up
  • Final Exam

By enrolling in this course, you'll gain a solid foundation for AP Calculus, refresh your precalculus skills, and develop a deeper appreciation for the power and beauty of advanced mathematics. Don't miss this opportunity to get ahead and boost your confidence in your mathematical abilities!