Introduction

Welcome to AP Calculus BC! This rigorous course covers all topics in AP Calculus AB plus additional concepts, making it equivalent to two semesters of college calculus. To ensure you're prepared for the rich mathematical challenges ahead, this summer work is designed to strengthen your foundational knowledge and refresh key concepts from your previous mathematics courses.

Completing this summer work will allow us to move quickly through review material at the beginning of the school year and spend more time on the advanced BC-specific topics. The material should be completed before the first day of class, with all problems worked out clearly.

Purpose of Summer Work

The summer work serves several important purposes:

  • To review essential algebra, trigonometry, and pre-calculus concepts that form the foundation of calculus
  • To identify any areas where additional practice might be needed
  • To establish familiarity with the types of problems we'll encounter throughout the course
  • To develop mathematical stamina and problem-solving skills required for the pace of AP Calculus BC

Topics to Review

The following topics from previous mathematics courses should be thoroughly reviewed prior to the start of AP Calculus BC:

Algebra Topics

  • Factoring polynomials
  • Solving equations (linear, quadratic, polynomial, rational, exponential, logarithmic)
  • Working with inequalities
  • Function operations and composition
  • Inverse functions
  • Properties of exponents and logarithms

Trigonometry

  • Unit circle values
  • Graphs of trigonometric functions and their transformations
  • Trigonometric identities
  • Inverse trigonometric functions
  • Solving trigonometric equations
  • Law of Sines and Law of Cosines

Pre-Calculus Topics

  • Limits and their properties
  • Continuity
  • Definition of derivative using limits
  • Basic differentiation rules
  • Applications of derivatives (optimization, related rates, etc.)
  • Basic integration techniques
  • Applications of integrals (area, volume)

Summer Work Assignments

Problem Set 1: Algebra Review

Complete all problems in sections 1-4 of the provided worksheet, focusing on:

  • Simplifying complex expressions
  • Solving multi-step equations
  • Factoring challenging polynomials
  • Working with rational expressions

Suggested completion: July 15

Problem Set 2: Trigonometry Review

Complete all problems in sections 5-7 of the provided worksheet, focusing on:

  • Evaluating trigonometric expressions without a calculator
  • Proving trigonometric identities
  • Solving trigonometric equations
  • Graphing transformed trigonometric functions

Suggested completion: July 30

Problem Set 3: Pre-Calculus Review

Complete all problems in sections 8-10 of the provided worksheet, focusing on:

  • Evaluating limits (algebraic and graphical approaches)
  • Determining continuity
  • Basic differentiation and integration problems
  • Applications of derivatives and integrals

Suggested completion: August 15

Practice Test

Complete the practice test under timed conditions (90 minutes) to simulate exam conditions. This will help identify any remaining areas of weakness before the school year begins.

Suggested completion: August 25

Submitting Your Work

All summer work should be completed clearly and neatly, with all steps shown. On the first day of class, you will turn in:

  • All completed problem sets stapled or bound in a folder
  • A one-page reflection on your experience with the summer work, including any concepts that were particularly challenging
  • Three questions you have about calculus that you hope to have answered during the course