AP Calculus AB/BC Summer Assignment
Introduction
Welcome to AP Calculus! This summer assignment is designed to help you prepare for the rigorous curriculum that awaits you. Completing this assignment will refresh your knowledge of essential pre-calculus concepts and introduce you to some fundamental calculus ideas that will be covered in the first weeks of the course.
All students planning to take AP Calculus AB or BC should complete this assignment before the first day of class. If you are currently unsure which course you will be taking, please complete all sections of this assignment.
Important Submission Information
This assignment is due on the first day of class. Please show all work for each problem. Answers alone are not sufficient. All work should be completed on separate paper, clearly labeled with your name and the problem number. Late submissions will result in a penalty of 10 points per day.
Purpose of the Summer Assignment
The summer assignment serves several important purposes:
- Reviewing critical algebraic skills needed for calculus
- Introducing fundamental calculus concepts at a manageable pace
- Allowing students to identify areas where additional review may be needed
- Ensuring a smooth transition into the AP Calculus curriculum
- Providing a baseline assessment of students' mathematical preparedness
- Giving you a head start on material that will be covered in the first weeks of class
Topics Covered
The summer assignment focuses on the following pre-calculus topics:
- Algebra Review: Solving equations, factoring, rational expressions, inequalities
- Functions: Domain, range, composition, transformations, inverse functions
- Graphing: Analyzing and sketching functions piecewise defined functions
- Exponential and Logarithmic Functions: Properties, graphs, equations
- Trigonometry: Unit circle, trigonometric identities, solving trigonometric equations
- Limits: Evaluating limits graphically, numerically, and algebraically
Assignment Outline
| Topic | Problem Numbers | Points |
|---|---|---|
| Algebra Review | Problems 1-20 | 20 points |
| Functions and Graphs | Problems 21-40 | 20 points |
| Exponential and Logarithmic Functions | Problems 41-55 | 15 points |
| Trigonometry | Problems 56-70 | 15 points |
| Introduction to Limits | Problems 71-85 | 15 points |
| Limits and Continuity (BC only) | Problems 86-100 | 15 points |
Submission Guidelines
- All work should be completed on 8.5 x 11-inch paper
- Write clearly and legibly using pen or pencil
- Show all work necessary to arrive at your answers
- Staple pages together in the correct order
- Include a cover sheet with your name, intended course (AB or BC), and date
- Solutions should be simplified and properly formatted
- Graphs should be drawn with appropriate scaling and labels
- Circle or highlight your final answers
Resources
If you encounter difficulties with any of the problems, the following resources may be helpful:
- Khan Academy (khanacademy.org) - Offers free tutorials on all prerequisite topics
- Paul's Online Math Notes (tutorial.math.lamar.edu) - Comprehensive notes with examples
- Purple Math (purplemath.com) - Clear explanations of algebraic concepts
- PatrickJMT (patrickjmt.com) - Video tutorials on calculus topics
- Your pre-calculus or algebra textbook
- Forming study groups with classmates
Getting Started
We recommend beginning this assignment in mid-July to avoid last-minute stress. Break the work into manageable chunks, perhaps completing one topic per week. This will give you time to seek help if needed and to practice each concept thoroughly.
Remember that the effort you put into this assignment will pay dividends throughout the year as we build upon these foundational concepts. Calculus is a beautiful and powerful branch of mathematics, and we're excited to explore it with you!
Frequently Asked Questions
What if I don't understand a problem?
Try to solve the problem to the best of your ability, showing your work. If you're still stuck, look up the concept in your resources or ask for help. It's okay to have questionsthis assignment is partly to identify areas where you may need additional support.
Can I use a calculator?
For most problems, calculators should be used only to check your work. On the AP exam, there are sections where calculators are not allowed, so it's important to develop your problem-solving skills without relying on them.
What happens if I don't complete the assignment?
This assignment constitutes your first grade of the course. Incomplete assignments will result in partial credit according to the amount of work completed. Students who do not submit the assignment by the third day of class will be required to attend mandatory tutoring sessions.
How much time should I expect to spend on this assignment?
Most students find that 10-15 hours spread over the course of the summer is sufficient to complete the assignment well.
Where can I get help during the summer?
Feel free to email your questions to your instructor, who will respond within 2-3 business days. You may also utilize the online resources listed in this document.
Contact Information
If you have questions about the assignment over the summer, please contact:
Dr. Sarah Martinez
AP Calculus Teacher
Email: smartinez@school.edu
Office Hours: Available for virtual appointments by request
Mr. James Wilson
Mathematics Department Chair
Email: jwilson@school.edu
Office Hours: Available for virtual appointments by request
