There is no greater frustration than scoring less than full credit on a problem, especially if you knew exactly how to find the answer but didn’t show any steps. Unfortunately, if the instructions ask you to show your work, then the grader is looking for more than just a final answer. This article is all about showing your math on the AP Calculus exam.
Why Showing Your Work is Important
First, let’s talk about why it’s important to show your work.
It’s not just about weeding out the cheaters who copy their final answers from a neighbor.
Instead, showing your math steps demonstrates that you know the process well enough to explain it to someone else. That’s an important part of learning mathematics.
Furthermore, half of the AP Calculus exam requires you to show work. You must show a logical progression of mathematical steps to receive credit on the free response questions. (More info about those can be found here: Understanding AP Free Response Questions.)
10 Tips to Showing your Math Work
Here are a few tips to help you out.
1. Think Before you Write
The most important tip is to make sure that you understand what the question is asking before writing anything down.
Think about the givens and the goal. Do you have a strategy for solving the problem? What major steps go into the solution?
2. Build a Narrative
It may sound strange, but the solution of a mathematical problem should read like a story. You will lead the reader from the given information to the final answer through a series of logical steps.
3. Use Scratch Work Effectively
It’s important to separate scratch from mathematical steps.
Scratch includes mundane numerical computations, verification of your work, and other items that do not fit with the flow of your mathematical argument for the question.
Designate a small area of the page for scratch work. This might be where you work out sums and products, or verify your antiderivatives by taking a derivative, etc.
4. Write Down Your Formulas and Equations
In calculus, much of the work is in setting up and solving equations, working out derivatives or integrals, etc.
Be sure to write down each expression or equation clearly before working with it.
5. Write Down Major Calculator Steps
You are encouraged to used built-in features of the calculator. However, you must indicate when and where you use a calculator function or program.
Now this doesn’t mean you have to write, “I added 14.5 to 54.2 in the calculator to get 68.7.” Instead, the graders want to know when you have used the solver or numerical integration features, for example.
6. Don’t Over-Use the Calculator
Some approved calculators can do calculus procedures, including finding extreme values, intervals of increase/decrease, and concavity. While it’s great for checking your work, don’t rely on those calculator features to solve the problem completely.
You know you’ve over-used the calculator if your “work” consists of the phrase “The answer is ___ because my calculator said so.”
7. Review the Problem Statement
After answering a question, go back and re-read the problem. Does your last line of work answer the question? Did you address all parts of the question? Are your units correct?
8. Don’t Erase
Erasing takes up valuable time. Moreover, you might find that you needed that work later anyway.
If you absolutely must get rid of work on your page, simply cross it out. But be careful not to cross out good work. The graders will ignore anything that is crossed-out.
9. Practice, Practice, Practice!
Plan to complete a few practice tests in the weeks and months leading up to the real deal. A good AP Calculus test prep book includes detailed solutions which you can use as models.
10. Get Feedback
Make sure you understand what kind of work the graders are looking for.
Your teacher or a tutor can help evaluate whether your work meets the standards of the AP Calculus exam.
Hopefully these tips will help you out. Showing your math is essential for achieving a high score on the AP Calculus exams, so sharpen your pencils and get to work!
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About Shaun Ault
Shaun earned his Ph. D. in mathematics from The Ohio State University in 2008 (Go Bucks!!). He received his BA in Mathematics with a minor in computer science from Oberlin College in 2002. In addition, Shaun earned a B. Mus. from the Oberlin Conservatory in the same year, with a major in music composition. Shaun still loves music -- almost as much as math! -- and he (thinks he) can play piano, guitar, and bass. Shaun has taught and tutored students in mathematics for about a decade, and hopes his experience can help you to succeed!
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