Calculators on the AP Calculus AB Exam

 

Calculators are good—that’s what professional organizations for math teachers have decided. This is lucky for you, because it means you can use a calculator on the AP exam. In fact, on some parts of the exam, you are expected to use a calculator, a graphing calculator, to be specific. Graphing calculators have become a standard, essential part of AP Calculus. You should be using yours on a regular basis to become comfortable with it.
You’ll need your calculator for Section I, Part B (which consists of 15 multiple-choice questions) and Section II, Part A (which consists of 2 free-response questions). Let’s do the math here. This means that for 34 out of the 51 questions on the test (more than 60 percent of the exam), you cannot use a calculator. It’s not a crutch or a cure-all, even if you have a calculator that takes derivatives, computes integrals, and does your laundry. The bottom line is that you need to know calculus and know it well to succeed on the AP exam.

As a general rule, you can expect to:

• Adjust the viewing window to zoom in on a particular part of a function’s graph
• Find the zeros of a complicated function (for example, to determine where a particle is at rest)
• Evaluate a messy derivative at a specified value (for example, to find an instantaneous rate of change)
• Calculate a definite integral (for example, to find the volume of a solid of revolution)

You can bring up to two graphing calculators into the exam with you, along with whatever pro-grams they contain. You can use whatever shortcuts you’ve programmed into your calculator. To maintain the integrity of the test, you can’t take any test information out in your calculator.

There is a huge variety of graphing calculators available on the market, and their capabilities have increased as technology has advanced. Some of the newer models are much more powerful than their older, first-generation siblings. It does not really matter which particular brand or type of calculator you have, though you should make certain the calculator meets your needs. What is truly important is that you know how to use your calculator.
The AP Calculus committee works hard to develop questions that can be solved with any appropriate calculator, but it can’t develop tests that are fair to all students if the range of calculator capabilities is too large. To level the playing field, your calculator must meet a minimum performance level to ensure that you can solve all of the problems on the test. Some calculators with more advanced, complicated features are not allowed because the AP Calculus exam committee feels that they would give students who use them an unfair advantage. The trick, then, is to find a calculator that can do everything you need it to do, but not so much that it will be barred from the exam.
The people who write the test assume that your calculator can:

1. Plot a graph in the appropriate viewing window.
2. Find the zeros of a function (a technique often used to solve equations).
3. Calculate the value of the derivative of a function at a point.
4. Calculate the value of a definite integral numerically.

If you can perform these functions with your calculator, then you have enough computational power to solve any problem on the AP exam.
A non-graphing scientific calculator simply isn’t enough on the exam—they don’t give you enough computing power. You can’t use tools that provide too much computing power either, which means no computers—like laptops—and no mini-computers—including pocket organizers, pen-input devices like tablets, or anything with a QWERTY keyboard, such as a TI-92 Plus. The AP Course Description has a list of approved calculators; read it and make sure yours is on the list. Then make sure that you really know your calculator. Your calculator is your friend, so treat it like one. Use it often. Take it with you. Learn its secrets. Let it help you find answers in class and on tests.

The authors of the AP exam try to write questions that present an equal challenge to students, regardless of what sort of calculators they may have. They try, but they don’t always succeed, and it is definitely to your advantage to have the most advanced calculator you can.

Lower-level calculators cannot perform symbolic manipulations. That is, they cannot multiply or factor polynomials, differentiate or integrate symbolically, or take limits. They evaluate a polynomial at a point; they can evaluate the derivative of a function at the point, but they can’t tell you the derivative function. They can compute a numerical approximation of a definite integral, but they can’t tell you the exact value.
The TI-83 Plus is an example of a lower-level graphing calculator. A more powerful graphing calculator can perform symbolic manipulations. It can multiply and factor polynomials, differentiate and integrate symbolically, and take limits of functions. It shows the answer symbolically as an equation, when appropriate. It can show a precise answer with square roots and fractions. The TI-89 is an example of a more powerful model.


 
There are lots of other calculators that fall into each of these categories. Yours, whatever it is, is just fine as long as you know how to use it. Many calculators use similar keystrokes. The important thing is to become familiar with your calculator. If you want to perform an operation and don’t know how to do it, refer to your owner’s manual. If you’ve lost yours (have you cleaned your room lately?), most calculator companies have a free copy of the instruction manual on their websites.