In my final post on reviewing for the AP Calculus exams I return to calculator use.
I hope everyone has been using calculators all year long. (My opinion is that students should be given a CAS calculator, or CAS computer program, or now even an iPad CAS app on the first day of Algebra 1 before they get their books – or earlier. But we’ll save that for another post.)
The exam will not instruct students when or if to use a calculator on a particular question. Sometimes the multiple-choice answers will provide a big hint (if the choices are decimals), other times not. On the free-response questions if the problem can be done by calculator it is expected that students will use their calculator – they don’t have to, but there is no credit for finding an antiderivative or a derivative by hand. It is the numerical answer that counts.
Here again is what students are allowed to do on the exams with their calculator without showing any additional work.
- Graph a function in a window. They may have to determine the window themselves.
- Solve an equation. This is usually best done by graphing both sides and finding the point(s) of intersection, but any equation solving routine in the calculator may be used.
- Find the numerical value of a derivative at a point.
- Evaluate a definite integral.
For the last three items students should write what they are doing on their paper. That is, write the equation, the definite integral or followed by the number from their calculator. Use standard notation not calculator syntax.
For anything else, the work must be shown. Calculators can find extreme values, but readers will look for the appropriate “calculus” and not just the answer. In fact, a correct answer with no supporting work may not receive any credit.
Another handy skill is to be able to store and recall the numbers found without retyping them on their calculator. This saves time, students are less likely to make a typing mistake, and it avoids round off error.
Answers from calculators should be correct to three places after the decimal point. This does not mean they must be rounded or truncated; more places may be given as long as the first three are correct.
Remember that arithmetic simplification is not required. Only answers from calculators need to be given as decimals. If the computation gives 1 + 1, or or ½ + cos(3) or then the answer may be left that way. This also applies to a long expression resulting from a Riemann sum. Once the answer consists of all numbers, stop! You cannot make the answer any better and if you make a mistake or type the wrong key, then the final answer will be wrong and the point will be lost.
Be careful not to round too soon. If, for example, a student find the limits of integration and rounds them to three places to write on their paper, they will have earned the point given for limits of integration. BUT if these rounded values are then used to compute the integral and the rounding causes the final answer to not be correct to three places then they will lose the answer point.
Finally, get a copy of the directions for the two parts of the exam and go over them with your students before the test. Be sure students understand them.
Good luck to your students on the exam. Nah, luck has nothing to do with it. You prepared them well, they will do well.