How to Approach Each Question Type on the AP Calculus Exam (page 2)

The Multiple-Choice Questions

• There are 45 multiple-choice questions for both AP Calculus AB and BC exams. These questions are divided into Section 1-Part A which consists of 27 questions for which the use of a calculator is not permitted, and Section 1-Part B with 17 questions, for which the use of a graphing calculator is allowed. The multiple-choice questions account for 50% of the grade for the whole test.

• Do the easy questions first because all multiple-choice questions are worth the same amount of credit. You have 55 minutes for the 27 questions in Section I Part A and 50 minutes for the 17 questions in Section I Part B. Do not linger on any one question. Time yourself accordingly.

• There is no partial credit for multiple-choice questions, and you do not need to show work to receive credit for the correct answer. TIP

• Read the question carefully. If there is a graph or a chart, look at it carefully. For example, be sure to know if the given graph is that of f (x ) or f '(x ). Pay attention to the scale of the x and y axes, and the unit of measurement.

• If you can eliminate some of the given choices, guess. The odds are in your favor for getting a higher score.

• If you have no clue as to what the question is about, leave it blank. There is a penalty for an incorrect answer. TIP

• If a question involves finding the derivative of a function, you must first find the derivative, and then see if you need to need to do additional work to get the final answer to the question. For example, if a question asks for an equation of the tangent line to a curve at a given point, you must first find the derivative, evaluate it at the given point (which gives you the slope of the line), and then proceed to find an equation of the tangent line. For some questions, finding the derivative of a given function (or sometimes, the antiderivative), is only the first step to solving the problem. It is not the final answer to the question. You might need to do more work to get the final answer. STRATEGY

• Sometimes, it is easier to work backward by trying each of the given choices as the final answer. Often, you will able to eliminate some of the given choices quickly.

• If a question involves decimal numbers, do not round until the final answer, and at that point, the final answer is usually rounded to 3 decimal places. Look at the number of decimal places of the answers in the given choices.

• Trust your instincts. Usually your first approach to solving a problem is the correct one.

The Free-Response Questions

• There are 6 free-response questions, divided into Section 2-PartAconsisting of 3 questions which allow the use of a calculator, and Section 2-Part B with 3 questions which do not permit the use of a calculator. The 6 free-response questions account for 50% of the grade for the whole test.

• Read, Read, Read. Read the question carefully. Know what information is given, what quantity is being sought, and what additional information you need to find in order to answer the question. TIP

• Always show a sufficient amount of work so that your line of reasoning is clear. This is particularly important in determining partial credit. In general, use complete sentences to explain your reasoning. Include all graphs, charts, relevant procedures, and theorems. Clearly indicate all the important steps that you have taken in solving the problem. A correct answer with insufficient work will receive minimal credit.

• When appropriate, represent the given information in calculus notations. For example, if it is given that the volume of a cone is decreasing at 2 cm3 per second, write dV dt = − 2 cm3sec. Similarly, represent the quantity being sought in calculus notations. For example, if the question asks for the rate of change of the radius of the cone at 5 seconds, write “Find dr dt at t =5 sec.” TIP

• Do not forget to answer the question. Free-Response questions tend to involve many computations. It is easy to forget to indicate the final answer. As a habit, always state the final answer as the last step in your solution, and if appropriate, include the unit of measurement in your final answer. For example, if a question asks for the area of a region, you may want to conclude your solution by stating that “The area of the region is 20 square units.”

• Do the easy questions first. Each of the 6 free-response questions is worth the same amount of credit. There is no penalty for an incorrect solution.

• Pay attention to the scales of the x and y axes, the unit of measurement, and the labeling of given charts and graphs. For example, be sure to know whether a given graph is that of f (x ) or f '(x ).

• When finding relative extrema or points of inflection, you must show the behavior of the function that leads to your conclusion. Simply showing a sign chart is not sufficient. TIP

• Often a question has several parts. Sometimes, in order to answer a question in one part of the question, you might need the answer to an earlier part of the question. For example, to answer the question in part (b), you might need the answer in part (a). If you are not sure how to answer part (a), make an educated guess for the best possible answer and then use this answer to solve the problem in part (b). If your solution in part (b) uses the correct approach but your final answer is incorrect, you could still receive full or almost full credit for your work.

• As with solving multiple-choice questions, trust your instincts. Your first approach to solving a problem is usually the correct one.

Tips for Taking the Exam

General Tips

TIP

• Write legibly.

• Label all diagrams.

• Organize your solution so that the reader can follow your line of reasoning.

• Use complete sentences whenever possible. Always indicate what the final answer is.

More Tips

• Do easy questions first.

• Write out formulas and indicate all major steps.

• If you can eliminate some of the choices in a multiple-choice question, guess.

• Leave a multiple-choice question blank if you have no clue what the answer is.

• Be careful to bubble in the right grid, especially if you skip a question.

• Move on. Don’t linger on a problem too long.

• Go with your first instinct if you are unsure.

Still More Tips

• Indicate units of measure.

• Simplify numeric or algebraic expressions only if the question asks you to do so.

• Carry all decimal places and round only at the end. • Round to 3 decimal places unless the question indicates otherwise.

• Watch out for different units of measure, e.g., the radius, r, is 2 feet, find dr dt in inches per second. •

• Use calculus notations and not calculator syntax 

• Use only the four specified capabilities of your calculator to get your answer: plotting graph, finding zeros, calculating numerical derivatives, and evaluating definite integrals. All other built-in capabilities can only be used to check your solution.

• Answer all parts of a question from Section II even if you think your answer to an earlier part of the question might not be correct.

Enough Already . . . Just 3 More Tips

• Be familiar with the instructions for the different parts of the exam before the day of the exam. Visit the College Board website at: www.collegeboard.com/ap for more information.

• Get a good night sleep the night before.

• Have a light breakfast before the exam.