AP Calculus BC Free-Response Questions Strategies
The AP Calculus BC Free-Response Questions Strategies
There are 6 free-response questions in Section II-Part A consisting of 2 questions that allow the use of a calculator, and Part B with 4 questions that 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.
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 cm3/sec. 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.”
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.
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.