The following strategies for answering the free-response questions will help you on exam day.
Keep an eye on your time.
Monitor your time carefully. As you begin Part A and Part B of the free-response section, you may wish to look over both questions for that part before starting to work on them. You are encouraged to use the allotted time to respond to all parts of all questions. All work must be written in the separate Section II: Free Response booklet.
During the second timed portion for Part B, you are permitted to continue to work on questions 1 and 2 in Part A, but you are not permitted to use a calculator during this time.
If you do work that you think is incorrect, simply put an “X” through it instead of spending time erasing it completely; crossed-out work won’t be graded.
Show your work, even when you’re using a graphing calculator.
The exam reader wants to see if you know how to solve the problem. Answers without supporting work may not receive credit in cases where supporting work is requested.
Use your graphing calculator to help you be successful on Part A of the free-response section.
You are expected to use your graphing calculator for tasks such as producing graphs and tables, evaluating functions, solving equations, and performing computations.
Your calculator must be in radian mode. Avoid rounding intermediate computations on the way to the final result. Unless otherwise specified, any decimal approximations reported in your work should be accurate to three places after the decimal point.
It may be helpful to use your graphing calculator to store information such as computed values for constants, functions you are working with, solutions to equations, and any intermediate values. Computations with the graphing calculator that use the stored information help to maintain as much precision as possible and ensure the desired accuracy in final answers.
Try to solve each part of each question.
Each free-response question is divided into parts (a), (b), and (c), with each part calling for a different response. Credit for each part is awarded independently, so you should attempt to solve each part. For example, you may receive no credit for your answer to part (a), but still receive full credit for part (b) or part (c). If the answer to a later part of a question depends on the answer to an earlier part, you may still be able to receive full credit for the later part, even if that earlier answer is incorrect.
Be sure to fully answer the question being asked.
Read each question carefully to understand what is being asked. For example, if a question asks for the maximum value of a function, do not stop after finding the x-value at which the maximum value occurs.
When asked to explain or give a reason for your answer, think about how that can be done.
Your explanation can use things such as information from the question or function representation, a mathematical definition, or a function property. The exam reader wants to know why something is true and see your mathematical reasoning in your response.
Familiarize yourself with the free-response questions from the AP Precalculus Course and Exam Description. These sample questions illustrate the four types of free-response questions and their formats. For example, question 3 (Modeling a Periodic Context) always includes a graph where you are asked to label coordinates of points and includes developing a sinusoidal function model. Question 4 (Symbolic Manipulations) always includes the same standard directions paragraph.
Look for the task verbs in the free-response questions.
Pay close attention to the task verbs used in the free-response questions. Each one directs you to complete a specific type of response. Here are the task verbs you’ll see on the exam:
- Construct/write a function/expression/equation/model: Develop an analytical representation, with and without technology, that is consistent with a scenario, data set, or other criteria.
- Describe: Develop a verbal representation that is consistent with a scenario, data set, function representation, or other criteria.
- Determine/Find/Identify: Apply appropriate methods or processes for answering a question.
- Estimate/Compare: Use a function representation to find approximate values and/or compare results.
- Explain/Give a reason/Provide a rationale/Justify: Use information from the scenario or function representation to provide reasons or rationales for solutions or conclusions.
- Express/Indicate: Provide information or a result in a desired form or include units as part of the answer to a question.
- Interpret: Describe the connection between a mathematical expression or solution and its meaning within the realistic context of a problem, often including consideration of units.
- Plot and label, sketch and label: Develop a graphical representation that is consistent with a scenario, data set, or other criteria.
- Rewrite: Apply appropriate methods to determine/find equivalent analytical representations of an expression.
- Solve: Apply appropriate methods to determine/find solutions to an equation or inequality.