Section II is four free-response questions worth 6 points each, 37.5 percent of the exam score. The four are fixed task types that appear in the same order every year, drawn only from Units 1, 2, and 3. Two of them sit in a real-world modeling context, and the section splits down the middle by calculator: Part A (Questions 1 and 2) requires a graphing calculator, Part B (Questions 3 and 4) allows none. Points come from correct work as much as correct answers, so show every step.
Questions
4
6 points each
Time
70 min
35 per part
Weighting
37.5%
of the exam score
Content
Units 1-3
Unit 4 excluded
The four task types
What each question asks
1
Function Concepts
Units 1-2 · Part A · Graphing calculator · No context
A pure, context-free question on the behavior of polynomial, rational, exponential, or logarithmic functions. You use the calculator to graph, evaluate, and find zeros or intersections, then reason about what the function is doing.
Read behavior precisely: increasing and decreasing intervals, concavity, extrema, zeros, and asymptotes are all fair game.
Use the calculator's strengths: real zeros and intersection points are meant to be found on the device, not by hand.
Answer the question asked. A request to justify wants a reason tied to the function's behavior, not just a recomputed number.
2
Modeling a Non-Periodic Context
Units 1-2 · Part A · Graphing calculator · Real-world context
Build and use a non-periodic model, typically polynomial, rational, exponential, or logarithmic, for a real situation. This is where data modeling and regression on the calculator earn their keep, followed by interpreting the model in the context's own units.
Fit with the calculator when the question gives data, then state the model with its parameters.
Carry the units through every answer, and read rates of change and predicted values back into the context.
Respect the domain the context imposes, and flag when a prediction runs past the data the model was built on.
3
Modeling a Periodic Context
Unit 3 · Part B · No calculator · Real-world context
Build and use a sinusoidal model for a periodic situation such as a rotating wheel, a tide, or a daylight cycle, entirely by hand. Amplitude, midline, period, and phase come from the context, and every value is exact.
Extract the parameters carefully: amplitude is half the swing (from the radius, not the diameter), the midline is the center height, and the period is the time for one full cycle.
Pick the form the starting position dictates: starting at a maximum points to cosine; starting at the midline points to sine.
Work in radians and keep values exact, since no calculator is available here.
4
Symbolic Manipulations
Units 2-3 · Part B · No calculator · No context
Pure algebra: rewrite expressions, prove equivalences, and solve equations across exponential, logarithmic, and trigonometric functions, all by hand. This is the fluency question, where the log and trig properties either serve you or trip you.
Apply the properties exactly: a log of a sum does not split, and a trig function does not distribute over addition.
Check for extraneous solutions when you solve logarithmic and trigonometric equations, and keep every solution in a given interval.
Show the manipulation. The points are in the steps, so a correct final line without the work in between can still lose credit.
Earning the points
What the rubric rewards
Show all of your work. Your response is scored on the correctness and completeness of your supporting work as well as the answer. Answers without supporting work may not receive credit where work is requested.
Do not round early. Avoid rounding intermediate computations. Unless a question says otherwise, report decimal approximations accurate to three places after the decimal point.
Store, do not retype. On the calculator questions, storing constants, functions, and solutions preserves precision far better than copying rounded numbers back in by hand.
Stay in radian mode for the whole exam, and keep periodic-model work exact on the no-calculator Part B.
Interpret in context. On the two modeling questions, an answer is not finished until it is stated in the situation's units and reads as a sentence a person could act on.
Justify when asked. Communication and Reasoning is 30 to 40 percent of the exam. A justification names the specific feature of the function or model that forces the conclusion.
The fastest way to stop losing FRQ points
Most free response points are lost to a small set of documented misconceptions: splitting a log over addition, reading amplitude off the diameter, keeping an extraneous root, or shifting a graph the wrong way. Diagnose which ones are costing you, then drill only those.
College Board publishes free response questions with scoring guidelines and sample student responses. Working released questions against the rubric is the single best way to learn where the points actually sit. Find them on the AP Precalculus exam page, and use the Course and Exam Description for the full framework behind each question type.
Common questions
FAQ
How many free response questions are on AP Precalculus?
Four, each worth 6 points, for 37.5 percent of the exam score. They are four fixed task types in a fixed order: Function Concepts, Modeling a Non-Periodic Context, Modeling a Periodic Context, and Symbolic Manipulations.
Which FRQs allow a calculator?
Part A, which is Questions 1 and 2, requires a graphing calculator and gets 35 minutes. Part B, which is Questions 3 and 4, allows no calculator and gets another 35 minutes. Keep the calculator in radian mode.
What content do the AP Precalculus FRQs cover?
Only Units 1, 2, and 3. Question 1 draws on Units 1 and 2, Question 2 on Units 1 and 2 in a modeling context, Question 3 on Unit 3 in a periodic context, and Question 4 on Units 2 and 3. Unit 4 is not assessed.
How precise do my decimal answers need to be?
Unless a question specifies otherwise, report decimal approximations accurate to three places after the decimal point, and avoid rounding intermediate computations along the way. Storing values in your calculator keeps the final result precise.
Do I lose points for a right answer with no work?
You can. Responses are scored on the correctness and completeness of the supporting work as well as the answer, and answers without supporting work may not receive credit in cases where work is requested. Show the steps.
