AP Precalculus Exam Guide and Score Calculator

AP Precalculus is the newest maths course in the AP catalogue, introduced for the 2023-24 school year, and it is not the precalculus course most parents remember. It is organised around function families and how they behave, and the exam rewards describing behaviour in words at least as much as it rewards computing values. This guide covers the units, the exam structure, the free-response question types, how to estimate a score, and an honest read on difficulty.

(AI-Math is independent and has no affiliation with the College Board. The Course and Exam Description is revised periodically; verify unit weightings and format against the current official version.)

The four units

Unit	Topic	Approx. exam weight
1	Polynomial and rational functions	30–40%
2	Exponential and logarithmic functions	27–40%
3	Trigonometric and polar functions	30–35%
4	Functions involving parameters, vectors, and matrices	Not assessed on the exam

Unit 4 is real course content that teachers may cover, but it is not tested. If exam preparation is your goal, your time belongs in units 1 to 3.

Unit 1 is about polynomial and rational behaviour: rates of change, extrema, end behaviour, zeros and multiplicity, asymptotes, holes, and transformations. The idea of "rate of change of the rate of change" appears here and is deliberate preparation for calculus. Use the polynomial calculator and the asymptote finder while you build fluency.

Unit 2 covers arithmetic and geometric sequences, exponential models, logarithms, log properties, semi-log plots, and inverse functions. Semi-log plots are the topic students most often meet for the first time: if data is linear on a semi-log plot, the underlying model is exponential. Practise log manipulation on the logarithm calculator.

Unit 3 covers the unit circle, sinusoidal modelling with amplitude, period, phase and midline, the six trigonometric functions, inverse trig, identities, and polar functions. Sinusoidal modelling from a described context is the highest-yield single skill in the course. Our unit circle reference and trig equation solver cover the mechanics.

Exam format and length

The exam is 3 hours long.

Section I — Multiple choice, 40 questions, 120 minutes, 50%

• Part A: 28 questions, 80 minutes, no calculator
• Part B: 12 questions, 40 minutes, graphing calculator required

Section II — Free response, 4 questions, 60 minutes, 50%

• Part A: 2 questions, 30 minutes, graphing calculator required
• Part B: 2 questions, 30 minutes, no calculator

Each free-response question is worth 6 points, so the section totals 24 points.

The four free-response question types

The FRQ set has a fixed design, which makes it unusually easy to prepare for. Every year you get one of each:

1. Question 1 (calculator): function concepts. You are given a table, a graph or an equation and asked about rates of change, average rate of change over an interval, and behaviour. Answers must be justified with reference to the given representation.
2. Question 2 (calculator): modelling a non-periodic context. Usually exponential or polynomial. You construct a model from data or a description, use it to predict, and interpret a value with correct units.
3. Question 3 (no calculator): modelling a periodic context. Build a sinusoidal function from a described situation — amplitude from the range of values, midline from the average, period from the repeat interval, phase from the starting point.
4. Question 4 (no calculator): symbolic manipulation. Algebraic work with functions: composition, inverses, transformations, solving equations exactly.

Two habits raise FRQ scores more than anything else. First, always answer with units and in context — "the population is increasing by about 340 fish per year" rather than "340". Second, justify from the representation you were given; if the data is a table, cite the table values you used.

Estimating your score

There is no official published conversion, and the cut points shift a little each year with the difficulty of the form. But the structure gives you a defensible estimate, and this is what any "AP Precalculus score calculator" is doing under the bonnet.

Both sections are worth 50%, so:

\text{composite %} = 0.5 \times \frac{\text{MC correct}}{40} \times 100 + 0.5 \times \frac{\text{FRQ points}}{24} \times 100

Then apply approximate cut points, which for AP maths exams have historically sat near:

Composite	Likely score
70%+	5
57–69%	4
43–56%	3
30–42%	2
below 30%	1

Worked example. You get 27 of 40 multiple choice and 15 of 24 free-response points. Section I contributes $0.5 \times (27/40) \times 100 = 33.75$, Section II contributes $0.5 \times (15/24) \times 100 = 31.25$, for a composite of 65% — comfortably in 4 territory and a few points short of a 5.

Treat this as a planning tool, not a prediction. Its real use is showing you the trade: on this exam, 3 extra free-response points are worth about the same as 5 extra multiple-choice questions, because there are fewer FRQ points in total. That makes the free-response section the cheaper place to gain.

Is AP Precalculus hard?

Honestly, no — it is one of the more approachable AP maths courses, and the score distributions from its first administrations have been favourable, with roughly three quarters of candidates earning a 3 or higher. Check the College Board's current published distribution rather than relying on that figure.

Three reasons it is manageable:

• Most of the content is a normal precalculus course you would take anyway, so there is little extra ground to cover.
• Unit 4 is not assessed, which removes the least familiar material from the exam.
• The FRQ design is fixed, so you can practise exactly four question types.

The one place students are genuinely caught out is the verbal justification. The exam repeatedly asks you to describe behaviour: is the rate of change increasing or decreasing, and how do you know? That is a writing skill, and a student who can compute everything but cannot write a clean two-sentence justification will land at a 3.

Is AP Precalculus worth taking?

If your school offers it and you are heading toward AP Calculus, yes — it is the same content you would take anyway, with the possibility of a score to show for it. Do not expect university credit: many institutions do not grant credit for precalculus at all, and where they do it usually only satisfies a placement requirement rather than a degree requirement. The value is preparation and demonstrated rigour, not credit.

How to pass, in four weeks

1. Week 1. Do a set of no-calculator multiple choice. Every miss goes into one of three buckets: algebra fluency, function behaviour vocabulary, or trigonometry recall.
2. Week 2. Rebuild the weakest bucket. For algebra fluency this means daily short drills, not long problem sets.
3. Week 3. One of each FRQ type per sitting, twice, graded against the published scoring guidelines. Write full sentences for every justification.
4. Week 4. Two full timed exams with the correct calculator restrictions, plus a final pass over the unit circle and log properties, which are the two things most often forgotten under pressure.

Related: AP Calculus AB and BC complete exam guide