United States · Grades 10 to 12 · Exam on Tuesday, May 11, 2027

AP Precalculus tutoring online

AP Precalculus is easy to misread. It is not a quick review before calculus. College Board designs it as the equivalent of a first-semester college precalculus course and organizes it around two ideas, covariation and rates of change, that run through every function type from polynomials to polar curves. The exam is 2 hours and 55 minutes on the morning of Tuesday, May 11, 2027, and more of the score comes from the no-calculator parts than from the calculator parts. This page sets out the units and their weights, the calculator rules section by section, the four free-response question types, and worked examples our teachers wrote, all from College Board's own documents checked on October 31, 2026.

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In short

AP Precalculus is a College Board Advanced Placement course designed as the equivalent of a first-semester college precalculus course. Its exam, on Tuesday, May 11, 2027, lasts 2 hours 55 minutes: 42 multiple-choice questions worth 62.5% of the score and four six-point free-response questions worth 37.5%, covering Units 1 to 3 (polynomial and rational, exponential and logarithmic, trigonometric and polar functions). Modern Age Coders tutors AP Precalculus live online, in a batch of 15 to 20 or 1-on-1, through our AP Precalculus exam prep course.

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Courses for an AP Precalculus student

The AP course first, then the algebra behind it and the calculus after it.

AP Precalculus course thumbnail

APP / 01

AP Precalculus exam prep

Units 1 to 3 in College Board's order, with calculator and no-calculator practice and free-response writing.

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High School Mathematics course thumbnail

APP / 02

High school mathematics

For a student whose Algebra 2 still slows down the precalculus.

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AP Calculus AB & BC Exam Prep, Live Online, Score 5 Goal course thumbnail

APP / 03

AP Calculus AB and BC

Where rates of change go next, for the year after.

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The exam

What is on the AP Precalculus exam, and when is it?

The 2027 exam is on Tuesday, May 11, 2027, in the morning session. It has 42 multiple-choice questions in 1 hour 45 minutes and four free-response questions in 1 hour 10 minutes, and it covers Units 1, 2 and 3 only.

AP Precalculus exam format, from AP Central (checked October 31, 2026)
SectionQuestions and timeShare of scoreCalculator
I, Part A: multiple choice29 questions, 65 minutes43.75%Not permitted
I, Part B: multiple choice13 questions, 40 minutes18.75%Graphing calculator required
II, Part A: free response2 questions, 35 minutes (FRQ 1 and 2)18.75%Graphing calculator required
II, Part B: free response2 questions, 35 minutes (FRQ 3 and 4)18.75%Not permitted
Total46 questions, 2 hours 55 minutes100%

The date and the day

College Board's 2027 schedule runs AP Exams over two weeks, May 3 to 7 and May 10 to 14, 2027. AP Precalculus is in Session 1 on Tuesday, May 11, and for most schools in the lower 48 states, Hawaii and Washington, D.C., Session 1 starts at 8 a.m. local time.

The same Tuesday has AP Statistics in Session 2, and AP Calculus AB and BC fall on Monday, May 10. A student taking two of these should plan the week, not just the morning.

What kind of exam it is

College Board describes AP Precalculus as a hybrid digital exam. It publishes test previews in the Bluebook app and a sample free-response booklet so students can see in advance how they will answer the free-response questions.

The free-response questions are each worth 6 points, and two of them, according to the AP Students page, "incorporate a real-world function modeling context". Students are expected to explain, not only to compute.

Sources: AP Central AP Precalculus exam page and 2027 AP Exam dates, and the AP Students AP Precalculus exam page, checked October 31, 2026. AP and Advanced Placement are trademarks of College Board, which is not affiliated with Modern Age Coders.

The course

What are the AP Precalculus units and how much is each worth?

Four units, three of them on the exam. On the multiple-choice section, College Board weights Unit 1 at 30 to 40 percent, Unit 2 at 25 to 40 percent and Unit 3 at 30 to 35 percent. Unit 4 is taught where states or districts require it and is not assessed.

AP Precalculus units, from the course page and the Course and Exam Description
UnitTopicsSuggested pacingMultiple-choice weighting
1. Polynomial and Rational Functions1.1 Change in Tandem to 1.14 Function Model Construction and Application6 to 8 weeks30 to 40%
2. Exponential and Logarithmic Functions2.1 Change in Arithmetic and Geometric Sequences to 2.15 Semi-log Plots6 to 9 weeks25 to 40%
3. Trigonometric and Polar Functions3.1 Periodic Phenomena to 3.15 Rates of Change in Polar Functions7 to 10 weeks30 to 35%
4. Functions Involving Parameters, Vectors, and Matrices4.1 to 4.14, ending with matrices modeling7 weeksNot assessed
The three mathematical practices and their share of the whole exam, from AP Central
PracticeWhat College Board meansExam weighting
1. Procedural and Symbolic FluencyAlgebraically manipulate functions, equations, and expressions35 to 50%
2. Multiple RepresentationsTranslate mathematical information between representations20 to 30%
3. Communication and ReasoningCommunicate with precise language, and provide rationales for conclusions30 to 40%

The two ideas under every unit

The Course and Exam Description opens Unit 1 with two concepts: covariation, "how output values change in tandem with changing input values", and rates of change, "including average rate of change, rate of change at a point, and changing rates of change". Topic 1.1 is literally called Change in Tandem.

Those ideas return for every function type. An exponential model is a function whose output changes by a constant ratio; a sinusoidal one has rates of change that repeat. Students who learn each function as a separate list of rules miss the thread the exam is built on.

Precise language is assessed

Up to 40 percent of the exam weighting goes to Communication and Reasoning, and the CED shows the standard it means with a model sentence: "On the closed interval 0 to 1, as the value of x increases, the value of y increases then decreases."

Its pool example goes further, naming inputs, outputs and units: the average rate of change of volume from 2 to 5 minutes "is 0.4 cubic meters per minute". We teach students to write like that from the first week, because the free-response scoring expects it.

Sources: AP Central AP Precalculus course page and the Course and Exam Description (PDF), whose pacing assumes 45-minute class periods five days a week for a full year; checked October 31, 2026.

Calculator rules, our arithmetic

Can you use a calculator on the AP Precalculus exam?

On some parts only. A graphing calculator is required for multiple-choice Part B and free-response Part A, and not permitted on multiple-choice Part A or free-response Part B. Adding College Board's published shares, 62.5 percent of the score is earned without a calculator.

Our sum of College Board's published score shares, by calculator rule
Calculator rulePartsShare of score (our sum)Minutes per question (our division)
Not permittedMC Part A (29 questions) and FRQ Part B (2 questions)43.75% + 18.75% = 62.5%About 2.2 for MC; 17.5 for each FRQ
Graphing calculator requiredMC Part B (13 questions) and FRQ Part A (2 questions)18.75% + 18.75% = 37.5%About 3.1 for MC; 17.5 for each FRQ

What the calculator is for

The CED is specific: "students must learn to identify zeros, points of intersection, and extrema using graphing calculator technology", and they also fit linear, quadratic, cubic and quartic regressions to data. AP Students adds that the calculator parts are answered in radian mode.

So the calculator sections are not easier versions of the others. They test whether a student can set up a model and read a graph correctly, which is its own skill and needs its own practice.

What it means for study time

Most of the marks need algebra by hand: exact values, log rules, factoring, rewriting trigonometric expressions. A student who practices everything with a calculator at their elbow is practicing for the smaller share of the exam.

We split practice the same way the exam does: hand-only sessions for symbolic work, and separate calculator sessions for modeling, regression and graph reading.

Shares and timings from the AP Central exam page; calculator uses from the Course and Exam Description; radian mode from AP Students; checked October 31, 2026. The sums and the minutes per question are our arithmetic. College Board keeps the list of approved calculators on its AP calculator policy page.

Free response, ours

What are the four AP Precalculus free-response questions?

College Board names them: Function Concepts and Modeling a Non-Periodic Context, both with a graphing calculator, then Modeling a Periodic Context and Symbolic Manipulations, both without. Each is worth 6 points. The examples below are our own, written in that style, not College Board questions.

Our periodic model, in the style of FRQ 3. A Ferris wheel seat is 5 meters above the ground at its lowest point and 45 meters at its highest, and the wheel turns once every 8 minutes. A rider boards at the lowest point at t = 0. A model is h(t) = 25 − 20 cos(πt / 4), with h in meters and t in minutes. (i) State the midline, amplitude and period. (ii) When is the rider first 35 meters up? (iii) Describe how the rate of change of h behaves on 0 ≤ t ≤ 4.

(i) Reading the model

The midline is h = 25, halfway between 5 and 45. The amplitude is 20, half of the 40-meter difference. The period is 8 minutes, since πt / 4 reaches 2π when t = 8.

(ii) Solving without a calculator

25 − 20 cos(πt / 4) = 35 gives cos(πt / 4) = −1/2. The first positive solution is πt / 4 = 2π/3, so t = 8/3 minutes, about 2 minutes 40 seconds after boarding.

(iii) The rate of change

On 0 < t < 4, h is increasing. Its rate of change increases on 0 < t < 2 and decreases on 2 < t < 4, so h is concave up and then concave down, with the fastest climb at t = 2, at the midline.

Our check: average rate of change of h over each minute (meters per minute)
Intervalh at starth at endAverage rate of change
t = 0 to 15.0010.865.86
t = 1 to 210.8625.0014.14
t = 2 to 325.0039.1414.14
t = 3 to 439.1445.005.86

How the answer should be written

Part (iii) is where most of the points sit, and the language matters. Our model answer: "On the interval 0 < t < 4, h is increasing. The average rates of change over successive one-minute intervals increase from 5.86 to 14.14 meters per minute and then decrease to 5.86, so the rate of change of h increases and then decreases." That is the CED's precise-language standard applied.

A student who writes "it goes up faster then slower" has the right idea and may not earn the reasoning point. The difference is naming the function, the interval and the units.

A symbolic example, FRQ 4 style

Our problem: solve log2(x) + log2(x − 2) = 3. Combine the logs: log2(x(x − 2)) = 3, so x(x − 2) = 8, x2 − 2x − 8 = 0 and (x − 4)(x + 2) = 0. Only x = 4 is in the domain of both logarithms; x = −2 must be rejected, with a reason.

The rejection is the point. Symbolic Manipulations questions reward a correct answer with a justified domain check, not just the algebra.

Question types and point values from the AP Central and AP Students exam pages. The Ferris wheel model, the log equation, the table and the model answers are ours, checked in Python on October 31, 2026. Past free-response questions and scoring guidelines are on AP Central's exam page; we link to them and reproduce none.

Practice set, ours

Seven AP Precalculus practice problems

One or two from each assessed unit, at exam level. Written by our teachers; answers checked in Python. Try them without a calculator first.

Our practice set
#UnitOur problemAnswer
1Unit 1What is the average rate of change of f(x) = x3 − 4x on the interval [0, 2]?0, because f(0) = f(2) = 0
2Unit 1Find all real zeros of f(x) = x3 − 4x.−2, 0 and 2
3Unit 2A geometric sequence has first term 5 and common ratio 3. What is the sixth term?5 × 35 = 1215
4Unit 2Find the inverse of f(x) = 2x − 1 + 3.f−1(x) = 1 + log2(x − 3), for x > 3
5Unit 2Solve e2x − 5ex + 6 = 0.x = ln 2 or x = ln 3
6Unit 3State the amplitude, period and midline of y = 5 sin(3x) + 2.5; 2π/3; y = 2
7Unit 3Convert the polar point r = 2, θ = π/3 to rectangular coordinates.(1, √3)

Why problem 1 is a trap

An average rate of change of 0 does not mean f is constant. On [0, 2] the cubic dips below the axis and comes back; the start and end heights happen to match. The CED separates average rate of change from rate of change at a point for exactly this reason.

A good free-response answer would say so: "the average rate of change over [0, 2] is 0, although f is not constant on that interval".

A semi-log check, Unit 2

Topic 2.15 is Semi-log Plots. Our example: for y = 3 × 2x, log y = log 3 + x log 2, so plotting log y against x gives a straight line with slope log 2, about 0.301 in base 10. A straight semi-log plot is how data reveals an exponential model.

Students meeting this for the first time often expect the curve to stay curved. Seeing the line appear is one of the more satisfying moments in the course.

All seven problems, the explanations and the semi-log example are ours. For official practice, College Board publishes past free-response questions with scoring guidelines on AP Central and test previews in Bluebook; AP Classroom progress checks are available through a student's AP class section.

A school-year plan, ours

From August to May 11, 2027

Our suggested pacing, close to the CED's week ranges. If the school is ahead or behind, we match the class, not this table.

Our AP Precalculus year
WhenFocusThe sign it is secure
August to OctoberUnit 1: rates of change, polynomials, rational functionsDescribes concavity in words and from a table of values
November to JanuaryUnit 2: exponentials, logarithms, semi-log plotsSolves log equations by hand and rejects extraneous roots
February to AprilUnit 3: trigonometric and polar functionsBuilds a sinusoidal model from a description, no calculator
Late April to May 11Full timed exams, split by calculator ruleFinishes MC Part A with time to check, and writes FRQ reasons in full

If the exam is weeks away

Sit one full practice exam in the four timed parts, then rework every free-response answer that lost a reasoning point.

Spend more of the remaining time on no-calculator work, since that is where most of the score sits.

If the course is just starting

Make sure the Algebra 2 prerequisites are solid: College Board lists linear and quadratic functions, factoring, systems of equations, exponents, radicals and complex numbers.

Our precalculus tutoring page covers non-AP precalculus, and Algebra 2 tutoring covers what comes before.

The full list

Math courses around AP Precalculus

Grouped by where the student is in the high school sequence.

I

The AP course

Grades 10 to 12

APP / AP / 01

AP Precalculus exam prep

Units 1 to 3 and the May exam.

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II

Before and alongside

Algebra and functions
III

Using the functions

Modeling and data

APP / USE / 03

Data science for teens

Exponential growth in real data.

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How lessons run

Live AP Precalculus classes through the school year

Weekdays or weekends, flexible: choose your batch, or for a very personalised plan choose 1-on-1 at your convenience, weekend mornings or weekdays.

Weekdays

After school, matched to the class unit.

Weekends

Timed practice exams in four parts.

1-on-1

One student, one teacher, one weak unit.

Two kinds of session

Hand-only practice and calculator practice, kept apart as on the exam.

Written reasons

Every free-response answer is rewritten until it names the interval and the units.

Unit by unit

Lessons follow the school's pace, so tutoring supports the class rather than competing with it.

Original problems

Ours, in College Board style; official released questions are for students to try themselves.

Every US time zone

Live online, scheduled around the school day.

Batch size

Fifteen to twenty students, or one student alone.

Student work

Projects from our students

Work our learners have published across math, programming and AI. The student labs page shows more.

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Fees

Schools order AP Exams through College Board; our monthly fee is only for tutoring. Families can start at any unit and stop after May 11.

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Questions from parents

AP Precalculus: what students and parents ask

When is the AP Precalculus exam in 2027?

College Board schedules it for Tuesday, May 11, 2027, in Session 1. For most US schools, Session 1 starts at 8 a.m. local time.

How long is the AP Precalculus exam?

2 hours and 55 minutes: 42 multiple-choice questions in 1 hour 45 minutes, then four free-response questions in 1 hour 10 minutes.

What units are on the AP Precalculus exam?

Units 1, 2 and 3: polynomial and rational functions, exponential and logarithmic functions, and trigonometric and polar functions. Unit 4, on parameters, vectors and matrices, is not assessed.

Do I need a graphing calculator for AP Precalculus?

Yes. A graphing calculator is required for multiple-choice Part B and free-response Part A, in radian mode, and not permitted on the other two parts. College Board lists approved models on its calculator policy page.

How much of the exam is without a calculator?

Adding College Board's published shares, multiple-choice Part A (43.75 percent) and free-response Part B (18.75 percent) make 62.5 percent of the score with no calculator allowed.

What are the free-response questions on AP Precalculus?

Four, each worth 6 points: Function Concepts, Modeling a Non-Periodic Context, Modeling a Periodic Context and Symbolic Manipulations. The first two allow a graphing calculator; the last two do not.

Is AP Precalculus the same as regular precalculus?

College Board designs it as the equivalent of a first-semester college precalculus course, with a set framework and an end-of-course exam. Regular precalculus varies by school and has no AP Exam.

Can AP Precalculus earn college credit?

It can, depending on the college. College Board says qualifying scores may earn credit, placement or both, and its AP Credit Policy Search shows each college's rule.

What should my child know before AP Precalculus?

College Board lists the Algebra 1, Geometry and Algebra 2 sequence, including quadratics, factoring, right-triangle trigonometry, systems of equations, exponent rules, radicals and complex numbers.

Which days and times can my child take classes?

Weekdays or weekends, flexible: choose your batch, or for a very personalised plan choose 1-on-1 at your convenience, weekend mornings or weekdays.

Are you affiliated with College Board?

No. Modern Age Coders is an independent tutoring school. AP and Advanced Placement are College Board trademarks, and College Board has no connection with our classes.

Elsewhere on this site

More high school math help

The courses on either side of AP Precalculus, and help by grade.

Precalculus tutoring

For non-AP precalculus courses.

AP Calculus tutoring

AB and BC, the year after.

AP Statistics tutoring

The other AP exam on May 11.

Algebra 2 tutoring

The prerequisite College Board lists.

11th grade math tutor

The usual year for AP Precalculus.

10th grade math tutor

For students taking it early.

Related pages in this guide

Part of the guide: US math placement and college readiness tests

High school math courses

School placement and growth tests

PSAT and PreACT

College placement and credit

More guides: US state math tests by state · US gifted and selective school tests · Homeschool and school math curricula guide · US math and coding competitions guide

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