AP Calculus ABAP Exams

AP Calculus AB Review: The Most-Tested Questions, Unit by Unit

Sigma Prep

Math Instructor · 10+ Years Experience

October 24, 2026·14 min read

Key takeaways

Unit weight: Units 5 and 6 carry the most multiple choice (20.6% and 19.4% of the 315 official questions, 2012–2018); Unit 8 carries the most free response (28.1% of the points, 2012–2026).
Top types: separable differential equations, position from velocity, amounts from a rate and Riemann sums from a table.
Practice: the free-response work multiple choice never asks for: justifications, slope-field sketches and what an integral means, with units.

We sorted every public official AP Calculus AB question by what it actually asks: 760 multiple choice questions from 17 released and practice exams (1969–2018) and 416 free-response questions (1969–2026). Then we ranked the question types by how much of a recent exam they make up. The short version: 29 question types make up half the exam, the free-response section leans hard on Unit 8, and widely used practice material leans toward limits and derivative rules, not toward what the exam rewards.

Below are the top 20 types, each with its numbers and one practice problem we wrote ourselves.

The 20 most-tested question types

Ranked by how much of a recent exam they make up. Each type lists its unit, its share of the exam, how many of the 7 practice exams from 2012–2018 had it in multiple choice, and how many of the 86 free-response questions from 2012–2026 used it in at least one part. These 20 add up to about 39% of the exam.

1. Separable differential equation with an initial condition

Separate the variables, integrate both sides, use the given point to find $C$ , then solve for $y$ .

Unit 74.6% of the exam6 of 7 practice exams12 FRQs since 2012

Try it

Solve

\frac{dy}{dx} = xy^2

with

y(0) = 1

Solution

$y = \frac{2}{2 - x^2}$ .

Practice: Separable Differential Equations worksheet · AP Unit 7 worksheet

2. Position or velocity from an initial condition

Start at a known position and add the integral of velocity.

Unit 82.9% of the exam5 of 7 practice exams11 FRQs since 2012

Try it

A particle has velocity

v(t) = 3t^2 - 4t

and

x(1) = 5

. Find

x(3)

Solution

$5 + \int_1^3 v(t)\,dt = 15$ .

Practice: Displacement and Distance worksheet · AP Unit 8 worksheet

3. Amount from a rate in context

A rate is given (water, people, cars); find how much there is at a later time. Usually a calculator question.

Unit 82.7% of the examall 7 practice exams11 FRQs since 2012

Try it

Water flows into a tank at

r(t) = 20 + 5\sin\left(\frac{t}{2}\right)

liters per minute. The tank holds 100 liters at

t = 0

. How much does it hold at

t = 10

Solution

$100 + \int_0^{10} r(t)\,dt \approx 307.163$ liters.

Practice: Net Change worksheet · AP Unit 8 worksheet

4. Riemann or trapezoidal sum from a table

Approximate an integral from a table of values, often with unequal intervals.

Unit 62.3% of the exam5 of 7 practice exams15 FRQs since 2012, on every exam from 2012 to 2026

Try it

Selected values of

R(t)

are in the table.

$t$	0	2	5	9
$R(t)$	4	7	6	10

Use a trapezoidal sum with these four points to estimate

\int_0^9 R(t)\,dt

Solution

$11 + 19.5 + 32 = 62.5$ .

Practice: Riemann Sums From a Table worksheet · AP Unit 6 worksheet

5. Displacement and total distance

Displacement is $\int v$ ; total distance is $\int |v|$ , so split where $v$ changes sign.

Unit 82.1% of the exam6 of 7 practice exams8 FRQs since 2012

Try it

v(t) = t^2 - 4t + 3

[0, 3]

. Find the displacement and the total distance.

Solution

displacement 0, total distance $\frac{8}{3}$ .

Practice: Displacement and Distance worksheet · AP Unit 8 worksheet

6. Average value of a function

The integral divided by the length of the interval.

Unit 82.0% of the exam3 of 7 practice exams9 FRQs since 2012

Try it

Find the average value of

f(x) = 3x^2 - 2x

[1, 3]

Solution

$\frac{18}{2} = 9$ .

Practice: Average Value of a Function worksheet · AP Unit 8 worksheet

7. Tangent-line (linear) approximation

Use the tangent line at a known point to estimate a nearby value, often from a differential equation.

Unit 41.9% of the exam3 of 7 practice exams10 FRQs since 2012

Try it

\frac{dy}{dx} = x + y

and

y(1) = 2

. Use the tangent line at

x = 1

to approximate

y(1.2)

Solution

slope 3, so $y(1.2) \approx 2 + 3(0.2) = 2.6$ .

Practice: Linear Approximation worksheet · AP Unit 4 worksheet

8. Particle at rest or changing direction

At rest where $v = 0$ ; changing direction only where $v$ also changes sign.

Unit 41.8% of the exam3 of 7 practice exams8 FRQs since 2012

Try it

x(t) = t^3 - 6t^2 + 9t

for

t \ge 0

. When does the particle change direction?

Solution

$v = 3(t - 1)(t - 3)$ changes sign at $t = 1$ and $t = 3$ .

Practice: Motion Along a Line worksheet · AP Unit 4 worksheet

9. Area between curves (integrating in $x$ )

Find where the curves meet, then integrate top minus bottom.

Unit 81.8% of the exam2 of 7 practice exams6 FRQs since 2012

Try it

Find the area between

y = x

and

y = x^2 - 2x

Solution

they meet at $x = 0$ and 3; $\int_0^3 (3x - x^2)\,dx = \frac{9}{2}$ .

Practice: Area Between Two Curves worksheet · AP Unit 8 worksheet

10. Equation of a tangent line

Point plus slope from the derivative.

Unit 21.7% of the exam4 of 7 practice exams13 FRQs since 2012

Try it

Write the tangent line to

f(x) = x^3 - 2x

x = 2

Solution

$y - 4 = 10(x - 2)$ .

Practice: Tangent and Normal Lines worksheet · AP Unit 2 worksheet

11. Volume with square or rectangle cross sections

Integrate the area of one cross section across the region.

Unit 81.7% of the exam3 of 7 practice exams9 FRQs since 2012

Try it

The base is the region under

y = \sqrt{x}

from

x = 0

to 4. Cross sections perpendicular to the

x

-axis are squares. Find the volume.

Solution

$\int_0^4 x\,dx = 8$ .

Practice: Known Cross Sections worksheet · AP Unit 8 worksheet

12. Concavity and inflection from the graph of $f'$

$f$ is concave up where $f'$ is increasing; inflection points are where $f'$ switches between increasing and decreasing.

Unit 51.6% of the exam4 of 7 practice exams6 FRQs since 2012

Try it

f'

increases on

(0, 2)

and decreases on

(2, 5)

. Where is

f

concave up, and where does it have an inflection point?

Solution

concave up on $(0, 2)$ ; inflection at $x = 2$ .

Practice: Reading f From the Graph of f′ worksheet · AP Unit 5 worksheet

13. Velocity and acceleration from position

Differentiate once for velocity, twice for acceleration.

Unit 41.6% of the exam4 of 7 practice exams11 FRQs since 2012

Try it

s(t) = t^3 - 3t^2 + 2

for

t \ge 0

. Find the acceleration when the velocity is 9.

Solution

$3t^2 - 6t = 9$ gives $t = 3$ , and $a(3) = 12$ .

Practice: Motion Along a Line worksheet · AP Unit 4 worksheet

14. Behavior of $g(x) = \int_a^x f(t)\,dt$

Since $g' = f$ , read the graph of $f$ as the derivative of $g$ .

Unit 61.6% of the exam4 of 7 practice exams7 FRQs since 2012

Try it

The graph of

f

0 \le x \le 7

is shown.

Let

g(x) = \int_0^x f(t)\,dt

. Where does

g

have a relative maximum?

Solution

$x = 3$ , where $g' = f$ changes from positive to negative.

Practice: Accumulation Functions worksheet · AP Unit 6 worksheet

15. Related rates with a given equation

The equation is given; differentiate with respect to $t$ and plug in.

Unit 41.5% of the exam3 of 7 practice exams8 FRQs since 2012

Try it

xy = 12

, and

x

increases at 3 units per second. Find

\frac{dy}{dt}

when

x = 4

Solution

$4\frac{dy}{dt} + 3(3) = 0$ , so $\frac{dy}{dt} = -\frac{9}{4}$ .

16. Absolute extrema from the graph of $f'$ and areas

Check the endpoints and the critical points, using areas under $f'$ to get the values of $f$ .

Unit 51.5% of the exam2 of 7 practice exams9 FRQs since 2012

Try it

f(0) = 5

f'

is positive on

(0, 2)

, enclosing area 3 with the

x

-axis, and negative on

(2, 6)

, enclosing area 7. Find the absolute minimum of

f

[0, 6]

Solution

candidates are $f(0) = 5$ , $f(2) = 8$ , $f(6) = 1$ , so the minimum is 1.

Practice: Reading f From the Graph of f′ worksheet · AP Unit 5 worksheet

17. Implicit differentiation

Differentiate both sides, treating $y$ as a function of $x$ , then solve for $\frac{dy}{dx}$ .

Unit 31.5% of the exam5 of 7 practice exams5 FRQs since 2012

Try it

Find

\frac{dy}{dx}

for

x^2 + xy + y^2 = 7

(1, 2)

Solution

$-\frac{4}{5}$ .

Practice: Implicit Differentiation worksheet · AP Unit 3 worksheet

18. Derivative of an accumulation function (FTC)

The derivative of $\int_a^{u(x)} f(t)\,dt$ is $f(u(x)) \cdot u'(x)$ .

Unit 61.5% of the exam4 of 7 practice exams12 FRQs since 2012

Try it

g(x) = \int_2^{3x} \sqrt{t^2 + 1}\,dt

. Find

g'(1)

Solution

$3\sqrt{10}$ .

Practice: The Second Fundamental Theorem worksheet · AP Unit 6 worksheet

19. Product or quotient rule from a table

Same rules, but the values come from a table or graph instead of formulas.

Unit 21.5% of the exam4 of 7 practice exams7 FRQs since 2012

Try it

f(2) = 3

f'(2) = -1

g(2) = 4

g'(2) = 5

, and

h = f \cdot g

. Find

h'(2)

Solution

$(-1)(4) + (3)(5) = 11$ .

Practice: Derivatives From a Table worksheet · AP Unit 2 worksheet

20. Chain rule with trig, exponential and log functions

Derivative of the outside, times the derivative of the inside.

Unit 31.4% of the exam4 of 7 practice exams3 FRQs since 2012

Try it

y = e^{\sin 3x}

. Find

\frac{dy}{dx}

x = 0

Solution

$3\cos(3x) \cdot e^{\sin 3x} = 3$ .

Practice: The Chain Rule worksheet · AP Unit 3 worksheet

Which units are tested most

College Board gives a weight range for each unit, but those ranges describe the multiple choice section only. Here is how the recent exams compare.

Unit	CED weight (MC)	Official MC, 2012–18	FRQ points, 2012–26
1. Limits and Continuity	10–15%	10.5%	2.5%
2. Derivative definition and basic rules	10–15%	14.0%	8.0%
3. Chain rule, implicit, inverse	5–10%	8.6%	3.6%
4. Contextual applications of derivatives	10–15%	8.9% (below)	19.5%
5. Analytical applications of derivatives	15–20%	20.6% (above)	15.0%
6. Integration and accumulation	15–20%	19.4%	13.5%
7. Differential equations	5–10%	4.4% (below)	9.8%
8. Applications of integration	10–15%	13.7%	28.1%

The multiple choice column is the 315 questions on the 7 practice exams from 2012–2018. The free-response column is the share of scoring points on the 2012–2026 exams.

Unit 5 runs at or just above its range in multiple choice. Increasing and decreasing, extrema, concavity and the “which graph is $f'$ ” questions are the biggest block of the section.
Units 4 and 7 run below their ranges in multiple choice, then make up for it in free response: Unit 4 (motion and rates in context) takes 19.5% of FRQ points and Unit 7 takes 9.8%.
Unit 8 is the heavyweight of free response. Accumulation, motion, area and volume take 28.1% of FRQ points, more than any other unit.
Limits are a multiple choice topic. Unit 1 is about a tenth of the multiple choice but only 2.5% of FRQ points.

What’s rising and what’s fading since 2012

We compared each type’s share of the recent exams (multiple choice 2012–18, free response 2012–26) with its share across all years. We call a type Rising when its recent share is at least double its long-run share, and Fading when it is under half. Moves smaller than that are labeled Steady, even when they point clearly one way.

Question type	Since 2012	All years	Label
Riemann or trapezoidal sum from a table	2.79%	1.59%	Steady, up
Amount from a rate in context	3.17%	2.33%	Steady, up
Tangent-line approximation	2.20%	1.23%	Steady, up
Product or quotient rule from a table	2.26%	0.85%	Rising
Related rates with a given equation	1.98%	0.95%	Rising
Estimate a derivative from a table or graph	1.75%	0.82%	Rising
Speeding up or slowing down	1.73%	0.63%	Rising
L’Hospital’s Rule	1.17%	0.40%	Rising
Equation of a tangent line	1.26%	3.16%	Fading
Area between curves	1.49%	3.16%	Fading
Washer method	0.16%	1.47%	Fading
Optimization	0.16%	1.37%	Fading
Related rates: circles and spheres	0.16%	0.96%	Fading
Related rates: cones and similar triangles	0.16%	0.75%	Fading

Things to take from it:

Tables and accumulation are up. A table-based Riemann or trapezoidal sum has been in at least one free-response question on every exam from 2012 to 2026.
Related rates has split in two. The geometry kind (spheres, cones and similar shapes) is fading. The kind where the equation is given to you is rising.
Optimization is nearly gone. It had a single multiple choice item on the 2012–2018 practice exams.
Tangent-line equations are fading on the exam but not in classrooms. Teacher review material written since 2019 still drills them heavily.

The newest exams, read with care. Comparing the free-response questions from 2019–2026 with those from 1998–2018 points the same way. “Is the speed increasing or decreasing?” went from 6% of questions to 16%, the derivative of an accumulation function from 12% to 20%, L’Hospital’s Rule from 1% to 9%, and table Riemann sums from 8% to 14%. The classic two-rate tank problem (water in, water out) went from 8% to 2%, though finding the greatest or least amount from a rate model was still part of the calculator question in 2019, 2022 and 2025. But there are only 44 free-response questions since 2019, so a single question moves a share by about 2 points. Treat these as directions, not as a forecast.

What students under-practice

We tagged 15,345 multiple choice questions from teacher worksheets, review packets and prep books. After removing reposted official questions and anything outside AB, 10,263 were left. That is a good picture of what is commonly practiced. Here is how it compares with the official multiple choice.

By unit, practice material puts 17.2% of its questions on Unit 2 (derivative rules), while the 719 in-scope official multiple choice questions from 1969–2018 put 14.9% there. It puts 16.8% on Unit 5, against 19.9% on the exams, and 9.6% on Unit 8, against 13.5%.

Under-practiced	Share of official MC vs share of practice	Why it matters
Relative extrema from a formula for f′	1.5% vs 0.6% (0.4×)	A calculator-section regular
Increasing and decreasing intervals	2.1% vs 1.1% (0.5×)	Among the most frequent official MC types
Position from velocity and a starting point	1.9% vs 1.1% (0.5×)	#2 on the list above
Concavity intervals from a formula	1.7% vs 0.9% (0.5×)	Steady in recent exams
Amount from a rate in context	1.5% vs 0.9% (0.6×)	Used in 52 FRQs since 1998
Average value from a graph	1.0% vs 0.3% (0.3×)	6 items on the 2012–18 practice exams

“Official MC” is the share of all 719 in-scope official multiple choice questions, 1969–2018.

Over-practiced, by the same measure: limits of piecewise functions (2.8× their official share), special trig limits (2.8×), limits by factoring (2.4×), higher-order derivatives (2.3×), the washer method (3.2×) and tangent-line equations (1.5×). None of these is off the exam. They just get far more practice time than the exam gives them points.

The biggest gap is free response. The practice material we collected is multiple choice, and several things the free-response section scores have no multiple choice version at all: justifying with the Mean Value Theorem (19 FRQs since 1998) or the Intermediate Value Theorem (12), sketching a slope field (17), explaining what an integral means in context with units (25), and volume about a line other than an axis (19). If you only drill multiple choice, you never practice writing these.

The calculator section

Multiple choice Part B (13 questions) and free response Part A (2 questions) require a graphing calculator. You need four things from it: graph a function in a window you choose, solve an equation numerically, find a derivative at a point, and evaluate a definite integral. On free response, write the setup along with the calculator’s answer.

What the calculator questions actually ask is narrower than you might expect:

Amount from a rate in context. It appeared on all 7 practice exams from 2012–2018, and all 8 of those items were in the calculator section.
Reading a formula for $f'$ . Finding where $f$ has a relative extremum from a messy formula for $f'$ : 6 of its 7 items on the 2012–2018 practice exams were calculator questions.

Both come down to graphing or integrating a function you could not handle by hand, which is exactly what the calculator is for.

Desmos is built in. The AP exam runs in the Bluebook app, and College Board’s calculator policy (checked October 2026) says the Desmos graphing calculator is built into Bluebook for the calculator parts of AP Calculus AB: multiple choice Part B and free response Part A. It is not available in the no-calculator parts. You can also bring up to two approved handheld calculators. Bluebook uses a test version of Desmos with some features turned off, so practice in Bluebook’s own AP Calculus practice test, not only on desmos.com.

AP Calculus AB exam format, and the May 2027 change

The exam has two sections, multiple choice and free response, each half of your score, and each split into a no-calculator part and a calculator part. Starting with the May 2027 exam, multiple choice gets shorter. Free response and course content do not change.

Section	Calculator	Through May 2026	From May 2027
MC Part A	Not allowed	30 questions, 60 min	29 questions, 62 min
MC Part B	Required	15 questions, 45 min	13 questions, 38 min
FRQ Part A	Required	2 questions, 30 min	2 questions, 30 min
FRQ Part B	Not allowed	4 questions, 60 min	4 questions, 60 min

That is 42 multiple choice questions instead of 45. Part A gets about 2.1 minutes per question (was 2.0) and Part B about 2.9 (was 3.0). Multiple choice is still half of your score. One more thing if you practice from old exams: older released exams have five answer choices, while the current exam has four.

How we counted

Official multiple choice. 760 items from 17 released and practice exams, 1969–2018. The 7 practice exams from 2012–2018 (315 items) are the closest to today’s exam. College Board has not made any multiple choice from after 2018 public.
Official free response. All 416 free-response questions, 1969–2026, split into 1,396 parts and weighted by their published scoring points.
Matching. Each question is tagged to one of College Board’s 8 units and 81 AB topics from the Course and Exam Description (the CED), and to a more specific question type inside the topic. Recent exams count most.
What gets practiced. For comparison, we also tagged 15,345 multiple choice questions from teacher worksheets and prep books: a picture of what is commonly practiced, not of the exam.

Questions that are no longer on AB (integration by parts, shells, Newton’s method and similar) are left out. No College Board question is reproduced here. The stats are counts of public College Board exams, and every example problem is our own.

Practice by unit

Every unit of the CED has a free worksheet: 20 original multiple choice questions in the exam’s four-choice format, weighted by how often the official exams ask each kind of question, split into a no-calculator Part A and a calculator Part B, with an answer key and a PDF. Each unit also has its own review post with the most-tested question types, worked examples and the most common mistakes.

Unit 1: Limits and ContinuityWorksheet · Free response · Review
Unit 2: Differentiation: Definition and Fundamental PropertiesWorksheet · Free response · Review
Unit 3: Differentiation: Composite, Implicit, and Inverse FunctionsWorksheet · Free response · Review
Unit 4: Contextual Applications of DifferentiationWorksheet · Free response · Review
Unit 5: Analytical Applications of DifferentiationWorksheet · Free response · Review
Unit 6: Integration and Accumulation of ChangeWorksheet · Free response · Review
Unit 7: Differential EquationsWorksheet · Free response · Review
Unit 8: Applications of IntegrationWorksheet · Free response · Review

All eight sheets are on the AP Calculus AB worksheets page.

For free response, each unit has a set of 4 multi-part questions scored out of 9 points, and the mixed AP Calculus AB FRQ set is shaped like Section II of the exam: two calculator questions, then four without, each with a scoring guide.

Common Questions

Separable differential equations with an initial condition: they appeared on 6 of the 7 official practice exams from 2012–2018 and in 12 of the 86 free-response questions from 2012–2026, each worth 4 to 6 of the question’s 9 points. A Riemann or trapezoidal sum from a table was on the free response of every exam from 2012 to 2026, and in multiple choice alone, finding an amount from a rate in context appeared on all 7 practice exams.

It depends on the section. In multiple choice, Unit 5 (analytical applications of derivatives) is the largest, at 20.6% of the 2012–2018 practice exam questions. In free response, Unit 8 (applications of integration) takes 28.1% of the scoring points on the 2012–2026 exams, more than any other unit.

From May 2027, 42 multiple choice questions: 29 without a calculator in 62 minutes, then 13 with a graphing calculator in 38 minutes. The free-response section is unchanged at 6 questions: 2 with a calculator in 30 minutes, then 4 without in 60 minutes.

The course covers about one semester of college calculus, and what makes the exam hard is mostly the mix, not any one topic. 29 question types make up half the exam, free response leans hard on Unit 8 (28.1% of the 2012–2026 scoring points), and a lot of common practice material spends its time on limits and derivative rules instead. Practicing the most-tested question types in the exam format, with and without a calculator, closes most of that gap.

Yes, in the calculator parts only. College Board's calculator policy (checked October 2026) says a Desmos graphing calculator is built into the Bluebook app for multiple choice Part B and free response Part A. You may also bring up to two approved handheld graphing calculators.

Mostly, yes. The core question types have barely changed, but older released exams use five answer choices instead of four, and some older questions are no longer on AB, such as integration by parts, shells and Newton's method. Of the 41 out-of-scope official multiple choice questions we found, 40 come from exams before 1994.

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Practice by unit: free AP Calculus AB worksheets

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AP Calculus AB Review: The Most-Tested Questions, Unit by Unit

The 20 most-tested question types

1. Separable differential equation with an initial condition

2. Position or velocity from an initial condition

3. Amount from a rate in context

4. Riemann or trapezoidal sum from a table

5. Displacement and total distance

6. Average value of a function

7. Tangent-line (linear) approximation

8. Particle at rest or changing direction

9. Area between curves (integrating in xxx)

10. Equation of a tangent line

11. Volume with square or rectangle cross sections

12. Concavity and inflection from the graph of f′f'f′

13. Velocity and acceleration from position

14. Behavior of g(x)=∫axf(t) dtg(x) = \int_a^x f(t)\,dtg(x)=∫ax​f(t)dt

15. Related rates with a given equation

16. Absolute extrema from the graph of f′f'f′ and areas

17. Implicit differentiation

18. Derivative of an accumulation function (FTC)

19. Product or quotient rule from a table

20. Chain rule with trig, exponential and log functions

Which units are tested most

What’s rising and what’s fading since 2012

What students under-practice

The calculator section

AP Calculus AB exam format, and the May 2027 change

How we counted

Practice by unit

Common Questions

What is the most common question type on the AP Calculus AB exam?+

Which unit is on the AP Calculus AB exam the most?+

How many questions are on the AP Calculus AB exam in 2027?+

Is AP Calculus AB hard?+

Can you use Desmos on the AP Calculus AB exam?+

Are old AP Calculus AB exams still good practice?+

Practice by unit: free AP Calculus AB worksheets

Keep reading

AP Calculus AB Unit 1 Review: The Most-Tested Limits and Continuity Questions

AP Calculus AB Unit 2 Review: The Most-Tested Derivative Questions

AP Calculus AB Unit 3 Review: The Most-Tested Chain Rule and Implicit Questions

9. Area between curves (integrating in $x$ )

12. Concavity and inflection from the graph of $f'$

14. Behavior of $g(x) = \int_a^x f(t)\,dt$

16. Absolute extrema from the graph of $f'$ and areas