AP Calculus AB · Reference

AP Calculus AB formula sheet the formulas you have to memorize.

Here is a complete AP Calculus AB formula sheet — also called the equation sheet — covering every limit, derivative, integral, and theorem the exam expects you to know. The catch worth knowing up front: the AP Calculus AB exam does not provide a formula sheet, so treat this as a study reference to memorize, not something you carry into the test.

Updated June 2026Part of AP Calculus AB Review

Is a formula sheet provided on the AP Calculus AB exam?

No. Unlike AP Statistics or the AP Physics exams, AP Calculus AB gives you no reference sheet at all — you are expected to have every derivative, antiderivative, and theorem memorized. A graphing calculator (or the built-in Desmos) is allowed on Part B of the multiple choice and Part A of the free response, but the formulas themselves are on you.

That makes a page like this more than a convenience: the list below is the toolkit you have to walk in already knowing. It is grouped the way the course is taught, so each formula sits next to the topic where you use it.

The AP Calculus AB formula sheet, by topic

Every formula you need on test day, with a plain-language note on when to use it.

Limits & continuity

Derivative as a limit: f′(x) = lim_h→0 [f(x+h) − f(x)] / h

The definition every derivative rule comes from.

Alternate form: f′(a) = lim_x→a [f(x) − f(a)] / (x − a)

The slope of the tangent line at a single point.

lim_x→0 (sin x)/x = 1

A special limit worth memorizing outright.

Continuous at a: lim_x→a f(x) = f(a)

What it means for a function to be continuous at a point.

Derivative rules

Power rule: d/dx[xⁿ] = n·xⁿ⁻¹

Differentiate any power of x.

Product rule: (fg)′ = f′g + fg′

For a product of two functions.

Quotient rule: (f/g)′ = (f′g − fg′) / g²

Order matters — top-derivative first.

Chain rule: d/dx[f(g(x))] = f′(g(x))·g′(x)

Never forget the inside derivative.

Common derivatives

d/dx[sin x] = cos x · d/dx[cos x] = −sin x

The two you build the rest of trig from.

d/dx[tan x] = sec²x · d/dx[sec x] = sec x tan x

The other trig derivatives worth memorizing.

d/dx[e^x] = e^x · d/dx[ln x] = 1/x

Exponential and natural log.

d/dx[arctan x] = 1/(1+x²) · d/dx[arcsin x] = 1/√(1−x²)

The inverse-trig derivatives that show up on the exam.

Integrals (antiderivatives)

∫ xⁿ dx = xⁿ⁺¹/(n+1) + C, n ≠ −1

The power rule in reverse.

∫ (1/x) dx = ln|x| + C

The exception to the reverse power rule.

∫ e^x dx = e^x + C · ∫ cos x dx = sin x + C

Two you reach for constantly.

∫ sec²x dx = tan x + C · ∫ 1/(1+x²) dx = arctan x + C

The derivative list, read backwards.

Key theorems

Fundamental Theorem (Part 2): ∫_a^b f(x) dx = F(b) − F(a)

Evaluate a definite integral using an antiderivative.

FTC (Part 1): d/dx ∫_a^x f(t) dt = f(x)

Differentiating an accumulation function.

Mean Value Theorem: f′(c) = [f(b) − f(a)] / (b − a)

A guaranteed instant where the slope equals the average rate.

Average value: (1/(b−a)) ∫_a^b f(x) dx

The average height of a function on [a, b].

Applications

Motion: v(t) = x′(t), a(t) = v′(t)

Velocity and acceleration from a position function.

Total distance = ∫_a^b |v(t)| dt

Distance vs displacement — use the absolute value.

Area between curves = ∫_a^b (top − bottom) dx

The setup for area problems.

Volume (disk): V = π ∫_a^b [R(x)]² dx

Rotating a region around an axis.

Exponential growth: dy/dt = ky → y = y₀e^kt

The one differential-equation model to know cold.

How to use this formula sheet

Do not just read the list — because none of it is provided on exam day, the goal is recall under pressure. Quiz yourself until you can reproduce each rule from a blank page, and pair every formula with a worked problem so you know not just the formula but when it applies.

For a faster, concept-first version that pairs each unit with its key idea and the mistake to avoid, use our AP Calc AB cheat sheet, work full problems against the rubric with the FRQ guide, and the score calculator turns a practice raw score into a 1–5.

Frequently asked questions

Quick answers — written by humans, not a chatbot.

Is a formula sheet provided on the AP Calculus AB exam?

No. AP Calculus AB does not provide a formula or reference sheet — you must memorize the derivatives, integrals, and theorems. Only a calculator is allowed, and only on the calculator sections.

What is the difference between the AP Calculus AB formula sheet and equation sheet?

They are the same thing — both names refer to the collected formulas you need to know. Because none is provided, it is a study reference you build and memorize.

Do I need to memorize formulas for AP Calculus AB?

Yes. Since no sheet is provided, you must know the derivative and integral rules, the common derivatives and antiderivatives, and the key theorems cold.

Is a calculator allowed on AP Calculus AB?

Yes, on Part B of the multiple choice and Part A of the free response. The other parts are no-calculator. A graphing calculator or the built-in Desmos is required.

What formulas are most important for AP Calculus AB?

The derivative rules (power, product, quotient, chain), the common derivatives and antiderivatives, and the Fundamental Theorem of Calculus.