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AP Precalculus · Reference

AP Precalculus formula sheet the formulas you have to memorize.

Here is a complete AP Precalculus formula sheet — also called the equation sheet — covering the polynomial, exponential, logarithmic, and trigonometric formulas the exam expects. The catch up front: the AP Precalculus exam provides no formula sheet, so treat this as a study reference to memorize, not something you carry into the test.

Updated June 2026Part of AP Precalculus Review

Is a formula sheet provided on the AP Precalculus exam?

No. Like AP Calculus, AP Precalculus gives you no reference sheet at all — the formulas, the unit circle, and the identities all have to be memorized. A graphing calculator is allowed on Part B of the multiple choice and Part A of the free response, but the formulas themselves are on you.

The list below is grouped by function family, the way the course is organized, so each formula sits next to the topic where you use it. Only Units 1–3 are tested, so those are the formulas that matter for the exam.

The AP Precalculus formula sheet, by topic

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

Functions & transformations

Average rate of change: (f(b) − f(a)) / (b − a)
The slope between two points on a function.
Transformations: g(x) = a·f(b(x − h)) + k
Stretches, reflections, and shifts of a parent function.
Inverses: f(f−1(x)) = x
Inverse functions undo each other; reflect across y = x.

Polynomial & rational functions

Quadratic formula: x = (−b ± √(b2 − 4ac)) / 2a
The roots of ax2 + bx + c = 0.
End behavior
Set by the leading term’s degree and sign.
Rational asymptotes
Vertical at zeros of the denominator; horizontal or slant from comparing degrees.

Exponential & logarithmic

Exponential model: f(x) = a·bx
Growth when b > 1, decay when 0 < b < 1.
Definition: logb(x) = y ⇔ by = x
Logs and exponentials are inverses.
Properties: log(xy) = log x + log y; log(xn) = n·log x
The product, quotient, and power rules.
Change of base: logb x = (ln x)/(ln b)
Evaluate any logarithm on a calculator.

Trigonometry

Unit circle point: (cosθ, sinθ)
The coordinates at angle θ on the unit circle.
Pythagorean identity: sin2θ + cos2θ = 1
The identity the others build on.
Ratios: tanθ = sinθ/cosθ, plus csc, sec, cot
The six trigonometric functions.
Sinusoidal model: f(x) = a·sin(b(x − c)) + d
Amplitude |a|, period 2π/|b|, phase shift c, midline d.

Polar & complex

Polar to rectangular: x = r cosθ,  y = r sinθ
Convert a polar point to (x, y).
r2 = x2 + y2,  tanθ = y/x
Recover the radius and angle from (x, y).

How to use this formula sheet

Because none of it is provided, the goal is recall under pressure — quiz yourself until you can reproduce each formula, and the unit circle, from a blank page. Pair every formula with a worked problem so you know not just the formula but when it applies, and give trigonometry extra time, since the unit circle and identities carry a third of the exam.

Drill the tools in context with the Progress Check walkthroughs, keep the full AP Precalculus review guide in view for the format and study plan, and run a practice raw score through the score calculator to see where you land.

Frequently asked questions

Quick answers — written by humans, not a chatbot.

Is a formula sheet provided on the AP Precalculus exam?

No. AP Precalculus does not provide a formula or reference sheet — you must memorize the formulas, the unit circle, and the identities. Only a calculator is allowed, and only on the calculator sections.

What is the difference between the AP Precalculus formula sheet and equation sheet?

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

Do I need to memorize the unit circle for AP Precalculus?

Yes. The unit circle, the Pythagorean identity, and the basic trig values are essential, since no reference sheet is provided.

Is a calculator allowed on AP Precalculus?

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

What formulas are most important for AP Precalculus?

The quadratic formula, the log properties and change of base, the unit circle and Pythagorean identity, and the sinusoidal and exponential models.

Related

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