AP®MathsCollege BoardCalculus ABRevision NotesCourse OverviewCourse OverviewPrerequisites

Prerequisites (College Board AP® Calculus AB): Revision Note

Written by: Roger B

Reviewed by: Jamie Wood

Updated on 6 May 2026

Prerequisites

What are the prerequisites to studying Calculus AB?

You should have studied:
- Algebra
- Geometry
- Trigonometry
- Analytic geometry
- Elementary functions

Functions you need to know

You need to know the following functions

Function	Form	Domain	Range
Linear	$f (x) = a x + b$	$x \in ℝ$	$f (x) \in ℝ$
Polynomial	$f (x) = a_{n} x^{n} + . . . + a_{1} x + a_{0}$	$x \in ℝ$	$f (x) \in ℝ$ if $n$ is odd $f (x)$ will be bounded either above or below if $n$ is even
Rational	$f (x) = \frac{a x + b}{c x + d}$	$x \neq - \frac{d}{c}$	$f (x) \neq \frac{a}{c}$
Exponential	$f (x) = a^{x}$ where $a > 0$	$x \in ℝ$	$f (x) \in (0, \infty)$
Logarithmic	$f (x) = \log_{a} x$ where $a > 0$	$x \in (0, \infty)$	$f (x) \in ℝ$
Sine	$f (x) = \sin x$	$x \in ℝ$	$f (x) \in [- 1, 1]$
Cosine	$f (x) = \cos x$	$x \in ℝ$	$f (x) \in [- 1, 1]$
Tangent	$f (x) = \tan x$	$x \neq \frac{(2 k + 1)}{2} π$ where $k \in ℤ$	$f (x) \in ℝ$
Secant	$f (x) = \sec x$	$x \neq \frac{(2 k + 1)}{2} π$ where $k \in ℤ$	$f (x) \in (- \infty, 1] \cup [1, \infty)$
Cosecant	$f (x) = \csc x$	$x \neq k π$ where $k \in ℤ$	$f (x) \in (- \infty, 1] \cup [1, \infty)$
Cotangent	$f (x) = \tan x$	$x \neq k π$ where $k \in ℤ$	$f (x) \in ℝ$
Inverse sine	$f (x) = \arcsin x$	$x \in [- 1, 1]$	$f (x) \in [- \frac{π}{2}, \frac{π}{2}]$
Inverse cosine	$f (x) = \arccos x$	$x \in [- 1, 1]$	$f (x) \in [0, π]$
Inverse tangent	$f (x) = \arctan x$	$x \in ℝ$	$f (x) \in (- \frac{π}{2}, \frac{π}{2})$

Language of functions

Domain is the set of values that are substituted into the function
Range is the set of values that can be obtained by the function given its domain
An odd function satisfies $f (- x) = - f (x)$
An even function satisfies $f (- x) = f (x)$
A periodic function with period $k$ satisfies $f (x + k) = f (x)$ for all $x$ in the domain
A function has symmetry at $x = k$ if $f (k - x) = f (k + x)$ for all $x$ in the domain
A function has a zero at $x = k$ if $f (k) = 0$
The $x$ intercept(s) of a function are the values of $x$ that satisfy $f (x) = 0$
The $y$ intercept of a function value $f (0)$
A function is increasing on an interval if $f (x) < f (y)$ whenever $x < y$ in the interval
A function is increasing on an interval if $f (x) > f (y)$ whenever $x < y$ in the interval

Trigonometric values

You need to know the values of trigonometric functions at the numbers $0, \frac{π}{6}, \frac{π}{4}, \frac{π}{3}, \frac{π}{2}$ and their multiples

$x$	$0$	$\frac{π}{6}$	$\frac{π}{4}$	$\frac{π}{3}$	$\frac{π}{2}$
$\sin x$	$0$	$\frac{1}{2}$	$\frac{\sqrt{2}}{2}$	$\frac{\sqrt{3}}{2}$	$1$
$\cos x$	$1$	$\frac{\sqrt{3}}{2}$	$\frac{\sqrt{2}}{2}$	$\frac{1}{2}$	$0$

The values at multiples of these can be found using the properties

	$\sin$	$\cos$
$(- x)$	$\sin (- x) = - \sin x$	$\cos (- x) = \cos x$
$(π - x)$	$\sin (π - x) = \sin x$	$\cos (π - x) = - \cos x$
$(π + x)$	$\sin (π + x) = - \sin x$	$\cos (π + x) = - \cos x$
$(2 π - x)$	$\sin (2 π - x) = - \sin x$	$\cos (2 π - x) = \cos x$
$(2 π + x)$	$\sin (2 π + x) = \sin x$	$\cos (2 π + x) = \cos x$

Trigonometric identities

Tangent identities
- $\tan x \equiv \frac{\sin x}{\cos x}$
Reciprocal identities
- $\sec x \equiv \frac{1}{\cos x}$
- $\csc x \equiv \frac{1}{\sin x}$
- $\cot x \equiv \frac{1}{\tan x}$
Pythagorean identities
- $\sin^{2} x + \cos^{2} x \equiv 1$
- $1 + \tan^{2} x \equiv \sec^{2} x$
- $1 + \cot^{2} x \equiv \csc^{2} x$

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