AP CALCULUS AB STUDY GUIDE |
COMPLETE EXAM REVIEW, FORMULAS,
PRACTICE QUESTIONS & EXAM PREP
2026| GRADED A+ | GUARANTEED
SUCCESS
Updated 2026 Questions and Answers | 100% Verified
Exam Prep and Comprehensive Rationales Included
,indeterminate form an expression involving two algebraic functions whose limits cannot be
determined from the limits of the individual functions
Squeeze Theorem If h(x) ≤ f(x) ≤ g(x) for specific values of x, and if (lim x→a h(x) = L) and (lim x→a
g(x) = L) then (lim x→a f(x) = L) also.
function is continuous if lim (x→c) f(x) = f(c)
Layman's definition of Continuity A function is continuous wherever you can draw it with a pen without ever having
to lift it
removable discontinuity a discontinuity at which the limit of the function exists but does not equal the
value of the function at that point
Infinite Discontinuity a discontinuity at which the limit of the function does not exist because both one-
sided limits are infinite
Jump Discontinuity a discontinuity at which the limit of the function does not exist because both one-
sided limits exist but have different values
PIVOT Procedures, Images, Vocabulary, Operations, Test
vertical asymptote exists when the graph of the function approaches positive or negative infinity as x
approaches some constant, c, and has equation x = c
x = (π/2) + nπ vertical asymptotes of tan(x)
finding a vertical asymptote simplify the function and set the denominator equal to 0
horizontal asymptote exists when the graph of the function approaches some constant, c, as x
approaches negative or positive infinity and has equation y = c
Relative Magnitude how fast a function grows or decays
there is no horizontal asymptote If the numerator has a higher degree than the denominator
, Graph is concave up
there is a horizontal asymptote at y = 0 If the denominator has a higher degree than the numerator
the horizontal asymptote is the ratio of the highest power If the numerator and the denominator have the same highest degree
coefficients
Intermediate Value Theorem (IVT) a theorem that states if f is a function that is continuous on the closed interval [a,
b] and d is any number between f(a) and f(b), then there must be at least one
number c, where a < c < b, such that f(c) = d
Definition of Derivative F'(x) = lim (h→0) of (ƒ(x+h) - ƒ(x))/(h)
Gives us the slope of ƒ(x) at any point x
Average rate of change the slope of the secant line on the interval [a, b] between the points at x = a and x
=b
difference quotient a formula used to calculate the slope of the secant line between two points on
the graph of a function
differential equation an equation that relates some unknown function with its derivative(s)
If a function f is differentiable at x = c then f is continuous at x = c
differentiability implies continuity but continuity does not imply differentiability.
equals 0 derivative of a constant
derivative of x This derivative equals 1
nx^(n-1) derivative of x^n
c ∙ (derivative of f(x)) derivative of (c ∙ f(x))
derivative of f(x) ± g(x) derivative of f(x) ± derivative of g(x)
f'g + fg' equals (fg)' ; which is the derivative of f times g
(f'g-fg')/g² (f/g)' ; which is the derivate of f divided by g
derivative graph The points of the term are x-coordinate and y being the slope of the tangent line
at the x-coordinate on the graph of the function; (x , slope)
COMPLETE EXAM REVIEW, FORMULAS,
PRACTICE QUESTIONS & EXAM PREP
2026| GRADED A+ | GUARANTEED
SUCCESS
Updated 2026 Questions and Answers | 100% Verified
Exam Prep and Comprehensive Rationales Included
,indeterminate form an expression involving two algebraic functions whose limits cannot be
determined from the limits of the individual functions
Squeeze Theorem If h(x) ≤ f(x) ≤ g(x) for specific values of x, and if (lim x→a h(x) = L) and (lim x→a
g(x) = L) then (lim x→a f(x) = L) also.
function is continuous if lim (x→c) f(x) = f(c)
Layman's definition of Continuity A function is continuous wherever you can draw it with a pen without ever having
to lift it
removable discontinuity a discontinuity at which the limit of the function exists but does not equal the
value of the function at that point
Infinite Discontinuity a discontinuity at which the limit of the function does not exist because both one-
sided limits are infinite
Jump Discontinuity a discontinuity at which the limit of the function does not exist because both one-
sided limits exist but have different values
PIVOT Procedures, Images, Vocabulary, Operations, Test
vertical asymptote exists when the graph of the function approaches positive or negative infinity as x
approaches some constant, c, and has equation x = c
x = (π/2) + nπ vertical asymptotes of tan(x)
finding a vertical asymptote simplify the function and set the denominator equal to 0
horizontal asymptote exists when the graph of the function approaches some constant, c, as x
approaches negative or positive infinity and has equation y = c
Relative Magnitude how fast a function grows or decays
there is no horizontal asymptote If the numerator has a higher degree than the denominator
, Graph is concave up
there is a horizontal asymptote at y = 0 If the denominator has a higher degree than the numerator
the horizontal asymptote is the ratio of the highest power If the numerator and the denominator have the same highest degree
coefficients
Intermediate Value Theorem (IVT) a theorem that states if f is a function that is continuous on the closed interval [a,
b] and d is any number between f(a) and f(b), then there must be at least one
number c, where a < c < b, such that f(c) = d
Definition of Derivative F'(x) = lim (h→0) of (ƒ(x+h) - ƒ(x))/(h)
Gives us the slope of ƒ(x) at any point x
Average rate of change the slope of the secant line on the interval [a, b] between the points at x = a and x
=b
difference quotient a formula used to calculate the slope of the secant line between two points on
the graph of a function
differential equation an equation that relates some unknown function with its derivative(s)
If a function f is differentiable at x = c then f is continuous at x = c
differentiability implies continuity but continuity does not imply differentiability.
equals 0 derivative of a constant
derivative of x This derivative equals 1
nx^(n-1) derivative of x^n
c ∙ (derivative of f(x)) derivative of (c ∙ f(x))
derivative of f(x) ± g(x) derivative of f(x) ± derivative of g(x)
f'g + fg' equals (fg)' ; which is the derivative of f times g
(f'g-fg')/g² (f/g)' ; which is the derivate of f divided by g
derivative graph The points of the term are x-coordinate and y being the slope of the tangent line
at the x-coordinate on the graph of the function; (x , slope)
