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AP®︎/College Calculus AB

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Limits and continuity

Content	Standards
☰ Defining limits and using limit notation	, , , , ,
📺 Limits intro	, , , ,
📝 Limits intro	, , , ,
✅ Limits intro	, , , ,
☰ Estimating limit values from graphs	, , , , , ,
📺 Estimating limit values from graphs	, , , ,
📺 Unbounded limits	, , ,
📝 Estimating limit values from graphs	, , , , ,
✅ Estimating limit values from graphs	, , ,
📺 One-sided limits from graphs	, , , , ,
📺 One-sided limits from graphs: asymptote	, , , , ,
✅ One-sided limits from graphs	, , , , ,
📺 Connecting limits and graphical behavior	, , , , ,
✅ Connecting limits and graphical behavior	, , , , ,
☰ Estimating limit values from tables	, , ,
📺 Approximating limits using tables	, ,
📺 Estimating limits from tables	, ,
📝 Using tables to approximate limit values	, ,
✅ Creating tables for approximating limits	, ,
✅ Estimating limits from tables	, ,
📺 One-sided limits from tables	, ,
✅ One-sided limits from tables	, ,
☰ Determining limits using algebraic properties of limits: limit properties	, , , ,
📺 Limit properties	, , ,
📺 Limits of combined functions	, , ,
📺 Limits of combined functions: piecewise functions	, , ,
✅ Limits of combined functions: sums and differences	, , ,
✅ Limits of combined functions: products and quotients	, , ,
📺 Limits of composite functions	, , ,
✅ Limits of composite functions	, , ,
☰ Determining limits using algebraic properties of limits: direct substitution	, , , ,
📺 Limits by direct substitution	, ,
✅ Limits by direct substitution	, ,
📺 Undefined limits by direct substitution	, ,
✅ Direct substitution with limits that don't exist	, ,
📺 Limits of trigonometric functions	, ,
✅ Limits of trigonometric functions	, ,
📺 Limits of piecewise functions	, ,
✅ Limits of piecewise functions	, ,
📺 Limits of piecewise functions: absolute value	, ,
☰ Determining limits using algebraic manipulation	, , ,
📺 Limits by factoring	, ,
✅ Limits by factoring	, ,
📺 Limits by rationalizing	, ,
✅ Limits using conjugates	, ,
📺 Trig limit using Pythagorean identity	, ,
📺 Trig limit using double angle identity	, ,
✅ Limits using trig identities	, ,
☰ Selecting procedures for determining limits	, , ,
📺 Strategy in finding limits	, ,
📝 Strategy in finding limits	, ,
✅ Conclusions from direct substitution (finding limits)	, ,
✅ Next steps after indeterminate form (finding limits)	, ,
✅ Strategy in finding limits	, ,
☰ Determining limits using the squeeze theorem	, , ,
📺 Squeeze theorem intro	, ,
✅ Squeeze theorem	, ,
📺 Limit of sin(x)/x as x approaches 0	, ,
📺 Limit of (1-cos(x))/x as x approaches 0	, ,
☰ Exploring types of discontinuities	, , ,
📺 Types of discontinuities	, ,
✅ Classify discontinuities	, ,
☰ Defining continuity at a point	, , ,
📺 Continuity at a point	, ,
📺 Worked example: Continuity at a point (graphical)	, ,
✅ Continuity at a point (graphical)	, ,
📺 Worked example: point where a function is continuous	, ,
📺 Worked example: point where a function isn't continuous	, ,
✅ Continuity at a point (algebraic)	, ,
☰ Confirming continuity over an interval	, , , ,
📺 Continuity over an interval	, ,
✅ Continuity over an interval	, ,
📺 Functions continuous on all real numbers	, , ,
📺 Functions continuous at specific x-values	, , ,
✅ Continuity and common functions	, , ,
☰ Removing discontinuities	, , , ,
📺 Removing discontinuities (factoring)	, , ,
📺 Removing discontinuities (rationalization)	, , ,
✅ Removable discontinuities	, , ,
☰ Connecting infinite limits and vertical asymptotes	, , , ,
📺 Introduction to infinite limits	, , ,
📺 Infinite limits and asymptotes	, , ,
✅ Infinite limits: graphical	, , ,
📺 Analyzing unbounded limits: rational function	, , ,
📺 Analyzing unbounded limits: mixed function	, , ,
✅ Infinite limits: algebraic	, , ,
☰ Connecting limits at infinity and horizontal asymptotes	, , , , ,
📺 Introduction to limits at infinity	, , ,
📺 Functions with same limit at infinity	, , ,
✅ Limits at infinity: graphical	, , ,
📺 Limits at infinity of quotients (Part 1)	, , , ,
📺 Limits at infinity of quotients (Part 2)	, , , ,
✅ Limits at infinity of quotients	, , , ,
📺 Limits at infinity of quotients with square roots (odd power)	, , , ,
📺 Limits at infinity of quotients with square roots (even power)	, , , ,
✅ Limits at infinity of quotients with square roots	, , , ,
☰ Working with the intermediate value theorem	, , ,
📺 Intermediate value theorem	, ,
📺 Worked example: using the intermediate value theorem	, ,
✅ Using the intermediate value theorem	, ,
📺 Justification with the intermediate value theorem: table	, ,
📺 Justification with the intermediate value theorem: equation	, ,
✅ Justification with the intermediate value theorem	, ,
📝 Intermediate value theorem review	, ,
☰ Optional videos
📺 Formal definition of limits Part 1: intuition review
📺 Formal definition of limits Part 2: building the idea
📺 Formal definition of limits Part 3: the definition
📺 Formal definition of limits Part 4: using the definition

Differentiation: definition and basic derivative rules

Content	Standards
☰ Defining average and instantaneous rates of change at a point	, , , , , , , , , ,
📺 Newton, Leibniz, and Usain Bolt	, , , ,
📺 Derivative as a concept	, , , ,
📺 Secant lines & average rate of change	, ,
✅ Secant lines & average rate of change	, ,
📝 Derivative notation review	, , ,
📺 Derivative as slope of curve	, , , , ,
✅ Derivative as slope of curve	, , , , ,
📺 The derivative & tangent line equations	, , , , ,
✅ The derivative & tangent line equations	, , , , ,
☰ Defining the derivative of a function and using derivative notation	, , , , , , ,
📺 Formal definition of the derivative as a limit	, , , ,
📺 Formal and alternate form of the derivative	, , , ,
📺 Worked example: Derivative as a limit	, , , ,
📺 Worked example: Derivative from limit expression	, , , ,
✅ Derivative as a limit	, , , ,
📺 The derivative of x² at x=3 using the formal definition	, , , ,
📺 The derivative of x² at any point using the formal definition	, , , ,
📝 Finding tangent line equations using the formal definition of a limit	, , , , , ,
☰ Estimating derivatives of a function at a point	, , ,
📺 Estimating derivatives	, ,
✅ Estimate derivatives	, ,
☰ Connecting differentiability and continuity: determining when derivatives do and do not exist	, , , ,
📺 Differentiability and continuity	, , ,
📺 Differentiability at a point: graphical	, , ,
✅ Differentiability at a point: graphical	, , ,
📺 Differentiability at a point: algebraic (function is differentiable)	, , ,
📺 Differentiability at a point: algebraic (function isn't differentiable)	, , ,
✅ Differentiability at a point: algebraic	, , ,
📝 Proof: Differentiability implies continuity	, , ,
☰ Applying the power rule	, , ,
📺 Power rule	, ,
✅ Power rule (positive integer powers)	, ,
✅ Power rule (negative & fractional powers)	, ,
📺 Power rule (with rewriting the expression)	, ,
✅ Power rule (with rewriting the expression)	, ,
📝 Justifying the power rule	, ,
☰ Derivative rules: constant, sum, difference, and constant multiple: introduction	, , ,
📺 Basic derivative rules	, ,
📺 Basic derivative rules: find the error	, ,
✅ Basic derivative rules: find the error	, ,
📺 Basic derivative rules: table	, ,
✅ Basic derivative rules: table	, ,
📝 Justifying the basic derivative rules	, ,
☰ Derivative rules: constant, sum, difference, and constant multiple: connecting with the power rule	, , ,
📺 Differentiating polynomials	, ,
✅ Differentiate polynomials	, ,
📺 Differentiating integer powers (mixed positive and negative)	, ,
✅ Differentiate integer powers (mixed positive and negative)	, ,
📺 Tangents of polynomials	, ,
✅ Tangents of polynomials	, ,
☰ Derivatives of cos(x), sin(x), 𝑒ˣ, and ln(x)	, , ,
📺 Derivatives of sin(x) and cos(x)	, ,
📺 Worked example: Derivatives of sin(x) and cos(x)	, ,
✅ Derivatives of sin(x) and cos(x)	, ,
📝 Proving the derivatives of sin(x) and cos(x)	, ,
📺 Derivative of 𝑒ˣ	, ,
📺 Derivative of ln(x)	, ,
✅ Derivatives of 𝑒ˣ and ln(x)	, ,
📝 Proof: The derivative of 𝑒ˣ is 𝑒ˣ	, ,
📝 Proof: the derivative of ln(x) is 1/x	, ,
☰ The product rule	, , ,
📺 Product rule	, ,
📺 Differentiating products	, ,
✅ Differentiate products	, ,
📺 Worked example: Product rule with table	, ,
📺 Worked example: Product rule with mixed implicit & explicit	, ,
✅ Product rule with tables	, ,
📝 Proving the product rule	, ,
📝 Product rule review	, ,
☰ The quotient rule	, , ,
📺 Quotient rule	, ,
✅ Differentiate quotients	, ,
📺 Worked example: Quotient rule with table	, ,
✅ Quotient rule with tables	, ,
📺 Differentiating rational functions	, ,
✅ Differentiate rational functions	, ,
📝 Quotient rule review	, ,
☰ Finding the derivatives of tangent, cotangent, secant, and/or cosecant functions	, , ,
📺 Derivatives of tan(x) and cot(x)	, ,
📺 Derivatives of sec(x) and csc(x)	, ,
✅ Derivatives of tan(x), cot(x), sec(x), and csc(x)	, ,
☰ Optional videos
📺 Proof: Differentiability implies continuity
📺 Justifying the power rule
📺 Proof of power rule for positive integer powers
📺 Proof of power rule for square root function
📺 Limit of sin(x)/x as x approaches 0	, ,
📺 Limit of (1-cos(x))/x as x approaches 0	, ,
📺 Proof of the derivative of sin(x)
📺 Proof of the derivative of cos(x)
📺 Product rule proof

Differentiation: composite, implicit, and inverse functions

Content	Standards
☰ The chain rule: introduction	, , ,
📺 Chain rule	, ,
📺 Common chain rule misunderstandings	, ,
📝 Chain rule	, ,
📺 Identifying composite functions	, ,
✅ Identify composite functions	, ,
📺 Worked example: Derivative of cos³(x) using the chain rule	, ,
📺 Worked example: Derivative of √(3x²-x) using the chain rule	, ,
📺 Worked example: Derivative of ln(√x) using the chain rule	, ,
✅ Chain rule intro	, ,
☰ The chain rule: further practice	, , ,
📺 Worked example: Chain rule with table	, ,
✅ Chain rule with tables	, ,
📺 Derivative of aˣ (for any positive base a)	, ,
📺 Derivative of logₐx (for any positive base a≠1)	, ,
✅ Derivatives of aˣ and logₐx	, ,
📺 Worked example: Derivative of 7^(x²-x) using the chain rule	, ,
📺 Worked example: Derivative of log₄(x²+x) using the chain rule	, ,
📺 Worked example: Derivative of sec(3π/2-x) using the chain rule	, ,
📺 Worked example: Derivative of ∜(x³+4x²+7) using the chain rule	, ,
✅ Chain rule capstone	, ,
📝 Proving the chain rule	, ,
📝 Derivative rules review	, ,
☰ Implicit differentiation	, , ,
📺 Implicit differentiation	, ,
📺 Worked example: Implicit differentiation	, ,
📺 Worked example: Evaluating derivative with implicit differentiation	, ,
✅ Implicit differentiation	, ,
📺 Showing explicit and implicit differentiation give same result	, ,
📝 Implicit differentiation review	, ,
☰ Differentiating inverse functions	, , ,
📺 Derivatives of inverse functions	, ,
📺 Derivatives of inverse functions: from equation	, ,
📺 Derivatives of inverse functions: from table	, ,
✅ Derivatives of inverse functions	, ,
☰ Differentiating inverse trigonometric functions	, , ,
📺 Derivative of inverse sine	, ,
📺 Derivative of inverse cosine	, ,
📺 Derivative of inverse tangent	, ,
✅ Derivatives of inverse trigonometric functions	, ,
📝 Differentiating inverse trig functions review	, ,
☰ Selecting procedures for calculating derivatives: strategy	,
📺 Differentiating functions: Find the error
📺 Manipulating functions before differentiation
📝 Strategy in differentiating functions
✅ Differentiating functions: Find the error
✅ Manipulating functions before differentiation
☰ Selecting procedures for calculating derivatives: multiple rules	,
📺 Differentiating using multiple rules: strategy
✅ Differentiating using multiple rules: strategy
📺 Applying the chain rule and product rule
📺 Applying the chain rule twice
📺 Derivative of eᶜᵒˢˣ⋅cos(eˣ)
📺 Derivative of sin(ln(x²))
✅ Differentiating using multiple rules
☰ Calculating higher-order derivatives	, , , ,
📺 Second derivatives	, , ,
✅ Second derivatives	, , ,
📺 Second derivatives (implicit equations): find expression	, , ,
📺 Second derivatives (implicit equations): evaluate derivative	, , ,
✅ Second derivatives (implicit equations)	, , ,
📝 Second derivatives review	, , ,
☰ Further practice connecting derivatives and limits	, , ,
📺 Disguised derivatives	, ,
✅ Disguised derivatives	, ,
☰ Optional videos
📺 Proof: Differentiability implies continuity
📺 If function u is continuous at x, then Δu→0 as Δx→0
📺 Chain rule proof
📺 Quotient rule from product & chain rules

Contextual applications of differentiation

Content	Standards
☰ Interpreting the meaning of the derivative in context	, , , , ,
📺 Interpreting the meaning of the derivative in context	, , , ,
📝 Analyzing problems involving rates of change in applied contexts	, , , ,
✅ Interpreting the meaning of the derivative in context	, , , ,
☰ Straight-line motion: connecting position, velocity, and acceleration	, , ,
📺 Introduction to one-dimensional motion with calculus	, ,
📺 Interpreting direction of motion from position-time graph	, ,
📺 Interpreting direction of motion from velocity-time graph	, ,
📺 Interpreting change in speed from velocity-time graph	, ,
✅ Interpret motion graphs	, ,
📺 Worked example: Motion problems with derivatives	, ,
✅ Motion problems (differential calc)	, ,
☰ Rates of change in other applied contexts (non-motion problems)	, , ,
📺 Applied rate of change: forgetfulness	, ,
✅ Rates of change in other applied contexts (non-motion problems)	, ,
📺 Marginal cost & differential calculus
☰ Introduction to related rates	, , , ,
📺 Related rates intro	, , ,
📝 Analyzing problems involving related rates	, , ,
📺 Analyzing related rates problems: expressions	, , ,
✅ Analyzing related rates problems: expressions	, , ,
📺 Analyzing related rates problems: equations (Pythagoras)	, , ,
📺 Analyzing related rates problems: equations (trig)	, , ,
✅ Analyzing related rates problems: equations	, , ,
📺 Differentiating related functions intro	, , ,
📺 Worked example: Differentiating related functions	, , ,
✅ Differentiate related functions	, , ,
☰ Solving related rates problems	, , ,
✅ Related rates intro	, ,
✅ Related rates (multiple rates)	, ,
📺 Related rates: Approaching cars	, ,
📺 Related rates: Falling ladder	, ,
✅ Related rates (Pythagorean theorem)	, ,
📺 Related rates: water pouring into a cone	, ,
✅ Related rates (advanced)	, ,
📺 Related rates: shadow	, ,
📺 Related rates: balloon	, ,
☰ Approximating values of a function using local linearity and linearization	, , ,
📺 Local linearity	, ,
📺 Local linearity and differentiability	, ,
📺 Worked example: Approximation with local linearity	, ,
✅ Approximation with local linearity	, ,
📺 Linear approximation of a rational function	, ,
☰ Using L’Hôpital’s rule for finding limits of indeterminate forms	, , , ,
📺 L'Hôpital's rule introduction	, , ,
📺 L'Hôpital's rule: limit at 0 example	, , ,
✅ L'Hôpital's rule: 0/0	, , ,
📺 L'Hôpital's rule: limit at infinity example	, , ,
✅ L'Hôpital's rule: ∞/∞	, , ,
📝 Proof of special case of l'Hôpital's rule	, , ,
☰ Optional videos
📺 Proof of special case of l'Hôpital's rule

Applying derivatives to analyze functions

Content	Standards
☰ Using the mean value theorem	, , ,
📺 Mean value theorem	, ,
📺 Mean value theorem example: polynomial	, ,
📺 Mean value theorem example: square root function	, ,
✅ Using the mean value theorem	, ,
📺 Justification with the mean value theorem: table	, ,
📺 Justification with the mean value theorem: equation	, ,
📝 Establishing differentiability for MVT	, ,
✅ Justification with the mean value theorem	, ,
📺 Mean value theorem application	, ,
📝 Mean value theorem review	, ,
☰ Extreme value theorem, global versus local extrema, and critical points	, , , , ,
📺 Extreme value theorem	, , , ,
📺 Critical points introduction	, , , ,
📺 Finding critical points	, , , ,
✅ Find critical points	, , , ,
☰ Determining intervals on which a function is increasing or decreasing	, , ,
📺 Finding decreasing interval given the function	, ,
📺 Finding increasing interval given the derivative	, ,
✅ Increasing & decreasing intervals	, ,
📝 Increasing & decreasing intervals review	, ,
☰ Using the first derivative test to find relative (local) extrema	, , ,
📺 Introduction to minimum and maximum points	, ,
📺 Finding relative extrema (first derivative test)	, ,
📺 Worked example: finding relative extrema	, ,
📺 Analyzing mistakes when finding extrema (example 1)	, ,
📺 Analyzing mistakes when finding extrema (example 2)	, ,
📝 Finding relative extrema (first derivative test)	, ,
✅ Relative minima & maxima	, ,
📝 Relative minima & maxima review	, ,
☰ Using the candidates test to find absolute (global) extrema	, , ,
📺 Finding absolute extrema on a closed interval	, ,
✅ Absolute minima & maxima (closed intervals)	, ,
📺 Absolute minima & maxima (entire domain)	, ,
✅ Absolute minima & maxima (entire domain)	, ,
📝 Absolute minima & maxima review	, ,
☰ Determining concavity of intervals and finding points of inflection: graphical	, , , ,
📺 Concavity introduction	, , ,
📺 Analyzing concavity (graphical)	, , ,
✅ Concavity intro	, , ,
📺 Inflection points introduction	, , ,
📺 Inflection points (graphical)	, , ,
✅ Inflection points intro	, , ,
☰ Determining concavity of intervals and finding points of inflection: algebraic	, , , , ,
📺 Analyzing concavity (algebraic)	, , , ,
📺 Inflection points (algebraic)	, , , ,
📺 Mistakes when finding inflection points: second derivative undefined	, , , ,
📺 Mistakes when finding inflection points: not checking candidates	, , , ,
📝 Analyzing the second derivative to find inflection points	, , , ,
✅ Analyze concavity	, , , ,
✅ Find inflection points	, , , ,
📝 Concavity review	, , , ,
📝 Inflection points review	, , , ,
☰ Using the second derivative test to find extrema	, , ,
📺 Second derivative test	, ,
✅ Second derivative test	, ,
☰ Sketching curves of functions and their derivatives	, , , ,
📺 Curve sketching with calculus: polynomial	, , ,
📺 Curve sketching with calculus: logarithm	, , ,
📺 Analyzing a function with its derivative	, , ,
☰ Connecting a function, its first derivative, and its second derivative	, , , ,
📺 Calculus based justification for function increasing	, , ,
📺 Justification using first derivative	, , ,
📝 Justification using first derivative	, , ,
✅ Justification using first derivative	, , ,
📺 Inflection points from graphs of function & derivatives	, , ,
📺 Justification using second derivative: inflection point	, , ,
📺 Justification using second derivative: maximum point	, , ,
📝 Justification using second derivative	, , ,
✅ Justification using second derivative	, , ,
📺 Connecting f, f', and f'' graphically	, , ,
📺 Connecting f, f', and f'' graphically (another example)	, , ,
✅ Connecting f, f', and f'' graphically	, , ,
☰ Solving optimization problems	, , , , ,
📺 Optimization: sum of squares	, , , ,
📺 Optimization: box volume (Part 1)	, , , ,
📺 Optimization: box volume (Part 2)	, , , ,
📺 Optimization: profit	, , , ,
📺 Optimization: cost of materials	, , , ,
📺 Optimization: area of triangle & square (Part 1)	, , , ,
📺 Optimization: area of triangle & square (Part 2)	, , , ,
✅ Optimization	, , , ,
📺 Motion problems: finding the maximum acceleration	, , , ,
☰ Exploring behaviors of implicit relations	, , , , , ,
📺 Horizontal tangent to implicit curve	, , , , ,
✅ Tangents to graphs of implicit relations	, , , , ,
☰ Calculator-active practice	, ,
✅ Analyze functions (calculator-active)	,

Integration and accumulation of change

Content	Standards
☰ Exploring accumulations of change	, , , , , ,
📺 Introduction to integral calculus	, , , , ,
📺 Definite integrals intro	, , , , ,
📝 Exploring accumulation of change	, , , , ,
📺 Worked example: accumulation of change	, , , , ,
✅ Accumulation of change	, , , , ,
☰ Approximating areas with Riemann sums	, , , , , ,
📺 Riemann approximation introduction	, , , , ,
📺 Over- and under-estimation of Riemann sums	, , , , ,
📝 Left & right Riemann sums	, , , , ,
📺 Worked example: finding a Riemann sum using a table	, , , , ,
✅ Left & right Riemann sums	, , , , ,
📺 Worked example: over- and under-estimation of Riemann sums	, , , , ,
✅ Over- and under-estimation of Riemann sums	, , , , ,
📺 Midpoint sums	, , , , ,
📺 Trapezoidal sums	, , , , ,
📝 Understanding the trapezoidal rule	, , , , ,
✅ Midpoint & trapezoidal sums	, , , , ,
📝 Riemann sums review	, , , , ,
☰ Riemann sums, summation notation, and definite integral notation	, , , , , , ,
📺 Summation notation
📝 Summation notation
📺 Worked examples: Summation notation
✅ Summation notation
📺 Riemann sums in summation notation	, ,
📝 Riemann sums in summation notation	, ,
📺 Worked example: Riemann sums in summation notation	, ,
✅ Riemann sums in summation notation	, ,
📺 Definite integral as the limit of a Riemann sum	, , , , , ,
📝 Definite integral as the limit of a Riemann sum	, , , , , ,
📺 Worked example: Rewriting definite integral as limit of Riemann sum	, , , , , ,
📺 Worked example: Rewriting limit of Riemann sum as definite integral	, , , , , ,
✅ Definite integral as the limit of a Riemann sum	, , , , , ,
☰ The fundamental theorem of calculus and accumulation functions	, , , ,
📺 The fundamental theorem of calculus and accumulation functions	, , ,
📺 Functions defined by definite integrals (accumulation functions)	, , ,
✅ Functions defined by definite integrals (accumulation functions)	, , ,
📺 Worked example: Finding derivative with fundamental theorem of calculus	, , ,
✅ Finding derivative with fundamental theorem of calculus	, , ,
✅ Finding derivative with fundamental theorem of calculus: chain rule	, , ,
☰ Interpreting the behavior of accumulation functions involving area	, , ,
📺 Interpreting the behavior of accumulation functions	, ,
📝 Interpreting the behavior of accumulation functions	, ,
✅ Interpreting the behavior of accumulation functions	, ,
☰ Applying properties of definite integrals	, , , ,
📺 Negative definite integrals	, ,
📺 Finding definite integrals using area formulas	, ,
✅ Finding definite integrals using area formulas	, ,
📺 Definite integral over a single point	, , ,
📺 Integrating scaled version of function	, , ,
📺 Switching bounds of definite integral	, , ,
📺 Integrating sums of functions	, , ,
📺 Worked examples: Finding definite integrals using algebraic properties	, , ,
✅ Finding definite integrals using algebraic properties	, , ,
📺 Definite integrals on adjacent intervals	, , ,
📺 Worked example: Breaking up the integral's interval	, , ,
📺 Worked example: Merging definite integrals over adjacent intervals	, , ,
✅ Definite integrals over adjacent intervals	, , ,
📺 Functions defined by integrals: switched interval	, , ,
📺 Finding derivative with fundamental theorem of calculus: x is on lower bound	, , ,
📺 Finding derivative with fundamental theorem of calculus: x is on both bounds	, , ,
📝 Definite integrals properties review	, , ,
☰ The fundamental theorem of calculus and definite integrals	, , , , ,
📺 The fundamental theorem of calculus and definite integrals	, , , ,
✅ The fundamental theorem of calculus and definite integrals	, , , ,
📺 Antiderivatives and indefinite integrals	, , , ,
✅ Antiderivatives and indefinite integrals	, , , ,
📝 Proof of fundamental theorem of calculus	, , , ,
☰ Finding antiderivatives and indefinite integrals: basic rules and notation: reverse power rule	, , , ,
📺 Reverse power rule	, , ,
✅ Reverse power rule	, , ,
✅ Reverse power rule: negative and fractional powers	, , ,
📺 Indefinite integrals: sums & multiples	, , ,
✅ Reverse power rule: sums & multiples	, , ,
📺 Rewriting before integrating	, , ,
✅ Reverse power rule: rewriting before integrating	, , ,
📝 Reverse power rule review	, , ,
☰ Finding antiderivatives and indefinite integrals: basic rules and notation: common indefinite integrals	, , , ,
📺 Indefinite integral of 1/x	, , ,
📺 Indefinite integrals of sin(x), cos(x), and eˣ	, , ,
✅ Indefinite integrals: eˣ & 1/x	, , ,
✅ Indefinite integrals: sin & cos	, , ,
📝 Common integrals review	, , ,
☰ Finding antiderivatives and indefinite integrals: basic rules and notation: definite integrals	, , ,
📺 Definite integrals: reverse power rule	, ,
✅ Definite integrals: reverse power rule	, ,
📺 Definite integral of rational function	, ,
📺 Definite integral of radical function	, ,
📺 Definite integral of trig function	, ,
📺 Definite integral involving natural log	, ,
✅ Definite integrals: common functions	, ,
📺 Definite integral of piecewise function	, ,
📺 Definite integral of absolute value function	, ,
✅ Definite integrals of piecewise functions	, ,
☰ Integrating using substitution	, , , ,
📺 𝘶-substitution intro	, ,
📺 𝘶-substitution: multiplying by a constant	, ,
📺 𝘶-substitution: defining 𝘶	, ,
📺 𝘶-substitution: defining 𝘶 (more examples)	, ,
📝 𝘶-substitution	, ,
✅ 𝘶-substitution: defining 𝘶	, ,
📺 𝘶-substitution: rational function	, ,
📺 𝘶-substitution: logarithmic function	, ,
📝 𝘶-substitution warmup	, ,
✅ 𝘶-substitution: indefinite integrals	, ,
📺 𝘶-substitution: definite integrals	, , ,
📝 𝘶-substitution with definite integrals	, , ,
✅ 𝘶-substitution: definite integrals	, , ,
📺 𝘶-substitution: definite integral of exponential function	, , ,
☰ Integrating functions using long division and completing the square	, , ,
📺 Integration using long division	, ,
✅ Integration using long division	, ,
📺 Integration using completing the square and the derivative of arctan(x)	, ,
✅ Integration using completing the square	, ,
☰ Optional videos
📺 Proof of fundamental theorem of calculus
📺 Intuition for second part of fundamental theorem of calculus

Differential equations

Content	Standards
☰ Modeling situations with differential equations	, , ,
📺 Differential equations introduction	, ,
📺 Writing a differential equation	, ,
✅ Write differential equations	, ,
☰ Verifying solutions for differential equations	, , , ,
📺 Verifying solutions to differential equations	, , ,
✅ Verify solutions to differential equations	, , ,
☰ Sketching slope fields	, , ,
📺 Slope fields introduction	, ,
📺 Worked example: equation from slope field	, ,
📺 Worked example: slope field from equation	, ,
📺 Worked example: forming a slope field	, ,
✅ Slope fields & equations	, ,
☰ Reasoning using slope fields	, , , ,
📺 Approximating solution curves in slope fields	, , ,
📺 Worked example: range of solution curve from slope field	, , ,
✅ Reasoning using slope fields	, , ,
☰ Finding general solutions using separation of variables	, , , ,
📺 Separable equations introduction	, , ,
📺 Addressing treating differentials algebraically	, , ,
📝 Separable differential equations	, , ,
✅ Separable differential equations: find the error	, , ,
📺 Worked example: separable differential equations	, , ,
✅ Separable differential equations	, , ,
📺 Worked example: identifying separable equations	, , ,
📝 Identifying separable equations	, , ,
✅ Identify separable equations	, , ,
☰ Finding particular solutions using initial conditions and separation of variables	, , , , ,
📺 Particular solutions to differential equations: rational function	, , , ,
📺 Particular solutions to differential equations: exponential function	, , , ,
✅ Particular solutions to differential equations	, , , ,
📺 Worked example: finding a specific solution to a separable equation	, , , ,
📺 Worked example: separable equation with an implicit solution	, , , ,
✅ Particular solutions to separable differential equations	, , , ,
☰ Exponential models with differential equations	, , , , , ,
📺 Exponential models & differential equations (Part 1)	, , , , ,
📺 Exponential models & differential equations (Part 2)	, , , , ,
📺 Worked example: exponential solution to differential equation	, , , , ,
✅ Differential equations: exponential model equations	, , , , ,
✅ Differential equations: exponential model word problems	, , , , ,

Applications of integration

Content	Standards
☰ Finding the average value of a function on an interval	, , ,
📺 Average value over a closed interval	, ,
📺 Calculating average value of function over interval	, ,
✅ Average value of a function	, ,
📺 Mean value theorem for integrals	, ,
☰ Connecting position, velocity, and acceleration functions using integrals	, , ,
📺 Motion problems with integrals: displacement vs. distance	, ,
📺 Analyzing motion problems: position	, ,
📺 Analyzing motion problems: total distance traveled	, ,
📝 Motion problems (with definite integrals)	, ,
✅ Analyzing motion problems (integral calculus)	, ,
📺 Worked example: motion problems (with definite integrals)	, ,
✅ Motion problems (with integrals)	, ,
📺 Average acceleration over interval	, ,
☰ Using accumulation functions and definite integrals in applied contexts	, , , , , ,
📺 Area under rate function gives the net change	, , , , ,
📺 Interpreting definite integral as net change	, , , , ,
📺 Worked examples: interpreting definite integrals in context	, , , , ,
✅ Interpreting definite integrals in context	, , , , ,
📺 Analyzing problems involving definite integrals	, , , , ,
📝 Analyzing problems involving definite integrals	, , , , ,
✅ Analyzing problems involving definite integrals	, , , , ,
📺 Worked example: problem involving definite integral (algebraic)	, , , , ,
✅ Problems involving definite integrals (algebraic)	, , , , ,
☰ Finding the area between curves expressed as functions of x	, , ,
📺 Area between a curve and the x-axis	, ,
📺 Area between a curve and the x-axis: negative area	, ,
✅ Area between a curve and the x-axis	, ,
📺 Area between curves	, ,
📺 Worked example: area between curves	, ,
✅ Area between two curves given end points	, ,
✅ Area between two curves	, ,
📺 Composite area between curves	, ,
☰ Finding the area between curves expressed as functions of y	, , ,
📺 Area between a curve and the 𝘺-axis	, ,
📺 Horizontal area between curves	, ,
✅ Horizontal areas between curves	, ,
☰ Finding the area between curves that intersect at more than two points	, , ,
✅ Area between curves that intersect at more than two points (calculator-active)	, ,
☰ Volumes with cross sections: squares and rectangles	, , ,
📺 Volume with cross sections: intro	, ,
✅ Volumes with cross sections: squares and rectangles (intro)	, ,
📺 Volume with cross sections: squares and rectangles (no graph)	, ,
📺 Volume with cross sections perpendicular to y-axis	, ,
✅ Volumes with cross sections: squares and rectangles	, ,
☰ Volumes with cross sections: triangles and semicircles	, , , ,
📺 Volume with cross sections: semicircle	, ,
📺 Volume with cross sections: triangle	, ,
✅ Volumes with cross sections: triangles and semicircles	, , ,
☰ Volume with disc method: revolving around x- or y-axis	, , ,
📺 Disc method around x-axis	, ,
📺 Generalizing disc method around x-axis	, ,
📺 Disc method around y-axis	, ,
✅ Disc method: revolving around x- or y-axis	, ,
☰ Volume with disc method: revolving around other axes	, , ,
📺 Disc method rotation around horizontal line	, ,
📺 Disc method rotating around vertical line	, ,
📺 Calculating integral disc around vertical line	, ,
✅ Disc method: revolving around other axes	, ,
☰ Volume with washer method: revolving around x- or y-axis	, , ,
📺 Solid of revolution between two functions (leading up to the washer method)	, ,
📺 Generalizing the washer method	, ,
✅ Washer method: revolving around x- or y-axis	, ,
☰ Volume with washer method: revolving around other axes	, , ,
📺 Washer method rotating around horizontal line (not x-axis), part 1	, ,
📺 Washer method rotating around horizontal line (not x-axis), part 2	, ,
📺 Washer method rotating around vertical line (not y-axis), part 1	, ,
📺 Washer method rotating around vertical line (not y-axis), part 2	, ,
✅ Washer method: revolving around other axes	, ,
☰ Calculator-active practice	, , , ,
✅ Contextual and analytical applications of integration (calculator-active)	, , ,

AP Calculus AB solved free response questions from past exams

Content	Standards
☰ AP Calculus AB 2017 free response
📺 2017 AP Calculus AB/BC 4a
📺 2017 AP Calculus AB/BC 4b
📺 2017 AP Calculus AB/BC 4c
☰ AP Calculus AB 2015 free response
📺 2015 AP Calculus AB/BC 1ab
📺 2015 AP Calculus AB/BC 1c
📺 2015 AP Calculus AB/BC 1d
📺 2015 AP Calculus AB 2a
📺 2015 AP Calculus AP 2b
📺 2015 AP Calculus 2c
📺 2015 AP Calculus AB/BC 3a
📺 2015 AP Calculus AB/BC 3b
📺 2015 AP Calculus AB/BC 3cd
📺 2015 AP Calculus AB/BC 4ab
📺 2015 AP Calculus AB/BC 4cd
📺 2015 AP Calculus AB 5a
📺 2015 AP Calculus AB 5b
📺 2015 AP Calculus AB 5c
📺 2015 AP Calculus AB 5d
📺 2015 AP Calculus AB 6a
📺 2015 AP Calculus AB 6b
📺 2015 AP Calculus AB 6c
☰ AP Calculus AB 2011 free response
📺 2011 Calculus AB free response #1a
📺 2011 Calculus AB Free Response #1 (b, c, & d)
📺 2011 Calculus AB free response #2 (a & b)
📺 2011 Calculus AB free response #2 (c & d)
📺 2011 Calculus AB free response #3 (a & b)
📺 2011 Calculus AB free response #3 (c)
📺 2011 Calculus AB free response #4a
📺 2011 Calculus AB free response #4b
📺 2011 Calculus AB free response #4c
📺 2011 Calculus AB free response #4d
📺 2011 Calculus AB free response #5a
📺 2011 Calculus AB free response #5b
📺 2011 Calculus AB free response #5c
📺 2011 Calculus AB free response #6a
📺 2011 Calculus AB free response #6b
📺 2011 Calculus AB free response #6c

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