AP Calculus Easy Worksheet™

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Free Response questions REQUIRE full explanations. Practice writing the Step-By-Step solutions! Calculus BC test consists of ALL topics, while the AB test consists of those topics not marked BC test
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Select the number of each type of equations: (Selecting Random will randomly generate all subtypes) Click on any title to see the free sample worksheet. (only the first few samples are free) A (Random) Limits and Continuity a. Limit Notation (includes 1-sided) b. Finding 1-sided Limits c. Determing if a limit exists d. Definition of Limit e. Estimating Limits Numerically f. Evaluating Basic Limits g. Limits of Polynomial, Trigonometric, and Rational Functions h. Limits of Composite Functions i. The Squeeze Theorem j. Definition of Continuity k. Properties of Continuity l. The Intermediate Value Theorem m. Vertical Asymptotes n. Determining Infinite limits and Holes in Rational Functions B (Random) Differentiation a. Finding the Slope of the Tangent Line at a point b. Definition of the Derivative c. Using the Definition of the Derivative d. Finding points of Differentiability e. Differentiability vs. Continuity C (Random) Derivative Rules a. Constant Rule and Power Rule b. Constant Multiple Rule c. Sum and Difference Rules d. Derivatives Involving Sine/Cosine e. Average Velocity f. Instantaneous Velocity g. Rate of Change Problems h. Product Rule i. Quotient Rule j. Derivatives of Trigonometric Functions k. Higher Order Derivatives l. Finding Average Acceleration m. Finding Instantaneous Acceleration n. The Chain Rule o. Simplifying Derivatives p. Repeated Applications of the Chain Rule q. Tangent Line of a Trigonometric Function r. Implicit Differentiation s. Finding Slope with Implicit Differentiation t. Related Rates Problems D (Random) Applications of Differentiation a. Finding Critical Points b. The Extreme Value Theorem c. Rolle's Theorem d. Mean Value Theorem e. Finding a Tangent Line f. Finding Instantaneous Rate of Change g. Finding Intervals where f is Increasing/Decreasing h. Applying the First Derivative Test i. The Path of a Projectile j. Determining Concavity k. Finding Points of Inflection l. Using the Second Derivative Test E (Random) Curve Sketching and Applications a. Limits at Infinity b. Finding Horizontal Asymptotes c. Graphing Rational Functions d. Graphing Radical Functions e. Graphing Polynomial Functions f. Graphing Trigonometric Functions g. Finding Minimum Volume/Area h. Finding Minimum Distance/Length i. Finding Maximal Area given Perimeter j. Using Newton's Method k. Using Tangent Line Approximations F (Random) Integrals a. Vocabulary and Symbolic Notation b. Solving Basic Differential Equations c. Applying Basic Integration Rules d. Rewriting before Integrating e. Finding Particular Solutions f. Evaluating Definite Intervals (Fundamental Theorem of Calculus) g. Solving Vertical Motion Problems h. Using the Mean Value Theorem for Integrals (Finding the Average Value) i. Using the Second Fundamental Theorem of Calculus j. Integrating a Composite Function k. Integrating using Change of Variables l. Integrating Definite Integrals using Change of Variables m. Integrating Odd/Even Functions G (Random) Approximating and Finding Area a. Using Riemann sums to approximate Area b. Using the Trapezoidal Rule to approximate Area c. Doing Error Analysis with the Trapezoidal Rule d. Using Simpson's Rule to approximate Area e. Doing Error Analysis with Simpson's Rule f. Using Definite Intervals to find Area H (Random) Logarithms and Exponential Functions a. Differentiating Logarithmic Functions b. Differentiation involving Logs and Absolute Value c. Finding Relative Extrema with Logarithmic Functions d. Integrating Using Logarithms e. Integrating Logs with Change of Variable f. Finding Area with the Log Rule g. Change of Variable with the Log Rule h. Solving Differential Equations involving Logs i. Finding an Average Value j. Differentiating Exponential Functions k. Locating Relative Extrema for Exponential Functions l. Integrating Exponential Functions m. Finding Area with Exponential Functions n. Derivatives for Bases other than e o. Integration for Bases other than e p. Solving Word Problems about Compound Interest q. Solving Word Problems with Logistic Growth r. Solving Word Problems about Logistic Decay I (Random) Trigonometric Functions and Inverse Functions a. Integrating Trigonometric Functions b. Evaluating the Derivative of an Inverse Function c. Domain/Range of Inverse Trigonometric Functions d. Differentiating Inverse Trigonometric Functions e. Maximizing Angles f. Integration with Inverse Trigonometric Functions g. Integration by Substitution h. Completing the Square to help Integrate J (Random) Differential Equations a. Sketching Slope Fields b. Using Slope Fields to sketch a Particular Solution c. (BC TEST) Approximating Solutions using Euler's Method d. Solve Differential Equations e. Exponential Growth and Decay f. Using Separation of Variables g. Finding a Particular Solution h. Finding a Particular Solution Curve i. (BC TEST) Solving Logistic Differential Equations j. Solving First-Order Linear Differential Equations	K (Random) Area, Volume, and Arc Length a. Finding the Area of a Region Between Two Curves b. Finding the Area of a Region cut Horizontally Between Two Curves c. Finding Volume when Revolving around an Axis d. Finding Volume when Revolving not no an Axis e. Finding Volume when you know the Cross Section f. Finding the Length of an Arc g. Finding the Area of a Surface created by Revolution L (Random) Integration Techniques a. (BC TEST) Integrating with Disguised Log Rules b. (BC TEST) Integrating with Disguised Power Rules c. Integrating Using Trigonometric Identities d. (BC TEST) Integration By Parts e. (BC TEST) Integrating Complex Trigonometric Integrals f. (BC TEST) Integrating Using Trigonometric Substitution g. (BC TEST) Converting Limits when Integrating Using Trigonometric Substitution h. (BC TEST) Finding Arc Length i. (BC TEST) Integrating With Partial Fractions M Indeterminate Forms and L'Hopital's Rule (Random) a. (BC TEST) Identifying Indeterminate Forms where you can use L'Hopital's Rule b. (BC TEST) Using L'Hopitals' Rule in the Basic Cases c. (BC TEST) Using L'Hopital's Rule in More Advanced Cases d. (BC TEST) Evaluating Improper Integrals with one Infinite Limit e. (BC TEST) Evaluating Improper Integrals with two Infinite Limits N (Random) Sequences and Series a. (BC TEST) Determining Convergence / Divergence of the Limit of a Sequence b. (BC TEST) Using L'Hopital's Rule to Determine Convergence of the Limit of a Sequence c. (BC TEST) Using the Squeeze Theorem for Sequences d. (BC TEST) Identifying Bounded Monotonic Sequences e. (BC TEST) Finding the n^th Partial Sum f. (BC TEST) Identifying Series Tests and Their Conditions g. (BC TEST) Using Geometric Series h. (BC TEST) Using the n^th-Term Test for Divergence i. (BC TEST) Using the Integral Test j. (BC TEST) Using Telescoping Series k. (BC TEST) Using p-Series and Harmonic Series l. (BC TEST) Using the Direct Comparison Test m. (BC TEST) Using the Limit Comparison Test n. (BC TEST) Using the Alternating Series Test o. (BC TEST) Using the Alternating Series Remainder to Approximate Eror p. (BC TEST) Using Absolute and Conditional Convergence q. (BC TEST) Using the Ratio Test r. (BC TEST) Using the Root Test O (Random) Polynomial Approximations a. (BC TEST) Using Taylor and Maclaurin Polynomial Approximations b. (BC TEST) Finding Lagrange Error for A Taylor Polynomial c. (BC TEST) Finding Radius of Convergence d. (BC TEST) Finding the Interval of Convergence e. (BC TEST) Finding Geometric Power Series f. (BC TEST) Finding Power Series by Integration g. (BC TEST) Taylor and Maclaurin Series for Composite Functions h. (BC TEST) Finding A Binomial Series i. (BC TEST) Approximating Definite Integrals With Power Series P (Random) Parametric Equations a. (BC TEST) Converting From Parametric Equations b. (BC TEST) Creating Parametric Equations for a Graph/Relation c. (BC TEST) Parametric Equations and Orientation (note: sketching a curve..) d. (BC TEST) Graphing a Cycloid e. (BC TEST) Differentiation of Parametric Equations f. (BC TEST) Finding Slope of Parametric Equations f. (BC TEST) Finding Tangent Lines of Parametric Equations g. (BC TEST) Finding Concavity of Parametric Equations h. (BC TEST) Finding Arc Length of a Parametric Curve i. (BC TEST) Finding the Area of a Surface of Revolution (Parametric) Q (Random) Polar Coordinates a. (BC TEST) Converting Points from Rectangular to Polar Form b. (BC TEST) Converting Points from Polar to Rectangular Form c. (BC TEST) Converting Equations from Rectangular to Polar Form d. (BC TEST) Converting Equations from Polar to Rectangular Form e. (BC TEST) Sketching Special Polar Graphs f. (BC TEST) Finding Horizontal and Vertical Tangent Lines g. (BC TEST) Finding Tangent Lines at the Pole h. (BC TEST) Finding Area of a Polar Region (One curve) i. (BC TEST) Finding Area of a Polar Region (Two curves) j. (BC TEST) Finding Arc Length of a Polar Curve k. (BC TEST) Finding the Area of a Surface of Revolution l. (BC TEST) Classifying Conics by Eccentricity R (Random) Vectors a. (BC TEST) Identifying Vector Vocabulary b. (BC TEST) Finding the Length of a Vector (Magnitude) c. (BC TEST) Using Basic Vector Operations (addition, subtraction, scalar multiplication) d. (BC TEST) Identifying and Using Properties of Vector Operations e. (BC TEST) Finding a Unit Vector f. (BC TEST) Writing Vectors as a Linear Combination of Unit Vectors g. (BC TEST) Writing a Vector given Magnitude and Direction h. (BC TEST) Finding a Resultant Force i. (BC TEST) Finding a Velocity j. (BC TEST) Writing Vectors in Space with Unit Vectors k. (BC TEST) Writing Vectors in Space in Component Form l. (BC TEST) Measuring Force in Space m. (BC TEST) Finding the Dot Product of Vectors n. (BC TEST) Finding the Angle Between Two Vectors o. (BC TEST) Finding Orthogonal Vectors p. (BC TEST) Finding Projections q. (BC TEST) Decomposing a Vector into Vector Components r. (BC TEST) Finding a Force s. (BC TEST) Finding Work t. (BC TEST) Finding the Cross Product u. (BC TEST) Using the Cross Product v. (BC TEST) Finding Derivatives of Vector Valued Functions w. (BC TEST) Finding Intervals where the Curve is Smooth x. (BC TEST) Finding Velocity and Acceleration
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