AP Calculus

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AP Calculus-AB worksheets by topics

 

Functions, Limits, & Continuity Differentiation
  1. Interesting Graphs – A few equations to graph that have interesting (and hidden) features.  pdf   
  2. Functions – Properties of functions and the Rule of Four (equations, tables, graphs, and words).  pdf   
  3. Reading a Position Graph – Answer questions about motion using a position graph.  pdf   
  4. Reading Graphs – Four graphs and questions using function notation.  pdf   
  5. Find a Function – Find an example of a function in the media.  pdf   
  6. INDY 500 – Sketch graphs based on traveling one lap along an oval racetrack.  pdf   
  7. Farenheit – The relationship between Farenheit and Celsius.  pdf   
  8. Linear Functions – Applications.  pdf   
  9. Exponential Functions – Recognizing exponential functions and their properties.  pdf   
  10. Inverse Functions – Relationships between a function and its inverse.  pdf   
  11. New Functions From Old – Transformations, compositions, and inverses of functions.  pdf   
  12. Transformations – A matching exercise using symbolic expressions and tables.  pdf   
  13. More Transformations – Graphing transformation.   pdf   
  14. Logarithms – Using logarithms to solve problems. Properties of logas.  pdf   
  15. Trig Reference Sheet – List of basic identities and rules.   pdf   
  16. Trig (part I) -Interpreting trig functions and practice with inverses.  pdf   
  17. Trig (part II) – More practice.  pdf   
  18. Denise & Chad – An illustration of the effects of changes in amplitude and period.  pdf   
  19. Polynomials & Rational Functions – Recognizing polynomials and rational functions and their properties.  pdf   
  20. Power Functions – Use graphs to explore power functions.  pdf   
  21. Limits and Continuity – Graphical and numerical exercises.  pdf   
  22. More Continuity – Basics about continuity.  pdf   
  1. Introduction to Rates – Introduction to rates of change using position and velocity.   pdf   
  2. Representations – Symbolic recognition and illustration of rates. Practical interpretation of rates of change using the rule of four.   pdf   
  3. Practical Example – Reading information about rates from a graph.  pdf   
  4. Estimation – Estimation using tables and equations. Practice with notation and terminology.  pdf   
  5. Derivative Graphs – Graphing a derivative function given a graph.  pdf   
  6. More Derivative Graphs – Matching exercise.  pdf   
  7. Terminology – Fill in the blank exercise. Practice with terminology  pdf   
  8. Differentiability – Determine when a function is not differentiable at a point.  pdf   
  9. More Differentiability – More practice.   pdf   
  10. Practice – Additional practice covering this section.  pdf   
Derivatives
  1. Product & Quotient Rules – Practice using these rules.   pdf   
  2. Chain Rule – Practice using this rule.   pdf   
  3. Base e – Derivation of e using derivatives.  pdf   
  4. Rules – Practice with tables and derivative rules in symbolic form.  pdf   
  5. More Practice – More practice using all the derivative rules.  pdf   
  6. More Practice – More practice using all the derivative rules.  pdf   
  7. Derivative (& Integral) Rules – A table of derivative and integral rules.   pdf   
Applications of Derivatives Definite & Indefinite Integrals/Applications
  1. Reading Graphs – Reading information from first and second derivative graphs.  pdf   
  2. Critical Points Part I – Terminology and characteristics of critical points.  pdf   
  3. Critical Points Part II – Finding critical points and graphing.  pdf   
  4. Families of Functions – Finding critical points for families of functions.  pdf   
  5. More Families of Functions – Finding values of parameters in families of functions.  pdf   
  6. Optimization Part I – Optimization problems emphasizing geometry.  pdf   
  7. Optimization Part II – More optimization problems.  pdf   
  8. Parametric Equations (Circles) – Sketching variations of the standard parametric equations for the unit circle.  pdf   
  9. Parametric Equations (Misc) – Fun graphs using parametric equations.   pdf   
  10. Parametric Equations – Finding direction of motion and tangent lines using parametric equations.  pdf  
  11. Holiday Parametric Equations – Halloween surprise.   pdf   
  12. L’Hopital’s Rule – Practice in recognizing when to use L’Hopital’s Rule.  pdf   
  13. Limit Practice -Additional practice with limits including L’Hopital’s Rule.   pdf   
  14. Introduction to Related Rates – Finding various derivatives using volume of a sphere and surface area of a cylinder.  pdf   
  15. Related Rates – Additional practice.  pdf   
  16. More Related Rates -Additional practice.   pdf   
  1. Intro to Velocity and Area – Relationship between velocity, position, and area.  pdf   
  2. Representations – Practice with notation, estimation, and interpretations.  pdf   
  3. Rocket – Application of velocity and position for a model rocket.  pdf   
  4. Mice – Application of velocity and position for two mice.  pdf   
  5. Cars – Application of velocity, position, and acceleration of two cars.  pdf   
  6. Fundamental Theorem Part I – Graphical approach.  pdf   
  7. Fundamental Theorem Part II – Illustrations and notation.  pdf   
  8. Position, Velocity, & Acceleration – Graphical relationships between position, velocity, and acceleration. pdf   
  9. Sketching Antiderivatives – Graphing antiderivatives.   pdf   
  10. Area Between Graphs – Using the Fundamental Theorem to find area between graphs.  pdf   
  11. Practice – Problems from chapters 5 and 6.  pdf   
  12. Integration – Recognizing when to use substitution. Integrands look similar.  pdf   
  13. Substitution – Practice, including definite integrals.  pdf   
  14. More Substitution – More practice.  pdf   
Differential Equations
  1. Separation of variables
  2. Slope fields
  3. Exponential growth and decay
  4. Particle motion