West Windsor-Plainsboro Regional School District AP Calculus AB Grades 9-12
18 days Unit 1: Limits and Continuity What is a limit? The informal definition of a limit, definition of continuous Estimate the slope of a line tangent to a given point Estimate the average velocity and instantaneous velocity at a given time Determine the limit of a function by applying the limit laws Show, by definition, if a function is continuous Calculate slopes of tangents, velocities, and other rates of change by applying the learned techniques to compute limits
Core Text: Calculus, 4 th Edition, Brooks, Cole Suggested :
Unit 2: Derivatives 18 days What is a derivative? How do we use derivatives? Terms: Derivative, chain rule, implicit differentiation, linear approximation, differentials, differentiable Apply the definition of derivative as a function Interpret the derivative as a rate of change Apply the power rule, product rule, and quotient rule to evaluate derivatives of functions Extend the concept of rates of change to the natural sciences and social sciences Differentiate trigonometric functions Differentiate a function by applying the chain rule Apply the method of implicit differentiation Evaluate higher order derivatives Solve related rate applications Find the linearization of a function and use it to approximate values
Compute the differential of a function Core Text: Calculus, 4 th Edition, Brooks, Cole Suggested :
Unit 3: Applications of Derivatives 18 days How can we use derivatives solve problems? The Mean Value Theorem, Newton s Method and the terms extreme values and anti derivative Apply calculus to find the maximum/minimum values of a function Apply the Mean Value Theorem Analyze and make the connections between and Evaluate limits at infinity Sketch the curve of a function by applying the first and second derivative tests Solve real world optimization problems Approximate roots by using Newton s method Determine the anti derivative of a function
Core Text: Calculus, 4 th Edition, Brooks, Cole Suggested :
Unit 4: Integrals 18 days How can we use integrals to find areas under a curve? How can we use integrals to solve problems? The Fundamental Theorem of Calculus, the Total Change Theorem and the term integral Approximate the area under a curve Approximate the total distance traveled Apply the definition of definite integral Approximate the definite integral Approximate definite integrals by applying the trapezoidal rule Apply the Fundamental Theorem of Calculus Solve applications involving the Total Change Theorem Evaluate definite and indefinite integrals by applying the substitution rule
Core Text: Calculus, 4 th Edition, Brooks, Cole Suggested :
Unit 5: Inverse Functions Course & Grade Level: Calculus Honors, 9 12 Calculus is a final course in the college preparatory sequence. It is designed for students who have successfully completed Pre calculus, but who need a less rigorous pace than Advanced Placement Calculus, as well as reinforcement of fundamental pre calculus concepts. The curriculum is designed to introduce students to a variety of calculus concepts while promoting critical thinking and fine tuning their pre calculus skills. This course will prepare students to continue on in higher level mathematics courses with confidence. Topics covered include a review of functions, limits, differentiation, applications of the derivative, integration and its applications, and trigonometric functions. 22 days What are the properties of inverse functions? How can we evaluate derivatives of inverse trigonometric functions? Properties of inverse functions Evaluate the derivative of an inverse function at a given point Compute the derivative of an exponential function Integrate exponential functions Differentiate logarithmic functions Integrate logarithmic functions Apply the method of logarithmic differentiation Evaluate derivatives of inverse trigonometric functions Integrate inverse trigonometric functions
Core Text: Calculus, Seventh Edition, Larson, Hostetler, Edwards Suggested :
Unit 6: Applications of Integration 18 days How can we use integration to solve real world problems? How can we find the area of a region? The disk, washer and shell method to find volume of a solid The meaning of the term: average value of a function Find the area of a region bounded by two curves Find the volume of a solid obtained by a rotation, using the disk method Find the volume of a solid obtained by a rotation, using the washer method Find the volume of a solid obtained by a rotation, using the shell method Find the volume of a solid with a known cross section Solve real world application problems involving area Solve application problems involving volume Find the average value of a function
Core Text: Calculus, 4 th Edition, Brooks, Cole Suggested :
Unit 7: Slope Fields and Differential Equations 18 days How can we construct a slope field? How do you solve differential equations using separation of variables? Terms: slope fields and differential equations Construct a slope field Sketch an anti derivative using a slope field Solve a differential equation by using separation of variables Core Text: Calculus, 4 th Edition, Brooks, Cole Suggested :
Unit 8: Improper Integrals 18 days How can we evaluate and use improper integrals? Terms: Divergence, convergence, improper integral, l hopital s rule Evaluate improper integrals with infinite integration limits Evaluate improper integrals with infinite discontinuities Apply improper integrals to finding the volume of an infinite solid Evaluate limits applying l hopital s rule Core Text: Calculus, 4 th Edition, Brooks, Cole Suggested :
Unit 9: Techniques of Integration This unit is optional enrichment at the teacher s discretion 18 days How do we apply the techniques of integration to differentiate functions? Terms: Partial fraction decomposition Apply integration by parts to differentiate functions Apply trigonometric substitution to differentiate functions Apply partial fraction decomposition to differentiate functions Core Text: Calculus, 4 th Edition, Brooks, Cole
Unit 10: Applications of Integration This unit is optional enrichment at the teacher s discretion 18 days How can we use integration to find the length of an arc? How can we use integration to evaluate the surface area of a function? Definition of arc length Find the length of an arc Evaluate the surface area of a function Core Text: Calculus, 4 th Edition, Brooks, Cole