AP+Calculus

Links Legend: [T] - Teacher Created [S] - Student Created [E] - External Link

1. Limits
[|Video (S)] [|Video (T)] [|Video (T)] || [|Video (S)] || Video (T) ||
 * 1) Students will be able to determine a limit (even if it DNE) graphically, numerically and algebraically || [|Podcast (T)]
 * 2) Students will be able to determine a limit that involves infinity || [|Pencast (T)]
 * 3) Students will be able to apply limits to determine whether continuity exists for a given function || [|Pencast (T)]
 * 4) Students will be able to find a constant that will make a piece-wise function continuous || [|Pencast (T)] ||
 * 5) Students will be able to apply the Intermediate Value Thm || [|Pencast (T)] ||
 * 6) Students will be able to use l’Hopital’s rule to evaluate limits of rational functions || [|Pencast (T)] ||

2. Derivatives
[|Video (T)] || [|Video (S)] || Video (T) || Product Rule (T) Quotient Rule (T) || Video (T) || Video (T) ||
 * 1) Students will be able to recognize and use the definition(s) and meanings of a derivative || [|Pencast (T)]
 * 2) Students will be able to use the derivative to solve problems involving equations of the tangent line || [|Pencast (T)] ||
 * 3) Students will be able to use the relationship between differentiability and continuity to solve for a constant in a piece-wise function || [|Pencast (T)] ||
 * 4) Students will be able to determine the algebraic derivative of polynomial functions || [|Pencast (T)]
 * 5) Students will be able to determine the algebraic derivative of trigonometric functions || [|Pencast (T)] ||
 * 6) Students will be able to determine the algebraic derivative of composite functions || [|Pencast (T)]
 * 7) Students will be able to determine the algebraic derivative of inverse functions || [|Pencast (T)] ||
 * 8) Students will be able to determine the algebraic derivatives of functions that are products or quotients || [|Pencast (T)]
 * 9) Students will be able to determine the algebraic derivative of exponential, logarithmic and natural exponential functions || [|Pencast (T)] ||
 * 10) Students will be able to use derivatives with position, velocity and acceleration functions || [|Pencast (T)]
 * 11) Students will be able to determine the speed of a function by determining the relationship between velocity and acceleration of a moving object || [|Pencast (T)] ||
 * 12) Students will be able to use derivatives to determine the critical points of a given function || [|Pencast (T)] ||
 * 13) Students will be able to use graphs to represent the relationships between a function and its first and second derivatives || [|Pencast (T)]
 * 14) Students will be able to use number lines of first and second derivatives to determine the behavior of graphs of functions || [|Pencast (T)] ||
 * 15) Students will be able to use derivatives to solve maximum/minimum problems || Podcast ||
 * 16) Students will be able to implicitly determine the algebraic derivative of functions || [|Pencast (T)] ||
 * 17) Students will be able to determine the derivative of an integral using the Fundamental Thm of Calculus (other form) || [|Pencast (T)] ||
 * 18) Students will be able to use the Mean Value Theorem to solve problems or justify conclusions || [|Pencast (T)] ||
 * 19) Students will be able to use derivatives to solve related rates problems || [|Pencast (T)] ||

3. Integrals
Video (T) || [|Video (T)] ||
 * 1) Students will be able to determine the anti-derivative of polynomial functions || [|Pencast (T)] ||
 * 2) Students will be able to determine the anti-derivative of trigonometric functions || [|Pencast (T)] ||
 * 3) Students will be able to determine the anti-derivative of composite functions || [|Pencast (T)]
 * 4) Students will be able to determine the anti-derivative of exponential, logarithmic and natural exponential functions || [|Pencast (T)] ||
 * 5) Students will be able to use anti-derivatives with position, velocity and acceleration functions || [|Pencast (T)] ||
 * 6) Students will be able to approximate the area under a curve using trapezoids || [|Pencast (T)]
 * 7) Students will be able to approximate the area under a curve using Riemann Sums (upper, lower, right, middle and left) || Podcast ||
 * 8) Students will be able to calculate the area under a curve by using the Fundamental Theorem of Calculus || Podcast ||
 * 9) Students will be able to solve differential equations (including exponential growth/decay) by separating and integrating || Podcast ||
 * 10) Students will be able to represent a differential equation graphically with a slope field || Podcast ||
 * 11) Students will be able to use properties of integrals to solve problems || Podcast ||
 * 12) Students will be able to use integrals to find the area between two functions || Podcast ||
 * 13) Students will be able to use integrals to find the volume of solid formed by plane slicing || Podcast ||
 * 14) Students will be able to use integrals to find the volume of a solid formed by rotation around an axis using the disk and/or washer method || Podcast ||
 * 15) Students will be able to determine distance and displacement of a moving object that changes direction in a given time interval || Podcast ||
 * 16) Students will be able to determine the average value of a given function over a given time interval || Podcast ||
 * 17) Students will be able to use u-substitution to evaluate definite integrals || Podcast ||

4. Use of Technology

 * 1) Students will be able to determine the numerical derivative of a function using a graphing calculator || Video (T) ||
 * 2) Students will be able to approximate the area under a curve numerically using a graphing calculator || Podcast ||
 * 3) Students will be able to numerically solve equations using a graphing calculator || Podcast ||
 * 4) Students will be able graph functions and create corresponding tables with a graphing calculator || Podcast ||

AP Calculus Review for Exam