AP+Calculus+Targets

AP Calculus

Target 1: I can estimate a limit from a graph and a table of data.

Target 2: I can find a limit using algebraic methods including substitution, factoring, rationalization, and simplification of complex fractions.

Target 3: I can find limits of functions involving trigonometry.

Target 4: I can find asymptotes analytically and using graphs and limits involving infinity.

Target 5: I can use limits to discuss the continuity of a function.

Target 6: I can use the Intermediate Value Theorem to prove that a function equals a given value on an interval.

Target 7: I can explain the difference between the average rate of change and the instantaneous rate of change, and find both.

Target 8: I can find the derivative using the limit of the difference quotient.

Target 9: I can find the derivative using the constant rule, power rule, constant multiple rule, the sum rule and the difference rule.

Target 10: I can find derivatives using the product and quotient rules.

Target 11: I can find position, velocity, speed and acceleration when given one of the functions.

Target 12: I can find the derivatives of trigonometric functions.

Target 13: I can find the derivative using the chain rule.

Target 14: I can find the derivative using implicit differentiation.

Target 15: I can use implicit differentiation to find the derivative of inverse functions, including inverse trigonometric functions.

Target 16: I can find the derivatives of exponential and logarithmic functions.

Target 17: I can use the Extreme Value Theorem to prove that a function has an absolute maximum and an absolute minimum on an interval.

Target 18: I can use the Mean Value Theorem to prove that a function has a specific instantaneous rate of change on a given interval.

Target 19: I can approximate the rate of change from graphs and tables of values.

Target 20: I can use the first derivative of a function to describe the behavior of the function.

Target 21: I can use the second derivative of a function to describe the behavior of a function.

Target 22: I can sketch a curve using information obtained from the first and second derivatives.

Target 23: I can find the maximum or minimum of a situation using optimization.

Target 24: I can find the slope of a curve at a point in order to find the equation of the tangent line, normal line and do a local linear approximation.

Target 25: I can solve problems involving rates using the related rates technique.

Target 26: I can write a definite integral as a limit of Riemann sums.

Target 27: I can find anti-derivatives of basic functions.

Target 28: I can use the basic properties of integrals to solve integral equations and simplify expressions.

Target 29: I can use the Fundamental Theorem of Calculus to evaluate definite integrals.

Target 30: I can find the average value of a function, and explain the relationship between average value and average rate of change.

Target 31: I can use the Fundamental Theorem of Calculus to do analytical and graphical analysis of functions.

Target 32: I can find numerical approximations using Riemann sums (Left, Right, and Midpoint) and trapezoid sums.

Target 33: I can sketch a slope field when given a differential.

Target 34: I can use substitution to find the anti-derivatives, including change of limits and change of variables.

Target 35: I can find the anti-derivatives of exponential and logarithmic functions.

Target 36: I can use separation of variables to solve a differential equation and use the solution in modeling.

Target 37: I can solve growth and decay equations algebraically.

Target 38: I can use the net change theorem.

Target 39: I can find particular anti-derivatives using an initial condition, including applications to motion.

Target 40: I can find the total distance traveled by a particle.

Target 41: I can find the area of a region between two curves.

Target 42: I can find the volume of a three-dimensional solid with known cross sections or by rotation around an axis.

Target 43: I can use L'Hopital's Rule to find limits.