Posted: Tue, 07/03/2018 - 2:12pm Updated: Thu, 07/25/2019 - 8:59am

This Teacher Resource Guide has been developed to provide supporting materials to help educators successfully implement the Indiana Academic Standards for Calculus. These resources are provided to help you in your work to ensure all students meet the rigorous learning expectations set by the Indiana Academic Standards. Use of these resources are optional; teachers should decide which resources will work best in their classroom for their students.

The resources on this webpage are for illustrative purposes only, to promote a base of clarity and common understanding. Each item illustrates a standard but please note that the resources are not intended to limit interpretation or classroom applications of the standards.

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LIMITS AND CONTINUITY

Activities, Examples, or Resources

C.LC.1: Understand the concept of limit and estimate limits from graphs and tables of values.

Limits & Continuity

C.LC.2: Find limits by substitution.

C.LC.3: Find limits of sums, differences, products, and quotients.

C.LC.4: Find limits of rational functions that are undefined at a point.

C.LC.5: Find limits at infinity.

C.LC.6: Decide when a limit is infinite and use limits involving infinity to describe asymptotic behavior.

C.LC.7: Find one-sided limits.

C.LC.8: Understand continuity in terms of limits.

Polygraph: Continuity

C.LC.9: Decide if a function is continuous at a point.

C.LC.10: Find the types of discontinuities of a function.

C.LC.11: Understand and use the Intermediate Value Theorem on a function over a closed interval.

The Intermediate Value Theorem

C.LC.12: Understand and apply the Extreme Value Theorem: If f(x) is continuous over a closed interval, then f has a maximum and a minimum on the interval.

Exploring the Extreme Value Theorem

DIFFERENTIATION

Activities, Examples, or Resources

C.D.1: Understand the concept of derivative geometrically, numerically, and analytically, and interpret the derivative as a rate of change.

C.D.2: State, understand, and apply the definition of derivative.

C.D.3: Find the derivatives of functions, including algebraic, trigonometric, logarithmic, and exponential functions.

C.D.4: Find the derivatives of sums, products, and quotients.

C.D.5: Find the derivatives of composite functions, using the chain rule.

C.D.6: Find the derivatives of implicitly-defined functions.

C.D.7: Find the derivatives of inverse functions.

C.D.8: Find second derivatives and derivatives of higher order.

C.D.9: Find derivatives using logarithmic differentiation.

C.D.10: Understand and apply the relationship between differentiability and continuity.

C.D.11: Understand and apply the Mean Value Theorem.

Mean Value Theorem

APPLICATIONS OF DERIVATIVES

Activities, Examples, or Resources

C.AD.1: Find the slope of a curve at a point, including points at which there are vertical tangents and no tangents.

C.AD.2: Find a tangent line to a curve at a point and a local linear approximation.

C.AD.3: Decide where functions are decreasing and increasing. Understand the relationship between the increasing and decreasing behavior of f and the sign of f'.

C.AD.4: Solve real-world and other mathematical problems finding local and absolute maximum and minimum points with and without technology.

C.AD.5: Analyze real-world problems modeled by curves, including the notions of monotonicity and concavity with and without technology.

C.AD.6: Find points of inflection of functions. Understand the relationship between the concavity of f and the sign of f".  Understand points of inflection as places where concavity changes.

C.AD.7: Use first and second derivatives to help sketch graphs modeling real-world and other mathematical problems with and without technology. Compare the corresponding characteristics of the graphs of f, f', and f".

Graphles to Graphles

C.AD.8: Use implicit differentiation to find the derivative of an inverse function.

C.AD.9: Solve optimization real-world problems with and without technology.

C.AD.10: Find average and instantaneous rates of change. Understand the instantaneous rate of change as the limit of the average rate of change. Interpret a derivative as a rate of change in applications, including distance, velocity, and acceleration.

Average Versus Instantaneous Speed

C.AD.11: Find the velocity and acceleration of a particle moving in a straight line.

C.AD.12: Model rates of change, including related rates problems.

INTEGRALS

Activities, Examples, or Resources

C.I.1: Use rectangle approximations to find approximate values of integrals.

C.I.2: Calculate the values of Riemann Sums over equal subdivisions using left, right, and midpoint evaluation points.

C.I.3: Interpret a definite integral as a limit of Riemann Sums.

C.I.4: Understand the Fundamental Theorem of Calculus: Interpret a definite integral of the rate of change of a quantity over an interval as the change of the quantity over the interval, that is

C.I.5: Use the Fundamental Theorem of Calculus to evaluate definite and indefinite integrals and to represent particular antiderivatives. Perform analytical and graphical analysis of functions so defined.

Explore the FTC Using a Graphing Calculator

C.I.6: Understand and use these properties of definite integrals.

C.I.7: Understand and use integration by substitution (or change of variable) to find values of integrals.

C.I.8: Understand and use Riemann Sums, the Trapezoidal Rule, and technology to approximate definite integrals of functions represented algebraically, geometrically, and by tables of values.

APPLICATIONS OF INTEGRALS

Activities, Examples, or Resources

C.AI.1: Find specific antiderivatives using initial conditions, including finding velocity functions from acceleration functions, finding position functions from velocity functions, and applications to motion along a line.

C.AI.2: Solve separable differential equations and use them in modeling real-world problems with and without technology.

C.AI.3: Solve differential equations of the form y' = ky as applied to growth and decay problems.

C.AI.4: Use definite integrals to find the area between a curve and the x-axis, or between two curves.

C.AI.5: Use definite integrals to find the average value of a function over a closed interval.

A Visual Approach to Average Value

C.AI.6: Use definite integrals to find the volume of a solid with known cross-sectional area.

C.AI.7: Apply integration to model and solve (with and without technology) real-world problems in physics, biology, economics, etc., using the integral as a rate of change to give accumulated change and using the method of setting up an approximating Riemann Sum and representing its limit as a definite integral.