# Academic standards list

### Calculus — Mathematics

### Introduction

Academic standards define the expectations for knowledge and skills that students are to learn in a subject by a certain age or at the end of a school grade level. This page contains a list of standards for a specific content area, grade level, and/or course. The list of standards may be structured using categories and sub-categories.

### Limits of Functions

TSS.Math.C.AM.F.LF — Conceptual Category: Functions

Understand the concept of the limit of a function.

Estimate limits of functions (including one-sided limits) from graphs or tables of data. Apply the definition of a limit to a variety of functions,…

Draw a sketch that illustrates the definition of the limit; develop multiple real-world scenarios that illustrate the definition of the limit.

### Behavior of Functions

TSS.Math.C.F.BF — Conceptual Category: Functions

Describe the asymptotic and unbounded behavior of functions.

Describe asymptotic behavior (analytically and graphically) in terms of infinite limits and limits at infinity.

Discuss the various types of end behavior of functions; identify prototypical functions for each type of end behavior.

### Continuity

TSS.Math.C.F.C — Conceptual Category: Functions

Develop an understanding of continuity as a property of functions.

Determine and define different types of discontinuity (point, jump, infinite) in terms of limits.

### Understand the Concept of the Derivative

TSS.Math.C.D.CD — Conceptual Category: Derivatives

Demonstrate an understanding of the derivative.

Define the derivative as the limit of the difference quotient; illustrate with the sketch of a graph.

Understand the derivative at a point.

Interpret the derivative as the slope of a curve (which could be a line) at a point, including points at which there are vertical tangents and points at…

Approximate both the instantaneous rate of change and the average rate of change given a graph or table of values.

### Computing and Apply Derivatives

TSS.Math.C.D.AD — Conceptual Category: Derivatives

Apply differentiation techniques.

Describe in detail how the basic derivative rules are used to differentiate a function; discuss the difference between using the limit definition of the…

Calculate the derivative of basic functions (power, exponential, logarithmic, and trigonometric).

Use first and second derivatives to analyze a function.

Relate the increasing and decreasing behavior of f to the sign of f' both analytically and graphically.

Apply derivatives to solve problems.

Model rates of change, including related rates problems. In each case, include a discussion of units.

Use tangent lines to approximate function values and changes in function values when inputs change (linearization).

### Understanding Integrals

TSS.Math.C.I.UI — Conceptual Category: Integrals

Demonstrate understanding of a definite integral.

Use Riemann sums (left, right, and midpoint evaluation points) and trapezoid sums to approximate definite integrals of functions represented graphically,…

Understand and apply the Fundamental Theorem of Calculus.

Use the Fundamental Theorem of Calculus to represent a particular antiderivative of a function and to understand when the antiderivative so represented is…

### Calculate and Apply Intergrals

TSS.Math.C.I.AI — Conceptual Category: Integrals

Apply techniques of antidifferentiation.

Develop facility with finding antiderivatives that follow directly from derivatives of basic functions (power, exponential, logarithmic, and trigonometric).

Use substitution of variables to calculate antiderivatives (including changing limits for definite integrals).

Apply integrals to solve problems.

Use a definite integral to find the volume of a solid formed by rotating a region around a given axis.

Use integrals to solve a variety of problems (e.g., distance traveled by a particle along a line, exponential growth/decay).

♦ Academic Standards marked with a diamond are "

*Supporting Content*" within the grade level or course.

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