## AP Calculus 12

AP Calculus AB Course Overview

Big Ideas

 ChangeUsing derivatives to describe rates of change of one variable with respect to another or using definite integrals to describe the net change in one variable over an interval of another allows students to understand change in a variety of contexts. It is critical that students grasp the relationship between integration and differentiation as expressed in the Fundamental Theorem of Calculus—a central idea in AP Calculus. LimitsBeginning with a discrete model and then considering the consequences of a limiting case allows us to model real-world behavior and to discover and understand important ideas, definitions, formulas, and theorems in calculus: for example, continuity, differentiation, integration. Analysis of FunctionsCalculus allows us to analyze the behaviors of functions by relating limits to differentiation, integration, and infinite series and relating each of these concepts to the others.

Introduction

AP Calculus AB is an introductory college-level calculus course. Students cultivate their understanding of differential and integral calculus through engaging with real-world problems represented graphically, numerically, analytically, and verbally and using definitions and theorems to build arguments and justify conclusions as they explore concepts like change, limits, and the analysis of functions.

Where does this course fit?

• Pre-Requisite: Requires Pre-Calculus 11 and some of Pre-Calculus 12
• An optional AP exam in May (requires exam fee) where a score of 4 or 5 may be used as university course credit.

Course Materials

• Graphing calculator is recommended
• Graphing calculator is required if you are writing the AP exam

Brief Outline

 Unit Description Limits and Continuity Limits introduce the subtle distinction between evaluating a function at a point and what value the function is approaching. This distinction allows us to extend understanding of asymptotes and holes in graphs with formal definitions of continuity. Differentiation Derivatives allow us to determine instantaneous rates of change. You will learn how to differentiate functions using various rules and apply that understanding to determine derivatives of implicit and inverse functions Applications of Differentiation We study how derivatives can be applied to solve real world problems. Integration and Accumulation of Change This unit establishes the relationship between differentiation and integration using the Fundamental Theorem of Calculus. We begin by exploring the contextual meaning of areas of certain regions bounded by rate functions. Differential Equations We learn to set up and solve separable differential equations. Slope fields can be used to represent solution curves to a differential equation, leading to the idea that there are infinitely many general solutions, varying only by a constant of integration Applications of Integration We learn how to find the average value of a function, model particle motion and net change, and determine areas, volumes. We also learn how to apply the Fundamental Theorem of Calculus to various problems.

Assessment Percentage Breakdown

 Assessment Type Percentage of the Course Assignments 41% Quizzes 24% Midterm exam 15% Final exam 20%

You have up to a year to complete your course.