• ### Course Overview

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.

HCC Equivalent Course

MATH 2413  Calculus I  /Sem. Hr. 4

PREREQUISITES

Before studying calculus, all students should complete the equivalent of four years of secondary mathematics designed for college-bound students: courses that should prepare them with a strong foundation in reasoning with algebraic symbols and working with algebraic structures. Prospective calculus students should take courses in which they study algebra, geometry, trigonometry, analytic geometry, and elementary functions. These functions include linear, polynomial, rational, exponential, logarithmic, trigonometric, inverse trigonometric, and piecewise-defined functions. In particular, before studying calculus, students must be familiar with the properties of functions, the composition of functions, the algebra of functions, and the graphs of functions. Students must also understand the language of functions (domain and range, odd and even, periodic, symmetry, zeros, intercepts, and descriptors such as increasing and decreasing). Students should also know how the sine and cosine functions are defined from the unit circle and know the values of the trigonometric functions at the numbers 0, π/6, π/4, π/3, π/2, and their multiples

### Course Content

Based on the Understanding by Design® (Wiggins and McTighe) model, this course framework provides a clear and detailed description of the course requirements necessary for student success. The framework specifies what students must know, be able to do, and understand, with a focus on big ideas that encompass core principles, theories, and processes of the discipline. The framework also encourages instruction that prepares students for advanced coursework in mathematics or other fields engaged in modeling change (e.g., pure sciences, engineering, or economics) and for creating useful, reasonable solutions to problems encountered in an ever-changing world.

The AP Calculus AB framework is organized into eight commonly taught units of study that provide one possible sequence for the course. As always, you have the flexibility to organize the course content as you like.

Unit

Exam Weighting (Multiple-Choice)

Unit 1: Limits and Continuity

10%–12%

Unit 2: Differentiation: Definition and Fundamental Properties

10%–12%

Unit 3: Differentiation: Composite, Implicit, and Inverse Functions

9%–13%

Unit 4: Contextual Applications of Differentiation

10%–15%

Unit 5: Analytical Applications of Differentiation

15%–18%

Unit 6: Integration and Accumulation of Change

17%–20%

Unit 7: Differential Equations

6%–12%

Unit 8: Applications of Integration

10%–15%

### Mathematical Practices

The AP Calculus AB framework included in the course and exam description outlines distinct skills, called mathematical practices, that students should practice throughout the year—skills that will help them learn to think and act like mathematicians.

Skill

Description

1.  Implementing Mathematical Processes

Determine expressions and values using mathematical processes.

2. Connecting Representations

Translate mathematical information from a single representation.

3.  Justification

Justify reasoning and solutions.

4.  Communication and Notation

Use correct notation, language, and mathematical conventions.

### AP and Higher Education

Higher education professionals play a key role developing AP courses and exams, setting credit and placement policies, and scoring student work. The AP Higher Education site features information on recruitment and admission, advising and placement, and more.

This chart shows recommended scores for granting credit, and how much credit should be awarded, for each AP course. Your students can look up credit and placement policies for colleges and universities on the AP Credit Policy Search .

Meet the Development Committee for AP Calculus AB.