# AP Calculus AB

#### Course Features

#### Course Details

Course Overview

Acellus AP Calculus is a two-part advanced placement course providing students with the curriculum required by the College Board for AP Calculus AB and BC. Students completing this course will be able to take the AP Calculus exam, enabling them to earn college credit for taking this course while still in high school.
Besides learning how to use the basic tools of Calculus, students completing this course learn on a deeper level what they are really doing and why it works. This provides insight few students experience in more conventional Calculus courses, empowering them with the knowledge required to solve real world problems.
Acellus AP Calculus is taught by veteran AP Calculus teacher, Patrick Mara. This course has been audited and approved by the College Board.
Acellus AP Calculus is A-G Approved through the University of California.
### Course Objectives & Student Learning Outcomes

Acellus AP Calculus is a two part-series consisting of Acellus AP Calculus AB and BC. Students completing this series will have taken the equivalent of two-semesters of college Calculus. (These courses have been audited and approved by the College Board to carry the AP designation and have been acknowledged to provide students with a college-level learning experience.) Students successfully completing these courses will know what limits are and how to compute them. They know how to differentiate functions and use various differentiation rules including the combination rules and the chain rule. They know how to use Calculus to analyze various functions and sketch graphs based on their derivatives. They are familiar using derivatives in real world situations. Students know how to approximate the area under curves using numerical methods and how to calculate the exact area using integration. Students are familiar with various integration techniques, including the chain rule, u-substitution, integration by parts, trig substitution, and partial fractions. They know how to use integration to calculate volumes of solids of revolution and surface area. Students know how to use integration to solve various real world problems including work problems and problems based upon liquid pressure and fluid force. They also know how to use separable differential equations and are familiar with slope fields. Students are familiar with sequences and various series and converge tests. Students also know how to work with parametric equations, polar coordinates and functions, and vector quantities and know how to calculate dot and cross products.This course was developed by the International Academy of Science. Learn More

**Scope and Sequence**

**Unit 1 – Pre-Calculus Review**In this unit students discuss parent functions, polynomial – power functions, and trigonometric functions. The study radical, rational, inverse, logarithmic, and exponential functions, and polynomial inequalities.

**Unit 2 – Limits and Continuity**In this unit students learn about computations of limits, indeterminate forms, limits to infinity, and proving continuity. They discuss intermediate value theorem, and types of discontinuity.

**Unit 3 – Derivatives: Part I**In this unit students explore average versus instantaneous velocity, and the tangent of y=x2 and of y=1/x. They learn about the general rule of the derivative, derivatives of constant and linear functions, the power rule for derivatives, and combination rules: sum and difference, product rule, and quotient rule.

**Unit 4 – Derivatives: Part II**In this unit students investigate tangent and normal lines, and approximating values of functions using local linearization, local linearity and differentiability. They explore derivatives of trigonometric functions, product and quotient rules with trigonometric and algebraic functions, numerical derivative with a calculator, predicting what f'(x) looks like graphically, and the graph of the derivative (calculator based).

**Unit 5 – Derivatives: Part III**In this unit students study the chain rule and chain rule activity, and velocity of a particle in motion. They investigate acceleration with analysis, implicit differentiation: the differential method and the y’ method.

**Unit 6 – Derivatives: Part IV**In this unit students discuss the derivative of the exponential function, inverse functions and derivatives, properties of logarithms, and derivative of the logarithmic functions. They study logarithmic differentiation, combination rules, and derivatives of inverse trigonometric functions. Following this unit students are presented with the Mid-Term Review and Exam

**Unit 7 – Derivatives: Part V**In this unit students learn about analysis using first and second derivatives, and absolute extrema. They discuss optimization problems, related rates, and mean value theorem for derivatives.

**Unit 8 – Anti-Differentiation: Part I**In this unit students explore anti-differentiation, the chain rule and anti-differentiation, U-substitution, anti-derivatives with initial conditions, and particle motion. They learn about exponential growth, decay and Newton’s law of cooling, slope fields, and slope fields with initial value problems.

**Unit 9 – Anti-Differentiation: Part II**In this unit students investigate definite integrals, the fundamental theorem of calculus, approximate area using numerical methods, and Riemann Sums – midpoint. They explore net area, definite integrals with calculator, properties of the definite integral, U-substitution with definite integrals, and the velocity/position connection.

**Unit 10 – Anti-Differentiation: Part III**In this unit students study numerical approximations: the trapezoid rule. They investigate area under a curve, area of a region between two curves, and the average rule.

**Unit 11 – Anti-Differentiation: Part IV**In this unit students discuss volumes of solids of revolution: the disc, washer, and shell methods. They study volume of solids with known cross sections, arc length and surfaces of revolution, integration to find surface area, work problems, and liquid pressure and fluid force.

**Unit 12 – Anti-Differentiation: Part V**In this unit students review integrals and learn about integration by parts, Newton’s Method, indeterminate forms and L'Hopital’s Rule, and inverse trigonometric integrals. They discuss velocity, acceleration, and preparing for the AP Calculus AB Exam. Following this unit students are presented with the Final Review and Exam, which completes this course and their preparation for the AP Calculus AB Exam.