# 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**This unit covers parent functions, polynomial – power functions, and trigonometric functions, as well as radical, rational, inverse, logarithmic, and exponential functions, and polynomial inequalities.

**Unit 2 – Limits and Continuity**This unit discusses computations of limits, indeterminate forms, limits to infinity, proving continuity, intermediate value theorem, and types of discontinuity.

**Unit 3 – Derivatives: Part I**This unit covers average versus instantaneous velocity, the tangent of y=x2 and of y=1/x, 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**This unit discusses tangent and normal lines, approximating values of functions using local linearization, local linearity and differentiability, derivatives of trigonometric functions, product and quotient rules with trigonometric and algebraic functions, numerical derivative with a calculator, predicting what f'(x0 looks like graphically, and the graph of the derivative (calculator based).

**Unit 5 – Derivatives: Part III**This unit covers the chain rule and chain rule activity, velocity of a particle in motion, acceleration with analysis, implicit differentiation: the differential method and the y’ method.

**Unit 6 – Derivatives: Part IV**This unit discusses the derivative of the exponential function, inverse functions and derivatives, properties of logarithms, derivative of the logarithmic functions, logarithmic differentiation, combination rules, and derivatives of inverse trigonometric functions.

**Unit 7 – Derivatives: Part V**This unit discusses analysis using first and second derivatives, absolute extrema, optimization problems, related rates, and mean value theorem for derivatives.

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

**Unit 9 – Anti-Differentiation: Part II**This unit covers definite integrals, the fundamental theorem o f calculus, approximate area using numerical methods, Riemann Sums – midpoint, 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**This unit discusses numerical approximations: the trapezoid rule, area under a curve, area of a region between two curves, and the average rule.

**Unit 11 – Anti-Differentiation: Part IV**This unit discusses volumes of solids of revolution: the disc, washer, and shell methods, as well as 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**This unit reviews integrals and discusses integration by parts, Newton’s Method, indeterminate forms and L”Hopital’s Rule, inverse trigonometric integrals, velocity, acceleration, and preparing for the AP Calculus AP Exam.