- Review 11ap Calculus Definition
- Review 11ap Calculus Test
Version #1
The course below follows CollegeBoard's Course and Exam Description. Lessons will begin to appear starting summer 2020.
BC Topics are listed, but there will be no lessons available for SY 2020-2021Unit 0 - Calc Prerequisites (Summer Work)
0.1 Summer Packet Unit 1 - Limits and Continuity
1.1 Can Change Occur at an Instant?
1.2 Defining Limits and Using Limit Notation
1.3 Estimating Limit Values from Graphs
1.4 Estimating Limit Values from Tables
1.5 Determining Limits Using Algebraic Properties
(1.5 includes piecewise functions involving limits)
1.6 Determining Limits Using Algebraic Manipulation
1.7 Selecting Procedures for Determining Limits
(1.7 includes rationalization, complex fractions, and absolute value)
1.8 Determining Limits Using the Squeeze Theorem
1.9 Connecting Multiple Representations of Limits
Mid-Unit Review - Unit 1
1.10 Exploring Types of Discontinuities
1.11 Defining Continuity at a Point
1.12 Confirming Continuity Over an Interval
1.13 Removing Discontinuities
1.14 Infinite Limits and Vertical Asymptotes
1.15 Limits at Infinity and Horizontal Asymptotes
1.16 Intermediate Value Theorem (IVT)
Review - Unit 1 Unit 2 - Differentiation: Definition and Fundamental Properties
2.1 Defining Average and Instantaneous Rate of
Change at a Point
2.2 Defining the Derivative of a Function and Using
Derivative Notation
(2.2 includes equation of the tangent line)
2.3 Estimating Derivatives of a Function at a Point
2.4 Connecting Differentiability and Continuity
2.5 Applying the Power Rule
2.6 Derivative Rules: Constant, Sum, Difference, and
Constant Multiple
(2.6 includes horizontal tangent lines, equation of the
normal line, and differentiability of piecewise)
2.7 Derivatives of cos(x), sin(x), e^x, and ln(x)
2.8 The Product Rule
2.9 The Quotient Rule
2.10 Derivatives of tan(x), cot(x), sec(x), and csc(x)
Review - Unit 2 Unit 3 - Differentiation: Composite, Implicit, and Inverse Functions
3.1 The Chain Rule
3.2 Implicit Differentiation
3.3 Differentiating Inverse Functions
3.4 Differentiating Inverse Trigonometric Functions
3.5 Selecting Procedures for Calculating Derivatives
3.6 Calculating Higher-Order Derivatives
Review - Unit 3
Unit 4 - Contextual Applications of Differentiation
4.1 Interpreting the Meaning of the Derivative in Context
4.2 Straight-Line Motion: Connecting Position, Velocity,
and Acceleration
4.3 Rates of Change in Applied Contexts Other Than
Motion
4.4 Introduction to Related Rates
4.5 Solving Related Rates Problems
4.6 Approximating Values of a Function Using Local
Linearity and Linearization
4.7 Using L'Hopital's Rule for Determining Limits of
Indeterminate Forms
Review - Unit 4 Unit 5 - Analytical Applications of Differentiation
5.1 Using the Mean Value Theorem
5.2 Extreme Value Theorem, Global Versus Local
Extrema, and Critical Points
5.3 Determining Intervals on Which a Function is
Increasing or Decreasing
5.4 Using the First Derivative Test to Determine Relative
Local Extrema
5.5 Using the Candidates Test to Determine Absolute
(Global) Extrema
5.6 Determining Concavity of Functions over Their
Domains
5.7 Using the Second Derivative Test to Determine
Extrema
Mid-Unit Review - Unit 5
5.8 Sketching Graphs of Functions and Their Derivatives
5.9 Connecting a Function, Its First Derivative, and Its
Second Derivative
(5.9 includes a revisit of particle motion and
determining if a particle is speeding up/down.)
5.10 Introduction to Optimization Problems
5.11 Solving Optimization Problems
5.12 Exploring Behaviors of Implicit Relations
Review - Unit 5 Unit 6 - Integration and Accumulation of Change
6.1 Exploring Accumulation of Change
6.2 Approximating Areas with Riemann Sums
6.3 Riemann Sums, Summation Notation, and Definite
Integral Notation
6.4 The Fundamental Theorem of Calculus and
Accumulation Functions
6.5 Interpreting the Behavior of Accumulation Functions
Involving Area
Mid-Unit Review - Unit 6
6.6 Applying Properties of Definite Integrals
6.7 The Fundamental Theorem of Calculus and Definite
Integrals
6.8 Finding Antiderivatives and Indefinite Integrals:
Basic Rules and Notation
6.9 Integrating Using Substitution
6.10 Integrating Functions Using Long Division
and Completing the Square
6.11 Integrating Using Integration by Parts (BC topic)
6.12 Integrating Using Linear Partial Fractions (BC topic)
6.13 Evaluating Improper Integrals (BC topic)
6.14 Selecting Techniques for Antidifferentiation
Review - Unit 6 Unit 7 - Differential Equations
7.1 Modeling Situations with Differential Equations
7.2 Verifying Solutions for Differential Equations
7.3 Sketching Slope Fields
7.4 Reasoning Using Slope Fields
7.5 Euler's Method (BC topic)
7.6 General Solutions Using Separation of Variables
7.7 Particular Solutions using Initial Conditions and
Separation of Variables
7.8 Exponential Models with Differential Equations
7.9 Logistic Models with Differential Equations (BC topic)
Review - Unit 7 Unit 8 - Applications of Integration
8.1 Average Value of a Function on an Interval
8.2 Position, Velocity, and Acceleration Using Integrals
8.3 Using Accumulation Functions and Definite Integrals
in Applied Contexts
8.4 Area Between Curves (with respect to x)
8.5 Area Between Curves (with respect to y)
8.6 Area Between Curves - More than Two Intersections
Mid-Unit Review - Unit 8
8.7 Cross Sections: Squares and Rectangles
8.8 Cross Sections: Triangles and Semicircles
8.9 Disc Method: Revolving Around the x- or y- Axis
8.10 Disc Method: Revolving Around Other Axes
8.11 Washer Method: Revolving Around the x- or y- Axis
8.12 Washer Method: Revolving Around Other Axes
8.13 The Arc Length of a Smooth, Planar Curve and
Distance Traveled (BC topic)
Review - Unit 8 Unit 9 - Parametric Equations, Polar Coordinates, and Vector-Valued Functions (BC topics)
9.1 Defining and Differentiating Parametric Equations
9.2 Second Derivatives of Parametric Equations
9.3 Arc Lengths of Curves (Parametric Equations)
9.4 Defining and Differentiating Vector-Valued Functions
9.5 Integrating Vector-Valued Functions
9.6 Solving Motion Problems Using Parametric and
Vector-Valued Functions
9.7 Defining Polar Coordinates and Differentiating in
Polar Form
9.8 Find the Area of a Polar Region or the Area Bounded
by a Single Polar Curve
9.9 Finding the Area of the Region Bounded by Two
Polar Curves
Review - Unit 9 Unit 10 - Infinite Sequences and Series (BC topics)
10.1 Defining Convergent and Divergent Infinite Series
10.2 Working with Geometric Series
10.3 The nth Term Test for Divergence
10.4 Integral Test for Convergence
10.5 Harmonic Series and p-Series
10.6 Comparison Tests for Convergence
10.7 Alternating Series Test for Convergence
10.8 Ratio Test for Convergence
10.9 Determining Absolute or Conditional Convergence
10.10 Alternating Series Error Bound
10.11 Finding Taylor Polynomial Approximations of
Functions
10.12 Lagrange Error Bound
10.13 Radius and Interval of Convergence of Power
Series
10.14 Finding Taylor Maclaurin Series for a Function
10.15 Representing Functions as a Power Series
Review - Unit 8 | Version #2
The course below covers all topics for the AP Calculus AB exam, but was built for a 90-minute class that meets every other day.
Lessons and packets are longer because they cover more material.Unit 0 - Calc Prerequisites (Summer Work)
0.1 Things to Know for Calc
0.2 Summer Packet
0.3 Calculator Skillz Unit 1 - Limits
1.1 Limits Graphically
1.2 Limits Analytically
1.3 Asymptotes
1.4 Continuity
Review - Unit 1 Unit 2 - The Derivative
2.1 Average Rate of Change
2.2 Definition of the Derivative
2.3 Differentiability [Calculator Required]
Review - Unit 2 Unit 3 - Basic Differentiation
3.1 Power Rule
3.2 Product and Quotient Rules
3.3 Velocity and other Rates of Change
3.4 Chain Rule
3.5 Trig Derivatives
Review - Unit 3 Unit 4 - More Deriviatvies
4.1 Derivatives of Exp. and Logs
4.2 Inverse Trig Derivatives
4.3 L'Hopital's Rule
Review - Unit 4 Unit 5 - Curve Sketching
5.1 Extrema on an Interval
5.2 First Derivative Test
5.3 Second Derivative Test
Review - Unit 5 Unit 6 - Implicit Differentiation
6.1 Implicit Differentiation
6.2 Related Rates
6.3 Optimization
Review - Unit 6 Unit 7 - Approximation Methods
7.1 Rectangular Approximation Method
7.2 Trapezoidal Approximation Method
Review - Unit 7 Unit 8 - Integration
8.1 Definite Integral
8.2 Fundamental Theorem of Calculus (part 1)
8.3 Antiderivatives (and specific solutions)
Review - Unit 8 Unit 9 - The 2nd Fundamental Theorem of Calculus
9.1 The 2nd FTC
9.2 Trig Integrals
9.3 Average Value (of a function)
9.4 Net Change
Review - Unit 9 Unit 10 - More Integrals
10.1 Slope Fields
10.2 u-Substitution (indefinite integrals)
10.3 u-Substitution (definite integrals)
10.4 Separation of Variables
Review - Unit 10 Unit 11 - Area and Volume
11.1 Area Between Two Curves
11.2 Volume - Disc Method
11.3 Volume - Washer Method
11.4 Perpendicular Cross Sections
Review - Unit 11 |
Show Mobile NoticeADVANCED PLACEMENT CALCULUS BC. CHAPTER 10 Review. TI-89 Titanium Guidebook - FULL Version. AP Calc BC Course Outline. Course Overview. AP Calculus BC 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,.
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Chapter 1 : Review
Review 11ap Calculus Definition
Technically a student coming into a Calculus class is supposed to know both Algebra and Trigonometry. Unfortunately, the reality is often much different. Most students enter a Calculus class woefully unprepared for both the algebra and the trig that is in a Calculus class. This is very unfortunate since good algebra skills are absolutely vital to successfully completing any Calculus course and if your Calculus course includes trig (as this one does) good trig skills are also important in many sections.
The intent of this chapter is to do a very cursory review of some algebra and trig skills that are vital to a calculus course. This chapter does not include all the algebra and trig skills that are needed to be successful in a Calculus course. It only includes those topics that most students are particularly deficient in. For instance, factoring is also vital to completing a standard calculus class but is not included here as it is assumed that if you are taking a Calculus course then you do know how to factor. For a more in depth review you should check out the full set of Algebra notes at http://tutorial.math.lamar.edu.
Note that even though these topics are very important to a Calculus class I rarely cover all of them in the actual class itself. We simply don’t have the time to do that. I do cover certain portions of this chapter in class, but for the most part I leave it to the students to read this chapter on their own.
Here is a list of topics that are in this chapter.
Functions – In this section we will cover function notation/evaluation, determining the domain and range of a function and function composition.
Inverse Functions – In this section we will define an inverse function and the notation used for inverse functions. We will also discuss the process for finding an inverse function.
Trig Functions – In this section we will give a quick review of trig functions. We will cover the basic notation, relationship between the trig functions, the right triangle definition of the trig functions. We will also cover evaluation of trig functions as well as the unit circle (one of the most important ideas from a trig class!) and how it can be used to evaluate trig functions.
Solving Trig Equations – In this section we will discuss how to solve trig equations. The answers to the equations in this section will all be one of the “standard” angles that most students have memorized after a trig class. However, the process used here can be used for any answer regardless of it being one of the standard angles or not.
Solving Trig Equations with Calculators, Part I – In this section we will discuss solving trig equations when the answer will (generally) require the use of a calculator (i.e. they aren’t one of the standard angles). Note however, the process used here is identical to that for when the answer is one of the standard angles. The only difference is that the answers in here can be a little messy due to the need of a calculator. Included is a brief discussion of inverse trig functions.
Solving Trig Equations with Calculators, Part II – In this section we will continue our discussion of solving trig equations when a calculator is needed to get the answer. The equations in this section tend to be a little trickier than the 'normal' trig equation and are not always covered in a trig class.
Exponential Functions – In this section we will discuss exponential functions. We will cover the basic definition of an exponential function, the natural exponential function, i.e. ({bf e}^{x}), as well as the properties and graphs of exponential functions
Logarithm Functions – In this section we will discuss logarithm functions, evaluation of logarithms and their properties. We will discuss many of the basic manipulations of logarithms that commonly occur in Calculus (and higher) classes. Included is a discussion of the natural ((ln(x))) and common logarithm ((log(x))) as well as the change of base formula.
Exponential and Logarithm Equations – In this section we will discuss various methods for solving equations that involve exponential functions or logarithm functions.
Common Graphs – In this section we will do a very quick review of many of the most common functions and their graphs that typically show up in a Calculus class.
Review 11ap Calculus Test