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AP Calculus AB – Mohammad Al-Khuffash

  • Course Duration: 10H 21M

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Mohammad Al-Khuffash

Mohammad Al-Khuffash

High school Mathematics teacher

Course Type

Full Course
Program

Level

AP
Subject

Mathematics

Course Curriculum

  • General
    • forumAnnouncements
    • resourceAP Calculus AB - Course Syllabus
  • Unit 1: Limits and Continuity (Big Ideas: Change, Limits, Analysis of Functions)
    • hvp1.1 Introducing Calculus
    • page1.1 Introducing Calculus
    • hvp1.2 Defining Limits
    • page1.2 Defining Limits
    • hvp1.3 Finding Limits From Graphs
    • page1.3 Finding Limits From Graphs
    • hvp1.4 Finding Limits from Tables
    • page1.4 Finding Limits from Tables
    • hvp1.5 Determining Limits Using Algebraic Properties of Limits
    • page1.5 Determining Limits Using Algebraic Properties of Limits
    • hvp1.6 Determining Limits Using Algebraic Manipulation
    • page1.6 Determining Limits Using Algebraic Manipulation
    • hvp1.7 Selecting Procedures for Determining Limits
    • page1.7 Selecting Procedures for Determining Limits
    • hvp1.8 Determining Limits Using the Squeeze Theorem
    • page1.8 Determining Limits Using the Squeeze Theorem
    • hvp1.9 Connecting Multiple Representations of Limits
    • page1.9 Connecting Multiple Representations of Limits
    • hvp1.10 Exploring Types of Discontinuities
    • page1.10 Exploring Types of Discontinuities
    • hvp1.11 Defining Continuity at a Point
    • page1.11 Defining Continuity at a Point
    • hvp1.12 Confirming Continuity Over an Interval
    • page1.12 Confirming Continuity Over an Interval
    • hvp1.13 Removing Discontinuities
    • page1.13 Removing Discontinuities
    • hvp1.14 Infinite Limits and Vertical Asymptotes
    • page1.14 Infinite Limits and Vertical Asymptotes
    • hvp1.15 Limits at Infinity and Horizontal Asymptotes
    • page1.15 Limits at Infinity and Horizontal Asymptotes
    • hvp1.16 Intermediate Value Theorem (IVT)
    • page1.16 Intermediate Value Theorem (IVT)
  • Unit 2: Differentiation: Definition and Fundamental Properties (Big Ideas: Change, Limits, Analysis of Functions)
    • hvp2.1 Defining Average and Instantaneous Rate of Change at a Point
    • page2.1 Defining Average and Instantaneous Rate of Change at a Point
    • hvp2.2 Defining the Derivative of a Function and Using Derivative Notation
    • page2.2 Defining the Derivative of a Function and Using Derivative Notation
    • hvp2.3 Estimating Derivatives of a Function at a Point
    • page2.3 Estimating Derivatives of a Function at a Point
    • hvp2.4 Connecting Differentiability and Continuity
    • page2.4 Connecting Differentiability and Continuity
    • hvp2.5 Applying the Power Rule
    • page2.5 Applying the Power Rule
    • hvp2.6 Derivative Rules: Constant, Sum, Difference, and Constant Multiple
    • page2.6 Derivative Rules: Constant, Sum, Difference, and Constant Multiple
    • hvp2.7 Derivatives of cos(x), sin(x), e^x, and ln(x)
    • page2.7 Derivatives of cos(x), sin(x), e^x, and ln(x)
    • hvp2.8 The Product Rule
    • page2.8 The Product Rule
    • hvp2.9 The Quotient Rule
    • page2.9 The Quotient Rule
    • hvp2.10 Derivatives of tan(x), cot(x), sec(x), and csc(x)
    • page2.10 Derivatives of tan(x), cot(x), sec(x), and csc(x)
  • Unit 3: Differentiation: Composite, Implicit, and Inverse Functions (Big Idea: Analysis of Functions)
    • hvp3.1 The Chain Rule
    • page3.1 The Chain Rule
    • hvp3.2 Implicit Differentiation
    • page3.2 Implicit Differentiation
    • hvp3.3 Differentiating Inverse Functions
    • page3.3 Differentiating Inverse Functions
    • hvp3.4 Differentiating Inverse Trigonometric Functions
    • page3.4 Differentiating Inverse Trigonometric Functions
    • hvp3.5 Selecting Procedures for Calculating Derivatives
    • page3.5 Selecting Procedures for Calculating Derivatives
    • hvp3.6 Calculating Higher-Order Derivatives
    • page3.6 Calculating Higher-Order Derivatives
  • Unit 4: Contextual Applications of Differentiation and Rates of Change (Big Ideas: Change, Limits)
    • hvp4.1 Interpreting the Meaning of the Derivative in Context (copy)
    • page4.1 Interpreting the Meaning of the Derivative in Context
    • hvp4.2 Straight-Line Motion: Connecting Position, Velocity and Acceleration
    • page4.2 Straight-Line Motion: Connecting Position, Velocity and Acceleration
    • hvp4.3 Rates of Change in Applied Contexts Other Than Motion
    • page4.3 Rates of Change in Applied Contexts Other Than Motion
    • hvp4.4 Introduction to Related Rates
    • page4.4 Introduction to Related Rates
    • hvp4.5 Solving Related Rates Problems
    • page4.5 Solving Related Rates Problems
    • hvp4.6 Approximating Values of a Function Using Local Linearity and Linearization
    • page4.6 Approximating Values of a Function Using Local Linearity and Linearization
    • hvp4.7 Using L'Hopital's Rule for Determining Limits of Indeterminate Forms
    • page4.7 Using L'Hopital's Rule for Determining Limits of Indeterminate Forms
  • Unit 5: Analytical Applications of Differentiation including Analysis of Functions (Big Idea: Analysis of Functions)
    • page5.1 Using the Mean Value Theorem
    • page5.2 Critical Points
    • page5.3 Increasing and Decreasing Intervals
    • page5.4 The First Derivative Test
    • page5.5 Determine Absolute Extrema Using the Candidates Test
    • page5.11 Solving Optimization Problems
    • page5.12 Behaviors Of Implicit Relations
  • Unit 6: Integration and Accumulation of Change (Big Ideas: Change, Limits, Analysis of Functions)
    • page6.1 Accumulation of Change
    • page6.2 Approximating Areas with Riemann Sums
    • page6.3 Summation on notation
    • page6.4 Accumulation Functions
    • page6.5 Behavior of accumulation functions
    • page6.6 Properties of Definite integrals
    • page6.7 Definite Integrals
    • page6.8 Indefinite Integrals
    • page6.9 Integrating Using substitution

About Course

Course Overview 

The AP Calculus AB course provides a comprehensive introduction to the concepts and techniques of calculus, focusing on limits, derivatives, and integrals. Students begin by exploring limits and continuity, which lay the groundwork for understanding how functions behave. They then learn to compute derivatives using various rules and apply them to real-world problems, such as optimization and rates of change. The course also covers integration, teaching students to find both indefinite and definite integrals while highlighting the Fundamental Theorem of Calculus, which connects differentiation and integration. Throughout the course, emphasis is placed on analytical methods, problem-solving skills, and the ability to communicate mathematical ideas effectively, all of which prepare students for the AP exam and further studies in mathematics and related fields.



What you'll learn?

  • Understanding limits and their role in determining function behavior.
  • Calculating and applying derivatives to analyze rates of change and optimize functions.
  • Learning to compute integrals and applying the Fundamental Theorem of Calculus to find areas and volumes.

Material Includes

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