MATH Courses for School GPA STARPREP® MATHEMATICS PROGRAMSAP® Calculus AB
The course frameworks for AP® Calculus AB define content students must know and skills
students must master in order to earn transferable, long-term understandings of calculus. The frameworks reflect
a commitment to what college faculty value and mirror the curricula in corresponding college courses. Teachers
may adjust the frameworks to meet state and local requirements.
The frameworks are organized into logical sequences, based on teacher input and commonly used textbooks.
These sequences represent one reasonable learning pathway for each course, among many. Teachers may adjust
the suggested sequencing of units or topics, although they will want to carefully consider how to account for
such changes as they access course resources for planning, instruction, and assessment.
Balancing guidance and flexibility, this approach helps to prepare students for college credit and placement.
AP® Calculus AB
STARPREP®에서 제공하는 AP® Calculus AB 프로그램은 총 2개의 PHASES (GPA-Boosting Course / 2023 MAY' TEST-PREP Course)으로 나뉘어지며 학생/반의 수준에 따라 진도가 정해집니다.
[학생의 성적/수업 이해도을 고려하는 수업 진행]
for Graders 9-12 (STARPREP® course code: APCAB)
Professor Dr. Jerome E Lee MIT Mathematical Physics 졸업 KAIST Multi-physics 졸업 티칭 경력 23년차
professor Kathy Lee Texas A&M University, Applied Mathematics, BS 학사졸업 Massachusetts College of Pharmacy & Health Sciences, Pharmacy, Doctor of Pharmacy 약학박사졸업 Mathematics Expert 수학전문강사
Professor Dr. Jerome E Lee MIT Mathematical Physics 졸업 KAIST Multi-physics 졸업 티칭 경력 23년차
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AP® Calculus AB
AP® Calculus AB
Curriculum Guide
High School AP® Calculus AB
01Limits and Continuity
1-1 Introducing Calculus: 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 of Limits 1-6 Determining Limits Using Algebraic Manipulation 1-7 Selecting Procedures for Determining Limits 1-8 Determining Limits Using the queeze Theorem 1-9 Connecting Multiple Representations of Limits 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 Connecting Infinite Limits and Vertical Asymptotes 1-15 Connecting Limits at Infinity and Horizontal Asymptotes 1-16 Working with the Intermediate Value Theorem (IVT)
02Differentiation: Definition and Basic Derivative Rules
2-1 Defining Average and Instantaneous Rates of Change at a Point 2-2 Defining the Derivative of a Function and Using Derivative Notation 2-3 Estimating Derivatives of a Function at a Point 2-4 Connecting Differentiability and Continuity: Determining When Derivatives Do and Do Not Exist 2-5 Applying the Power Rule 2-6 Derivative Rules: Constant, Sum, Difference, and Constant Multiple 2-7 Derivatives of cos x, sin x, ex, and ln x 2-8 The Product Rule 2-9 The Quotient Rule 2-10 Finding the Derivatives of Tangent, Cotangent, Secant, and/or Cosecant Functions
03Differentiation: 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
04Contextual 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’Hospital’s Rule for Determining Limits of Indeterminate Forms
05Analytical 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 5-8 Sketching Graphs of Functions and Their Derivatives 5-9 Connecting a Function, Its First Derivative, and Its Second Derivative 5-10 Introduction to Optimization Problems 5-11 Solving Optimization Problems 5-12 Exploring Behaviors of Implicit Relations
06Integration and Accumulation of Change
6-1 Exploring Accumulations of Change 6-2 Approximating Areas 1 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 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 Selecting Techniques for Antidifferentiation
07Differential 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 Finding General Solutions Using Separation of Variables 7-6 Finding Particular Solutions Using Initial Conditions and Separation of Variables 7-7 Exponential Models with Differential Equations
08Applications of Integration
8-1 Finding the Average Value of a Function on an Interval 8-2 Connecting Position, Velocity, and Acceleration of Functions Using Integrals 8-3 Using Accumulation Functions and Definite Integrals in Applied Contexts 8-4 Finding the Area Between Curves Expressed as Functions of x 8-5 Finding the Area Between Curves Expressed as Functions of y 8-6 Finding the Area Between Curves that Intersect at More Than Two Points 8-7 Volumes with Cross Sections: Squares and Rectangles 8-8 Volumes with Cross Sections: Triangles and Semicircles 8-9 Volume with Disc Method: Revolving Around the x- or y-Axis 8-10 Volume with Disc Method: Revolving 2 Around Other Axes 8-11 Volume with Washer Method: Revolving 4 Around the x- or y-Axis 8-12 Volume with Washer Method: Revolving 2 Around Other Axes
01Limits and Continuity
1-1 Introducing Calculus: 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 of Limits 1-6 Determining Limits Using Algebraic Manipulation 1-7 Selecting Procedures for Determining Limits 1-8 Determining Limits Using the queeze Theorem 1-9 Connecting Multiple Representations of Limits 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 Connecting Infinite Limits and Vertical Asymptotes 1-15 Connecting Limits at Infinity and Horizontal Asymptotes 1-16 Working with the Intermediate Value Theorem (IVT)
02Differentiation: Definition and Basic Derivative Rules
2-1 Defining Average and Instantaneous Rates of Change at a Point 2-2 Defining the Derivative of a Function and Using Derivative Notation 2-3 Estimating Derivatives of a Function at a Point 2-4 Connecting Differentiability and Continuity: Determining When Derivatives Do and Do Not Exist 2-5 Applying the Power Rule 2-6 Derivative Rules: Constant, Sum, Difference, and Constant Multiple 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 Finding the Derivatives of Tangent, Cotangent, Secant, and/or Cosecant Functions
03Differentiation: 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
04Contextual 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’Hospital’s Rule for Determining Limits of Indeterminate Forms
05Analytical 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 5-8 Sketching Graphs of Functions and Their Derivatives 5-9 Connecting a Function, Its First Derivative, and Its Second Derivative 5-10 Introduction to Optimization Problems 5-11 Solving Optimization Problems 5-12 Exploring Behaviors of Implicit Relations
06Integration and Accumulation of Change
6-1 Exploring Accumulations of Change 6-2 Approximating Areas 1 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 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 Selecting Techniques for Antidifferentiation
07Differential 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 Finding General Solutions Using Separation of Variables 7-6 Finding Particular Solutions Using Initial Conditions and Separation of Variables 7-7 Exponential Models with Differential Equations
08Applications of Integration
8-1 Finding the Average Value of a Function on an Interval 8-2 Connecting Position, Velocity, and Acceleration of Functions Using Integrals 8-3 Using Accumulation Functions and Definite Integrals in Applied Contexts 8-4 Finding the Area Between Curves Expressed as Functions of x 8-5 Finding the Area Between Curves Expressed as Functions of y 8-6 Finding the Area Between Curves that Intersect at More Than Two Points 8-7 Volumes with Cross Sections: Squares and Rectangles 8-8 Volumes with Cross Sections: Triangles and Semicircles 8-9 Volume with Disc Method: Revolving Around the x- or y-Axis 8-10 Volume with Disc Method: Revolving 2 Around Other Axes 8-11 Volume with Washer Method: Revolving 4 Around the x- or y-Axis 8-12 Volume with Washer Method: Revolving 2 Around Other Axes