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AP Calculus AB - 8th / 9th Grade

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  • Taught by Dr. Ahn

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  • Among students who are trained for competition math, Dr. Ahn selects a handful of extremely talented 8th and 9th graders and invites them to this Elite class.

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  • These students take the real AP Calculus AB test administered by College Board in May each year.

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  • Their training starts in June (Summer) as they enter 8th and 9th grade.

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  • They have extra intensive courses during Summer, Thanksgiving break, Winter break and Spring break.

Picture above: Shows Dr. Ahn training 3 exceptionally talented 8th graders for AP Calculus AB that was taken in May 2018. Two students got 5/5 and one student 4/5.  - Image is blurred for privacy.

TEST FORMAT

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  • 2 Parts (Free Response Questions / Multiple Choice)

  • These two parts are given 50% / 50% in scores.

  • FRQ: Part A (2 Questions/ 30 min/ Graphing Calculator)

  • FRQ: Part B (4 Questions/ 60 min/ No Calculator)

  • M/C: Part A (28 Questions/ 55 min/ No Calculator)

  • M/C: Part B (17 Questions/ 50 min/ Graphing Calculator) 

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Preparation for Calculus

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  • Math II materials needed for Calculus

  • Math III materials needed for Calculus

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Limits and Their Properties

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  • Finding Limits Graphically and Numerically

  • Evaluating Limits Analytically

  • Continuity  and One-Sided Limits

  • Infinite Limits

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Differentiation

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  • The Derivatives and Tangent Line Problems

  • Basic Differentiation Rules

  • Rates of Change

  • Product and Quotient Rules

  • Higher Order Derivatives

  • Chain Rule

  • Implicit Differentiation

  • Derivatives of Inverse Functions

  • Related Rates​

OVERVIEW

Applications of Differentiation

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  • Extrema on an Interval

  • Rolle's Theorem and Mean Value Theorem

  • Increasing and Decreasing Functions

  • First Derivative Test

  • Concavity and Second Derivative Test

  • Limits at Infinity

  • Optimization Problems

  • Differentials

  • Slope Fields

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Integration

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  • Antiderivatives

  • Indefinite Integrals

  • Riemann Sums

  • Definite Integrals

  • Fundamental Theorem of Calculus

  • Integration by Substitution

  • Numerical Integration

  • Integration of Natural Logarithmic Functions

  • Integration of Inverse Trigonometric Functions

  • Hyperbolic Function

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Applications of Integration

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  • Area of a Region Between Two Curves

  • Volume: The Disk Method

  • Volume: The Shell Method

  • Arc Length

  • Surfaces of Revolution

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