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About the AP Calculus Exam  
The AP Calculus exam is conducted for two levels, Calculus AB and Calculus BC.

AP Calculus AB Exam.

Duration : 3 HOURS

Exam Format : The AP Calculus AB exam has two sections: a Multiple Choice Section and a Free Response Section. The multiple-choice section is for one hour and 45 minutes (105-minutes) and has 45-questions. The free-response section is for one hour and 30 minutes (90 minutes) and has six-problems.

Section I: Multiple-Choice Section. This section has two parts. Part A has 28 questions to be answered in 55 minutes without a calculator Part B has 17 questions to be answered in 50 minutes using a graphing calculator.

Scoring: Scores on the multiple-choice section are given as per the number of questions answered correctly. There is no negative marking and no marks are allotted for unanswered questions.

Section II: Free-Response Section: This section is divided into two parts. Part A of the free-response section has two problems to be solved in 30 minutes using a graphing calculator. Part B of the free-response section comprises four problems to be answered in 60 minutes and NO calculators are permitted for this part. During the Part B, students can continue to work on problems in Part A however no calculators can be used during this time.

Scoring: To gain full credit, students must show the complete line of reasoning and must communicate their methods and conclusions clearly.

Final Scores.
The multiple-choice and free-response sections each account for one-half of the final exam grade.

Use of Calculators
The use of a graphing calculator is permissible on parts of the AP Calculus Exams as given out above. The exams have questions which can be answered using a graphing calculator which has the following basic capabilities:

  • Plot the graph of a function within an arbitrary viewing window
  • Find the zeros of functions (solve equations numerically)
  • Numerically calculate the derivative of a function
  • Numerically calculate the value of a definite integral
Following are not permitted on the exams: nongraphing scientific calculators, portable and handheld computers, laptops, electronic writing pads, pocket organizers. Also calculators with QWERTY (typewriter-like) keypad as part of hardware or software, pen-input, stylus or touch-screen wireless or Bluetooth capabilities are not permitted. For detailed calculator instructions, please visit Collegeboard site.

AP Calculus BC Exam:

Duration : 3 HOURS

Exam Format : The AP Calculus AB exam has two sections: a Multiple Choice Section and a Free Response Section. The multiple-choice section is for one hour and 45 minutes (105-minutes) and has 45-questions. The free-response section is for one hour and 30 minutes (90 minutes) and has six-problems.

Section I: Multiple-Choice Section. This section has two parts. Part A has 28 questions to be answered in 55 minutes without a calculator Part B has 17 questions to be answered in 50 minutes using a graphing calculator.

Scoring: Scores on the multiple-choice section are given as per the number of questions answered correctly. There is no negative marking and no marks are allotted for unanswered questions.

Section II: Free-Response Section: This section is divided into two parts. Part A of the free-response section has two problems to be solved in 30 minutes using a graphing calculator. Part B of the free-response section comprises four problems to be answered in 60 minutes and NO calculators are permitted for this part. During the Part B, students can continue to work on problems in Part A however no calculators can be used during this time.

Scoring: To gain full credit, students must show the complete line of reasoning and must communicate their methods and conclusions clearly.

Final Scores.
The multiple-choice and free-response sections each account for one-half of the final exam grade. Use of

Calculators
The use of a graphing calculator is permissible on parts of the AP Calculus Exams as given out above. The exams have questions which can be answered using a graphing calculator which has the following basic capabilities:

  • Plot the graph of a function within an arbitrary viewing window
  • Find the zeros of functions (solve equations numerically)
  • Numerically calculate the derivative of a function
  • Numerically calculate the value of a definite integral
Following are not permitted on the exams: nongraphing scientific calculators, portable and handheld computers, laptops, electronic writing pads, pocket organizers. Also calculators with QWERTY (typewriter-like) keypad as part of hardware or software, pen-input, stylus or touch-screen wireless or Bluetooth capabilities are not permitted. For detailed calculator instructions, please visit Collegeboard site.

Study Packages

The study packages for AP Calculus Exam are available here. The packages can be customized as per your requirements.

Diagnostic Test. The students are first put through a diagnostic test to assess their strengths and areas where they may need greater emphasis.

Study Topics .The study topics which are covered in the AP Calculus AB and AP Calculus BC exam have been given out below.

Study Topics: AP Calculus AB
A.     Functions, Graphs and Limits
A.1   Analysis of Graphs
 
A.1.1 
 Geometric and Analytic Analysis of Graphs of Different Functions
    A.1.2   Prediction and Explanation of Local and Global Behaviour of a Function by using both Geometric and Analytic and Calculus
A.2   Limits of Functions [Including One-Sided Limits]
  A.2.1 Solving the Limits of a function using Algebra
    A.2.2 Estimating Limits from Graphs
A.3  Asymptotic and Unbounded Behaviour of Graphs
  A.3.1 Concept of Asymptotes as a Graphical Behaviour
A.3.2 Describing Asymptotic Behavior in terms of Limits Involving Infinity
A.3.3 Comparing Relative Magnitudes of Functions and their Rates of Change
A.4   Continuity
A.4.1 Continuous Function and Concept of Continuity
A.4.2 Continuity in terms of Limits [Right Hand Limit and Left Hand Limit]
A.4.3 Graphical Representation of Continuous Functions
A.4.4 Intermediate Value Theorem and Extreme Value Theorem
B.   Derivatives
B.1   Concept of the Derivative
B.1.1 Graphical, Numerical and Analytical concept of Differentiation
B.1.2 Instantaneous Rate of Change
B.1.3 Derivative as the Limit of the Difference Quotient [First Principle Method]
B.1.4 Relationship between Differentiability and Continuity
B.2   Derivative at a Point
B.2.1 Slope of a Curve at a Point [Points having Vertical Tangents and No Tangents]
B.2.2 Tangent Line to a Curve at a Point and Local Linear Approximation
B.2.3 Instantaneous Rate of Change as the Limit of Average Rate of Change
B.2.4 Approximate Rate of Change from Graphs
B.3   Derivative as a Function
B.3.1 Corresponding Characteristics of Graphs of ƒ and ƒ'

B.3.2 Relationship between the Increasing and Decreasing behavior of ƒ and the sign of ƒ'

B.3.3 The Mean Value Theorem and its Geometric Interpretation
B.3.4 Equations Involving Derivatives
B.3.5 Verbal Descriptions Translation into Equations Involving Derivatives and vice versa
B.4   Second Derivatives
B.4.1 Corresponding Characteristics of the graphs of ƒ , ƒ' and ƒ''

B.4.2 Relationship between the Concavity of ƒ and the Sign of ƒ''

B.4.3 Points of Inflection as Places where Concavity Changes
B.5   Applications of Derivatives
B.5.1 Analysis of Curves
B.5.2 Optimization both Absolute/Global and Relative/Local Extrema
    B.5.3 Modelling Rtes of Change [including related rates problems]
    B.5.4 Implicit Differentiation for differentiating an inverse function
    B.5.5 Derivation as a rate of change [velocity and acceleration]
    B.5.6 Geometric Interpretation of Differential Equations [including curves]
  B.6    Computation of Derivatives
    B.6.1 Differentiation of functions[for example basic functions, including power, exponential, logarithmic, trigonometric and inverse trigonometric functions ]
    B.6.2 Basic Differentiating Rules [Sums, Products and Quotients Rules]
B.6.3 Chain Rule and Implicit Differentiation
C.   Integration
C.1  Interpretations and Properties of Definite Integrals
C.1.1 Basic Properties of Definite Integral.
C.1.2 Definite Integral as a limit of Riemann Sums.
C.1.3 Definite Integral of the Rate of Change of a Quantity over an Interval Interpreted as the Change of the quantity over that Interval [Including Additivity and Linearity].
C.2   Applications of Integrals
C.2.1 Basic Application Models of Integral.
C.2.2 Approximation Method [Riemann Sums].
C.2.3 Concept of Some Basic Applications [Area of a Region, Volume of a Solid with known cross-sections, Average Value of a Function, Distance Travelled by a Particle along a line and Accumulated Change from a Rate of Change].  
C.3   Fundamental Theorem of Calculus
C.3.1 Using of Fundamental Theorem to Evaluate Definite Integrals.
C.3.2 Using of Fundamental Theorem to Represent and Analyze a Particular Anti-Derivative Analytically and Graphically.
C.4    Techniques of Anti-Differentiation
C.4.1 Anti-Differentiation by using Substitution Technique [accompanied with Changing of Limits in the case of Definite Integral].
C.4.2 Differentiation of a Basic Function followed by its respective Anti-Differe

Study Topics: AP Calculus- BC
A.   Functions, Graphs and Limits
  A.1   Analysis of Graphs
    A.1.1 Geometric and Analytic Analysis of Graphs of Different Functions
    A.1.2 Prediction and Explanation of Local and Global Behaviour of a Function by using both Geometric and Analytic and Calculus
  A.2    Limits of Functions [Including One-Sided Limits]
    A.2.1 Solving the Limits of a function using Algebra
    A.2.2 Estimating Limits from Graphs
  A.3   Asymptotic and Unbounded Behaviour of Graphs
    A.3.1 Concept of Asymptotes as a Graphical Behaviour
    A.3.2 Describing Asymptotic Behavior in terms of Limits Involving Infinity
    A.3.3 Comparing Relative Magnitudes of Functions and their Rates of Change
  A.4   Continuity
    A.4.1 Continuous Function and Concept of Continuity
    A.4.2 Continuity in terms of Limits [Right Hand Limit and Left Hand Limit]
    A.4.3 Graphical Representation of Continuous Functions
    A.4.4 Intermediate Value Theorem and Extreme Value Theorem
  A.5   Parametric, Polar and Vector Functions
    A.5.1 Analysis of Planar Curves given in Parametric, Polar and Vector.
B.  Derivatives
  B.1  Concept of the Derivative
    B.1.1 Graphical, Numerical and Analytical concept of Differentiation
    B.1.2 Instantaneous Rate of Change
    B.1.3 Derivative as the Limit of the Difference Quotient [First Principle Method]
    B.1.4 Relationship between Differentiability and Continuity
  B.2   Derivative at a Point
    B.2.1 Slope of a Curve at a Point [Points having Vertical Tangents and No Tangents]
    B.2.2 Tangent Line to a Curve at a Point and Local Linear Approximation
    B.2.3 Instantaneous Rate of Change as the Limit of Average Rate of Change
    B.2.4 Approximate Rate of Change from Graphs
 
B.3   Derivative as a Function
    B.3.1 Corresponding Characteristics of Graphs of ƒ and ƒ'

    B.3.2   Relationship between the Increasing and Decreasing behavior of ƒ and the sign of ƒ'

    B.3.3 The Mean Value Theorem and its Geometric Interpretation
    B.3.4 Equations Involving Derivatives
    B.3.5 Verbal Descriptions Translation into Equations Involving Derivatives and vice versa
  B.4   Second Derivatives
    B.4.1   Corresponding Characteristics of the graphs of ƒ , ƒ' and ƒ''

    B.4.2 Relationship between the Concavity of ƒ and the Sign of ƒ''

    B.4.3 Points of Inflection as Places where Concavity Changes
  B.5   Applications of Derivatives
    B.5.1 Analysis of Curves
    B.5.2 Planar Curves Analysis [in Parametric, Polar and Vector Form including Velocity and Acceleration]
    B.5.3 Optimization both Absolute/Global and Relative/Local Extrema
    B.5.4 Modelling Rtes of Change [including related rates problems]
    B.5.5 Implicit Differentiation for differentiating an inverse function
    B.5.6 Derivation as a rate of change [velocity and acceleration]
    B.5.7 Geometric Interpretation of Differential Equations [including curves]
    B.5.8 Differential Equations Solution using Euler's Method
    B.5.9 L'Hospital's Rule [usage in determining Limits and Convergence of Improper Integrals and Series]
  B.6   Computation of Derivatives
    B.6.1 Differentiation of functions[for example basic functions, including power, exponential, logarithmic, trigonometric and inverse trigonometric functions ]
    B.6.2 Basic Differentiating Rules [Sums, Products and Quotients Rules]
    B.6.3 Chain Rule and Implicit Differentiation
    B.6.4 Derivative of Parametric, Polar and Vector functions
C.   Integration
  C.1    Interpretations and Properties of Definite Integrals
    C.1.1 Basic Properties of Definite Integral.
    C.1.2   Definite Integral as a limit of Riemann Sums.
    C.1.3 Definite Integral of the Rate of Change of a Quantity over an Interval Interpreted as the Change of the quantity over that Interval [Including Additivity and Linearity].
  C.2   Applications of Integrals
    C.2.1 Basic Application Models of Integral.
    C.2.2 Approximation Method [Riemann Sums].
    C.2.3 Concept of Some Basic Applications [Area of a Region, Volume of a Solid with known cross-sections, Average Value of a Function, Distance Travelled by a Particle along a line and Accumulated Change from a Rate of Change].
  C.3    Fundamental Theorem of Calculus
    C.3.1 Using of Fundamental Theorem to Evaluate Definite Integrals.
    C.3.2 Using of Fundamental Theorem to Represent and Analyze a Particular Anti-Derivative Analytically and Graphically.
  C.4    Techniques of Anti-Differentiation
    C.4.1 Anti-Differentiation directly from Derivatives of basic Functions
    C.4.2 Anti-Differentiation by using Substitution Technique [accompanied with Changing of Limits in the case of Definite Integral], By-Parts and Simple Fraction [for non-repeating linear factors.]
    C.4.3 Differentiation of a Basic Function followed by its respective Anti-Differentiation
    C.4.4 Improper Integrals
  C.5   Applications of Anti-Differentiation
    C.5.1 Anti-Differentiation of functions given with some Initial Condition[Study of motion Along a Line].
    C.5.2 Separable Differential Equations
    C.5.3 Study of the Equations related to Exponential Growth.
    C.5.4 Logistic Differential Equations and using them in Modelling.
  C.6   Numerical Approximation of Definite Integrals
    C.6.1 Use of Riemann Sum Approximation Equation [Left, Right and Midpoint Evaluation Points]
    C.6.2 Use of T rapezoidal Sums Approximation Equation for Definite Integrals of Functions represented Algebraically, Graphically and from Tabulated Values
D.   Polynomial Approximations and Series
  D.1   Concept of Series
    D.1.1 Sequence of Partial Sums and Concept of Convergence
    D.1.2 Convergence and Divergence Series
  D.2   Series of Constants
    D.2.1 Decimal Expansion
    D.2.2 Arithmetic, Geometric and Harmonic Series with Applications
    D.2.3 Alternating Series with Error Bound.
    D.2.4 Series as Areas of Rectangles and their Relationship to Improper Integrals [including the Integral Test for the convergence of p -series].
    D.2.5 Ratio Test for Convergence and Divergence.
    D.2.6 Comparing Series to test for convergence or divergence.
  D.3   Taylor Series
    D.3.1 Taylor Polynomial Approximation [including Graphical Demonstration of Convergence]
    D.3.2 Maclaurin Series and the General Taylor Series centered at x = a .
    D.3.3 Maclaurin Series for the Different Functions such as e x , sin x , cos x , and 1/[1-x]
    D.3.4 Formal Manipulation of Taylor Series and Shortcuts to compute Taylor Series[including Substitution, Differentiation, Anti-differentiation and the formation of new series from known series]
    D.3.5 Functions defined by Power Series
    D.3.6 Radius and Interval of Convergence of Power Series
    D.3.7 Lagrange Error Bound for Ta

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