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Introduction
Ordering Info
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© 2004 by Bloomsburg Area School District and Scantron Corporation.
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Bloomsburg Area School District
Math 9-12 10/22/04
Mathematics - Calculus AP

Algebraic Concepts
Rate: Change
The learner will be able to illustrate rates of change, including associated rates problems.
Strand Scope Source
Rates Master Advanced Placement Tests (AP), 2000, Calculus AB, II
  
Connecting: Functions/Geometric/Analytic
The learner will be able to understand the correlation between the geometric and analytic information of a function.
Strand Scope Source
Connecting Master Advanced Placement Tests (AP), 2000, Calculus AB.; I
  
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Calculus and Pre-Calculus
Definite Integral: Rate of Change
The learner will be able to determine the definite integral of the rate of change of a quantity over an interval as the change of the quantity over the interval: the integral from a to b of f'(x)dx = f(b) - f(a).
Strand Scope Source
Definite Integral Master Advanced Placement Tests (AP), 2000, Calculus AB, III
  
Definite Integral: Riemann Sums
The learner will be able to compute the values of Riemann Sums over equal subdivisions applying left, right, and midpoint evaluation points.
Strand Scope Source
Definite Integral Master Advanced Placement Tests (AP), 2000, Calculus AB, III
  
Definite Integral: Apply
The learner will be able to apply integrals to illustrate concrete, social, or economic scenarios to include determining the area of a region and the distance traveled by a particle along a line.
Strand Scope Source
Definite Integral Master Advanced Placement Tests (AP), 2000, Calculus AB, III
  
Definite Integral: Riemann Sum
The learner will be able to apply Riemann sums and the Trapezoidal Rule to estimate definite integrals of functions illustrated algebraically, geometrically, and by tables of values.
Strand Scope Source
Definite Integral Master Advanced Placement Tests (AP), 2000, Calculus AB, III
  
Integration: Use/Model/Solve
The learner will be able to use integration to model and obtain solutions to problems in other areas outside of mathematics applying the integral as a rate of change to give accumulated change and applying the method of setting up and approximating Riemann Sum and illustrating its limit as a definite integral.
Strand Scope Source
Integration Master Advanced Placement Tests (AP), 2000, Calculus AB, III
  
Integration: Understanding/Methods
The learner will be able to apply an understanding of integration and methods of integration to obtain applied problem solutions.
Strand Scope Source
Integration Master Advanced Placement Tests (AP), 2000, Calculus AB, III
  
Derivatives: Comprehend
The learner will be able to comprehend the idea of the derivative geometrically, numerically, and analytically.
Strand Scope Source
Derivatives/Antiderivatives Master Advanced Placement Tests (AP), 2000, Calculus AB, II
  
Intermediate Value Theorem: Comprehend
The learner will be able to comprehend the Intermediate Value Theorem on a function over a closed interval.
Strand Scope Source
Applying Calculus Concepts Master Advanced Placement Tests (AP), 2000, Calculus AB.; I
  
Extreme Value Theorem: Comprehend
The learner will be able to comprehend the Extreme Value Theorem.
Strand Scope Source
Applying Calculus Concepts Master Advanced Placement Tests (AP), 2000, Calculus AB.; I
  
Applying: Fundamental Theorem
The learner will be able to illustrate particular antiderivatives both graphically and analytically applying the Fundamental Theorem.
Strand Scope Source
Applying Calculus Concepts Master Advanced Placement Tests (AP), 2000, Calculus AB, III
  
Curves: Examine/Monotone/Concave
The learner will be able to examine curves as well as the ideas of monotonicity and concavity of the curve.
Strand Scope Source
Curve Sketching Master Advanced Placement Tests (AP), 2000, Calculus AB, II
  
Definite Integral: Fundamental Theorems
The learner will be able to evaluate definite integrals by applying the Fundamental Theorem of calculus.
Strand Scope Source
Definite Integral Master Advanced Placement Tests (AP), 2000, Calculus AB, III
  
Definite Integral: Average Value
The learner will be able to use concepts of the definite integral to calculate the average value of a function.
Strand Scope Source
Definite Integral Master Advanced Placement Tests (AP), 2000, Calculus AB, III
  
Definite Integral: Use
The learner will be able to use the basic properties of definite integrals.
Strand Scope Source
Definite Integral Master Advanced Placement Tests (AP), 2000, Calculus AB, III
  
Definite Integral: Volume/Known Areas
The learner will be able to use concepts of the definite integral to calculate the volume of a solid of revolution where the cross-sectional area is a known value.
Strand Scope Source
Definite Integral Master Advanced Placement Tests (AP), 2000, Calculus AB, III
  
Definite Integral: Interpret/Riemann
The learner will be able to interpret the definite integral as the limit of Riemann Sums over subdivision of equal size.
Strand Scope Source
Definite Integral Master Advanced Placement Tests (AP), 2000, Calculus AB, III
  
Differential Equations: Solve
The learner will be able to obtain solutions to separable differential equations.
Strand Scope Source
Differential Equations Master Advanced Placement Tests (AP), 2000, Calculus AB, III
  
Differential Equation: Solve
The learner will be able to obtain solutions to differential equations of the form y' = ky as applied to growth and decay problems.
Strand Scope Source
Differential Equations Master Advanced Placement Tests (AP), 2000, Calculus AB, III
  
Differential Equation: Separable
The learner will be able to apply separable differential equations in modeling.
Strand Scope Source
Differential Equations Master Advanced Placement Tests (AP), 2000, Calculus AB, III
  
Integration: Substitution/Variables
The learner will be able to integrate by substitution of variables, including substituting for the limits of integration in a definite integral.
Strand Scope Source
Integration Master Advanced Placement Tests (AP), 2000, Calculus AB, III
  
Derivatives: Define
The learner will be able to give the definition of the derivative as the limit of the difference quotient.
Strand Scope Source
Derivatives/Antiderivatives Master Advanced Placement Tests (AP), 2000, Calculus AB, II
  
Derivatives: Mean Value Theorem
The learner will be able to illustrate an understanding of the Mean Value Theorem and its geometric consequence.
Strand Scope Source
Derivatives/Antiderivatives Master Advanced Placement Tests (AP), 2000, Calculus AB, II
  
Derivatives: Comprehend
The learner will be able to comprehend the relationship of the concavity of functions and the sign of the second order derivative.
Strand Scope Source
Derivatives/Antiderivatives Master Advanced Placement Tests (AP), 2000, Calculus AB, II
  
Derivatives: Basic Rules
The learner will be able to apply the basic rules for the sum, difference, and product of functions.
Strand Scope Source
Derivatives/Antiderivatives Master Advanced Placement Tests (AP), 2000, Calculus AB, II
  
Derivatives: Determine/Power Function
The learner will be able to determine the derivative of a power function.
Strand Scope Source
Derivatives/Antiderivatives Master Advanced Placement Tests (AP), 2000, Calculus AB, II
  
Derivatives: Inverse Trigonometric
The learner will be able to calculate the derivatives of inverse trigonometric functions.
Strand Scope Source
Derivatives/Antiderivatives Master Advanced Placement Tests (AP), 2000, Calculus AB, II
  
Derivative: Slope of a Curve/Point
The learner will be able to determine the slope of a curve at a point, including points at which there are vertical tangents and no tangents.
Strand Scope Source
Derivatives/Antiderivatives Master Advanced Placement Tests (AP), 2000, Calculus AB, II
  
Derivatives: Determine/Tangent
The learner will be able to determine tangent lines to a curve at a point and a local linear approximation.
Strand Scope Source
Derivatives/Antiderivatives Master Advanced Placement Tests (AP), 2000, Calculus AB, II
  
Derivatives: Translate
The learner will be able to make verbal descriptions into equations involving derivatives and vice versa.
Strand Scope Source
Derivatives/Antiderivatives Master Advanced Placement Tests (AP), 2000, Calculus AB, II
  
Derivatives: Determine
The learner will be able to apply implicit differentiation to determine derivatives of inverse functions.
Strand Scope Source
Derivatives/Antiderivatives Master Advanced Placement Tests (AP), 2000, Calculus AB, II
  
Antiderivatives: Determine
The learner will be able to determine specific antiderivatives applying initial conditions including applications to motion along a line.
Strand Scope Source
Derivatives/Antiderivatives Master Advanced Placement Tests (AP), 2000, Calculus AB, III
  
Derivatives: Compare
The learner will be able to make comparisons of the corresponding attributes of the graphs of f, f', and f".
Strand Scope Source
Derivatives/Antiderivatives Master Advanced Placement Tests (AP), 2000, Calculus AB, II
  
Derivatives: Compare/Characteristics
The learner will be able to compare the characteristics of the graphs of the function and the first derivative of the function.
Strand Scope Source
Derivatives/Antiderivatives Master Advanced Placement Tests (AP), 2000, Calculus AB, II
  
Derivatives: Rate of Change
The learner will be able to make an interpretation of the derivative as an instantaneous rate of change.
Strand Scope Source
Derivatives/Antiderivatives Master Advanced Placement Tests (AP), 2000, Calculus AB, II
  
Derivative: Interpret/Rate of Change
The learner will be able to interpret the derivative as a rate of change in different applied contexts including velocity, speed, and acceleration.
Strand Scope Source
Derivatives/Antiderivatives Master Advanced Placement Tests (AP), 2000, Calculus AB, II
  
Limits: Describe/Understanding
The learner will be able to describe an understanding of the limiting process.
Strand Scope Source
Limits Master Advanced Placement Tests (AP), 2000, Calculus AB.; I
  
Limits: Infinity
The learner will be able to explain asymptotic behavior in terms of limits involving infinity.
Strand Scope Source
Limits Master Advanced Placement Tests (AP), 2000, Calculus AB.; I
  
Limits: Comprehend/Rate of Change
The learner will be able to comprehend instantaneous rate of change as the limit of average rate of change.
Strand Scope Source
Limits Master Advanced Placement Tests (AP), 2000, Calculus AB, II
  
Limits: Algebraic
The learner will be able to calculate limits applying algebra.
Strand Scope Source
Limits Master Advanced Placement Tests (AP), 2000, Calculus AB.; I
  
Limits: Approximate/Graphs/Tables
The learner will be able to approximate limits from graphs or tables of data.
Strand Scope Source
Limits Master Advanced Placement Tests (AP), 2000, Calculus AB.; I
  
Differentiation: Comprehend
The learner will be able to comprehend the relationship between differentiability and continuity.
Strand Scope Source
Differentiation Master Advanced Placement Tests (AP), 2000, Calculus AB, II
  
Differentiation: Rate of Change/Point
The learner will be able to estimate the rate of change at a point when presented with the graph of a function or a table of values.
Strand Scope Source
Differentiation Master Advanced Placement Tests (AP), 2000, Calculus AB, II
  
Differentiation: Chain/Implicit
The learner will be able to apply the chain rule and implicit differentiation.
Strand Scope Source
Differentiation Master Advanced Placement Tests (AP), 2000, Calculus AB, II
  
Slope Fields
The learner will be able to identify, calculate, and complete a slope field.
Strand Scope Source
Differential Equations Master Bloomsburg Area School District(a)
  
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Functions: Predict/Describe
The learner will be able to predict and describe the observed local and global behavior of a function.
Strand Scope Source
Functions Master Advanced Placement Tests (AP), 2000, Calculus AB.; I
  
Graphing: Understand/Asymptotes
The learner will be able to illustrate an understanding of asymptotes in terms of graphical behavior.
Strand Scope Source
Graphing Functions Master Advanced Placement Tests (AP), 2000, Calculus AB.; I
  
Limits: Continuity
The learner will be able to illustrate a comprehension of continuity in terms of limits.
Strand Scope Source
Limits Master Advanced Placement Tests (AP), 2000, Calculus AB.; I
  
Functions: Comprehend
The learner will be able to comprehend the relationship between the increasing and decreasing behavior of functions and the sign of the first order derivative.
Strand Scope Source
Calculus with Functions Master Advanced Placement Tests (AP), 2000, Calculus AB, II
  
Functions: Comprehend/Point/Inflection
The learner will be able to comprehend that points of inflection are places where concavity changes.
Strand Scope Source
Calculus with Functions Master Advanced Placement Tests (AP), 2000, Calculus AB, II
  
Functions: Derivative
The learner will be able to find the derivative of a basic function by using the rules of differentiation.
Strand Scope Source
Calculus with Functions Master Advanced Placement Tests (AP), 2000, Calculus AB, II
  
Functions: Differentiating
The learner will be able to differentiate the following functions: trigonometric, logarithmic, and exponential.
Strand Scope Source
Calculus with Functions Master Advanced Placement Tests (AP), 2000, Calculus AB, II
  
Functions: Determine/Maxima/Minima
The learner will be able to determine local and absolute maximum and minimum points.
Strand Scope Source
Calculus with Functions Master Advanced Placement Tests (AP), 2000, Calculus AB, II
  
Functions: Antiderivative
The learner will be able to find the antiderivative of a basic function.
Strand Scope Source
Calculus with Functions Master Advanced Placement Tests (AP), 2000, Calculus AB, III
  
Functions: Continuous
The learner will be able to understand the concept of continuity of a function.
Strand Scope Source
Functions Master Advanced Placement Tests (AP), 2000, Calculus AB.; I
  
Functions: Continuous
The learner will be able to illustrate a geometric understanding of graphs of continuous functions.
Strand Scope Source
Functions Master Advanced Placement Tests (AP), 2000, Calculus AB.; I
  
Functions: Compare
The learner will be able to make a comparison of the relative magnitudes of functions and their rates of change.
Strand Scope Source
Functions Master Advanced Placement Tests (AP), 2000, Calculus AB.; I
  
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