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© 2003 by
Cobb County School District
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All Rights Reserved.
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Scantron Corporation
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Cobb County School District |
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Mathematics (Updated October 2003) |
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Mathematics - Calculus |
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Goals and Descriptions |
PS1: PATTERNS, RELATIONS, AND FUNCTIONS
The learner will be able to
apply and analyze functions, relations, and patterns in abstract and real world situations.
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M.CALC.1.1 Limits: Evaluate
The learner will be able to
evaluate the limits of a function algebraically and apply the properties of limits, including one-sided limits.
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M.CALC.1.2 Derivatives: Define
The learner will be able to
approximate the rate of change at a point, given the graph of a function or a table of values. define the derivative of a function in various ways. The limit of the difference quotient. The slope of the tangent line at a point. Instantaneous rate of change. The limit of the average rate of change.
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M.CALC.1.3 Differentiation: Apply
The learner will be able to
apply the derivative to determine the slope of a curve at a point, the equation of the tangent line to a curve at a point and the equation of the normal line to a curve at point.
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M.CALC.1.4 Differentiation: Use/Rules
The learner will be able to
use the rules of differentiation (power rule, product rule and quotient rule) with algebraic and transcendental functions.
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M.CALC.1.5 Differentiation: Chain Rule
The learner will be able to
apply the chain rule to composite functions, and implicitly defined functions.
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M.CALC.1.6 Derivatives: Inverse Function
The learner will be able to
differentiate the inverse of a function, including inverse trigonometric functions.
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M.CALC.1.7 Differentiation: Find/Apply
The learner will be able to
determine the successive derivatives of a function and apply them to problems, such as speed, velocity and acceleration.
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M.CALC.1.8 Differentiation: Apply/Relation
The learner will be able to
use the relationships between f(x), f'(x), and f''(x) to determine the increasing and decreasing behavior of f(x). Determine critical points of f(x). Determine the concavity of f(x) over an interval, the points of inflection of f(x), Sketch the graphs of f'(x) and f''(x) when given f(x), and sketch the graph of f(x) when given f'(x).
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M.CALC.1.9 Optimization Problems
The learner will be able to
apply derivative; solve optimization and related rate of changes problems.
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M.CALC.1.10 Integration: Define/Use/Properties
The learner will be able to
define the antiderivative and apply its properties to problems such as distance and velocity from acceleration with initial conditions, growth and decay.
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M.CALC.1.11 Apply Calculus Concepts: Fundamental Theorem of Calculus
The learner will be able to
identify and use the Fundamental Theorem of Calculus.
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M.CALC.1.12 Integration: Substitution
The learner will be able to
integrate using substitution, by using identities, by changing variables and by parts.
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M.CALC.1.13 Limits: Infinity
The learner will be able to
describe asymptotic behavior in terms of limits involving infinity.
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M.CALC.1.14 Applying Calculus Concepts:
The learner will be able to
apply the definition of continuity to a function at a point. Determine if a function is continuous over an interval.
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M.CALC.1.15 Differentiation: Function/Over/Interval
The learner will be able to
determine if a function is differentiable over an interval. Determine points where the derivative of a function fails to exist.
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M.CALC.1.16 Applying Calculus Concepts:
The learner will be able to
apply the Mean Value and Rolle's Theorem.
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M.CALC.1.17 Applying Calculus Concepts:
The learner will be able to
apply L'Hopital's Rule when appropriate.
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M.CALC.1.18 Applying Calculus Concepts:
The learner will be able to
use the Extreme Value Theorem in problem situations.
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M.CALC.1.19 Apply Calculus Concepts: Sums
The learner will be able to
evaluate sums using sigma notation.
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M.CALC.1.20 Integration: Apply/Mean Value
The learner will be able to
apply the integral to the average of mean value of a function on an interval.
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M.CALC.1.21 Functions: Transcendental/Rules
The learner will be able to
apply the rules of integration to algebraic and transcendental functions.
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M.CALC.1.22 Functions/Relations: Recognize
The learner will be able to
identify and apply non-calculus properties of algebraic, trigonometric, exponential, and logarithmic function. Include the following: polynomial (existence, number, and location of zeros), trigonometric (fundamental identities, addition formulas, graphs, amplitude, periodicity), exponential logarithmic (properties, graphs, inverse, the number, absolute value (f IxI), If (x) I and bounded/unbounded behavior.
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M.CALC.1.23 Operations: Functions/Algebra
The learner will be able to
identify the characteristics of functions and relations with respect to domain, range, intercepts, symmetries (including odd and even functions), asymptotes, and zeros.
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M.CALC.1.24 Graphs: Relate/Illustrate
The learner will be able to
graph functions and relationship with respect to these characteristics and identify these characteristics from graphs.
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M.CALC.1.25 Apply: Algebra of Functions
The learner will be able to
apply the algebra of functions by finding the sum. product, quotient, composition, and inverse where they exist.
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PS2: ALGEBRAIC MODELS IN PROBLEM SOLVING
The learner will be able to
use mathematical models to represent and understand quantitative relationships and change in real world situations.
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M.CALC.2.1 Solution: Reasonableness
The learner will be able to
solve problems including: selecting appropriate approaches and tools. Use estimating strategies to predict computational results. Judging reasonableness of results.
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M.CALC.2.2 Algebraic Concepts: Problem
The learner will be able to
solve problems that relate concepts to practical applications and to other concepts using appropriate tools.
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PS3: TOOLS, TECHNIQUES, AND FORMULAS
The learner will be able to
choose formulas and tools to solve problems involving measurement.
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M.CALC.3.1 Integration: Define/Apply
The learner will be able to
relate the definite integral to the concept of the area under a curve. Define and apply the properties of the definite integral.
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M.CALC.3.2 Integration: Find/Area/Curve
The learner will be able to
determine the area between curves using of integration formulas.
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M.CALC.3.3 Integration: Find/Volume/Solve
The learner will be able to
determine volumes by cross sections. Determine the volume of a solid of revolution using various methods such as disk, washer and shell.
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M.CALC.3.4 Integration: Estimate/Areas
The learner will be able to
approximate areas by using inscribed rectangles, circumscribed rectangles, trapezoids, and other appropriate methods.
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M.CALC.3.5 Integration: Natural Log
The learner will be able to
interpret the natural log ( ln x ) as the area under the curve of the function f(x) = 1/x.
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PS4: COMPUTATION AND ESTIMATION
The learner will be able to
estimate and judge reasonableness of numerical results.
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M.CALC.4.1 Limits: Approximate/Graphs/
The learner will be able to
estimate limits from graphs or tables of data. Estimate graphs from limits.
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й 2003 Cobb County School
District. All Rights Reserved
514 Glover Street | Marietta, Ga. 30060 | (770) 426-3300
Send your comments to Sue Brown
visitors since October 15, 2003
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