Chalkboard


Mission Statement
Introduction
Credits
Ordering Info

Sequencing & Pacing Guide

Calculus Terms

Vertical Alignment

Skills Packets

Vocabulary

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© 2003 by Cobb County School District and Scantron Corporation.
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Cobb County School District
Mathematics (Updated July 2004)
Mathematics - Calculus
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Goals and Descriptions

Priority Level:

High =      Mid =       Low =

Width of topic indicates suggested time to be allotted

Advanced Content Standards

Algebraic Concepts | Measurement | Number and Operations
 


Algebraic Concepts

PS1: PATTERNS, RELATIONS, AND FUNCTIONS
The learner will be able to apply and analyze functions, relations, and patterns in abstract and real world situations.
  
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.
Bloom's Scope Hours Source
Evaluation Master 3.0 GA: Quality Core Curriculum, December 2000, Calculus, #6
  
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.
Bloom's Scope Hours Source
Application Master 1.0 GA: Quality Core Curriculum, December 2000, Calculus, #10 and #14
  
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.
Bloom's Scope Hours Source
Application Master 2.0 GA: Quality Core Curriculum, December 2000, Calculus, #19
  
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.
Bloom's Scope Hours Source
Application Master 1.0 GA: Quality Core Curriculum, December 2000, Calculus, #12
  
M.CALC.1.5 Differentiation: Chain Rule
The learner will be able to apply the chain rule to composite functions, and implicitly defined functions.
Bloom's Scope Hours Source
Application Master 1.0 GA: Quality Core Curriculum, December 2000, Calculus, #13
  
M.CALC.1.6 Derivatives: Inverse Function
The learner will be able to differentiate the inverse of a function, including inverse trigonometric functions.
Bloom's Scope Hours Source
Analysis Master 1.0 GA: Quality Core Curriculum, December 2000, Calculus, #15
  
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.
Bloom's Scope Hours Source
Analysis Master 3.0 GA: Quality Core Curriculum, December 2000, Calculus, #16
  
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).
Bloom's Scope Hours Source
Application Master 4.0 GA: Quality Core Curriculum, December 2000, Calculus, #20
  
M.CALC.1.9 Optimization Problems
The learner will be able to apply derivative; solve optimization and related rate of changes problems.
Bloom's Scope Hours Source
Application Master 0.5 GA: Quality Core Curriculum, December 2000, Calculus, #22
  
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.
Bloom's Scope Hours Source
Application Master 4.0 GA: Quality Core Curriculum, December 2000, Calculus, #23
  
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.
Bloom's Scope Hours Source
Application Master 1.0 GA: Quality Core Curriculum, December 2000, Calculus, #27
  
M.CALC.1.12 Integration: Substitution
The learner will be able to integrate using substitution, by using identities, by changing variables and by parts.
Bloom's Scope Hours Source
Application Master 1.0 GA: Quality Core Curriculum, December 2000, Calculus, #28
  

 

M.CALC.1.13 Limits: Infinity
The learner will be able to describe asymptotic behavior in terms of limits involving infinity.
Bloom's Scope Hours Source
Comprehension Master 2.0 GA: Quality Core Curriculum, December 2000, Calculus, #8
  

 

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.
Bloom's Scope Hours Source
Application Master 1.0 GA: Quality Core Curriculum, December 2000, Calculus, #9
  

 

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.
Bloom's Scope Hours Source
Application Master 1.0 GA: Quality Core Curriculum, December 2000, Calculus, #11
  

 

M.CALC.1.16 Applying Calculus Concepts:
The learner will be able to apply the Mean Value and Rolle's Theorem.
Bloom's Scope Hours Source
Application Master 1.0 GA: Quality Core Curriculum, December 2000, Calculus, #17
  

 

M.CALC.1.17 Applying Calculus Concepts:
The learner will be able to apply L'Hopital's Rule when appropriate.
Bloom's Scope Hours Source
Application Master 1.0 GA: Quality Core Curriculum, December 2000, Calculus, #18
  

 

M.CALC.1.18 Applying Calculus Concepts:
The learner will be able to use the Extreme Value Theorem in problem situations.
Bloom's Scope Hours Source
Application Master 1.0 GA: Quality Core Curriculum, December 2000, Calculus, #21
  

 

M.CALC.1.19 Apply Calculus Concepts: Sums
The learner will be able to evaluate sums using sigma notation.
Bloom's Scope Hours Source
Application Master 2.0 GA: Quality Core Curriculum, December 2000, Calculus, #25
  

 

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.
Bloom's Scope Hours Source
Application Master 1.0 GA: Quality Core Curriculum, December 2000, Calculus, #29
  

 

M.CALC.1.21 Functions: Transcendental/Rules
The learner will be able to apply the rules of integration to algebraic and transcendental functions.
Bloom's Scope Hours Source
Application Master 4.0 Cobb County Schools
  

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.
Bloom's Scope Hours Source
Application Master 5.0 GA: Quality Core Curriculum, December 2000, Calculus, #3
  

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.
Bloom's Scope Hours Source
Comprehension Master 4.0 GA: Quality Core Curriculum, December 2000, Calculus, #4
  

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.
Bloom's Scope Hours Source
Application Master 3.0 GA: Quality Core Curriculum, December 2000, Calculus, #5
  

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.
Bloom's Scope Hours Source
Comprehension Master 2.0 Cobb County Schools
  
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.
  
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.
Bloom's Scope Hours Source
Evaluation Master 1.5 GA: Quality Core Curriculum, December 2000, Calculus, #1

 

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.
Bloom's Scope Hours Source
Analysis Master 8.0 GA: Quality Core Curriculum, December 2000, Calculus, #2
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Measurement

PS3: TOOLS, TECHNIQUES, AND FORMULAS
The learner will be able to choose formulas and tools to solve problems involving measurement.
  
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.
Bloom's Scope Hours Source
Analysis Master 3.0 GA: Quality Core Curriculum, December 2000, Calculus, #26
  
M.CALC.3.2 Integration: Find/Area/Curve
The learner will be able to determine the area between curves using of integration formulas.
Bloom's Scope Hours Source
Application Master 1.0 GA: Quality Core Curriculum, December 2000, Calculus, #30
  
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.
Bloom's Scope Hours Source
Application Master 2.0 GA: Quality Core Curriculum, December 2000, Calculus, #31
  

 

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.
Bloom's Scope Hours Source
Application Master 2.0 GA: Quality Core Curriculum, December 2000, Calculus, #24
  

 

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.
Bloom's Scope Hours Source
Analysis Master 1.5 GA: Quality Core Curriculum, December 2000, Calculus, #32
  
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Number and Operations

PS4: COMPUTATION AND ESTIMATION
The learner will be able to estimate and judge reasonableness of numerical results.
  

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.
Bloom's Scope Hours Source
Application Master 1.5 GA: Quality Core Curriculum, December 2000, Calculus, #7
  
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