mvsd
Math Curriculum 01/12/03

Mathematics - Calculus

Mathematics

The Idaho State Achievement Standards for Mathematics provides skills for kindergarten through twelfth grade.


Functions

    Functions/Relations: Recognize
The learner will be able to recognize the characteristics of functions and relations according to domain, range, intercepts, symmetry, odd, even, asymptotes, and zeros, as well as graph them according to these characteristics and recognize these characteristics according to the graphs.
Strand Bloom's Scope Hours Source
Functions/Relations Comprehension Master ID: State Achievement Standards, 2001, Grades 9-12, 353.03.a/353.01
  
    Functions: Properties
The learner will be able to recognize and apply the properties of algebraic, trigonometric, exponential, and logarithmic functions, including polynomials, absolute value, and functions with bounded/unbounded behavior.
Strand Bloom's Scope Hours Source
Functions Application Master ID: State Achievement Standards, 2001, Grades 9-12, 353.03.a
  
    Operations: Functions/Algebra
The learner will be able to apply the algebra of functions in determining the sum, product, quotient, composition, and inverse if they exist.
Strand Bloom's Scope Hours Source
Operations Comprehension Master District Expectation
  

Calculus and Pre-Calculus

    Limits: Approximate/Graphs/Tables
The learner will be able to approximate limits from graphs or tables of data.
Strand Bloom's Scope Hours Source
Limits Application Master 1.5 District Expectation
  
    Limits: Infinity
The learner will be able to explain asymptotic behavior in terms of limits involving infinity.
Strand Bloom's Scope Hours Source
Limits Comprehension Master 2.0 District Expectation
  
    Limits: Evaluate
The learner will be able to evaluate the limit of a function and apply the properties of limits, including one-sided limits.
Strand Bloom's Scope Hours Source
Limits Master District Expectation
  
    Apply Calculus Concepts: Fundamental
The learner will be able to recognize the Fundamental Theorem of Calculus.
Strand Bloom's Scope Hours Source
Applying Calculus Concepts Knowledge Master 1.0 District Expectation
  
    Applying Calculus Concepts: Continuity
The learner will be able to apply the definition of continuity of a function at a point & over an interval.
Strand Bloom's Scope Hours Source
Applying Calculus Concepts Application Master 1.0 District Expectation
  
    Applying Calculus Concepts: Extreme
The learner will be able to use the Extreme Value Theorem in problem scenarios.
Strand Bloom's Scope Hours Source
Applying Calculus Concepts Application Master 1.0 District Expectation
  
    Applying Calculus Concepts: L'Hopital
The learner will be able to appropriately apply L'Hopital's Rule.
Strand Bloom's Scope Hours Source
Applying Calculus Concepts Application Master 1.0 District Expectation
  
    Applying Calculus Concepts: Theorems
The learner will be able to apply the Mean Value and Rolle's Theorem.
Strand Bloom's Scope Hours Source
Applying Calculus Concepts Application Master 1.0 District Expectation
  
    Apply Calculus Concepts: Sums
The learner will be able to compute area values through the evaluation of sums and application of sigma notation.
Strand Bloom's Scope Hours Source
Applying Calculus Concepts Master District Expectation
  
    Derivatives: Slope of a Tangent/Define
The learner will be able to define a derivative as the slope of a line tangent to a curve at a given point.
Strand Bloom's Scope Hours Source
Derivatives/Antiderivatives Knowledge Master 0.5 District Expectation
  
    Derivatives: Define
The learner will be able to give the definition of the derivative as the limit of the difference quotient.
Strand Bloom's Scope Hours Source
Derivatives/Antiderivatives Knowledge Master 1.0 District Expectation
  
    Differentiation: Define/Instant/Limit
The learner will be able to define the derivative of a function as the instantaneous rate of change and as the limit of the average rate of change.
Strand Bloom's Scope Hours Source
Differentiation Knowledge Master 0.5 District Expectation
  
    Differentiation: Function/Over Interval
The learner will be able to determine whether a function is differentiable over an interval.
Strand Bloom's Scope Hours Source
Differentiation Application Master 1.0 District Expectation
  
    Differentiation: Function/Point
The learner will be able to find points where a function's derivative does not exist.
Strand Bloom's Scope Hours Source
Differentiation Application Master 1.0 District Expectation
  
    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 Bloom's Scope Hours Source
Differentiation Application Master 1.0 District Expectation
  
    Differentiation: Apply
The learner will be able to apply the derivative to find the slope of a curve at a given point, the equation of a tangent line to a point on the curve, and the equation of the normal line to a point on the curve.
Strand Bloom's Scope Hours Source
Differentiation Master District Expectation
  
    Differentiation: Apply/Relationships
The learner will be able to apply the relationships between f(x), f'(x), and f''(x) to find the increasing and decreasing behavior of f(x), the critical points of f(x), the concavity of f(x) over an interval, the points of inflection of f(x), to sketch the graphs of f'(x) and f''(x) when given f(x), and sketch the graph of f(x) when given f'(x).
Strand Bloom's Scope Hours Source
Differentiation Master District Expectation
  
    Differentiation: Find/Apply
The learner will be able to find and apply the successive derivatives of a function.
Strand Bloom's Scope Hours Source
Differentiation Master District Expectation
  
    Derivatives: Composite/Chain Rule
The learner will be able to calculate the derivative of composite functions using the chain rule.
Strand Bloom's Scope Hours Source
Derivatives/Antiderivatives Application Master 1.0 District Expectation
  
    Differentiation: Chain Rule/Implicit
The learner will be able to apply the chain rule to functions defined implicitly and related rates of change situations.
Strand Bloom's Scope Hours Source
Differentiation Application Master 1.0 District Expectation
  
    Derivatives: Inverse Functions
The learner will be able to calculate the derivative of the inverses of functions, including trigonometric inverses.
Strand Bloom's Scope Hours Source
Derivatives/Antiderivatives Application Master 1.0 District Expectation
  
    Differentiation: Use/Rules
The learner will be able to use the rules of differentiation with algebraic and transcendental functions.
Strand Bloom's Scope Hours Source
Differentiation Application Master 1.0 District Expectation
  
    Integration: Define/Apply
The learner will be able to make definitions of and/or use properties of the definite integral.
Strand Bloom's Scope Hours Source
Integration Master District Expectation
  
    Integration: Define/Use/Properties
The learner will be able to state the definition of the antiderivative and use its properties in problems.
Strand Bloom's Scope Hours Source
Integration Master District Expectation
  
    Definite Integral: Relate/Area
The learner will be able to relate the definite integral to the idea of the area under a curve.
Strand Bloom's Scope Hours Source
Definite Integral Analysis Master 1.0 District Expectation
  
    Definite Integral: Fundamental Theorems
The learner will be able to evaluate definite integrals by applying the Fundamental Theorem of calculus.
Strand Bloom's Scope Hours Source
Definite Integral Application Master 0.5 District Expectation
  
    Integration: Apply/Mean Value
The learner will be able to apply the integral to the mean value of a function over an interval.
Strand Bloom's Scope Hours Source
Integration Application Master 1.0 District Expectation
  
    Integration: Apply/Identities
The learner will be able to perform integration by applying identities.
Strand Bloom's Scope Hours Source
Integration Application Master 2.0 District Expectation
  
    Integration: Parts
The learner will be able to perform integration by parts.
Strand Bloom's Scope Hours Source
Integration Application Master 1.0 District Expectation
  
    Integration: Substitution
The learner will be able to integrate using substitution.
Strand Bloom's Scope Hours Source
Integration Application Master 1.0 District Expectation
  
    Integration: Changing Variables
The learner will be able to integrate by changing variables.
Strand Bloom's Scope Hours Source
Integration Application Master 2.0 District Expectation
  
    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.
Strand Bloom's Scope Hours Source
Integration Analysis Master 1.5 District Expectation
  
    Integration: Estimate/Areas
The learner will be able to estimate areas through the application of inscribed rectangles, circumscribed rectangles, trapezoids, and other suitable techniques.
Strand Bloom's Scope Hours Source
Integration Master District Expectation
  
    Integration: Find/Area/Curves
The learner will be able to find the area between curves through the use of integration formulas.
Strand Bloom's Scope Hours Source
Integration Application Master 1.0 District Expectation
  
    Integration: Find/Volume/Solid
The learner will be able to find the volume of a solid of revolution through the use of several different techniques.
Strand Bloom's Scope Hours Source
Integration Application Master 2.0 District Expectation
  

Probability/Statistics

    Optimization Problems
The learner will be able to solve optimization problems.
Strand Bloom's Scope Hours Source
Correlation/Deviation/Variance Application Master 0.5 ID: State Achievement Standards, 2001, Grades 9-12, 352.05.a
  

Problem Solving

    Problem Solving: Relate
The learner will be able to obtain solutions to problems that relate ideas to practical applications as well as to other ideas utilizing suitable instruments.
Strand Bloom's Scope Hours Source
Problem Solving Application Master ID: State Achievement Standards, 2001, Grades 9-12, 353.03.a; 352.05.a
  
    Problem Solving: Estimate/Predict
The learner will be able to apply estimation strategies to predict calculated results when solving problems.
Strand Bloom's Scope Hours Source
Problem Solving Application Master 1.0 District Expectation
  
    Solution: Reasonableness
The learner will be able to evaluate the reasonableness of a given solution.
Strand Bloom's Scope Hours Source
Solution Evaluation Master 1.5 District Expectation
  
    Strategies: Choose/Suitable
The learner will be able to choose suitable problem solving strategies.
Strand Bloom's Scope Hours Source
Strategies Application Master 1.0 District Expectation
  
    Strategies: Choose/Tools/Suitable
The learner will be able to choose suitable mathematical tools to obtain solutions to problems.
Strand Bloom's Scope Hours Source
Strategies Application Master 1.0 District Expectation
  

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