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Patterns, Functions, Algebra
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Patterns, Functions, Algebra
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CAL.PFA.1
The learner will be able to use and analyze elementary functions, including algebraic, trigonometric, exponential, and logarithmic functions.
| Strand |
Bloom's |
Scope |
| Functions |
Application |
Master |
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CAL.PFA.2
The learner will be able to analyze a function from its graph and its equation: maxima, minima, domain and range, end behavior, behavior near the asymptotes, intervals over which the function is increasing or decreasing, and critical points.
| Strand |
Bloom's |
Scope |
| Functions |
Analysis |
Master |
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CAL.PFA.3
The learner will be able to perform function operations, including composition, decomposition, and inverses.
| Strand |
Bloom's |
Scope |
| Functions: Operations |
Application |
Master |
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CAL.PFA.4
The learner will be able to apply the definition of continuity, find excluded values of a discontinuous function, and apply intermediate value theorem.
| Strand |
Bloom's |
Scope |
| Trigonometry: Concepts |
Application |
Master |
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CAL.PFA.5
The learner will be able to state and apply the definitions of the derivative and find the derivatives of elementary functions, inverses of functions, logarithmic functions, and higher order functions.
| Strand |
Bloom's |
Scope |
| Calculus: Derivatives/Antiderivatives |
Comprehension |
Master |
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CAL.PFA.6
The learner will be able to apply the Mean Value Theorem and L'Hopital's Rule.
| Strand |
Bloom's |
Scope |
| Calculus: Derivatives/Antiderivatives |
Application |
Master |
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CAL.PFA.7
The learner will be able to apply the concepts of a derivative by finding the slope of a tangent line to a curve.
| Strand |
Bloom's |
Scope |
| Calculus: Derivatives/Antiderivatives |
Knowledge |
Master |
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CAL.PFA.8
The learner will be able to find average, instantaneous, and related rates of change.
| Strand |
Bloom's |
Scope |
| Calculus: Concepts |
Comprehension |
Master |
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CAL.PFA.9
The learner will be able to use the concepts of integral calculus to find antiderivatives.
| Strand |
Bloom's |
Scope |
| Calculus: Derivatives/Antiderivatives |
Comprehension |
Master |
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CAL.PFA.10
The learner will be able to use antiderivatives to find distance and velocity from acceleration with given initial conditions.
| Strand |
Bloom's |
Scope |
| Calculus: Derivatives/Antiderivatives |
Application |
Master |
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CAL.PFA.11
The learner will be able to solve first order differentiable equations.
| Strand |
Bloom's |
Scope |
| Calculus: Differential Equations |
Application |
Master |
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CAL.PFA.12
The learner will be able to use integration formulas, use substitution to integrate, and do simple integration by parts.
| Strand |
Bloom's |
Scope |
| Calculus: Integration |
Application |
Master |
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CAL.PFA.13
The learner will be able to approximate the area under a curve.
| Strand |
Bloom's |
Scope |
| Calculus: Concepts |
Application |
Master |
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CAL.PFA.14
The learner will be able to describe and apply the properties of the definite integral.
| Strand |
Bloom's |
Scope |
| Calculus: Concepts |
Comprehension |
Master |
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CAL.PFA.15
The learner will be able to compute area values through the evaluation of sums and application of sigma notation.
| Strand |
Bloom's |
Scope |
| Calculus: Concepts |
Evaluation |
Master |
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CAL.PFA.16
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 |
| Calculus: Differential Equations |
Application |
Master |
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CAL.PFA.17
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 |
| Calculus: Differentiation |
Application |
Master |
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CAL.PFA.18
The learner will be able to find and apply the successive derivatives of a function.
| Strand |
Bloom's |
Scope |
| Calculus: Differentiation |
Application |
Master |
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CAL.PFA.19
The learner will be able to make definitions of and/or use properties of the definite integral.
| Strand |
Bloom's |
Scope |
| Calculus: Integration |
Application |
Master |
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CAL.PFA.20
The learner will be able to state the definition of the antiderivative and use its properties in problems.
| Strand |
Bloom's |
Scope |
| Calculus: Integration |
Application |
Master |
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CAL.PFA.21
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 |
| Calculus: Integration |
Application |
Master |
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CAL.PFA.22
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 |
| Calculus: Limits |
Evaluation |
Master |
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CAL.PFA.23
The learner will be able to recognize the Fundamental Theorem of Calculus.
| Strand |
Bloom's |
Scope |
| Calculus: Concepts |
Knowledge |
Master |
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CAL.PFA.24
The learner will be able to apply the definition of continuity of a function at a point.
| Strand |
Bloom's |
Scope |
| Calculus: Concepts |
Application |
Master |
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CAL.PFA.25
The learner will be able to determine whether a function is continuous over an interval.
| Strand |
Bloom's |
Scope |
| Calculus: Concepts |
Application |
Master |
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CAL.PFA.26
The learner will be able to use the Extreme Value Theorem in problem scenarios.
| Strand |
Bloom's |
Scope |
| Calculus: Concepts |
Application |
Master |
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CAL.PFA.27
The learner will be able to appropriately apply L'Hopital's Rule.
| Strand |
Bloom's |
Scope |
| Calculus: Concepts |
Application |
Master |
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CAL.PFA.28
The learner will be able to apply the Mean Value and Rolle's Theorem.
| Strand |
Bloom's |
Scope |
| Calculus: Concepts |
Application |
Master |
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CAL.PFA.29
The learner will be able to evaluate definite integrals by applying the Fundamental Theorem of calculus.
| Strand |
Bloom's |
Scope |
| Calculus: Concepts |
Application |
Master |
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CAL.PFA.30
The learner will be able to relate the definite integral to the idea of the area under a curve.
| Strand |
Bloom's |
Scope |
| Calculus: Integrals |
Analysis |
Master |
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CAL.PFA.31
The learner will be able to calculate the derivative of composite functions using the chain rule.
| Strand |
Bloom's |
Scope |
| Calculus: Derivatives/Antiderivatives |
Application |
Master |
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CAL.PFA.32
The learner will be able to give the definition of the derivative as the limit of the difference quotient.
| Strand |
Bloom's |
Scope |
| Calculus: Derivatives/Antiderivatives |
Knowledge |
Master |
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CAL.PFA.33
The learner will be able to calculate the derivative of the inverses of functions, including trigonometric inverses.
| Strand |
Bloom's |
Scope |
| Calculus: Derivatives/Antiderivatives |
Application |
Master |
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CAL.PFA.34
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 |
| Calculus: Derivatives/Antiderivatives |
Knowledge |
Master |
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CAL.PFA.35
The learner will be able to apply the chain rule to functions defined implicitly.
| Strand |
Bloom's |
Scope |
| Calculus: Differentiation |
Application |
Master |
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CAL.PFA.36
The learner will be able to apply the chain rule to related-rates of change situations.
| Strand |
Bloom's |
Scope |
| Calculus: Differentiation |
Application |
Master |
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CAL.PFA.37
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 |
| Calculus: Differentiation |
Knowledge |
Master |
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CAL.PFA.38
The learner will be able to determine whether a function is differentiable over an interval.
| Strand |
Bloom's |
Scope |
| Calculus: Differentiation |
Application |
Master |
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CAL.PFA.39
The learner will be able to find points where a function's derivative does not exist.
| Strand |
Bloom's |
Scope |
| Calculus: Differentiation |
Application |
Master |
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CAL.PFA.40
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 |
| Calculus: Differentiation |
Application |
Master |
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CAL.PFA.41
The learner will be able to use the rules of differentiation with algebraic and transcendental functions.
| Strand |
Bloom's |
Scope |
| Calculus: Differentiation |
Application |
Master |
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CAL.PFA.42
The learner will be able to perform integration by applying identities.
| Strand |
Bloom's |
Scope |
| Calculus: Integration |
Application |
Master |
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CAL.PFA.43
The learner will be able to apply the integral to the mean value of a function over an interval.
| Strand |
Bloom's |
Scope |
| Calculus: Integration |
Application |
Master |
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CAL.PFA.44
The learner will be able to integrate by changing variables.
| Strand |
Bloom's |
Scope |
| Calculus: Integration |
Application |
Master |
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CAL.PFA.45
The learner will be able to find the area between curves through the use of integration formulas.
| Strand |
Bloom's |
Scope |
| Calculus: Integration |
Application |
Master |
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CAL.PFA.46
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 |
| Calculus: Integration |
Application |
Master |
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CAL.PFA.47
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 |
| Calculus: Integration |
Analysis |
Master |
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CAL.PFA.48
The learner will be able to perform integration by parts.
| Strand |
Bloom's |
Scope |
| Calculus: Integration |
Application |
Master |
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CAL.PFA.49
The learner will be able to integrate using substitution.
| Strand |
Bloom's |
Scope |
| Calculus: Integration |
Application |
Master |
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CAL.PFA.50
The learner will be able to approximate limits from graphs or tables of data.
| Strand |
Bloom's |
Scope |
| Calculus: Limits |
Application |
Master |
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CAL.PFA.51
The learner will be able to explain asymptotic behavior in terms of limits involving infinity.
| Strand |
Bloom's |
Scope |
| Calculus: Limits |
Comprehension |
Master |
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CAL.PFA.52
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 |
| Functions: Relations |
Comprehension |
Master |
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CAL.PFA.53
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 |
| Functions |
Application |
Master |
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CAL.PFA.54
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 |
| Functions: Operations |
Application |
Master |
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CAL.PFA.55
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 |
| Problem Solving |
Application |
Master |
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CAL.PFA.56
The learner will be able to apply estimation strategies to predict calculated results when solving problems.
| Strand |
Bloom's |
Scope |
| Problem Solving |
Application |
Master |
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CAL.PFA.57
The learner will be able to evaluate the reasonableness of a given solution.
| Strand |
Bloom's |
Scope |
| Estimation |
Evaluation |
Master |
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CAL.PFA.58
The learner will be able to choose suitable problem solving strategies.
| Strand |
Bloom's |
Scope |
| Problem Solving |
Application |
Master |
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CAL.PFA.59
The learner will be able to choose suitable mathematical tools to obtain solutions to problems.
| Strand |
Bloom's |
Scope |
| Problem Solving |
Application |
Master |
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CAL.PFA.60
The learner will be able to solve optimization problems.
| Strand |
Bloom's |
Scope |
| Problem Solving |
Application |
Master |
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