Calculus

Tuesday, 21 August 2007

Patterns, Functions, Algebra   Patterns, Functions, Algebra Patterns, Functions, Algebra Description 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 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 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 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 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 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 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 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 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 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 CAL.PFA.11 The learner will be able to solve first order differentiable equations. Strand Bloom's Scope Calculus: Differential Equations Application Master 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 CAL.PFA.13 The learner will be able to approximate the area under a curve. Strand Bloom's Scope Calculus: Concepts Application Master 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 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 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 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 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 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 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 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 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 CAL.PFA.23 The learner will be able to recognize the Fundamental Theorem of Calculus. Strand Bloom's Scope Calculus: Concepts Knowledge Master 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 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 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 CAL.PFA.27 The learner will be able to appropriately apply L'Hopital's Rule. Strand Bloom's Scope Calculus: Concepts Application Master 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 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 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 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 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 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 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 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 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 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 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 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 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 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 CAL.PFA.42 The learner will be able to perform integration by applying identities. Strand Bloom's Scope Calculus: Integration Application Master 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 CAL.PFA.44 The learner will be able to integrate by changing variables. Strand Bloom's Scope Calculus: Integration Application Master 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 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 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 CAL.PFA.48 The learner will be able to perform integration by parts. Strand Bloom's Scope Calculus: Integration Application Master CAL.PFA.49 The learner will be able to integrate using substitution. Strand Bloom's Scope Calculus: Integration Application Master 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 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 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 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 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 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 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 CAL.PFA.57 The learner will be able to evaluate the reasonableness of a given solution. Strand Bloom's Scope Estimation Evaluation Master CAL.PFA.58 The learner will be able to choose suitable problem solving strategies. Strand Bloom's Scope Problem Solving Application Master 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 CAL.PFA.60 The learner will be able to solve optimization problems. Strand Bloom's Scope Problem Solving Application Master top