Calculus

MACA: Calculus

MACA.A: Process Skills

MACA.B: Functions

MACA.C: Limits and Continuity

MACA.D: Derivatives

MACA.E: Applications of Derivatives

MACA.F: Integrals

MACA.G: Applications of the Integral

MACA.H: Reading Across the Curriculum

MACA.A.1: use appropriate technology to solve mathematical problems

MACA.A.2: build new mathematical knowledge through problem-solving

MACA.A.3: solve problems that arise in mathematics and in other areas

MACA.A.4: apply and adapt a variety of appropriate strategies to solve problems

MACA.A.5: monitor and reflect on the process of mathematical problem-solving

MACA.A.6: recognize reasoning and proof (evidence) as fundamental aspects of mathematics

MACA.A.7: make and investigate mathematical conjectures

MACA.A.8: investigate, develop, and evaluate mathematical arguments and proofs

MACA.A.9: select and use various types of reasoning and methods of proof

MACA.A.10: organize and consolidate mathematics thinking

MACA.A.11: communicate mathematical thinking coherently to peers, teachers, and others

MACA.A.12: analyze and evaluate the mathematical thinking and strategies of others

MACA.A.13: use the terminology and language of mathematics to express mathematical ideas precisely

MACA.A.14: recognize and use connections among mathematical ideas

MACA.A.15: explain how mathematical ideas interconnect and build on one another to produce a coherent whole

MACA.A.16: recognize and apply mathematics in contexts outside of mathematics

MACA.A.17: create and use pictures, manipulatives, models, and symbols to organize, record, and communicate mathematical ideas

MACA.A.18: select, apply, and translate among mathematical representations to solve problems

MACA.A.19: use representations to model and interpret physical, social, and mathematical phenomena

MACA.B.20: apply concepts of functions including domain, range, intercepts, symmetry, asymptotes, zeros, odd, even, and inverse

MACA.B.21: apply the algebra of functions by finding sum, product, quotient, composition, and inverse, where they exist

MACA.B.22: identify and apply properties of algebraic, trigonometric, piecewise, absolute value, exponential, and logarithmic functions

MACA.C.23: calculate limits using algebra

MACA.C.24: evaluate limits of functions and apply properties of limits, including one-sided limits

MACA.C.25: estimate limits from graphs or tables of data

MACA.C.26: describe asymptotic behavior in terms of limits involving infinity

MACA.C.27: indicate where a function is continuous and where it is discontinuous

MACA.C.28: identify types of discontinuities graphically and analytically

MACA.C.29: apply the definition of continuity to a function at a point

MACA.D.30: 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, and the limit of the average rate of change

MACA.D.31: determine if a function is differentiable over an interval

MACA.D.32: determine where a function fails to be differentiable

MACA.D.33: apply the rules of differentiation, such as product and quotient rules, to algebraic functions, including successive derivatives

MACA.D.34: interpret derivative as a rate of change in the context of speed, velocity, and acceleration

MACA.D.35: apply the chain rule to composite functions, implicitly defined relations, and related rates of change

MACA.D.36: apply the rules of differentiation to trigonometric functions, such as product, quotient, and chain rules, including successive derivatives

MACA.E.37: 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 a point

MACA.E.38: apply Rolle's Theorem and the Mean Value Theorem

MACA.E.39: use the relationships between f(x), f'(x), and f"(x) to determine the increasing/decreasing behavior of f(x); determine the critical point(s) of f(x); determine the concavity of f(x) over an interval; and determine the point(s) of inflection of f(x)

MACA.E.40: given various pieces of information, sketch of graph(s) of f(x), f'(x), and f"(x)

MACA.E.41: find absolute (global) and relative (local) extrema

MACA.E.42: solve optimization problems

MACA.E.43: apply the extreme value theorem to problem situations

MACA.E.44: model rates of change involved with related rates problems

MACA.F.45: define the antiderivative and apply its properties to problems such as distance and velocity from acceleration with initial condition, growth, and decay

MACA.F.46: compute Riemann sums using left, right, and midpoint evaluations and trapezoids

MACA.F.47: calculate area by a definite integral of Riemann sums over equal subdivisions

MACA.F.48: calculate areas by evaluation sums using sigma notation

MACA.F.49: relate the definite integral to the concept of the area under a curve; define and apply the properties of the definite integral

MACA.F.50: identify and use the Fundamental Theorem of Calculus in evaluation of definite integrals

MACA.F.51: evaluate integrals following directly from derivatives of basic functions

MACA.F.52: evaluate integrals by substitution of variables (including change of limits for definite integrals)

MACA.G.53: apply the integral to the average or mean value of a function on an interval

MACA.G.54: evaluate the area between curves using integration formulas

MACA.G.55: evaluate the volume of a solid using known cross-sections

MACA.G.56: evaluate the volume of a solid of revolutions using the disk or washer method

MACA.H.57: read and discuss mathematical material to establish context for subject matter, develop mathematical vocabulary, and develop an awareness of current research