F.1.MAA The student will graphically, numerically, and algebraically evaluate concepts of different types of functions; include recursively defined functions, series, and sequences; and apply them to programming applications
F.1.MAA.1 Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. [e.g., the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n ≥ 1]
F.1.MAA.2 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases: graph exponential and logarithmic functions showing intercepts, end behavior, and trigonometric functions, showing period, midline, and amplitude; graph linear and quadratic functions and show intercepts, maxima, and minima; graph rational functions identifying zeros and asymptotes when suitable factorizations are available and showing end behavior.
F.1.MAA.4 Compare properties of two functions each represented in a different way: algebraically, graphically, numerically in tables, or by verbal descriptions (e.g., given a graph of one quadratic function and an algebraic expression for another, determine which has the larger maximum).
F.1.MAA.5 Write a function that describes a relationship between two quantities: compose functions [e.g., if T(y) is the temperature in the atmosphere as a function of height, and h(t) is the height of a weather balloon as a function of time, then T(h(t)) is the temperature at the location of the weather balloon as a function of time]; combine standard function types using arithmetic operations (e.g., build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential and relate these functions to the model); determine an explicit expression, a recursive process, or steps for calculation from a context.
EF.2.MAA The student will manipulate formulas and equations and apply them to programming applications
EF.2.MAA.1 Represent constraints by equations or inequalities and by systems of equations and/or inequalities (two and three variable systems); interpret solutions as viable or nonviable options in a modeling context (e.g., represent inequalities describing nutritional and cost constraints on combinations of different foods).
EF.2.MAA.3 Give an informal argument for the formulas for the circumference of a circle, area of a circle, and volume of a cylinder, pyramid, and cone; use dissection arguments, Cavalieri's principle, and informal limit arguments.
EF.2.MAA.4 Give an informal argument using Cavalieri's principle for the formulas for the volume of a sphere and other solid figures.
EF.2.MAA.5 Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.
SEM.3.MAA.7 Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers; the determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse.