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Arkansas: F Math Standards

35 standards · 4 domains

F.1

F.1.ATMM.1 Interpret key features of graphs and tables in terms of two quantities for functions beyond the level of quadratic that model a relationship between the quantities
F.1.ATMM.2 Graph functions expressed symbolically and show key features of the graph using technology
F.1.ATMM.3 Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions
F.1.ATMM.4 Graph polynomial functions, identifying zeros when suitable factorizations are available and showing end behavior
F.1.ATMM.5 Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available and showing end behavior
F.1.ATMM.6 Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude
F.1.ATMM.7 Interpret the parameters of functions beyond the level of linear and quadratic in terms of a context
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:
F.1.MAA.3 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function
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:
F.1.MAA.6 Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms
F.1.MAA.7 Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed
F.1.MAA.8 Use inverse functions to solve trigonometric equations that arise in modeling contexts, evaluate the solutions using technology, and interpret them in terms of the context
F.1.MAA.9 Know there is a complex number i such that i^2 = –1, and every complex number has the form a + bi with a and b real
F.1.MAA.10 Use the relation i^2 = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers
F.1.MAA.11 Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers

F.2

F.2.ATMM.1 Model equations in two or more variables to represent relationships between quantities for functions beyond the level of linear and quadratic
F.2.ATMM.2 Represent constraints or inequalities using systems of equations and/or inequalities; interpret solutions as viable or non-viable options in a modeling context for functions beyond the level of linear and quadratic
F.2.ATMM.3 Compose functions (e.g., If T(y) is the temperature in the atmosphere as a function of height, and h(y) 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)
F.2.ATMM.4 Write arithmetic and geometric sequences both recursively and with an explicit formula; use the sequences to model situations and translate between the two forms
F.2.ATMM.5 Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed
F.2.ATMM.6 Use inverse functions to solve trigonometric equations that arise in modeling context; evaluate the solutions using technology and interpret them in terms of the context

F.6

F.6.PC.1 Write a function that describes a relationship between two quantities.
F.6.PC.2 Find inverse functions.
F.6.PC.3 Understand the inverse relationship between exponents and logarithms. Use the inverse relationship between exponents and logarithms to solve problems.

F.7

F.7.PC.1 Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example: The Fibonacci sequence is defined recursively by (0) = (1) = 1, f(n + 1) = f(n) + (n − 1) for n ≥ 1.
F.7.PC.2 Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. For example: Calculate mortgage payments.
F.7.PC.3 (+) Know and apply the Binomial Theorem for the expansion of (x + y)^n in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal's Triangle.
F.7.PC.4 For a function that models a relationship between two quantities: Interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Note: Key features may include but not limited to: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.
F.7.PC.5 Calculate and interpret the average rate of change of a function (presented algebraically or as a table) over a specified interval. Estimate the rate of change from a graph.
F.7.PC.6 Graph functions expressed algebraically and show key features of the graph, with and without technology.
F.7.PC.7 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
F.7.PC.8 Build functions to model real-world applications using algebraic operations on functions and composition, with and without appropriate technology (e.g., profit functions as well as volume and surface area, optimization subject to constraints)