Algebra II Strategies

MAA2: Algebra II Strategies

MAA2.A: Algebra

MAA2.B: Statistics and Probability

MAA2.C: Functions

MAA2.D: Number and Quantity

MAA2.A.1: solve quadratic equations in one variable

MAA2.A.2: solve quadratic equations by inspection, taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation; recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b; connect the solutions to the graph and real life application

MAA2.A.3: interpret expressions that represent a quantity in terms of its context

MAA2.A.4: interpret complicated expressions by viewing one or more of their parts as a single entity

MAA2.A.5: identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial

MAA2.A.6: prove polynomial identities and use them to describe numerical relationships

MAA2.A.7: create equations and inequalities in one variable and use them to solve problems; include equations arising from linear and quadratic functions, and simple rational and exponential functions

MAA2.A.8: create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales

MAA2.A.9: use the properties of exponents to transform expressions for exponential functions

MAA2.A.10: represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context

MAA2.A.11: rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations

MAA2.A.12: 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

MAA2.B.13: decide if a specified model is consistent with results from a given data-generating process

MAA2.B.14: use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling

MAA2.B.15: evaluate reports based on data

MAA2.C.16: combine standard function types using arithmetic operations

MAA2.C.17: compose polynomial functions

MAA2.C.18: interpret key features of graphs and tables in terms of the quantities for a function that models a relationship between two quantities, and sketch graphs showing key features given a verbal description of the relationship; key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity

MAA2.C.19: graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases

MAA2.C.20: use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context

MAA2.C.21: relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes

MAA2.C.22: use the properties of exponents to interpret expressions for exponential functions

MAA2.C.23: understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents

MAA2.C.24: express as a logarithm for exponential models the solution to ab raised to the (ct) power equals d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology

MAA2.C.25: calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval; estimate the rate of change from a graph; consider all types of functions

MAA2.C.26: compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions)

MAA2.C.27: identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs; experiment with cases and illustrate an explanation of the effects on the graph using technology; include recognizing even and odd functions from their graphs and algebraic expressions for them

MAA2.D.28: solve quadratic equations with real coefficients that have complex solutions; connect complex solutions to the graphs and examples using the quadratic formula

MAA2.D.29: use the relation i² = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers

MAA2.D.30: extend polynomial identities to the complex numbers

MAA2.D.31: rewrite expressions involving radicals and rational exponents using the properties of exponents