Algebra II (Arizona Mathematics Standards)

Number and Quantity

• A2.N-RN.A.1 Explain how rational exponents are defined by extending the rules for integer exponents (e.g. 5^(1/3) as the cube root of 5).
• A2.N-RN.A.2 Rewrite expressions with radicals and rational exponents using exponent properties.
• A2.N-Q.A.1 Use units to understand and guide multistep problems, read units in formulas and choose scales and origins for graphs and data displays.
• A2.N-Q.A.2 Define suitable quantities when building a descriptive model.
• A2.N-Q.A.3 Report quantities with a level of accuracy that fits the limits of measurement.
• A2.N-CN.A.1 Add, subtract and multiply complex numbers using i² = −1. (being checked)
• A2.N-CN.C.7 Solve quadratics with real coefficients whose solutions are complex.

Algebra

• A2.A-SSE.A.2 Use the structure of polynomial and rational expressions to find ways to rewrite them, including factoring patterns.
• A2.A-SSE.B.3 Rewrite an expression in an equivalent form that shows its properties, including real problems with rational exponents.
  • c. Use exponent properties to rewrite exponential expressions (e.g. annual to monthly rates).
• A2.A-SSE.B.4 Derive the finite geometric series sum formula (ratio not 1) and use it, e.g. for mortgage payments.
• A2.A-APR.B.2 Use the Remainder and Factor Theorems to link division remainders, values p(a) and factors.
• A2.A-APR.B.3 Find zeros from factored polynomials and use them to sketch quadratic, cubic and quartic graphs.
• A2.A-APR.C.4 Prove polynomial identities and use them to show number relationships (e.g. Pythagorean triples).
• A2.A-APR.D.6 Rewrite simple rational expressions as quotient plus remainder over divisor, by inspection, long division or technology.
• A2.A-CED.A.1 Create one-variable equations and inequalities (linear, quadratic, simple rational, exponential) and use them to solve problems.
• A2.A-REI.A.1 Justify each step of solving a simple equation and build a viable argument for the solution method.
• A2.A-REI.A.2 Solve simple rational and radical equations and show how extraneous solutions can appear.
• A2.A-REI.B.4 Solve quadratic equations fluently by several methods and write complex solutions in a + bi form.
• A2.A-REI.C.7 Solve a system of a linear and a quadratic equation (including a line and a circle) algebraically and graphically.
• A2.A-REI.D.11 Explain why intersections of y = f(x) and y = g(x) solve f(x) = g(x), for polynomial, rational, exponential and logarithmic functions.

Functions

• A2.F-IF.B.4 Interpret key graph and table features in context, including periodicity.
• A2.F-IF.B.6 Calculate and interpret average rate of change over an interval and estimate it from a graph.
• A2.F-IF.C.7 Graph functions from their equations and show key features, by hand or with technology. (being checked)
• A2.F-IF.C.8.b Use exponent properties to interpret exponential functions, e.g. as percent growth or decay. (being checked)
• A2.F-IF.C.9 Compare properties of two functions shown in different ways.
• A2.F-BF.A.1 Write a function for a relationship between two quantities.
  • a. Find an explicit expression, recursive process or calculation steps from a context.
  • b. Combine function types with arithmetic operations and composition to build new functions.
• A2.F-BF.A.2 Write arithmetic and geometric sequences recursively and explicitly, model with them and convert between forms.
• A2.F-BF.B.3 Describe how adding k, multiplying by k or replacing x by kx or x + k changes a graph; find k; recognize even and odd functions.
• A2.F-BF.B.4 Find inverse functions.
  • a. Understand inverse functions as f(x) = y and g(y) = x for every value in their domains.
  • b. Know that if (a, b) is on a function's graph, (b, a) is on its inverse's graph.
  • c. Interpret a function and its inverse in a real-world context.
• A2.F-LE.A.4 Write solutions of ab^(ct) = d as logarithms (base 2, 10 or e) and evaluate them with technology.
• A2.F-LE.B.5 Interpret the parameters of exponential functions with rational exponents in context.
• A2.F-TF.A.1 Understand radian measure as arc length on the unit circle.
• A2.F-TF.A.2 Explain how the unit circle extends trigonometric functions to all real numbers.
• A2.F-TF.B.5 Build and interpret sine, cosine and tangent models of periodic situations with given amplitude, frequency and midline.
• A2.F-TF.C.8 Prove that sine squared plus cosine squared equals 1, then use it to find other trig values from one value and the quadrant.

Statistics and Probability

• A2.S-ID.A.4 Use mean and standard deviation to fit a normal distribution and estimate percentages, knowing when this is not appropriate.
• A2.S-ID.B.6 Make a scatter plot of two quantitative variables, describe their relationship and fit polynomial or exponential models.
  • a. Fit a function (linear, quadratic or exponential) to data and use it to solve problems.
• A2.S-ID.C.10 Interpret the parameters of exponential models in the context of the data.
• A2.S-IC.A.1 Understand statistics as making inferences about a population from a random sample.
• A2.S-IC.A.2 Decide whether a model fits results from a data-generating process, e.g. by simulation.
• A2.S-IC.B.3 Know the purposes of sample surveys, experiments and observational studies and how randomization relates to each.
• A2.S-IC.B.4 Estimate a population mean or proportion from a sample survey and know larger samples give more precise estimates. (being checked)
• A2.S-CP.A.3 Understand conditional probability P(A|B) = P(A and B)/P(B) and independence as P(A|B) = P(A).
• A2.S-CP.A.4 Build and read two-way tables to decide independence and find conditional probabilities.
• A2.S-CP.A.5 Explain conditional probability and independence in plain language with everyday examples.
• A2.S-CP.B.6 Find the probability of A given B as the share of B's outcomes that are also in A, including using Bayes' Rule.
• A2.S-CP.B.7 Apply the Addition Rule for "A or B" (add the two probabilities, subtract the overlap) and interpret it.
• A2.S-CP.B.8 Apply the general Multiplication Rule for "A and B" in an equally-likely model and interpret it.