Algebra II (West Virginia CCR Standards)

Number and Quantity – Complex numbers

• M.A2HS.1 Know the imaginary unit i and that complex numbers are made of a real part and an imaginary part.
• M.A2HS.2 Add, subtract and multiply complex numbers using i² = –1 and the usual properties of operations.
• M.A2HS.3 Solve quadratic equations with real coefficients that have complex solutions.
• M.A2HS.4 Factor special real polynomials whose zeros are complex.
• M.A2HS.5 Show that the Fundamental Theorem of Algebra holds for quadratic polynomials with real coefficients.

Algebra – Expressions, polynomials, rational expressions, equations and inequalities

• M.A2HS.6 Interpret rational and polynomial expressions that represent a quantity in context.
  • a. Interpret parts of an expression such as terms, factors and coefficients.
  • b. Interpret complicated expressions by viewing one or more parts as a single quantity.
• M.A2HS.7 Use the structure of polynomial and rational expressions to find ways to rewrite them.
• M.A2HS.8 Derive the formula for the sum of a finite geometric series and use it to solve problems.
• M.A2HS.9 Understand that polynomials are closed under addition, subtraction and multiplication, and carry out these operations for any degree.
• M.A2HS.10 Know and apply the Remainder Theorem for polynomials.
• M.A2HS.11 Find zeros of a factored polynomial and use them to sketch a rough graph of the function.
• M.A2HS.12 Prove polynomial identities and use them to describe numerical relationships.
• M.A2HS.13 Know and apply the Binomial Theorem to expand (x + y)^n for a positive integer n.
• M.A2HS.14 Rewrite simple rational expressions in different forms using a range of methods.
• M.A2HS.15 Understand that rational expressions are closed under the four operations and add, subtract, multiply and divide them.
• M.A2HS.16 Solve simple rational and radical equations in one variable and explain how extraneous solutions can arise.
• M.A2HS.17 Explain why the x-coordinates of intersection points solve f(x) = g(x) and find approximate solutions.
• M.A2HS.18 Solve a system of a linear and a quadratic equation algebraically and graphically.
• M.A2HS.19 Create one-variable equations and inequalities from common relationships and use them to solve problems.
• M.A2HS.20 Create equations in two or more variables for linear, exponential and quadratic relationships.
• M.A2HS.21 Represent constraints with equations or inequalities and interpret solutions as viable or not in context.

Functions – Interpret, analyze and build functions

• M.A2HS.22 For a function modeling a relationship, read key features (intercepts, intervals, extrema, symmetry, end behavior) from graphs and tables and relate the domain to the context.
• M.A2HS.23 Calculate and interpret the average rate of change of a function over an interval and estimate it from a graph.
• M.A2HS.24 Graph functions given symbolically, show key features by hand and with technology, and choose a suitable model.
  • a. Graph polynomial functions, showing zeros and end behavior.
  • b. Graph exponential and logarithmic functions, showing intercepts and end behavior.
• M.A2HS.25 Write a function in different but equivalent forms to show and explain its properties.
• M.A2HS.26 Compare properties of two functions each represented in a different way.
• M.A2HS.27 Write a function for a relationship between two quantities by combining standard function types with arithmetic operations.
• M.A2HS.28 Describe how transformations change graphs, and recognize even and odd functions from graphs and equations.
• M.A2HS.29 Find inverses of simple functions, restricting the domain where needed.
• M.A2HS.30 Write solutions of exponential models as logarithms and evaluate them with technology.

Statistics and Probability – Data, inference and decisions

• M.A2HS.31 Fit a normal distribution to data using mean and standard deviation, estimate percentages and know when this is not suitable.
• M.A2HS.32 Understand statistics as making inferences about populations from random samples; compare theoretical and empirical results.
• M.A2HS.33 Decide whether a model is consistent with results from a data-generating process, for example by simulation.
• M.A2HS.34 Tell sample surveys, experiments and observational studies apart and explain how randomization relates to each.
• M.A2HS.35 Use sample survey data to estimate a population mean or proportion and develop a margin of error by simulation.
• M.A2HS.36 Use data from randomized experiments to compare two treatments and use simulation to judge whether differences matter.
• M.A2HS.37 Evaluate reports based on data, looking at how the data were collected and whether conclusions follow.
• M.A2HS.38 Use probabilities to make fair decisions, including in quality control and with false positive or negative results.
• M.A2HS.39 Analyze decisions and strategies with probability, including quality control and false positive or negative results.