Algebra II (South Dakota Content Standards)

Number and Quantity (N)

• A2.N.CN.1 Know the unit i with i squared = −1 and that complex numbers have the form a + bi with a and b real.
• A2.N.CN.2 Add, subtract and multiply complex numbers using i squared = −1 and the usual properties.
• A2.N.CN.7 Solve quadratics with real coefficients that have complex solutions.

Algebra (A)

• A2.A.SSE.1 Interpret expressions that stand for a quantity in context (shared with Algebra I; modeling).
  • A2.A.SSE.1a Identify an expression's terms, factors and coefficients.
  • A2.A.SSE.1b Read complicated expressions by treating some parts as a single quantity.
• A2.A.SSE.2 Spot and use an expression's structure to find ways to rewrite it (shared with Algebra I).
• A2.A.APR.2 Know and use the Remainder Theorem.
• A2.A.APR.3 Find polynomial zeros by factoring.
  • A2.A.APR.3a Use zeros from a suitable factorization to sketch a rough graph.
  • A2.A.APR.3b Use zeros on a given graph to suggest a factorization.
• A2.A.APR.6 Rewrite simple rational expressions by inspection, synthetic or long division, the box method or a computer algebra system.
• A2.A.CED.1 Write one-variable equations and inequalities and use them to solve problems (modeling).
• A2.A.CED.2 Write equations in two or more variables for relationships and graph them with labeled axes and scales (shared; modeling).
• A2.A.CED.3 Express constraints with equations, inequalities or systems and judge which solutions are viable (shared; modeling).
• A2.A.CED.4 Solve a formula for a chosen quantity using equation-solving steps (shared; modeling).
• A2.A.REI.2 Solve one-variable rational and radical equations and show how extraneous solutions arise, with limits on rational degree.
• A2.A.REI.4 Choose, justify and use methods to solve one-variable quadratics, writing complex solutions as a ± bi (shared).
• A2.A.REI.11 Explain why intersections of y = f(x) and y = g(x) solve f(x) = g(x) and approximate them, e.g. with technology (shared).

Functions (F)

• A2.F.IF.4 Interpret key features of graphs and tables of functions in context and sketch graphs from descriptions (shared).
• A2.F.IF.5 Connect a function's domain to its graph and choose a sensible domain in context (shared; modeling).
• A2.F.IF.6 Find and interpret average rate of change from a formula or table over an interval and estimate it from a graph (modeling).
• A2.F.IF.7 Graph parent functions and their transformations by hand and with technology, showing key features (shared; modeling).
  • A2.F.IF.7b Graph square root, cube root and piecewise functions, including step and absolute value.
  • A2.F.IF.7c Graph polynomials showing zeros from suitable factorizations and end behavior.
  • A2.F.IF.7d Graph rational functions showing zeros, asymptotes and end behavior.
  • A2.F.IF.7e Graph log functions, marking intercepts and end behavior.
  • A2.F.IF.7f Graph sine and cosine curves, marking period, midline and amplitude.
• A2.F.IF.9 Compare two functions given in different representations (shared).
• A2.F.BF.1 Write a function for a relationship between two quantities (modeling).
  • A2.F.BF.1a Find an explicit expression, recursive process or calculation steps from a context.
  • A2.F.BF.1b Find an explicit expression from a graph.
  • A2.F.BF.1c Combine standard function types with arithmetic operations.
  • A2.F.BF.1d Compose functions.
• A2.F.BF.3 Describe how adding or multiplying by k inside or outside f changes a graph, and find k from graphs (shared).
• A2.F.BF.4 Find inverse functions.
  • A2.F.BF.4a Solve y = f(x) for x to write an inverse expression.
  • A2.F.BF.4b Check by composition that two functions are inverses.
  • A2.F.BF.4c Read inverse values from a graph or table.
• A2.F.BF.5 Use the inverse link between exponents and logarithms to solve problems (plus standard).
• A2.F.LE.4 Express solutions of a·b^(ct) = d as logarithms for base 2, 10 or e and evaluate with technology (modeling).
• A2.F.TF.1 Understand radian measure as arc length on the unit circle.
• A2.F.TF.2 Explain how the unit circle extends sine and cosine to all real numbers.
• A2.F.TF.5 Choose sine or cosine functions to model periodic situations with a given amplitude, frequency and midline (modeling).
• A2.F.TF.8 Prove sin² + cos² = 1 and use it to find trig ratios.

Statistics and Probability (S)

• A2.S.ID.4 Fit data to a normal curve with mean and standard deviation to estimate percentages, knowing when not to, using calculators or tables.
• A2.S.IC.1 See statistics as inferring population parameters from a random sample.
• A2.S.IC.2 Decide whether a model fits results from a data-generating process.
• A2.S.IC.3 Tell apart surveys, experiments and observational studies and explain the role of randomization in each.
• A2.S.IC.4 Estimate a population mean or proportion from a survey and build a margin of error by simulation.
• A2.S.IC.5 Compare two treatment groups in a randomized experiment and use simulation to judge whether differences are significant.
• A2.S.IC.6 Critically evaluate reports and claims based on data.