Algebra II (New York Next Generation)

Number and Quantity: The Real Number System

• Extend the properties of exponents to rational exponents
• AII-N.RN.1 Explore how the meaning of rational exponents comes from extending the rules for integer exponents.
• AII-N.RN.2 Convert between radical form and rational-exponent form using the properties of exponents.

Number and Quantity: The Complex Number System

• Perform arithmetic operations with complex numbers
• AII-N.CN.1 Know that i squared is −1 and that every complex number can be written a + bi with a and b real.
• AII-N.CN.2 Add, subtract and multiply complex numbers using i² = −1 and the usual properties, including powers of i.

Algebra: Seeing Structure in Expressions

• Interpret the structure of expressions
• AII-A.SSE.2 Spot an expression's structure to rewrite it, including factoring by grouping and sums or differences of cubes.
• Write expressions in equivalent forms to reveal their characteristics
• AII-A.SSE.3 Choose and write an equivalent form of an expression that reveals and explains properties of the quantity.
• AII-A.SSE.3a Factor a quadratic to show the zeros of the function it defines.
• AII-A.SSE.3c Rewrite exponential expressions with exponent properties, including rational coefficients in the exponent.

Algebra: Arithmetic with Polynomials and Rational Expressions

• Understand the relationship between zeros and factors of polynomials
• AII-A.APR.2 Use the Remainder Theorem: dividing p(x) by x − a leaves p(a), so x − a is a factor exactly when p(a) = 0.
• AII-A.APR.3 Find the zeros of polynomial functions when they can be factored suitably.
• Rewrite rational expressions
• AII-A.APR.6 Rewrite simple rational expressions as a polynomial plus a remainder over the divisor, dividing by inspection in easy cases.

Algebra: Creating Equations

• Create equations that describe numbers or relationships
• AII-A.CED.1 Write one-variable equations and inequalities for real situations, including linear, quadratic, rational and exponential models.

Algebra: Reasoning with Equations and Inequalities

• Understand solving equations as a process of reasoning and explain the reasoning
• AII-A.REI.1b Justify each step in solving rational or radical equations and build a sound argument for the method.
• AII-A.REI.2 Solve one-variable rational and radical equations, find extraneous solutions and explain why they appear.
• Solve equations and inequalities in one variable
• AII-A.REI.4 Solve one-variable quadratic equations, simplifying radicals in the answers when needed.
• AII-A.REI.4b Solve quadratics by inspection, square roots, factoring, completing the square, the formula or graphing, writing complex roots as a + bi.
• Solve systems of equations
• AII-A.REI.7b Solve a system of a linear equation and a quadratic (parabola or circle) in two variables, algebraically and by graphing.
• Represent and solve equations and inequalities graphically
• AII-A.REI.11 Solve f(x) = g(x) from where the graphs meet, estimate with technology, solve inequalities by graphing and interpret in context.

Functions: Interpreting Functions

• Understand the concept of a function and use function notation
• AII-F.IF.3 Know that a sequence is a function defined on integers, and write sequences recursively and in subscript notation.
• Interpret functions that arise in applications in terms of the context
• AII-F.IF.4 Read key features of graphs and tables in context and sketch graphs from a description of key features.
• AII-F.IF.6 Work out and interpret a function's average rate of change over a given interval.
• Analyze functions using different representations
• AII-F.IF.7 Graph functions and show their key features, by hand and with technology where suitable.
• AII-F.IF.7c Graph polynomials, showing zeros when they can be factored and showing end behavior.
• AII-F.IF.7e Graph cube root, exponential and log functions with intercepts and end behavior, and trig functions with period, midline and amplitude.
• AII-F.IF.8 Write a function in different equivalent forms to show and explain its properties.
• AII-F.IF.8b Use exponent rules to read exponential functions as growth or decay, including compound and continuous models.
• AII-F.IF.9 Compare properties of two functions given in different forms: equation, graph, table or words.

Functions: Building Functions

• Build a function that models a relationship between two quantities
• AII-F.BF.1 Write a function that describes how two quantities are related.
• AII-F.BF.1a Find a function from a context as an explicit formula, a recursive process or a list of calculation steps.
• AII-F.BF.1b Combine standard functions with arithmetic operations and relate the combined model to the situation, such as a cooling object.
• AII-F.BF.2 Give arithmetic and geometric sequences in recursive and explicit form, model with them and convert between forms.
• Build new functions from existing functions
• AII-F.BF.3b Recognize how f(x) + k, kf(x), f(kx) and f(x + k) change a graph, find k from graphs and identify even and odd functions.
• AII-F.BF.4a Find the inverse of a one-to-one function algebraically and graphically.
• AII-F.BF.5a Understand that exponentials and logarithms are inverses, algebraically and graphically.
• AII-F.BF.6 Write and evaluate finite arithmetic or geometric series in sigma (summation) notation.
• AII-F.BF.7 Explore how the formulas for finite arithmetic and geometric series are derived and use them in problems.

Functions: Linear, Quadratic, and Exponential Models

• Construct and compare linear, quadratic, and exponential models and solve problems
• AII-F.LE.2 Build a linear or exponential function from a graph, a described relationship or two input-output pairs.
• AII-F.LE.4 Solve exponential equations a·b^(ct) = d with logarithms and evaluate them with technology.
• Interpret expressions for functions in terms of the situation they model
• AII-F.LE.5 Explain what the parameters of a linear or exponential function mean in context.

Functions: Trigonometric Functions

• Extend the domain of trigonometric functions using the unit circle
• AII-F.TF.1 Understand a radian as the length of unit-circle arc cut off by an angle.
• AII-F.TF.2 Use the unit circle to find the values of all six trig functions for angles in radians.
• AII-F.TF.4 Use the unit circle to explain the odd/even symmetry and periodicity of trig functions.
• Model periodic phenomena with trigonometric functions
• AII-F.TF.5 Choose trig functions to model periodic events with a given amplitude, frequency, horizontal shift and midline.
• Prove and apply trigonometric identities
• AII-F.TF.8 Prove sin²θ + cos²θ = 1 and use it, with the quadrant, to find other trig values from one value.

Statistics and Probability: Interpreting Categorical and Quantitative Data

• Summarize, represent, and interpret data on a single count or measurement variable
• AII-S.ID.4a Decide whether a normal curve suits a data set.
• AII-S.ID.4b Where suitable, use a graphing calculator and a normal curve to find population percentages.
• Summarize, represent, and interpret data on two categorical and quantitative variables
• AII-S.ID.6 Plot two-variable data as a scatter plot and describe the relationship between the variables.
• AII-S.ID.6a Fit a function to real data and use it to solve problems in that context.

Statistics and Probability: Making Inferences and Justifying Conclusions

• Understand and evaluate random processes underlying statistical experiments
• AII-S.IC.2 Use simulation to judge whether a sample proportion or mean is likely under a given model.
• Make inferences and justify conclusions from sample surveys, experiments, and observational studies
• AII-S.IC.3 Know what surveys, experiments and observational studies are for, how they differ and how randomization fits each.
• AII-S.IC.4 Build a 95% interval around a simulated statistic and decide whether a suggested parameter is plausible.
• Evaluate reports based on data
• AII-S.IC.6a Use statistical tools to draw conclusions from numerical summaries.
• AII-S.IC.6b Use statistical language to critique claims in reports, such as causation versus correlation and bias.

Statistics and Probability: Conditional Probability and the Rules of Probability

• Understand independence and conditional probability and use them to interpret data
• AII-S.CP.1 Describe events as parts of a sample space using features of outcomes, unions, intersections and complements.
• AII-S.CP.4 Use two-way frequency tables to decide whether events are independent and to find conditional probabilities.
• Use the rules of probability to compute probabilities of compound events in a uniform probability model
• AII-S.CP.7 Apply the Addition Rule for P(A or B) and explain the result using the model.