Algebra 2 (Virginia SOL)

Expressions and Operations (EO)

• A2.EO.1 Perform operations on and simplify rational algebraic expressions.
• Add, subtract, multiply, and divide rational expressions and simplify the results.
• Justify equivalent rational expressions with linear or quadratic monomial or binomial factors.
• Recognize complex fractions and simplify them as products or quotients.
• Show that rational expressions written in different forms are equivalent.
• A2.EO.2 Simplify and perform operations on radical expressions and convert them to rational exponents.
• Simplify and find equivalent radical expressions with numerical or algebraic radicands.
• Add, subtract, multiply, and divide radical expressions, rationalising denominators where needed.
• Convert between radical expressions and expressions with rational exponents.
• A2.EO.3 Perform operations on and factor polynomials in one and two variables.
• Find sums, differences, and products of polynomials.
• Factor polynomials completely over the integers, up to four terms.
• Divide polynomials by monomial, binomial, or factorable trinomial divisors.
• Show polynomial forms are equivalent and verify difference of squares, sum/difference of cubes, and perfect squares.
• A2.EO.4 Perform operations on complex numbers.
• Explain the meaning of i.
• Write square roots of negative numbers in a + bi form and identify equivalent forms.
• Add, subtract, and multiply complex numbers using their properties.

Equations and Inequalities (EI)

• A2.EI.1 Represent, solve, and interpret absolute value equations and inequalities in one variable.
• Write an absolute value equation to model a contextual situation.
• Solve absolute value equations algebraically and verify graphically.
• Write an absolute value inequality to model a contextual situation.
• Solve absolute value inequalities and write solutions in set, interval, and number-line form.
• Verify solutions in several ways, explain methods, and interpret in context.
• A2.EI.2 Represent, solve, and interpret quadratic equations over the complex numbers and solve quadratic inequalities.
• Write a quadratic equation or inequality to model a situation.
• Solve quadratic equations over the complex numbers algebraically.
• Find real-number solutions of quadratic inequalities algebraically.
• Verify solutions in several ways, explain methods, and interpret in context.
• A2.EI.3 Solve systems of two equations in which at least one is quadratic.
• Write linear-quadratic or quadratic-quadratic systems to model a situation.
• Determine the number of solutions of such systems.
• Solve such systems algebraically and graphically, including in context.
• Verify solutions in several ways, explain methods, and interpret in context.
• A2.EI.4 Represent, solve, and interpret equations containing rational algebraic expressions.
• Write an equation with a rational expression to model a situation.
• Solve factorable rational equations with real solutions algebraically and graphically.
• Verify solutions in several ways, explain methods, and interpret in context.
• Justify why a possible solution of a rational equation may be extraneous.
• A2.EI.5 Represent, solve, and interpret equations containing a radical expression.
• Solve equations with at most one radical expression algebraically and graphically.
• Verify solutions in several ways, explain methods, and interpret in context.
• Justify why a possible solution of a square-root equation may be extraneous.
• A2.EI.6 Represent, solve, and interpret polynomial equations.
• Write a factored form of a polynomial of degree three or more from its zeros or x-intercepts.
• Determine the number and type (real or imaginary) of solutions.
• Solve polynomial equations over the complex numbers.
• Verify solutions in several ways, explain methods, and interpret in context.

Functions (F)

• A2.F.1 Investigate, analyze, and compare square root, cube root, rational, exponential, and logarithmic function families using transformations.
• Distinguish the parent graphs of these function families.
• Write a function's equation from its graph using transformations.
• Graph a function from its equation using transformations and verify with technology.
• Identify direct, inverse, or neither variation from a table, and write equations and graphs.
• Compare and contrast graphs, tables, and equations of these function families.
• A2.F.2 Investigate and analyze characteristics of square root, cube root, rational, polynomial, exponential, logarithmic, and piecewise-defined functions.
• Find domain, range, zeros, and intercepts, including graphs with discontinuities.
• Compare and contrast characteristics of these function types.
• Identify intervals on which a function is increasing, decreasing, or constant.
• Locate and find absolute (global) maximum and minimum values.
• Locate and find relative (local) maximum and minimum values.
• Evaluate f(x) from a graph or equation and explain x and f(x) in context.
• Describe the end behavior of a function.
• Find vertical and horizontal asymptotes of rational, exponential, and logarithmic functions.
• Find inverses of linear, quadratic, and square root functions and justify that they are inverses.
• Graph an inverse function as a reflection over the line y = x.
• Find the composition of two functions algebraically and graphically.

Statistics (ST)

• A2.ST.1 Apply the data cycle to univariate quantitative data that can be modeled by smooth curves, including normal curves.
• Formulate questions needing large univariate data sets or summary statistics.
• Collect or acquire univariate data through surveys, experiments, polls, or similar methods.
• Judge whether a histogram is skewed or symmetric and sketch a smooth curve to model it.
• Identify the properties of a normal distribution.
• Describe and interpret a smooth-curve distribution by center, spread, and shape.
• Calculate and interpret the z-score of a value in a data set.
• Compare data points from different distributions using z-scores.
• Solve problems linking mean, standard deviation, and z-scores for normal or smooth curves.
• Apply the Empirical Rule to answer investigative questions.
• Compare several distributions by center, spread, and shape.
• A2.ST.2 Apply the data cycle to bivariate data using scatterplots and curves of best fit.
• Formulate questions needing bivariate data and investigate them using the data cycle.
• Collect or acquire bivariate data through research, surveys, experiments, or polls.
• Represent bivariate data in a scatterplot using technology.
• Decide whether a relationship is linear, quadratic, exponential, or a combination.
• Find equations of best-fit models with technology, including piecewise combinations.
• Use the correlation coefficient to judge the goodness of fit of a linear model.
• Make predictions, decisions, and judgments from data, scatterplots, or models.
• Evaluate whether a mathematical model reasonably fits a real-world situation.
• A2.ST.3 Compute and distinguish between permutations and combinations.
• Compare and contrast permutations and combinations as counting methods.
• Calculate permutations of n objects taken r at a time.
• Calculate combinations of n objects taken r at a time.
• Apply permutations and combinations to contextual counting problems.
• Calculate and verify permutations and combinations using technology.