Algebra 2

Extend the understanding of numbers and operations to include complex numbers, radical expressions, and expressions written with rational exponents.

• A2.N.1.1(Objective)

  Find the value of 𝑖ⁿ for any whole number 𝑛.

• A2.N.1.2(Objective)

  Simplify, add, subtract, multiply, and divide complex numbers.

• A2.N.1.3(Objective)

  Understand and apply the relationship between rational exponents to integer exponents and radicals to solve problems.

Extend the understanding of numbers and operations to matrices.

• A2.N.2.1(Objective)

  Use matrices to organize and represent data. Identify the order (dimension) of a matrix.

• A2.N.2.2(Objective)

  Use addition, subtraction, and scalar multiplication of matrices to solve problems.

Represent and solve mathematical and real-world problems using nonlinear equations, systems of linear equations, and systems of linear inequalities; interpret the solutions in the original context.

• A2.A.1.1(Objective)

  Use mathematical models to represent quadratic relationships and solve using factoring, completing the square, the quadratic formula, and various methods (including graphing calculator or other appropriate technology). Find non-real roots when they exist.

• A2.A.1.2(Objective)

  Use mathematical models to represent exponential relationships, such as compound interest, depreciation, and population growth. Solve these equations algebraically or graphically (including graphing calculator or other appropriate technology).

• A2.A.1.3(Objective)

  Solve one-variable rational equations and check for extraneous solutions.

• A2.A.1.4(Objective)

  Solve polynomial equations with real roots using various methods (e.g., polynomial division, synthetic division, using graphing calculators or other appropriate technology).

• A2.A.1.5(Objective)

  Solve square and cube root equations with one variable, and check for extraneous solutions.

• A2.A.1.6(Objective)

  Solve common and natural logarithmic equations using the properties of logarithms.

• A2.A.1.7(Objective)

  Represent and evaluate mathematical models using systems of linear equations with a maximum of three variables. Graphing calculators or other appropriate technology may be used.

• A2.A.1.8(Objective)

  Use tools to solve systems of equations containing one linear equation and one quadratic equation. Graphing calculators or other appropriate technology may be used.

• A2.A.1.9(Objective)

  Solve systems of linear inequalities in two variables, with a maximum of three inequalities; graph and interpret the solutions on a coordinate plane. Graphing calculators or other appropriate technology may be used.

Generate and evaluate equivalent algebraic expressions and equations using various strategies.

• A2.A.2.1(Objective)

  Factor polynomial expressions including, but not limited to, trinomials, differences of squares, sum and difference of cubes, and factoring by grouping, using a variety of tools and strategies.

• A2.A.2.2(Objective)

  Add, subtract, multiply, divide, and simplify polynomial expressions.

• A2.A.2.3(Objective)

  Add, subtract, multiply, divide, and simplify rational expressions.

• A2.A.2.4(Objective)

  Solve rational equations with real roots.

• A2.A.2.5(Objective)

  Rewrite algebraic expressions involving radicals and rational exponents using the properties of exponents.

Represent and solve mathematical and real-world problems involving arithmetic and geometric sequences and series.

• A2.A.3.1(Objective)

  Recognize that arithmetic sequences are linear using equations, tables, graphs, and verbal descriptions. Using the pattern, find the next term.

• A2.A.3.2(Objective)

  Recognize that geometric sequences are exponential using equations, tables, graphs, and verbal descriptions. Given the formula 𝑓(𝑥) = 𝑎(𝑟)ˣ, find the next term and define the meaning of 𝑎 and 𝑟 within the context of the problem.

• A2.A.3.3(Objective)

  Solve problems that can be modeled using arithmetic sequences or series given the 𝑛th terms and sum formulas. Graphing calculators or other appropriate technology may be used.

• A2.A.3.4(Objective)

  Solve problems that can be modeled using finite geometric sequences and series given the 𝑛th terms and sum formulas. Graphing calculators or other appropriate technology may be used.

Understand functions as descriptions of covariation (how related quantities vary together).

• A2.F.1.1(Objective)

  Use algebraic, interval, and set notations to specify the domain and range of various types of functions, and evaluate a function at a given point in its domain.

• A2.F.1.2(Objective)

  Identify the parent forms of exponential, radical (square root and cube root only), quadratic, and logarithmic functions. Predict the effects of transformations [𝑓(𝑥 + 𝑐), 𝑓(𝑥) + 𝑐, 𝑓(𝑐𝑥), and 𝑐𝑓(𝑥)] algebraically and graphically.

• A2.F.1.3(Objective)

  Graph a quadratic function. Identify the domain, range, x- and y-intercepts, maximum or minimum value, axis of symmetry, and vertex using various methods and tools that may include a graphing calculator or appropriate technology.

• A2.F.1.4(Objective)

  Graph exponential and logarithmic functions. Identify the domain, range, asymptotes, and x- and y-intercepts using various methods and tools that may include calculators or other appropriate technology. Recognize exponential decay and growth graphically and algebraically.

• A2.F.1.5(Objective)

  Analyze the graph of a polynomial function by identifying the domain, range, intercepts, zeros, relative maxima, relative minima, and intervals of increase and decrease.

• A2.F.1.6(Objective)

  Graph a rational function and identify the domain (including holes), range, x- and y-intercepts, vertical and horizontal asymptotes, using various methods and tools that may include a graphing calculator or other appropriate technology (excluding slant or oblique asymptotes).

• A2.F.1.7(Objective)

  Graph a radical function (square root and cube root only). Identify the domain, range, and x- and y-intercepts using various methods and tools that may include a graphing calculator or other appropriate technology.

Summarize, interpret, and compare data sets using descriptive statistics.

• A2.D.1.1(Objective)

  Calculate measures of center and spread (i.e., mean, median, mode, range, interquartile range, standard deviation). Use these quantities to draw conclusions about the data.

• A2.D.1.2(Objective)

  Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of outliers.

Interpret and analyze linear models and data to make inferences based on the line of best fit.

• A2.D.2.1(Objective)

  Use technology to find the least squares regression line and use it to make predictions.

• A2.D.2.2(Objective)

  Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.

• A2.D.2.3(Objective)

  Use the correlation coefficient to assess the fit of a linear model.

Use probability to evaluate outcomes of decisions.

• A2.D.3.1(Objective)

  Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).

• A2.D.3.2(Objective)

  Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game).