Algebra II

Other South Dakota Mathematics sets

• Grade K
• Grade 1
• Grade 2
• Grade 3
• Grade 4
• Grade 5
• Grade 6
• Grade 7
• 8th Grade
• Grade 8
• Algebra I
• Grades 9, 10, 11, 12
• Geometry
• Pre-Calculus

Compose functions and evaluate their compositionA2.AF.1

Graph rational functions, identifying zeros and asymptotes (vertical and horizontal) when suitable factorizations are available and showing end behavior, with or without the appropriate technology.A2.AF.2

Compare properties of graphs, tables, equations, and verbal descriptions of two functions.A2.AF.3

Calculate and interpret the average rate of change of a function, both symbolically and from a table over a specified interval. Estimate the rate of change from a graph.A2.AF.4

 Given a graph, explain the effects of the transformation from the parent function including square root and cubic functions, rational, and absolute value functions. A2.AF.5

Describe the transformation of functions in the coordinate plane including translation, reflection, and dilation.A2.AF.6

Explain how restricting the domain of a function allows for the creation of its inverse.A2.AF.7

rite and graph the inverse of a given function; understand that the graph of an inverse function is a reflection of the function over the line 𝑦 = 𝑥. A2.AF.8

Verify if two functions are inverses of each other using composition of functionsA2.AF.9

Using ordered pairs, determine the inverse of a function given a graph or tableA2.AF.10

Write and use arithmetic sequences recursively and explicitly to model situations; translate between the two forms when given a graph, a description of the relationship, or two input-output pairs.A2.LF.1

Multiply a matrix by a scalarA2.LF.2

Add and subtract matrices.A2.LF.3

Solve systems of linear equations in three variablesA2.LF.4

Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context.A2.LF.5

Select, justify and apply appropriate methods to solve quadratic equations in one variable. Recognize complex solutions and write them as a +/- bi for real numbers a and b.A2.QF.1

Represent and solve real-world problems using quadratic equations and inequalities. A2.QF.2

Use the discriminant to determine the number and type of solutions of a quadratic equation.A2.QF.3

Sketch the graph of a quadratic function given a verbal description and show key features.A2.QF.4 

Solve a system of equations consisting of a linear equation and a nonlinear equation in two variables algebraically or graphically with or without technology.A2.QF.5

Use the properties of exponents to find equivalent expressions and to solve equations, including those involving rational exponents.A2.EL.1

Interpret the solution of a logarithmic equation as reasonable or unreasonable in context. A2.EL.2

 Translate between logarithmic and exponential forms of an equation. A2.EL.3

Use properties of logarithms to simplify and evaluate logarithmic expressions, with or without technology.A2.EL.4

Use the inverse relationship between exponents and logarithms to solve problems. A2.EL.5

Graph logarithmic functions, showing intercepts and end behavior.A2.EL.6

Select trigonometric functions that model real-world contexts. A2.TF.1

Develop the Pythagorean identity, sin^2(𝜃) + cos^2(𝜃) = 1. A2.TF.2

Apply the Pythagorean identity to find the remaining trigonometric functions when given sin (𝜃), cos (𝜃), or tan (𝜃) and the quadrant of the angle.A2.TF.3

Explain how changes in amplitude, period, and midline affect the graph of sine and cosine functions, using transformations and real-world contexts to support understanding. A2.TF.4

Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.A2.TF.5

Explain how the unit circle can be used to model sine, cosine, tangent, secant, cosecant, and cotangent for all real numbersA2.TF.6

Construct a possible polynomial given a graph.A2.PR.1

Create equations and inequalities with one variable and use them to solve problems, including absolute value functionsA2.PR.2

Solve formulas for a specific variable.A2.PR.3

Solve rational and radical equations containing one variable specifying extraneous solutions.A2.PR.4

Explain how the multiplicity of zeros affects the shape of a polynomial graph, using reasoning and visual patterns to justify the behavior at each intercept.A2.PR.5

Interpret the key features of polynomial functions that model a relationship between two quantities in a given context; translate between different representations of the function, especially graphs, tables, and equations.A2.PR.6

Determine the domain and range of polynomial and rational functions. A2.PR.7

Graph polynomial functions, identifying zeros when suitable factorizations are available and showing end behavior, with or without the appropriate technology. A2.PR.8

Apply the remainder and factor theorems to identify factors and find solutions to polynomial equations of degree greater than 2 and explain how each theorem supports the reasoning process.A2.PR.9

Factor polynomials using polynomial identities, including difference of squares, sum and difference of cubes, and the square of a sum or difference.A2.PR.10

Divide polynomial expressions using factorization, long division, and synthetic division, with and without a remainder.A2.PR.11

Explain why a solution to the equation 𝑓(𝑥) = 𝑔(𝑥) is the x-coordinate where the y-coordinate of 𝑓(𝑥) and 𝑔(𝑥) are the same using graphs, tables, or approximations, include cases where 𝑓(𝑥) and/or 𝑔(𝑥) are linear, polynomial, exponential, or rational and where at least one of the functions is not linear. A2.PR.12

Represent and use mathematical models for bivariate data sets to answer questions, draw conclusions, and make decisions.A2.SP.1

Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriateA2.SP.2

Distinguish between sample surveys, experiments, and observational studies and explain the purpose of randomization in statistical studies.A2.SP.3

Use data from a random sample to make inferences about a population.A2.SP.4

Compare theoretical and experimental probabilities using simulations.A2.SP.5

Read and explain, in context, the validity of data from outside reports by identifying the variables as quantitative or categorical and describing how the data was collected.A2.SP.6

Indicate any potential biases or flaws and identifying inferences the author of the report made from sample data.A2.SP.7