Algebra 2

Other Iowa Mathematics sets

• Kindergarten
• Grade 1
• Grade 2
• Grade 3
• Grade 4
• Grade 5
• Grade 6
• Grade 7
• Grade 8
• Algebra 1
• Calculus
• Geometry
• Precalculus
• Statistics and Probability
• Standards for Mathematical Practice: Grades 6–8
• Standards for Mathematical Practices: Grades K–5
• Standards of Mathematical Practice: High School

Interpret expressions that represent a quantity in terms of its context. For example, interpret 𝑃𝑃(1 + 𝑟𝑟)𝑛𝑛 as the product of 𝑃𝑃 and 𝑎𝑎 factor not depending on 𝑃𝑃. ★A2.A-SSE.A.1b

Use the structure of an expression to identify ways to rewrite it. For example, see 𝑥𝑥4 − 𝑦𝑦4 as (𝑥𝑥2)2 – (𝑦𝑦2)2, thus recognizing it as a difference of squares that can be factored as (𝑥𝑥2 – 𝑦𝑦2)(𝑥𝑥2 + 𝑦𝑦2). A2.A-SSE.A.2

Choose and produce an equivalent form of an expression or equation to reveal and explain properties of the quantity represented by the expression. (A1 and A2)A2.A-SSE.B.3

Apply the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. For example, calculate mortgage payments. ★A2.A-SSE.B.4

Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.A2.A-APR.A.1

Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by 𝑥𝑥 – 𝑎𝑎 is 𝑝𝑝(𝑎𝑎), so 𝑝𝑝(𝑎𝑎) = 0 if and only if (𝑥𝑥 − 𝑎𝑎) is a factor of 𝑝𝑝(𝑥𝑥).A2.A-APR.B.2

Identify zeros of polynomials when suitable factorizations are available and use the zeros to construct a rough graph of the function defined by the polynomial. A2.A-APR.B.3

Rewrite simple rational expressions in different forms; write 𝑎𝑎(𝑥𝑥) 𝑏𝑏(𝑥𝑥) in the form 𝑞𝑞(𝑥𝑥) + 𝑟𝑟(𝑥𝑥) 𝑏𝑏(𝑥𝑥) , where 𝑎𝑎(𝑥𝑥), 𝑏𝑏(𝑥𝑥), 𝑞𝑞(𝑥𝑥), and 𝑟𝑟(𝑥𝑥) are polynomials with the degree of r(x) less than the degree of b(x). For example, in the same way one may view 11 7 as (7+4) 7 = 1 + 4 7 , one can view (𝑥𝑥+7) (𝑥𝑥+3) as ((𝑥𝑥+3)+4) (𝑥𝑥+3) = 1 + 4 𝑥𝑥+3A2.A-APR.D.6

Create equations and inequalities in one variable and use them to solve problems. (A1 and A2) A2.A-CED.A.1

Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. (A1 and A2) A2.A-CED.A.2

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. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. (A1 and A2)  A2.A-CED.A.3

Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange the formula for the area of a trapezoid, A =(b1 +b2)/2*h for the length of one of the bases. (A1 and A2) A2.A-CED.A.4

Explain each step in solving an equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. (A1 and A2)A2.A-REI.A.1

Solve rational and radical equations in one variable and give examples showing how extraneous solutions may arise. (A1 and A2)A2.A-REI.A.2

Solve quadratic equations in one variable. (A1 and A2)A2.A-REI.B.4

Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. (A1 and A2)A2.A-REI.C.7

Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). (A1 and A2)A2.A-REI.D.10

Explain why the solution(s) of a system of equations are the point(s) of intersection(s) on a coordinate plane. Find the solutions approximately. For example, using technology to graph the functions, make tables of values, or find successive approximations. Include cases where 𝑓𝑓(𝑥𝑥) and/or 𝑔𝑔(𝑥𝑥) are quadratic, exponential, rational, absolute value functions, polynomial, exponential, and logarithmic functions. ★ (A1 and A2)A2.A-REI.D.11

Graph and interpret (with the use of technology) the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. (A1 and A2)A2.A-REI.D.12

For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features may include intercepts; intervals where the function is increasing, decreasing, positive, or negative; maximum and minimum; and symmetries. ★ (A1 and A2)A2.F-IF.B.4

Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function. ★ (A1 and A2)A2.F-IF.B.5

Calculate and interpret the average rate of change of a nonlinear function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. ★ (A1 and A2)A2.F-IF.B.6

Graph functions expressed symbolically and show key features of the graph by hand in simple cases and using technology for more complicated cases. ★ (A1 and A2)A2.F-IF.C.7

Note: a exists and can be found in A1. 

Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. For example, rewrite rational expressions to show the vertical transformation. (A1 and A2)A2.F-IF.C.8

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.A2.F-IF.C.9

Write a function that describes a relationship between two quantities. Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. ★A2.F-BF.A.1b

Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. ★ (A1 and A2)A2.F-BF.A.2

Identify the effect on linear and quadratic graphs of replacing 𝑓𝑓(𝑥𝑥) by 𝑓𝑓(𝑥𝑥) + 𝑘𝑘 , 𝑘𝑘𝑘𝑘(𝑥𝑥), 𝑓𝑓(𝑘𝑘𝑘𝑘), and 𝑓𝑓(𝑥𝑥 + 𝑘𝑘) for specific values of 𝑘𝑘 (both positive and negative); find the value of 𝑘𝑘 given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. (A1 and A2)A2.F-BF.B.3

Find inverse functions. A2.F-BF.B.4

Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). (A1 and A2)A2.F-LE.A.2

For exponential models, express as a logarithm the solution to 𝑎𝑎, 𝑏𝑏𝑐𝑐𝑐𝑐 = 𝑑𝑑 where 𝑎𝑎, 𝑏𝑏, 𝑐𝑐, and 𝑑𝑑 are numbers and the base 𝑎𝑎 is 2, 10, or 𝑒𝑒, evaluate the logarithm using technology.A2.F-LE.A.4

Interpret the parameters in a linear or exponential function in terms of a context. (A1 and A2) A2.F-LE.B.5

Understand the radian measure of an angle as the length of the arc on the unit circle subtended by the angle. A2.F-TF.A.1

Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.A2.F-TF.A.2

Use special triangles to determine geometrically the values of sine, cosine for 𝜋𝜋 3 , 𝜋𝜋 4 , and 𝜋𝜋 6 , and use the unit circle to express the values of sine and cosine for 𝜋𝜋 − 𝑥𝑥, 𝜋𝜋 + 𝑥𝑥, and 2𝜋𝜋 − 𝑥𝑥 in terms of their values for 𝑥𝑥, where 𝑥𝑥 is any real number. Note: Does not include tangent.A2.F-TF.A.3

Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.A2.F-TF.A.4

Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline. ★A2.F-TF.B.5

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 appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve. ★A2.S-ID.A.4

Understand statistics as a process for making inferences about population parameters based on a random sample from that population. ★A2.S-IC.A.1

Decide if a specified model is consistent with results from a given data-generating process. For example, using simulation or a model says a spinning coin falls heads up with probability 0.5. Would a result of 5 tails in a row cause you to question the model? ★A2.S-IC.A.2

Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. ★A2.S-IC.B.3

Use data from a sample survey to estimate a population mean or proportion; develop a margin of error using simulation models for random sampling. ★A2.S-IC.B.4

Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant. ★A2.S-IC.B.5

Evaluate reports based on data. ★A2.S-IC.B.6