Targets & Standards

In Algebra 2, students analyze and apply operations using multiple representations of functions to compare, interpret data, and make inferences. Functions include (but not limited to) linear, exponential, quadratic, absolute value, inverse, piecewise, cubic, polynomial, trigonometric, logarithms, etc. They use statistics in real world contexts to develop solutions.

Essential Standards

Level 3 of Target G - Create equations that describe numbers or relationships. (DOK 1,2)

Level 4 of Target I - Use complex numbers in polynomial identities and equations.

[Polynomials with real coefficients] (DOK 1, 2)

Level 3 of Target M - Analyze functions using different representations. (DOK 1, 2)

Target L: Interpret functions that arise in applications in terms of the context. (DOK 1, 2)

Target D: Interpret the structure of expressions. (DOK 1,2)

Target F: Perform arithmetic operations on polynomials. (DOK 2)

Level 3 of Target J - Represent and solve equations and inequalities graphically. (DOK 1, 2)

A-CED.A.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions and simple rational and exponential functions. Modeling Standard

There are no substandards for this standard.

N-CN.C.7 Solve quadratic equations with real coefficients that have complex solutions.

There are no substandards for this standard.

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

There are no substandards for this standard.

F-IF.C.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. Modeling Standard

b. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.

F-IF.B.4 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. Modeling Standard

Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.

A-SSE.A.2 Use the structure of an expression to identify ways to rewrite it.

For example, see x^4 – y^4 as (x^2)^2 – (y^2)^2, thus recognizing it as a difference of squares that can be factored as (x^2 – y^2)(x^2 + y^2).

A-APR.B.3 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.

There are no substandards for this standard.

A−REI.D.11 Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. Modeling Standard

b. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.

Level 3 of Target G - Create equations that describe numbers or relationships. (DOK 1,2)

Achievement Level Descriptors & Evidence

Achievement Level Descriptors

Evidence

Level 4 of Target I - Use complex numbers in polynomial identities and equations.

Supporting Standards

A-SSE.1 Interpret expressions that represent a quantity in terms of its context. Modeling Standard

a. Interpret parts of an expression, such as terms, factors, and coefficients.

b. Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret as the product of and a factor not depending on .

G-GPE.3.1 Given a quadratic equation of the form ax^2+by^2+cx+dy+e=0 use the method for completing the square to put the equation into stnadard form; identify whether the graph of the equation is a circle, ellipse, parabola, or hyperbola & graph the equation. CA only.

[In Algebra 2, this standard only addresses circles & parabolas.]

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

There is no substandard for this standard.

A-APR.4 Prove polynomial identities and use them to describe numerical relationships.

For example, the polynomial identity (x^2+y^2)^2 = (x^2-y^2)^2 + (2xy)^2 can be used to generate Pythagorean triples.

A-APR.5 Know and apply the Binomial Theorem for the expansion of (x+y)^n in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal’s Triangle.

The Binomial Theorem can be proved by mathematical induction or by a combinatorial argument.

F-IF.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Modeling Standard

There are no substandards for this standard.

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

There are no substandards for this standard.

F-IF.8 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

There are no substandards for this standard.

F-IF.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

There are no substandards for this standard.