Gizmos for California - Mathematics: Algebra 2 (California Standards adopted 2014)

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.

N-CN: : The Complex Number System

N-CN.1: : Know there is a complex number i such that i² = -1, and every complex number has the form a + bi with a and b real.

N-CN.2: : Use the relation i² = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.

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

A-SSE: : Seeing Structure in Expressions

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

A-SSE.1.a: : Interpret parts of an expression, such as terms, factors, and coefficients.

A-SSE.1.b: : Interpret complicated expressions by viewing one or more of their parts as a single entity.

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

A-APR: : Arithmetic with Polynomials and Rational Expressions

A-APR.1: : 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.

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).

A-APR.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.

A-APR.5: : Know and apply the Binomial Theorem for the expansion of (x + y)? 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.

A-CED: : Creating Equations

A-CED.1: : Create equations and inequalities in one variable including ones with absolute value and use them to solve problems.

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

A-CED.3: : Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context.

A-CED.4: : Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

A-REI: : Reasoning with Equations and Inequalities

A-REI.2: : Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

A-REI.3.1: : Solve one-variable equations and inequalities involving absolute value, graphing the solutions and interpreting them in context.

A-REI.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.

F-IF: : Interpreting Functions

F-IF.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.

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

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.

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

F-IF.7.b: : Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.

F-IF.7.c: : Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.

F-IF.7.e: : Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.

F-BF: : Building Functions

F-BF.3: : Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology.

F-LE: : Linear, Quadratic, and Exponential Models

F-LE.4: : For exponential models, express as a logarithm the solution to ab to the c?? power = ?? where a, c, and ?? are numbers and the base b is 2, 10, or ??; evaluate the logarithm using technology.

F-TF: : Trigonometric Functions

F-TF.2: : 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.

F-TF.2.1: : Graph all 6 basic trigonometric functions.

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

G-GPE: : Expressing Geometric Properties with Equations

G-GPE.3.1: : Given a quadratic equation of the form ax² + by2 + cx + dy + e = 0, use the method for completing the square to put the equation into standard form; identify whether the graph of the equation is a circle, ellipse, parabola, or hyperbola, and graph the equation.

S-IC: : Making Inferences and Justifying Conclusions

S-IC.4: : Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling.

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

S-MD: : Using Probability to Make Decisions

S-MD.6: : Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).

S-MD.7: : Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game).

Correlation last revised: 12/27/2023

California - Mathematics: Algebra 2

California Standards | Adopted: 2014