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

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

N: : Number and Quantity

N-CN: : The Complex Number System

1.1.1: : Perform arithmetic operations with complex numbers.

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.

1.1.2: : Use complex numbers in polynomial identities and equations.

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

N-CN.8: : Extend polynomial identities to the complex numbers.

A: : Algebra

A-SSE: : Seeing Structure in Expressions

2.1.1: : Interpret the structure of expressions

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

A-APR: : Arithmetic with Polynomials and Rational Expressions

2.2.1: : Perform arithmetic operations on polynomials

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.

2.2.2: : Understand the relationship between zeros and factors of 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.

2.2.3: : Use polynomial identities to solve problems

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.

A-CED: : Creating Equations

2.3.1: : Create equations that describe numbers or relationships

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

2.4.2: : Solve equations and inequalities in one variable

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

2.4.3: : Represent and solve equations and inequalities graphically

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: : Functions

F-IF: : Interpreting Functions

3.1.1: : Interpret functions that arise in applications in terms of the context

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.

3.1.2: : Analyze functions using different representations

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

F-BF: : Building Functions

3.2.1: : Build a function that models a relationship between two quantities

F-BF.1: : Write a function that describes a relationship between two quantities.

F-BF.1.b: : Combine standard function types using arithmetic operations.

3.2.2: : Build new functions from existing functions

F-BF.3: : Identify the effect on the graph of replacing f(x) by f(x) + k, kf(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-BF.4: : Find inverse functions.

F-BF.4.a: : Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse.

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

3.3.1: : Construct and compare linear, quadratic, and exponential models and solve problems

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

F-LE.4.2: : Use the definition of logarithms to translate between logarithms in any base.

F-LE.4.3: : Understand and use the properties of logarithms to simplify logarithmic numeric expressions and to identify their approximate values.

F-TF: : Trigonometric Functions

3.4.1: : Extend the domain of trigonometric functions using the unit circle

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

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.

3.4.2: : Model periodic phenomena with trigonometric functions

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

3.4.3: : Prove and apply trigonometric identities

F-TF.8: : Prove the Pythagorean identity sin²(theta) + cos²(theta) = 1 and use it to find sin(theta), cos(theta), or tan(theta) given sin(theta), cos(theta), or tan(theta) and the quadrant of the angle.

G: : Geometry

G-GPE: : Expressing Geometric Properties with Equations

4.1.1: : Translate between the geometric description and the equation for a conic section

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 standard form; identify whether the graph of the equation is a circle, ellipse, parabola, or hyperbola, and graph the equation.

S: : Statistics and Probability

S-ID: : Interpreting Categorical and Quantitative Data

5.1.1: : Summarize, represent, and interpret data on a single count or measurement variable

S-ID.4: : 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.

S-IC: : Making Inferences and Justifying Conclusions

5.2.1: : Understand and evaluate random processes underlying statistical experiments

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

S-IC.2: : Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation.

5.2.2: : Make inferences and justify conclusions from sample surveys, experiments, and observational studies

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

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

5.3.1: : Use probability to evaluate outcomes of 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

Common Core State Standards | Adopted: 2014

N: : Number and Quantity

A: : Algebra

F: : Functions

G: : Geometry

S: : Statistics and Probability