Gizmos for Alabama - Mathematics: Algebra 2 (Course of Study adopted 2016)

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: : Students will: 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: : Students will: Use the relation i² = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.

N-CN.3: : Students will: Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.

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

N-CN.4: : Students will: Solve quadratic equations with real coefficients that have complex solutions.

N-VM: : Vector and Matrix Quantities

1.3.1: : Perform operations on matrices and use matrices in applications.

N-VM.7: : Students will: Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network.

N-VM.8: : Students will: Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled.

N-VM.9: : Students will: Add, subtract, and multiply matrices of appropriate dimensions.

N-VM.11: : Students will: Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers. The determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse.

A: : Algebra

A-SSE: : Seeing Structure in Expressions

2.1.1: : Interpret the structure of expressions.

A-SSE.12: : Students will: Interpret expressions that represent a quantity in terms of its context.

A-SSE.12.a: : Interpret parts of an expression such as terms, factors, and coefficients.

A-SSE.12.b: : Interpret complicated expressions by viewing one or more of their parts as a single entity.

A-SSE.13: : Students will: 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.15: : Students will: 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.16: : Students will: 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.17: : Students will: 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.18: : Students will: Prove polynomial identities and use them to describe numerical relationships.

2.2.4: : Rewrite rational expressions.

A-APR.19: : Students will: Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or for the more complicated examples, a computer algebra system.

A-CED: : Creating Equations

2.3.1: : Create equations that describe numbers or relationships.

A-CED.20: : Students will: Create equations and inequalities in one variable and use them to solve problems.

A-CED.21: : Students will: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

A-CED.22: : Students will: 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.

A-CED.23: : Students will: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

A-REI: : Reasoning with Equations and Inequalities

2.4.1: : Understand solving equations as a process of reasoning and explain the reasoning.

A-REI.24: : Students will: Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

2.4.3: : Solve equations and inequalities in one variable.

A-REI.25: : Students will: Recognize when the quadratic formula gives complex solutions, and write them as a ± bi for real numbers a and b.

2.4.4: : Solve systems of equations.

A-REI.26: : Students will: Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3 × 3 or greater).

2.4.5: : Represent and solve equations and inequalities graphically.

A-REI.27: : Students will: 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.

A-CS: : Conic Sections

2.5.1: : Understand the graphs and equations of conic sections.

A-CS.28: : Students will: Create graphs of conic sections, including parabolas, hyperbolas, ellipses, circles, and degenerate conics, from second-degree equations.

A-CS.28.a: : Formulate equations of conic sections from their determining characteristics.

F: : Functions

F-IF: : Interpreting Functions

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

F-IF.29: : Students will: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.

3.1.2: : Analyze functions using different representations.

F-IF.30: : Students will: 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.30.a: : Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.

F-IF.30.b: : Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.

F-IF.30.c: : Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.

F-IF.31: : Students will: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

F-IF.31.a: : Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.

F-IF.31.b: : Use the properties of exponents to interpret expressions for exponential functions.

F-IF.32: : Students will: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

F-BF: : Building Functions

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

F-BF.33: : Students will: Write a function that describes a relationship between two quantities.

F-BF.33.a: : Combine standard function types using arithmetic operations.

3.2.2: : Build new functions from existing functions.

F-BF.34: : Students will: 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.35: : Students will: Find inverse functions.

F-BF.35.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.36: : Students will: 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.

S: : Statistics and Probability

S-MD: : Using Probability to Make Decisions

4.1.1: : Use probability to evaluate outcomes of decisions.

S-MD.37: : Students will: Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).

S-MD.38: : Students will: Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game).

S-CP: : Conditional Probability and the Rules of Probability

4.4.1: : Understand independence and conditional probability and use them to interpret data.

S-CP.39: : Students will: Describe events as subsets of a sample space (the set of outcomes), using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (“or,” “and,” “not”).

S-CP.40: : Students will: Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B.

S-CP.41: : Students will: Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities.

S-CP.42: : Students will: Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations.

4.4.2: : Use the rules of probability to compute probabilities of compound events in a uniform probability model.

S-CP.43: : Students will: Find the conditional probability of A given B as the fraction of B’s outcomes that also belong to A, and interpret the answer in terms of the model.

S-CP.45: : Students will: Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)P(B|A) = P(B)P(A|B), and interpret the answer in terms of the model.

S-CP.46: : Students will: Use permutations and combinations to compute probabilities of compound events and solve problems.

Correlation last revised: 9/16/2020

Alabama - Mathematics: Algebra 2

Course of Study | Adopted: 2016

N: : Number and Quantity

A: : Algebra

F: : Functions

S: : Statistics and Probability