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Standards of Learning--Algebra II Resources

There are links at the bottom of this page and every page on GeoLibrary to link to other GeoLibrary pages. The standards below outline the content for a one-year course in Algebra II. Students enrolled in Algebra II are assumed to have mastered those concepts outlined in the Algebra I standards. A thorough treatment of advanced algebraic concepts is provided through the study of functions, polynomials, rational expressions, complex numbers, matrices, and sequences and series. Emphasis should be placed on practical applications and modeling throughout the course of study. Oral and written communication concerning the language of algebra, logic of procedures, and interpretation of results also should permeate the course.

These standards include a transformational approach to graphing functions. Transformational graphing uses translation, reflection, dilation, and rotation to generate a "family of graphs" from a given graph and builds a strong connection between algebraic and graphic representations of functions. Students will vary the coefficients and constants of an equation, observe the changes in the graph of the equation, and make generalizations that can be applied to many graphs.

Graphing utilities (graphing calculators or computer graphing simulators) and spreadsheets will be used by students and teachers. Graphing utilities enhance the understanding of realistic applications through mathematical modeling and aid in the investigation and study of functions and their inverses. They also provide an effective tool for solving/verifying equations and inequalities. Any other available technology that will enhance student learning should be used.

Tutorial Index of Terms
WebMath: Instant solutions to your math problems
Algebra II -- Math for Morons Like Us
S. O. S. Mathemataics - CyberExam

AII.1 The student will identify field properties, axioms of equality and inequality, and properties of order that are valid for the set of real numbers and its subsets, complex numbers, and matrices.
Math Forum - Ask Dr. Math -- Properties of Real Numbers
Algebra Postulates

AII.2 The student will add, subtract, multiply, divide, and simplify rational expressions, including complex fractions.
Algebraic Techniques - Rational Expressions
Lesson 14.03: Simplifying Rational Expressions

AII.3 The student will

add, subtract, multiply, divide, and simplify radical expressions containing positive rational numbers and variables and expressions containing rational exponents; and
write radical expressions as expressions containing rational exponents, and vice versa.

AII.4 The student will solve absolute value equations and inequalities graphically and algebraically. Graphing calculators will be used both as a primary method of solution and to verify algebraic solutions.
5.2 Properties of Absolute Value
Soliving Absolute Value Inequalities -- Using graphing calucuators
Chapter 2.6 Lesson. Math 101 - Fall 1997 -- Solving Absolute Value Equations
Name That Absolute Value

AII.5 The student will identify and factor completely polynomials representing the difference of squares, perfect square trinomials, the sum and difference of cubes, and general trinomials.
Math Forum - Ask Dr. Math -- Factoring Polynomials
Factoring Polynomials Given One Root
Webmath.com: Factoring a polynomial

AII.6 The student will select, justify, and apply a technique to solve a quadratic equation over the set of complex numbers. Graphing calculators will be used for solving and confirming algebraic solutions.
Algebra Ii _ Quadratic Equations - Math for Morons Like Us
Webmath.com: Solving Quadratic Equations
Joann -- Solving Quadratic Equations
Graphing Quadratic Equations
Quadratic, etc. equations
Math - Quadratic Equations

AII.7 The student will solve equations containing rational expressions and equations containing radical expressions algebraically and graphically. Graphing calculators will be used for solving and confirming algebraic solutions.

AII.8 The student will recognize multiple representations of functions (linear, quadratic, absolute value, step, and exponential functions) and convert between a graph, a table, and symbolic form. A transformational approach to graphing will be employed through the use of graphing calculators.
Absolute Value
Absolute Value Function
Graphing Linear Functions - Claris Works
Linear Functions
Step Functions
Graphing Exponential Functions
Exponential Functions
Exponential Functions

AII.9 The student will find the domain, range, zeros and inverse of a function, the value of a function for a given element in its domain, and the composition of multiple functions. Functions will include those that have domains and ranges that are limited and/or discontinuous. The graphing calculator will be used as a tool to assist in investigation of functions, including exponential and logarithmic.
Graphing Exponential Functions
Math Forum - Ask Dr. Math
3-2 More About Functions
3.1 Functions
One-to-One Functions and the Inverse Function
Inverse Functions

AII.10 The student will investigate and describe the relationships between the solution of an equation, zero of a function, x-intercept of a graph, and factors of a polynomial expression through the use of graphs.

AII.11 The student will use matrix multiplication to solve practical problems. Graphing calculators or computer programs with matrix capabilities will be used to find the product.
Algebraic Properties of Matrix Operations

AII.12 The student will represent problem situations with a system of linear equations and solve the system using the inverse matrix method. Graphing calculators or computer programs with matrix capability will be used to perform computations.
Numbers in the Real World
Inverse Matrix Calculator
ctoy\MAT121\topic06 -- The Matrix Inverse

AII.13 The student will solve systems of linear inequalities and linear programming problems and describe the results both orally and in writing. A graphing calculator will be used to facilitate solutions to linear programming problems.

AII.14 The student will solve nonlinear systems of equations, including linear-quadratic and quadratic-quadratic, algebraically and graphically. The graphing calculator will be used as a tool to visualize graphs and predict the number of solutions.

AII.15 The student will recognize the general shape of polynomial functions, locate the zeros, sketch the graphs, and verify graphical solutions algebraically. The graphing calculator will be used as a tool to investigate the shape and behavior of polynomial functions.

AII.16 The student will investigate and apply the properties of arithmetic and geometric sequences and series to solve problems, including writing the first n terms, finding the nth term, and evaluating summation formulas. Notation will include sigma and 'a sub n'.

AII.17 The student will perform operations on complex numbers and express the results in simplest form. Simplifying results will involve using patterns of the powers of i.

AII.18 The student will identify conic sections (circle, ellipse, parabola, and hyperbola) from his/her equations. Given the equations in (h, k) form, students will sketch graphs of conic sections, using transformations.

AII.19 The student will collect and analyze data to make predictions, write equations, and solve practical problems. Graphing calculators will be used to investigate scatterplots to determine the equation for a curve of best fit.

AII.20 The student will identify, create, and solve practical problems involving a combination of direct and inverse variations.