﻿ MTH.ALG2 FCPS Program of Studies
Mathematics Curriculum
Algebra 2

The standards below outline the content for a one-year course in Algebra II. This course is designed for students who have successfully completed the standards for Algebra I and Geometry. All students preparing for postsecondary and advanced technical studies are expected to achieve the Algebra II standards. A thorough treatment of advanced algebraic concepts will be provided through the study of functions, “families of functions,” equations, inequalities, systems of equations and inequalities, polynomials, rational and radical equations, complex numbers, and sequences and series. Emphasis will 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 should also 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), computers, spreadsheets, and other appropriate technology tools will be used to assist in teaching and learning. Graphing utilities enhance the understanding of realistic applications through mathematical modeling and aid in the investigation and study of functions. They also provide an effective tool for solving and verifying solutions to equations and inequalities.

Last Updated: 07/31/13 09:02 PM

MTH.ALG2
Standard 1
DEVELOP SKILLS INVOLVING RATIONAL, RADICAL, AND POLYNOMIAL EXPRESSIONS

Benchmark 1.a
Add, Subtract, Multiply, Divide, & Simplify Rational Expressions

 Indicator 1.a.1 Add, subtract, multiply, and divide rational algebraic expressions

 Indicator 1.a.2 Simplify rational algebraic expressions

 Indicator 1.a.3 Recognize and simplify a complex algebraic fraction

 Indicator 1.a.4 Perform operations on rational expressions

Benchmark 1.b
Add, Subtract, Multiply, Divide, and Simplify Radical Expressions

 Indicator 1.b.1 Simplify radical expressions

 Indicator 1.b.2 Add and subtract radical expressions

 Indicator 1.b.3 Multiply and divide radical expressions

 Indicator 1.b.4 Rationalize radical expressions in the denominator and then simplify

 Indicator 1.b.5 Simplify expressions with positive or negative rational exponents

Benchmark 1.c
Write Radical Expressions with Rational Exponents & Vice Versa

 Indicator 1.c.1 Convert from radical notation to exponential notation

 Indicator 1.c.2 Convert from exponential notation to radical notation

Benchmark 1.d
Factor Polynomials Completely

 Indicator 1.d.1 Factor polynomials by applying general patterns

 Indicator 1.d.2 Factor polynomials completely over the integers

 Indicator 1.d.3 Verify polynomial identities

Benchmark 1.e
Expand and condense logarithmic expressions.

 Indicator 1.e.1 Condense & expand logarithmic expressions using log properties

MTH.ALG2
Standard 2
INVESTIGATE/APPLY PROPERTIES OF ARITHMETIC/GEOMETRIC SEQUENCES/SERIES

Benchmark 2.a
Investigate/Apply Properties of Arithmetic/Geometric Sequences/Series

 Indicator 2.a.1 Distinguish between a sequence and a series

 Indicator 2.a.2 Generalize patterns in a sequence using explicit and recursive formula

 Indicator 2.a.3 Use and interpret notations

 Indicator 2.a.4 Find the nth term for an arithmetic or a geometric sequence

 Indicator 2.a.5 Find the sum of the first n terms of an arithmetic or geometric series

 Indicator 2.a.6 Given the formula, find the sum of a convergent infinite series

 Indicator 2.a.7 Model real-world situations using sequences and series

 Indicator 2.a.8 Write an explicit formula for an arithmetic or geometric sequence

 Indicator 2.a.9 Use sigma notation to express an arithmetic or geometric series

 Indicator 2.a.10 Find the position of a term in an arithmetic sequence

 Indicator 2.a.11 Represent sequences and series using a table or graph

 Indicator 2.a.12 Use the arithmetic or the geometric mean to find a missing term

MTH.ALG2
Standard 3
PERFORM OPERATIONS ON COMPLEX NUMBERS

Benchmark 3.a
Perform Operations on Complex Numbers

 Indicator 3.a.1 Recognize that the square root of -1 is represented as i

 Indicator 3.a.2 Determine which field properties apply to the complex number system

 Indicator 3.a.3 Simplify radical expressions containing negative rational numbers

 Indicator 3.a.4 Simplify powers of i

 Indicator 3.a.5 Add, subtract, and multiply complex numbers

 Indicator 3.a.6 Place identified sets of numbers in a hierarchy of subsets

 Indicator 3.a.7 Write a real number in a+bi form

 Indicator 3.a.8 Write a pure imaginary number in a+bi form

 Indicator 3.a.9 Divide complex numbers using complex conjugates

MTH.ALG2
Standard 4
SOLVE A VARIETY OF EQUATIONS, ALGEBRAICALLY AND GRAPHICALLY

Benchmark 4.a
Solve Absolute Value Equations and Inequalities

 Indicator 4.a.1 Solve absolute value equations algebraically and graphically

 Indicator 4.a.2 Solve absolute value inequalities algebraically and graphically

 Indicator 4.a.3 Apply an appropriate equation to solve a real-world problem

 Indicator 4.a.4 Verify possible solutions to absolute value equations

 Indicator 4.a.5 Verify possible solutions to absolute value inequalities

 Indicator 4.a.6 Recognize absolute value equations/inequalities with no solution

 Indicator 4.a.7 Express solutions to abs. val. ineq. in set and interval notation

 Indicator 4.a.8 Given the equation, graph a piecewise or step function

 Indicator 4.a.9 Given a graph, write an equation for a piecewise or step function

Benchmark 4.b
Solve a Quadratic Equation Over the Set of Complex Numbers

 Indicator 4.b.1 Solve a quadratic equation over the set of complex numbers

 Indicator 4.b.2 Use the discriminant to determine the number and type of solutions

 Indicator 4.b.3 Apply an appropriate equation to solve a real-world problem

 Indicator 4.b.4 Recognize that the quad form can be derived from completing the square

Benchmark 4.c
Solve Equations Containing Rational Algebraic Expressions

 Indicator 4.c.1 Solve equations containing rational algebraic expressions

 Indicator 4.c.2 Apply an appropriate equation to solve a real-world problem

 Indicator 4.c.3 Identify vertical and horizontal asymptotes

Benchmark 4.d
Solve Equations Containing Radical Expressions

 Indicator 4.d.1 Solve an equation containing radical expressions

 Indicator 4.d.2 Verify possible solutions to an equation

 Indicator 4.d.3 Apply an appropriate equation to solve a real-world problem

 Indicator 4.d.4 Identify possible extraneous solutions when solving equations

 Indicator 4.d.5 Solve radical equations involving more than one radical expression

Benchmark 4.e
Solve exponential and logarithmic equations

 Indicator 4.e.1 Solve exponential equations

 Indicator 4.e.2 Solve logarithmic equations

 Indicator 4.e.3 Solve exponential & logarithmic equations using properties of logs

MTH.ALG2
Standard 5
SOLVE NONLINEAR SYSTEMS OF EQUATIONS

Benchmark 5.a
Solve Nonlinear Systems of Equations

 Indicator 5.a.1 Predict number of solutions to a nonlinear system of two equations

 Indicator 5.a.2 Solve a linear-quadratic system of two equations

 Indicator 5.a.3 Solve a quadratic-quadratic system of two equations

 Indicator 5.a.4 Solve a circle-linear system of two equations graphically

 Indicator 5.a.5 Solve a circle-quadratic system of two equations graphically

 Indicator 5.a.6 Solve a circle-linear system of two equations algebraically

 Indicator 5.a.7 Solve a circle-quadratic system of two equations algebraically

 Indicator 5.a.8 Sketch graph of a conic section (parabola or hyperbola) in (h, k) form

 Indicator 5.a.9 Write the equation of a conic section in (h, k) form from a graph

 Indicator 5.a.10 Use conic sections to model practical problems

MTH.ALG2
Standard 6
RECOGNIZE MULTIPLE REPRESENTATIONS OF FUNCTIONS

Benchmark 6.a
Recognize Multiple Representations of Functions

 Indicator 6.a.1 Recognize graphs of parent functions

 Indicator 6.a.2 Identify the graph of the transformed function

 Indicator 6.a.3 Given equation & using a transformational approach, graph a function

 Indicator 6.a.4 Given the graph of a function, identify the parent function

 Indicator 6.a.5 Identify the transformations of a function to determine the equation

 Indicator 6.a.6 Given the graph, write the equation of the function

 Indicator 6.a.7 Write the equation of a linear function in point-slope form

 Indicator 6.a.8 Use parametric equations to represent a linear or quadratic function

MTH.ALG2
Standard 7
INVESTIGATE AND ANALYZE FUNCTIONS, ALGEBRAICALLY & GRAPHICALLY

Benchmark 7.a
Determine the Domain and Range of Functions

 Indicator 7.a.1 Identify the domain and range of a function

 Indicator 7.a.2 Describe restricted/discontinuous domains and ranges

 Indicator 7.a.3 Write domain and range of a function using interval notation

Benchmark 7.b
Determine the Zeros of Functions

 Indicator 7.b.1 Identify the zeros of a function

 Indicator 7.b.2 Use long division to find all zeroes of a polynomial

 Indicator 7.b.3 Use synthetic division/substitution to find all zeros

Benchmark 7.c
Determine the X- and Y-Intercepts of Functions

 Indicator 7.c.1 Identify the intercepts of a function

Benchmark 7.d
Determine Intervals in Which a Function is Increasing or Decreasing

 Indicator 7.d.1 Identify intervals on which the function is increasing and decreasing

Benchmark 7.e
Determine the Asymptotes of Functions

 Indicator 7.e.1 Find the equations of vertical and horizontal asymptotes of functions

 Indicator 7.e.2 Graph rational functions

Benchmark 7.f
Determine the End Behavior of Functions

 Indicator 7.f.1 Describe the end behavior of a function

 Indicator 7.f.2 Describe end behavior of a function as x approaches pos & neg infinity

Benchmark 7.g
Determine the Inverse of a Function

 Indicator 7.g.1 Find the inverse of a function

 Indicator 7.g.2 Graph the inverse of a function as a reflection across the line, y = x

 Indicator 7.g.3 Investigate exponential and logarithmic functions

 Indicator 7.g.4 Convert between logarithmic and exponential forms of an equation

Benchmark 7.h
Determine the Composition of Multiple Functions

 Indicator 7.h.1 Find the composition of two functions

 Indicator 7.h.2 Use composition of functions to verify two functions are inverses

 Indicator 7.h.3 Find the composition of multiple functions

 Indicator 7.h.4 Find the value of a composition of multiple functions

 Indicator 7.h.5 Find the domain and range of a piecewise function

MTH.ALG2
Standard 8
INVESTIGATE AND DESCRIBE RELATIONSHIPS

Benchmark 8.a
Investigate and Describe Relationships

 Indicator 8.a.1 Describe relationships among solutions/zeros/intercepts/factors

 Indicator 8.a.2 Define a polynomial function, given its zeros

 Indicator 8.a.3 Determine a factored form of a polynomial expression

 Indicator 8.a.4 Identify zeros of multiplicity greater than 1

 Indicator 8.a.5 Determine the number of real solutions and nonreal solutions

 Indicator 8.a.6 Use long division to find all zeroes of a polynomial function

 Indicator 8.a.7 Use synthetic division/substitution to find all zeros

MTH.ALG2
Standard 9
COLLECT/ANALYZE DATA TO MAKE PREDICTIONS & SOLVE PRACTICAL PROBLEMS

Benchmark 9.a
Collect & Analyze Data to Make Predictions & Solve Practical Problems

 Indicator 9.a.1 Collect and analyze data

 Indicator 9.a.2 Investigate scatterplots to determine if patterns exist

 Indicator 9.a.3 Find an equation for the curve of best fit for data

 Indicator 9.a.4 Make predictions, using data, scatterplots, or curve of best fit

 Indicator 9.a.5 Determine the model that would best describe the data

 Indicator 9.a.6 Determine how well a regression curve approximates data points

MTH.ALG2
Standard 10
SOLVE PROBLEMS INVOLVING DIRECT, JOINT, & INVERSE VARIATIONS

Benchmark 10.a
Solve Problems Involving Direct, Joint, and Inverse Variations

 Indicator 10.a.1 Translate "y varies jointly as x and z" as y=kxz

 Indicator 10.a.2 Translate "y is directly proportional to x" as y=kx

 Indicator 10.a.3 Translate "y is inversely proportional to x" as y=k/x

 Indicator 10.a.4 Determine the value of the constant of proportionality

 Indicator 10.a.5 Use combinations of direct/joint/inverse variation to solve problems

 Indicator 10.a.6 Identify inverse or direct variation

MTH.ALG2
Standard 11
IDENTIFY AND APPLY PROPERTIES OF A NORMAL DISTRIBUTION

Benchmark 11.a
Identify and Apply Properties of a Normal Distribution

 Indicator 11.a.1 Identify the properties of a normal probability distribution

 Indicator 11.a.2 Describe impact of standard deviation & mean on normal distribution

 Indicator 11.a.3 Use standard normal distribution and z-scores to compare data sets

 Indicator 11.a.4 Represent probability as area under the curve

 Indicator 11.a.5 Determine probabilities or percentiles based on z-scores.

MTH.ALG2
Standard 12
COMPUTE AND DISTINGUISH BETWEEN PERMUTATIONS AND COMBINATIONS

Benchmark 12.a
Compute and Distinguish Between Permutations and Combinations

 Indicator 12.a.1 Compare and contrast permutations and combinations

 Indicator 12.a.2 Calculate the number of combinations of n objects taken r at a time

 Indicator 12.a.3 Calculate the number of permutations of n objects taken r at a time

 Indicator 12.a.4 Use permutations and combinations to solve real-world problems

MTH.ALG2
Standard 13
USE MATRIX MULTIPLICATION TO SOLVE PRACTICAL PROBLEMS

Benchmark 13.a
Use Matrix Multiplication to Solve Practical Problems

 Indicator 13.a.1 Find the product of two 2 x 2 matrices by hand

 Indicator 13.a.2 Find the product of 2 matrices greater than 2 x 2 w/a graphing calc

 Indicator 13.a.3 Use matrix multiplication to solve practical problems

 Indicator 13.a.4 Represent and solve a system of linear equations in matrix form

 Indicator 13.a.5 Find the inverse of a matrix with a graphing calculator

 Indicator 13.a.6 Find the determinant of a matrix with a graphing calculator

 Indicator 13.a.7 Identify the identity matrix and its properties

Essential - Standard, benchmark, or indicator from the VDOE Standards of Learning document. In the absence of VDOE standards for a given course, content subject to testing such as AP and IB can be labeled Essential.
Expected - Standard, benchmark, or indicator added by the FCPS Program of Studies to provide a context, a bridge, or an enhancement to the Essential SBIs.
Extended - Standard, benchmark, or indicator added by the FCPS Program of Studies generally used to differentiate instruction for advanced learners (Honors/GT)