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)