Academic Standard

Algebra
Initiative: 
Tennessee Diploma Project
Set: 
Mathematics
Type: 
Standard
Code: 
3
Grade range: 
9 to 12
Conceptual StrandThe Algebra Standard emphasizes relationships among quantities, including functions, patterns, ways of representing mathematical relationships, and the analysis of change.Guiding QuestionHow does algebra encompass the relationships among quantities, the use of symbols, the modeling of phenomena, and the mathematical study of change?
 
Elements within this Standard
 
Course Level Expectation
Understand and apply properties of rational exponents and perform basic operations to simplify algebraic expressions.
Understand, analyze, transform and generalize mathematical patterns, relations and functions using properties and various representations.
Analyze and apply various methods to solve equations, absolute values, inequalities, and systems of equations over complex numbers.
Graph and compare equations and inequalities in two variables. Identify and understand the relationships between the algebraic and geometric properties of the graph.
Use mathematical models involving equations and systems of equations to represent, interpret and analyze quantitative relationships, change in various contexts,
Check For Understanding
Perform operations on algebraic expressions and justify the procedures.
Determine the domain of a function represented in either symbolic or graphical form.
Determine and graph the inverse of a function with and without technology.
Analyze the effect of changing various parameters on functions and their graphs.
Graph piece-wise and step functions.
Simplify expressions and solve equations containing radicals.
Solve quadratic equations by factoring, graphing, completing the square, extracting square roots and using the quadratic formula.
Solve a three by three system of linear equations algebraically and by using inverse matrices and determinants with and without technology.
Find an equation for a parabola when given its graph or when given its roots.
Given a quadratic equation use the discriminant to determine the nature of the roots.
Describe and articulate the characteristics and parameters of a parent function.
Understand the relationship between real zeros of a function and the x-intercepts of its graph.
Solve problems using exponential functions requiring the use of logarithms for their solutions.
Define and use arithmetic and geometric sequences and series including using sigma and pi notation.
Find the sum of an geometric series whose common ratio, r, is in the interval (-1,1).
Prove basic properties of logarithms using properties of exponents and apply those properties to solve problems.
Know that the logarithm and exponential functions are inverses and use this information to solve real-world problems.
Solve compound inequalities involving disjunction and conjunction and linear inequalities containing absolute values.
Solve linear programming problems.
Understand the relationships between the equations of conic sections and their graphs.
Factor polynomials using a variety of methods including the factor theorem, synthetic division, long division, sums and differences of cubes, and grouping.
Determine the number and possible types of zeros for a polynomial function and find the rational roots.
Understand the connection between the roots, zeros, x-intercepts, factors of polynomials, and solutions of polynomial equations.
State Performance Indicator
Add, subtract and multiply polynomials; divide a polynomial by a lower degree polynomial.
Solve quadratic equations and systems, and determine roots of a higher order polynomial.
Add, subtract, multiply, divide and simplify rational expressions including those with rational and negative exponents.
Use the formulas for the general term and summation of finite arithmetic and both finite and infinite geometric series.
Describe the domain and range of functions and articulate restrictions imposed either by the operations or by the contextual situations which the functions
Combine functions (such as polynomial, rational, radical and absolute value expressions) by addition, subtraction, multiplication, division, or by composition
Identify whether a function has an inverse, whether two functions are inverses of each other, and/or explain why their graphs are reflections over the line y = x.
Solve systems of three linear equations in three variables.
Graph the solution set of two or three linear or quadratic inequalities.
Identify and/or graph a variety of functions and their transformations.
Graph conic sections (circles, parabolas, ellipses and hyperbolas) and understand the relationship between the standard form and the key characteristics of the
Interpret graphs that depict real-world phenomena.
Solve contextual problems using quadratic, rational, radical and exponential equations, finite geometric series or systems of equations.
Solve problems involving the binomial theorem and its connection to Pascals Triangle, combinatorics, and probability.