IXL Skill Plan | Texas Essential Knowledge and Skills (TEKS): Algebra 2

Texas Essential Knowledge and Skills (TEKS): Algebra 2

Skills available for Texas Algebra 2 standards

Strand

Mathematical process standards
Attributes of functions and their inverses
Systems of equations and inequalities
Quadratic and square root functions, equations, and inequalities
Exponential and logarithmic functions and equations
Cubic, cube root, absolute value and rational functions, equations, and inequalities
Number and algebraic methods
Data

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1	Mathematical process standards
1 The student uses mathematical processes to acquire and demonstrate mathematical understanding.
A apply mathematics to problems arising in everyday life, society, and the workplace;		Systems of equations and inequalities 1. Solve a system of equations using any method: word problems 2. Solve a system of equations using augmented matrices: word problems Quadratic and square root functions, equations, and inequalities 3. Solve quadratic equations: word problems Exponential and logarithmic functions and equations 4. Exponential growth and decay: word problems 5. Compound interest: word problems 6. Continuously compounded interest: word problems Data 7. Interpret regression lines
A apply mathematics to problems arising in everyday life, society, and the workplace;
Systems of equations and inequalities 1. Solve a system of equations using any method: word problems 2. Solve a system of equations using augmented matrices: word problems Quadratic and square root functions, equations, and inequalities 3. Solve quadratic equations: word problems Exponential and logarithmic functions and equations 4. Exponential growth and decay: word problems 5. Compound interest: word problems 6. Continuously compounded interest: word problems Data 7. Interpret regression lines

B use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution;		Systems of equations and inequalities 1. Solve a system of equations using any method: word problems 2. Linear programming 3. Solve a system of equations using augmented matrices: word problems Quadratic and square root functions, equations, and inequalities 4. Solve quadratic equations: word problems Exponential and logarithmic functions and equations 5. Write exponential functions: word problems 6. Exponential growth and decay: word problems 7. Compound interest: word problems 8. Continuously compounded interest: word problems Data 9. Analyze a regression line of a data set 10. Exponential regression
B use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution;
Systems of equations and inequalities 1. Solve a system of equations using any method: word problems 2. Linear programming 3. Solve a system of equations using augmented matrices: word problems Quadratic and square root functions, equations, and inequalities 4. Solve quadratic equations: word problems Exponential and logarithmic functions and equations 5. Write exponential functions: word problems 6. Exponential growth and decay: word problems 7. Compound interest: word problems 8. Continuously compounded interest: word problems Data 9. Analyze a regression line of a data set 10. Exponential regression

C select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems;		Attributes of functions and their inverses 1. Identify inverse functions Systems of equations and inequalities 2. Solve a system of equations in three variables using substitution 3. Solve a system of equations in three variables using elimination 4. Solve systems of linear inequalities by graphing 5. Solve a system of linear and quadratic equations by graphing: parabolas Quadratic and square root functions, equations, and inequalities 6. Solve a quadratic equation using square roots 7. Solve a quadratic equation using the zero product property 8. Solve a quadratic equation by factoring 9. Solve a quadratic equation by completing the square 10. Solve a quadratic equation using the quadratic formula 11. Solve quadratic inequalities 12. Solve radical equations 13. Find properties of a parabola from equations in general form Exponential and logarithmic functions and equations 14. Solve exponential equations by rewriting the base 15. Solve exponential equations using common logarithms 16. Solve exponential equations using natural logarithms 17. Solve logarithmic equations I Cubic, cube root, absolute value and rational functions, equations, and inequalities 18. Solve absolute value equations 19. Solve absolute value inequalities 20. Solve rational equations Number and algebraic methods 21. Factor using a quadratic pattern 22. Factor by grouping 23. Factor sums and differences of cubes 24. Factor polynomials 25. Solve equations with rational exponents Data 26. Find the equation of a regression line
C select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems;
Attributes of functions and their inverses 1. Identify inverse functions Systems of equations and inequalities 2. Solve a system of equations in three variables using substitution 3. Solve a system of equations in three variables using elimination 4. Solve systems of linear inequalities by graphing 5. Solve a system of linear and quadratic equations by graphing: parabolas Quadratic and square root functions, equations, and inequalities 6. Solve a quadratic equation using square roots 7. Solve a quadratic equation using the zero product property 8. Solve a quadratic equation by factoring 9. Solve a quadratic equation by completing the square 10. Solve a quadratic equation using the quadratic formula 11. Solve quadratic inequalities 12. Solve radical equations 13. Find properties of a parabola from equations in general form Exponential and logarithmic functions and equations 14. Solve exponential equations by rewriting the base 15. Solve exponential equations using common logarithms 16. Solve exponential equations using natural logarithms 17. Solve logarithmic equations I Cubic, cube root, absolute value and rational functions, equations, and inequalities 18. Solve absolute value equations 19. Solve absolute value inequalities 20. Solve rational equations Number and algebraic methods 21. Factor using a quadratic pattern 22. Factor by grouping 23. Factor sums and differences of cubes 24. Factor polynomials 25. Solve equations with rational exponents Data 26. Find the equation of a regression line

D communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate;		Attributes of functions and their inverses 1. Domain and range of absolute value functions: graphs 2. Domain and range of absolute value functions: equations 3. Domain and range of radical functions 4. Domain and range of logarithmic functions Systems of equations and inequalities 5. Find the vertices of a solution set for a system of linear inequalities Quadratic and square root functions, equations, and inequalities 6. Find properties of a parabola from equations in general form Cubic, cube root, absolute value and rational functions, equations, and inequalities 7. Rational functions: asymptotes and excluded values Number and algebraic methods 8. Domain and range of linear functions: graphs 9. Domain and range 10. Domain and range of quadratic functions: graphs 11. Domain and range of polynomials Data 12. Interpret regression lines 13. Exponential regression
D communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate;
Attributes of functions and their inverses 1. Domain and range of absolute value functions: graphs 2. Domain and range of absolute value functions: equations 3. Domain and range of radical functions 4. Domain and range of logarithmic functions Systems of equations and inequalities 5. Find the vertices of a solution set for a system of linear inequalities Quadratic and square root functions, equations, and inequalities 6. Find properties of a parabola from equations in general form Cubic, cube root, absolute value and rational functions, equations, and inequalities 7. Rational functions: asymptotes and excluded values Number and algebraic methods 8. Domain and range of linear functions: graphs 9. Domain and range 10. Domain and range of quadratic functions: graphs 11. Domain and range of polynomials Data 12. Interpret regression lines 13. Exponential regression

E create and use representations to organize, record, and communicate mathematical ideas;		Attributes of functions and their inverses 1. Find values of inverse functions from tables 2. Find values of inverse functions from graphs Systems of equations and inequalities 3. Solve a system of equations by graphing: word problems 4. Solve systems of linear inequalities by graphing 5. Find the vertices of a solution set for a system of linear inequalities 6. Linear programming 7. Solve a system of linear and quadratic equations by graphing: parabolas Quadratic and square root functions, equations, and inequalities 8. Write a quadratic function in vertex form from its vertex and another point 9. Write a quadratic function in factored form from its x-intercepts and another point 10. Write a quadratic function from three points 11. Graph solutions to quadratic inequalities 12. Graph square root functions 13. Write equations of parabolas in vertex form from graphs 14. Write equations of parabolas in vertex form using properties Exponential and logarithmic functions and equations 15. Match exponential functions and graphs 16. Graph logarithmic functions Cubic, cube root, absolute value and rational functions, equations, and inequalities 17. Graph solutions to absolute value equations 18. Write absolute value equations from graphs 19. Graph solutions to absolute value inequalities 20. Graph an absolute value function 21. Graph cube root functions
E create and use representations to organize, record, and communicate mathematical ideas;
Attributes of functions and their inverses 1. Find values of inverse functions from tables 2. Find values of inverse functions from graphs Systems of equations and inequalities 3. Solve a system of equations by graphing: word problems 4. Solve systems of linear inequalities by graphing 5. Find the vertices of a solution set for a system of linear inequalities 6. Linear programming 7. Solve a system of linear and quadratic equations by graphing: parabolas Quadratic and square root functions, equations, and inequalities 8. Write a quadratic function in vertex form from its vertex and another point 9. Write a quadratic function in factored form from its x-intercepts and another point 10. Write a quadratic function from three points 11. Graph solutions to quadratic inequalities 12. Graph square root functions 13. Write equations of parabolas in vertex form from graphs 14. Write equations of parabolas in vertex form using properties Exponential and logarithmic functions and equations 15. Match exponential functions and graphs 16. Graph logarithmic functions Cubic, cube root, absolute value and rational functions, equations, and inequalities 17. Graph solutions to absolute value equations 18. Write absolute value equations from graphs 19. Graph solutions to absolute value inequalities 20. Graph an absolute value function 21. Graph cube root functions

F analyze mathematical relationships to connect and communicate mathematical ideas; and		Attributes of functions and their inverses 1. Composition of linear and quadratic functions: find an equation 2. Find inverse functions and relations Quadratic and square root functions, equations, and inequalities 3. Graph solutions to quadratic inequalities 4. Write equations of parabolas in vertex form from graphs 5. Write equations of parabolas in vertex form using properties 6. Convert equations of parabolas from general to vertex form Exponential and logarithmic functions and equations 7. Convert between exponential and logarithmic form: rational bases 8. Convert between natural exponential and logarithmic form 9. Convert between exponential and logarithmic form: all bases Cubic, cube root, absolute value and rational functions, equations, and inequalities 10. Graph solutions to absolute value equations 11. Convert between rational exponents and radicals Data 12. Analyze a regression line of a data set 13. Exponential regression
F analyze mathematical relationships to connect and communicate mathematical ideas; and
Attributes of functions and their inverses 1. Composition of linear and quadratic functions: find an equation 2. Find inverse functions and relations Quadratic and square root functions, equations, and inequalities 3. Graph solutions to quadratic inequalities 4. Write equations of parabolas in vertex form from graphs 5. Write equations of parabolas in vertex form using properties 6. Convert equations of parabolas from general to vertex form Exponential and logarithmic functions and equations 7. Convert between exponential and logarithmic form: rational bases 8. Convert between natural exponential and logarithmic form 9. Convert between exponential and logarithmic form: all bases Cubic, cube root, absolute value and rational functions, equations, and inequalities 10. Graph solutions to absolute value equations 11. Convert between rational exponents and radicals Data 12. Analyze a regression line of a data set 13. Exponential regression

G display, explain, or justify mathematical ideas and arguments using precise mathematical language in written or oral communication.		1. Linear programming 2. Interpret regression lines 3. Analyze a regression line of a data set
G display, explain, or justify mathematical ideas and arguments using precise mathematical language in written or oral communication.
1. Linear programming 2. Interpret regression lines 3. Analyze a regression line of a data set

2	Attributes of functions and their inverses
2 The student applies mathematical processes to understand that functions have distinct key attributes and understand the relationship between a function and its inverse.
A graph the functions f(x)=√x, f(x)=1/x, f(x)=x³, f(x)= ³√x, f(x)=b to the x power, f(x)=\|x\|, and f(x)=logb (x) where b is 2, 10, and e, and, when applicable, analyze the key attributes such as domain, range, intercepts, symmetries, asymptotic behavior, and maximum and minimum given an interval;		Absolute value functions 1. Domain and range of absolute value functions: graphs 2. Domain and range of absolute value functions: equations Radical functions 3. Domain and range of radical functions Rational functions 4. Rational functions: asymptotes and excluded values Exponential and logarithmic functions 5. Match exponential functions and graphs 6. Domain and range of logarithmic functions 7. Graph logarithmic functions
A graph the functions f(x)=√x, f(x)=1/x, f(x)=x³, f(x)= ³√x, f(x)=b to the x power, f(x)=\|x\|, and f(x)=logb (x) where b is 2, 10, and e, and, when applicable, analyze the key attributes such as domain, range, intercepts, symmetries, asymptotic behavior, and maximum and minimum given an interval;
Absolute value functions 1. Domain and range of absolute value functions: graphs 2. Domain and range of absolute value functions: equations Radical functions 3. Domain and range of radical functions Rational functions 4. Rational functions: asymptotes and excluded values Exponential and logarithmic functions 5. Match exponential functions and graphs 6. Domain and range of logarithmic functions 7. Graph logarithmic functions

B graph and write the inverse of a function using notation such as f-¹ (x);		1. Find values of inverse functions from graphs 2. Graphs of inverse functions 3. Find inverse functions and relations
B graph and write the inverse of a function using notation such as f-¹ (x);
1. Find values of inverse functions from graphs 2. Graphs of inverse functions 3. Find inverse functions and relations

C describe and analyze the relationship between a function and its inverse (quadratic and square root, logarithmic and exponential), including the restriction(s) on domain, which will restrict its range; and		1. Find values of inverse functions from tables 2. Find values of inverse functions from graphs 3. Find inverse functions and relations
C describe and analyze the relationship between a function and its inverse (quadratic and square root, logarithmic and exponential), including the restriction(s) on domain, which will restrict its range; and
1. Find values of inverse functions from tables 2. Find values of inverse functions from graphs 3. Find inverse functions and relations

D use the composition of two functions, including the necessary restrictions on the domain, to determine if the functions are inverses of each other.		Composition of two functions 1. Composition of linear functions: find a value 2. Composition of linear functions: find an equation 3. Composition of linear and quadratic functions: find a value 4. Composition of linear and quadratic functions: find an equation Identify inverse functions 5. Identify inverse functions
D use the composition of two functions, including the necessary restrictions on the domain, to determine if the functions are inverses of each other.
Composition of two functions 1. Composition of linear functions: find a value 2. Composition of linear functions: find an equation 3. Composition of linear and quadratic functions: find a value 4. Composition of linear and quadratic functions: find an equation Identify inverse functions 5. Identify inverse functions

3	Systems of equations and inequalities
3 The student applies mathematical processes to formulate systems of equations and inequalities, use a variety of methods to solve, and analyze reasonableness of solutions.
A formulate systems of equations, including systems consisting of three linear equations in three variables and systems consisting of two equations, the first linear and the second quadratic;		1. Solve a system of equations by graphing: word problems 2. Solve a system of equations using substitution: word problems 3. Solve a system of equations using elimination: word problems 4. Solve a system of equations using any method: word problems 5. Solve a system of equations using augmented matrices: word problems
A formulate systems of equations, including systems consisting of three linear equations in three variables and systems consisting of two equations, the first linear and the second quadratic;
1. Solve a system of equations by graphing: word problems 2. Solve a system of equations using substitution: word problems 3. Solve a system of equations using elimination: word problems 4. Solve a system of equations using any method: word problems 5. Solve a system of equations using augmented matrices: word problems

B solve systems of three linear equations in three variables by using Gaussian elimination, technology with matrices, and substitution;		1. Solve a system of equations in three variables using substitution 2. Solve a system of equations in three variables using elimination
B solve systems of three linear equations in three variables by using Gaussian elimination, technology with matrices, and substitution;
1. Solve a system of equations in three variables using substitution 2. Solve a system of equations in three variables using elimination

C solve, algebraically, systems of two equations in two variables consisting of a linear equation and a quadratic equation;		1. Solve a system of linear and quadratic equations: parabolas
C solve, algebraically, systems of two equations in two variables consisting of a linear equation and a quadratic equation;
1. Solve a system of linear and quadratic equations: parabolas

D determine the reasonableness of solutions to systems of a linear equation and a quadratic equation in two variables;		1. Solve a system of linear and quadratic equations by graphing: parabolas
D determine the reasonableness of solutions to systems of a linear equation and a quadratic equation in two variables;
1. Solve a system of linear and quadratic equations by graphing: parabolas

E formulate systems of at least two linear inequalities in two variables;
E formulate systems of at least two linear inequalities in two variables;


F solve systems of two or more linear inequalities in two variables; and		1. Solve systems of linear inequalities by graphing 2. Find the vertices of a solution set for a system of linear inequalities 3. Linear programming
F solve systems of two or more linear inequalities in two variables; and
1. Solve systems of linear inequalities by graphing 2. Find the vertices of a solution set for a system of linear inequalities 3. Linear programming

G determine possible solutions in the solution set of systems of two or more linear inequalities in two variables.		1. Is (x, y) a solution to the system of inequalities?
G determine possible solutions in the solution set of systems of two or more linear inequalities in two variables.
1. Is (x, y) a solution to the system of inequalities?

4	Quadratic and square root functions, equations, and inequalities
4 The student applies mathematical processes to understand that quadratic and square root functions, equations, and quadratic inequalities can be used to model situations, solve problems, and make predictions.
A write the quadratic function given three specified points in the plane;		1. Write a quadratic function from three points
A write the quadratic function given three specified points in the plane;
1. Write a quadratic function from three points

B write the equation of a parabola using given attributes, including vertex, focus, directrix, axis of symmetry, and direction of opening;		1. Write a quadratic function in vertex form from its vertex and another point 2. Write a quadratic function in factored form from its x-intercepts and another point 3. Write equations of parabolas in vertex form from graphs 4. Write equations of parabolas in vertex form using properties
B write the equation of a parabola using given attributes, including vertex, focus, directrix, axis of symmetry, and direction of opening;
1. Write a quadratic function in vertex form from its vertex and another point 2. Write a quadratic function in factored form from its x-intercepts and another point 3. Write equations of parabolas in vertex form from graphs 4. Write equations of parabolas in vertex form using properties

C determine the effect on the graph of f(x) = √x when f(x) is replaced by af(x), f(x) + d, f(bx), and f(x - c) for specific positive and negative values of a, b, c, and d;		1. Graph square root functions
C determine the effect on the graph of f(x) = √x when f(x) is replaced by af(x), f(x) + d, f(bx), and f(x - c) for specific positive and negative values of a, b, c, and d;
1. Graph square root functions

D transform a quadratic function f(x) = ax² + bx + c to the form f(x) = a(x - h)² + k to identify the different attributes of f(x);		1. Convert equations of parabolas from general to vertex form 2. Find properties of a parabola from equations in general form
D transform a quadratic function f(x) = ax² + bx + c to the form f(x) = a(x - h)² + k to identify the different attributes of f(x);
1. Convert equations of parabolas from general to vertex form 2. Find properties of a parabola from equations in general form

E formulate quadratic and square root equations using technology given a table of data;
E formulate quadratic and square root equations using technology given a table of data;


F solve quadratic and square root equations;		Quadratic equations 1. Solve a quadratic equation using square roots 2. Solve a quadratic equation using the zero product property 3. Solve a quadratic equation by factoring 4. Solve a quadratic equation by completing the square 5. Solve a quadratic equation using the quadratic formula 6. Solve quadratic equations: word problems Square root equations 7. Solve radical equations
F solve quadratic and square root equations;
Quadratic equations 1. Solve a quadratic equation using square roots 2. Solve a quadratic equation using the zero product property 3. Solve a quadratic equation by factoring 4. Solve a quadratic equation by completing the square 5. Solve a quadratic equation using the quadratic formula 6. Solve quadratic equations: word problems Square root equations 7. Solve radical equations

G identify extraneous solutions of square root equations; and
G identify extraneous solutions of square root equations; and


H solve quadratic inequalities.		1. Graph solutions to quadratic inequalities 2. Solve quadratic inequalities
H solve quadratic inequalities.
1. Graph solutions to quadratic inequalities 2. Solve quadratic inequalities

5	Exponential and logarithmic functions and equations
5 The student applies mathematical processes to understand that exponential and logarithmic functions can be used to model situations and solve problems.
A determine the effects on the key attributes on the graphs of f(x) = b to the x power and f(x) = logb (x) where b is 2, 10, and e when f(x) is replaced by af(x), f(x) + d, and f(x - c) for specific positive and negative real values of a, c, and d;		1. Match exponential functions and graphs
A determine the effects on the key attributes on the graphs of f(x) = b to the x power and f(x) = logb (x) where b is 2, 10, and e when f(x) is replaced by af(x), f(x) + d, and f(x - c) for specific positive and negative real values of a, c, and d;
1. Match exponential functions and graphs

B formulate exponential and logarithmic equations that model real-world situations, including exponential relationships written in recursive notation;		1. Write exponential functions: word problems 2. Exponential growth and decay: word problems 3. Compound interest: word problems 4. Continuously compounded interest: word problems
B formulate exponential and logarithmic equations that model real-world situations, including exponential relationships written in recursive notation;
1. Write exponential functions: word problems 2. Exponential growth and decay: word problems 3. Compound interest: word problems 4. Continuously compounded interest: word problems

C rewrite exponential equations as their corresponding logarithmic equations and logarithmic equations as their corresponding exponential equations;		1. Convert between exponential and logarithmic form: rational bases 2. Convert between natural exponential and logarithmic form 3. Convert between exponential and logarithmic form: all bases
C rewrite exponential equations as their corresponding logarithmic equations and logarithmic equations as their corresponding exponential equations;
1. Convert between exponential and logarithmic form: rational bases 2. Convert between natural exponential and logarithmic form 3. Convert between exponential and logarithmic form: all bases

D solve exponential equations of the form y = ab to the x power where a is a nonzero real number and b is greater than zero and not equal to one and single logarithmic equations having real solutions; and		1. Solve exponential equations by rewriting the base 2. Solve exponential equations using common logarithms 3. Solve exponential equations using natural logarithms 4. Solve logarithmic equations I
D solve exponential equations of the form y = ab to the x power where a is a nonzero real number and b is greater than zero and not equal to one and single logarithmic equations having real solutions; and
1. Solve exponential equations by rewriting the base 2. Solve exponential equations using common logarithms 3. Solve exponential equations using natural logarithms 4. Solve logarithmic equations I

E determine the reasonableness of a solution to a logarithmic equation.
E determine the reasonableness of a solution to a logarithmic equation.

6	Cubic, cube root, absolute value and rational functions, equations, and inequalities
6 The student applies mathematical processes to understand that cubic, cube root, absolute value and rational functions, equations, and inequalities can be used to model situations, solve problems, and make predictions.
A analyze the effect on the graphs of f(x) = x³ and f(x) = ³√x when f(x) is replaced by af(x), f(bx), f(x - c), and f(x) + d for specific positive and negative real values of a, b, c, and d;		1. Graph cube root functions
A analyze the effect on the graphs of f(x) = x³ and f(x) = ³√x when f(x) is replaced by af(x), f(bx), f(x - c), and f(x) + d for specific positive and negative real values of a, b, c, and d;
1. Graph cube root functions

B solve cube root equations that have real roots;
B solve cube root equations that have real roots;


C analyze the effect on the graphs of f(x) = \|x\| when f(x) is replaced by af(x), f(bx), f(x-c), and f(x) + d for specific positive and negative real values of a, b, c, and d;		1. Graph an absolute value function 2. Transformations of absolute value functions
C analyze the effect on the graphs of f(x) = \|x\| when f(x) is replaced by af(x), f(bx), f(x-c), and f(x) + d for specific positive and negative real values of a, b, c, and d;
1. Graph an absolute value function 2. Transformations of absolute value functions

D formulate absolute value linear equations;		1. Write absolute value equations from graphs
D formulate absolute value linear equations;
1. Write absolute value equations from graphs

E solve absolute value linear equations;		1. Solve absolute value equations 2. Graph solutions to absolute value equations
E solve absolute value linear equations;
1. Solve absolute value equations 2. Graph solutions to absolute value equations

F solve absolute value linear inequalities;		1. Solve absolute value inequalities 2. Graph solutions to absolute value inequalities
F solve absolute value linear inequalities;
1. Solve absolute value inequalities 2. Graph solutions to absolute value inequalities

G analyze the effect on the graphs of f(x) = 1/x when f(x) is replaced by af(x), f(bx), f(x-c), and f(x) + d for specific positive and negative real values of a, b, c, and d;
G analyze the effect on the graphs of f(x) = 1/x when f(x) is replaced by af(x), f(bx), f(x-c), and f(x) + d for specific positive and negative real values of a, b, c, and d;


H formulate rational equations that model real-world situations;
H formulate rational equations that model real-world situations;


I solve rational equations that have real solutions;		1. Solve rational equations
I solve rational equations that have real solutions;
1. Solve rational equations

J determine the reasonableness of a solution to a rational equation;		1. Solve rational equations
J determine the reasonableness of a solution to a rational equation;
1. Solve rational equations

K determine the asymptotic restrictions on the domain of a rational function and represent domain and range using interval notation, inequalities, and set notation; and		1. Rational functions: asymptotes and excluded values
K determine the asymptotic restrictions on the domain of a rational function and represent domain and range using interval notation, inequalities, and set notation; and
1. Rational functions: asymptotes and excluded values

L formulate and solve equations involving inverse variation.		1. Write and solve inverse variation equations
L formulate and solve equations involving inverse variation.
1. Write and solve inverse variation equations

7	Number and algebraic methods
7 The student applies mathematical processes to simplify and perform operations on expressions and to solve equations.
A add, subtract, and multiply complex numbers;		1. Add and subtract complex numbers 2. Complex conjugates 3. Multiply complex numbers
A add, subtract, and multiply complex numbers;
1. Add and subtract complex numbers 2. Complex conjugates 3. Multiply complex numbers

B add, subtract, and multiply polynomials;		1. Add and subtract polynomials 2. Multiply polynomials
B add, subtract, and multiply polynomials;
1. Add and subtract polynomials 2. Multiply polynomials

C determine the quotient of a polynomial of degree three and of degree four when divided by a polynomial of degree one and of degree two;		1. Divide polynomials using synthetic division 2. Divide polynomials using long division
C determine the quotient of a polynomial of degree three and of degree four when divided by a polynomial of degree one and of degree two;
1. Divide polynomials using synthetic division 2. Divide polynomials using long division

D determine the linear factors of a polynomial function of degree three and of degree four using algebraic methods;		1. Factor polynomials
D determine the linear factors of a polynomial function of degree three and of degree four using algebraic methods;
1. Factor polynomials

E determine linear and quadratic factors of a polynomial expression of degree three and of degree four, including factoring the sum and difference of two cubes and factoring by grouping;		1. Factor using a quadratic pattern 2. Factor by grouping 3. Factor sums and differences of cubes 4. Factor polynomials
E determine linear and quadratic factors of a polynomial expression of degree three and of degree four, including factoring the sum and difference of two cubes and factoring by grouping;
1. Factor using a quadratic pattern 2. Factor by grouping 3. Factor sums and differences of cubes 4. Factor polynomials

F determine the sum, difference, product, and quotient of rational expressions with integral exponents of degree one and of degree two;		1. Multiply and divide rational expressions 2. Add and subtract rational expressions 3. Simplify complex fractions
F determine the sum, difference, product, and quotient of rational expressions with integral exponents of degree one and of degree two;
1. Multiply and divide rational expressions 2. Add and subtract rational expressions 3. Simplify complex fractions

G rewrite radical expressions that contain variables to equivalent forms;		1. Simplify radical expressions with variables I 2. Simplify radical expressions with variables II 3. Convert between rational exponents and radicals
G rewrite radical expressions that contain variables to equivalent forms;
1. Simplify radical expressions with variables I 2. Simplify radical expressions with variables II 3. Convert between rational exponents and radicals

H solve equations involving rational exponents; and		1. Solve equations with rational exponents
H solve equations involving rational exponents; and
1. Solve equations with rational exponents

I write the domain and range of a function in interval notation, inequalities, and set notation.		1. Domain and range of linear functions: graphs 2. Domain and range 3. Domain and range of quadratic functions: graphs 4. Domain and range of polynomials 5. Domain and range of radical functions 6. Domain and range of logarithmic functions
I write the domain and range of a function in interval notation, inequalities, and set notation.
1. Domain and range of linear functions: graphs 2. Domain and range 3. Domain and range of quadratic functions: graphs 4. Domain and range of polynomials 5. Domain and range of radical functions 6. Domain and range of logarithmic functions

8	Data
8 The student applies mathematical processes to analyze data, select appropriate models, write corresponding functions, and make predictions.
A analyze data to select the appropriate model from among linear, quadratic, and exponential models;		1. Identify linear, quadratic, and exponential functions from graphs 2. Identify linear, quadratic, and exponential functions from tables
A analyze data to select the appropriate model from among linear, quadratic, and exponential models;
1. Identify linear, quadratic, and exponential functions from graphs 2. Identify linear, quadratic, and exponential functions from tables

B use regression methods available through technology to write a linear function, a quadratic function, and an exponential function from a given set of data; and		1. Find the equation of a regression line 2. Interpret regression lines 3. Analyze a regression line of a data set 4. Exponential regression
B use regression methods available through technology to write a linear function, a quadratic function, and an exponential function from a given set of data; and
1. Find the equation of a regression line 2. Interpret regression lines 3. Analyze a regression line of a data set 4. Exponential regression

C predict and make decisions and critical judgments from a given set of data using linear, quadratic, and exponential models.		1. Interpret regression lines 2. Analyze a regression line of a data set 3. Exponential regression
C predict and make decisions and critical judgments from a given set of data using linear, quadratic, and exponential models.
1. Interpret regression lines 2. Analyze a regression line of a data set 3. Exponential regression