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Skills available for Texas high school math standards

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College and Career Readiness Standards College and Career Readiness Standards
Texas Essential Knowledge and Skills (TEKS): 111.47 Statistics Texas Essential Knowledge and Skills (TEKS): 111.47 Statistics
Texas Essential Knowledge and Skills (TEKS): 111.48 Algebraic Reasoning Texas Essential Knowledge and Skills (TEKS): 111.48 Algebraic Reasoning
State of Texas Assessments of Academic Readiness (STAAR) State of Texas Assessments of Academic Readiness (STAAR)
Texas Essential Knowledge and Skills (TEKS): Algebra 1 Texas Essential Knowledge and Skills (TEKS): Algebra 1
Texas Essential Knowledge and Skills (TEKS): Algebra 2 Texas Essential Knowledge and Skills (TEKS): Algebra 2
Texas Essential Knowledge and Skills (TEKS): Algebraic Reasoning Texas Essential Knowledge and Skills (TEKS): Algebraic Reasoning
Texas Essential Knowledge and Skills (TEKS): Geometry Texas Essential Knowledge and Skills (TEKS): Geometry
Texas Essential Knowledge and Skills (TEKS): Precalculus Texas Essential Knowledge and Skills (TEKS): Precalculus
Texas College and Career Readiness Standards: Grades: 9-12 Texas College and Career Readiness Standards: Grades: 9-12

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These student expectations will not be listed under a separate reporting category. Instead, they will be incorporated into test questions across reporting categories since the application of mathematical process standards is part of each knowledge statement.

A.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;
- 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;
- 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;
- D communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate;
- E create and use representations to organize, record, and communicate mathematical ideas;
- F analyze mathematical relationships to connect and communicate mathematical ideas; and
- G display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.

1 The student will demonstrate an understanding of how to use algebraic methods to manipulate numbers, expressions, and equations.

A.10 The student applies the mathematical process standards and algebraic methods to rewrite in equivalent forms and perform operations on polynomial expressions.
- A add and subtract polynomials of degree one and degree two;
- B multiply polynomials of degree one and degree two;
- C determine the quotient of a polynomial of degree one and polynomial of degree two when divided by a polynomial of degree one and polynomial of degree two when the degree of the divisor does not exceed the degree of the dividend;
  - Divide powers: variable bases (8-C.17)
  - Divide polynomials using long division (A1-W.14)
- D rewrite polynomial expressions of degree one and degree two in equivalent forms using the distributive property;
- E factor, if possible, trinomials with real factors in the form ax² + bx + c, including perfect square trinomials of degree two; and
- F decide if a binomial can be written as the difference of two squares and, if possible, use the structure of a difference of two squares to rewrite the binomial.
  - Factor quadratics: special cases (A1-X.7)
A.11 The student applies the mathematical process standards and algebraic methods to rewrite algebraic expressions into equivalent forms.
- A simplify numerical radical expressions involving square roots; and
- B simplify numeric and algebraic expressions using the laws of exponents, including integral and rational exponents.
A.12 The student applies the mathematical process standards and algebraic methods to write, solve, analyze, and evaluate equations, relations, and functions.
- A decide whether relations represented verbally, tabularly, graphically, and symbolically define a function;
  - Identify functions (A1-M.4)
  - Identify functions: vertical line test (A1-M.5)
- B evaluate functions, expressed in function notation, given one or more elements in their domains;
- C identify terms of arithmetic and geometric sequences when the sequences are given in function form using recursive processes;
- D write a formula for the nth term of arithmetic and geometric sequences, given the value of several of their terms; and
  - Write variable expressions for arithmetic sequences (A1-U.7)
  - Write variable expressions for geometric sequences (A1-U.8)
- E solve mathematic and scientific formulas, and other literal equations, for a specified variable.

2 The student will demonstrate an understanding of how to describe and graph linear functions, equations, and inequalities.

A.3 The student applies the mathematical process standards when using graphs of linear functions, key features, and related transformations to represent in multiple ways and solve, with and without technology, equations, inequalities, and systems of equations.
- A determine the slope of a line given a table of values, a graph, two points on the line, and an equation written in various forms, including y = mx + b, Ax + By = C, and y - y? = m(x - x?);
- B calculate the rate of change of a linear function represented tabularly, graphically, or algebraically in context of mathematical and real-world problems;
- C graph linear functions on the coordinate plane and identify key features, including x-intercept, y-intercept, zeros, and slope, in mathematical and real-world problems;
- D graph the solution set of linear inequalities in two variables on the coordinate plane;
  - Graph a two-variable linear inequality (A1-P.3)
- E determine the effects on the graph of the parent function f(x) = x when f(x) is replaced by af(x), f(x) + d, f(x - c), f(bx) for specific values of a, b, c, and d;
- F graph systems of two linear equations in two variables on the coordinate plane and determine the solutions if they exist;
  - Solve a system of equations by graphing (A1-O.2)
  - Find the number of solutions to a system of equations by graphing (A1-O.4)
- G estimate graphically the solutions to systems of two linear equations with two variables in real-world problems; and
  - Solve a system of equations by graphing: word problems (A1-O.3)
- H graph the solution set of systems of two linear inequalities in two variables on the coordinate plane.
  - Solve systems of linear inequalities by graphing (A1-P.7)
A.4 The student applies the mathematical process standards to formulate statistical relationships and evaluate their reasonableness based on real-world data.
- A calculate, using technology, the correlation coefficient between two quantitative variables and interpret this quantity as a measure of the strength of the linear association;
  - Match correlation coefficients to scatter plots (A1-JJ.3)
  - Calculate correlation coefficients (A1-JJ.4)
- B compare and contrast association and causation in real-world problems; and
- C write, with and without technology, linear functions that provide a reasonable fit to data to estimate solutions and make predictions for real-world problems.

3 The student will demonstrate an understanding of how to write and solve linear functions, equations, and inequalities.

A.2 The student applies the mathematical process standards when using properties of linear functions to write and represent in multiple ways, with and without technology, linear equations, inequalities, and systems of equations.
- A determine the domain and range of a linear function in mathematical problems; determine reasonable domain and range values for real-world situations, both continuous and discrete; and represent domain and range using inequalities;
- B write linear equations in two variables in various forms, including y = mx + b, Ax + By = C, and y - y? = m(x - x?), given one point and the slope and given two points;
- C write linear equations in two variables given a table of values, a graph, and a verbal description;
  - Slope-intercept form: write an equation from a graph (A1-L.5)
  - Point-slope form: write an equation from a graph (A1-L.16)
- D write and solve equations involving direct variation;
  - Write direct variation equations (A1-J.2)
  - Write and solve direct variation equations (A1-J.3)
- E write the equation of a line that contains a given point and is parallel to a given line;
  - Write an equation for a parallel or perpendicular line (A1-L.19)
- F write the equation of a line that contains a given point and is perpendicular to a given line;
  - Write an equation for a parallel or perpendicular line (A1-L.19)
- G write an equation of a line that is parallel or perpendicular to the X or Y axis and determine whether the slope of the line is zero or undefined;
  - Equations of horizontal and vertical lines (A1-L.12)
- H write linear inequalities in two variables given a table of values, a graph, and a verbal description; and
- I write systems of two linear equations given a table of values, a graph, and a verbal description.
A.5 The student applies the mathematical process standards to solve, with and without technology, linear equations and evaluate the reasonableness of their solutions.
- A solve linear equations in one variable, including those for which the application of the distributive property is necessary and for which variables are included on both sides;
- B solve linear inequalities in one variable, including those for which the application of the distributive property is necessary and for which variables are included on both sides; and
- C solve systems of two linear equations with two variables for mathematical and real-world problems.

4 The student will demonstrate an understanding of how to describe, write, and solve quadratic functions and equations.

A.6 The student applies the mathematical process standards when using properties of quadratic functions to write and represent in multiple ways, with and without technology, quadratic equations.
- A determine the domain and range of quadratic functions and represent the domain and range using inequalities;
- B write equations of quadratic functions given the vertex and another point on the graph, write the equation in vertex form (f(x) = a(x - h)²+ k), and rewrite the equation from vertex form to standard form (f(x) = ax²+ bx + c); and
- C write quadratic functions when given real solutions and graphs of their related equations.
  - Match quadratic functions and graphs (A2-N.7)
  - Write a quadratic function from its zeros (A2-N.10)
A.7 The student applies the mathematical process standards when using graphs of quadratic functions and their related transformations to represent in multiple ways and determine, with and without technology, the solutions to equations.
- A graph quadratic functions on the coordinate plane and use the graph to identify key attributes, if possible, including x-intercept, y-intercept, zeros, maximum value, minimum values, vertex, and the equation of the axis of symmetry;
- B describe the relationship between the linear factors of quadratic expressions and the zeros of their associated quadratic functions; and
  - Solve a quadratic equation using the zero product property (A1-Z.2)
  - Solve a quadratic equation by factoring (A1-Z.3)
- C determine the effects on the graph of the parent function f(x) = x² when f(x) is replaced by af(x), f(x) + d, f(x - c), f(bx) for specific values of a, b, c, and d.
  - Transformations of quadratic functions (A1-Y.4)
A.8 The student applies the mathematical process standards to solve, with and without technology, quadratic equations and evaluate the reasonableness of their solutions. The student formulates statistical relationships and evaluates their reasonableness based on real-world data.
- A solve quadratic equations having real solutions by factoring, taking square roots, completing the square, and applying the quadratic formula; and
- B write, using technology, quadratic functions that provide a reasonable fit to data to estimate solutions and make predictions for real-world problems.

5 The student will demonstrate an understanding of how to describe and write exponential functions and equations.

A.9 The student applies the mathematical process standards when using properties of exponential functions and their related transformations to write, graph, and represent in multiple ways exponential equations and evaluate, with and without technology, the reasonableness of their solutions. The student formulates statistical relationships and evaluates their reasonableness based on real-world data.
- A determine the domain and range of exponential functions of the form f(x) = ab to the x power and represent the domain and range using inequalities;
- B interpret the meaning of the values of a and b in exponential functions of the form f(x) = ab to the x power in real-world problems;
  - Exponential growth and decay: word problems (A1-V.9)
- C write exponential functions in the form f(x) = ab to the x power (where b is a rational number) to describe problems arising from mathematical and real-world situations, including growth and decay;
  - Exponential growth and decay: word problems (A1-V.9)
- D graph exponential functions that model growth and decay and identify key features, including y-intercept and asymptote, in mathematical and real-world problems; and
  - Match exponential functions and graphs II (A1-V.4)
- E write, using technology, exponential functions that provide a reasonable fit to data and make predictions for real-world problems.

These student expectations will not be listed under a separate reporting category. Instead, they will be incorporated into test questions across reporting categories since the application of mathematical process standards is part of each knowledge statement.

2A.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;
- 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;
- 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;
- D communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate;
- E create and use representations to organize, record, and communicate mathematical ideas;
- F analyze mathematical relationships to connect and communicate mathematical ideas; and
- G display, explain, or justify mathematical ideas and arguments using precise mathematical language in written or oral communication.

1 The student will demonstrate an understanding of how to use algebraic methods to manipulate numbers, expressions, and equations.

2A.7 The student applies mathematical processes to simplify and perform operations on expressions and to solve equations.
- A add, subtract, and multiply complex numbers;
- B add, subtract, and multiply polynomials;
  - Add and subtract polynomials (A2-L.2)
  - Multiply polynomials (A2-L.3)
- 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;
  - Divide polynomials using long division (A2-L.4)
  - Divide polynomials using synthetic division (A2-L.5)
- D determine the linear factors of a polynomial function of degree three and of degree four using algebraic methods;
  - Factor polynomials (A2-M.9)
- 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;
- F determine the sum, difference, product, and quotient of rational expressions with integral exponents of degree one and of degree two;
  - Multiply and divide rational expressions (A2-X.5)
  - Add and subtract rational expressions (A2-X.6)
- G rewrite radical expressions that contain variables to equivalent forms;
  - Simplify radical expressions with variables I (A2-R.4)
  - Simplify radical expressions with variables II (A2-R.5)
- H solve equations involving rational exponents; and
- I write the domain and range of a function in interval notation, inequalities, and set notation.
  - Domain and range of radical functions (A2-S.1)
  - Domain and range of logarithmic functions (A2-BB.1)

2 The student will demonstrate an understanding of how to describe and graph various functions and their inverses.

2A.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;
- B graph and write the inverse of a function using notation such as f-¹ (x);
- 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
- D use the composition of two functions, including the necessary restrictions on the domain, to determine if the functions are inverses of each other.
  - Identify inverse functions (A2-V.1)
  - Find inverse functions and relations (A2-V.4)
2A.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;
- 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
  - Find the equation of a regression line (A2-SS.4)
- C predict and make decisions and critical judgments from a given set of data using linear, quadratic, and exponential models.
  - Interpret regression lines (A2-SS.5)
  - Analyze a regression line of a data set (A2-SS.6)

3 The student will demonstrate an understanding of how to write and solve systems of equations and inequalities.

2A.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;
- B solve systems of three linear equations in three variables by using Gaussian elimination, technology with matrices, and substitution;
- C solve, algebraically, systems of two equations in two variables consisting of a linear equation and a quadratic equation;
  - Solve a nonlinear system of equations (A2-P.4)
- D determine the reasonableness of solutions to systems of a linear equation and a quadratic equation 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
- G determine possible solutions in the solution set of systems of two or more linear inequalities in two variables.
  - Is (x, y) a solution to the system of inequalities? (A2-F.3)

4 The student will demonstrate an understanding of how to describe, write, and solve quadratic and square root functions, equations, and inequalities.

2A.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;
  - Write a quadratic function from its zeros (A2-N.10)
- B write the equation of a parabola using given attributes, including vertex, focus, directrix, axis of symmetry, and direction of opening;
  - Write equations of parabolas in vertex form from graphs (A2-DD.5)
  - Write equations of parabolas in vertex form using properties (A2-DD.6)
- 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;
  - Domain and range of square root functions: graphs (A1-FF.2)
- 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);
- E formulate quadratic and square root equations using technology given a table of data;
- F solve quadratic and square root equations;
- G identify extraneous solutions of square root equations; and
- H solve quadratic inequalities.
  - Graph solutions to quadratic inequalities (A2-O.9)
  - Solve quadratic inequalities (A2-O.10)

5 The student will demonstrate an understanding of how to describe, write, and solve exponential and logarithmic functions and equations.

2A.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;
- B formulate exponential and logarithmic equations that model real-world situations, including exponential relationships written in recursive notation;
- C rewrite exponential equations as their corresponding logarithmic equations and logarithmic equations as their corresponding exponential equations;
- 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
- E determine the reasonableness of a solution to a logarithmic equation.

6 The student will demonstrate an understanding of how to describe, write, and solve cubic, cube root, absolute value, and rational functions, equations, and inequalities.

2A.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;
  - Function transformation rules (A2-W.1)
  - Describe function transformations (A2-W.6)
- B solve cube root equations that have real roots;
  - Solve radical equations (A2-S.4)
- 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;
  - Domain and range of square root functions: graphs (A1-FF.2)
- D formulate absolute value linear equations;
- E solve absolute value linear equations;
- F solve absolute value linear inequalities;
  - Graph solutions to two-variable absolute value inequalities (A2-H.5)
- 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;
  - Function transformation rules (A2-W.1)
  - Describe function transformations (A2-W.6)
- H formulate rational equations that model real-world situations;
- I solve rational equations that have real solutions;
  - Solve rational equations (A2-X.8)
- J determine the reasonableness of a solution to a rational equation;
- 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
  - Rational functions: asymptotes and excluded values (A2-X.1)
- L formulate and solve equations involving inverse variation.

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These student expectations will not be listed under a separate reporting category. Instead, they will be incorporated into test questions across reporting categories since the application of mathematical process standards is part of each knowledge statement.

A.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;

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;

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;

D communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate;

E create and use representations to organize, record, and communicate mathematical ideas;

F analyze mathematical relationships to connect and communicate mathematical ideas; and

G display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.

1 The student will demonstrate an understanding of how to use algebraic methods to manipulate numbers, expressions, and equations.

A.10 The student applies the mathematical process standards and algebraic methods to rewrite in equivalent forms and perform operations on polynomial expressions.

A add and subtract polynomials of degree one and degree two;

B multiply polynomials of degree one and degree two;

C determine the quotient of a polynomial of degree one and polynomial of degree two when divided by a polynomial of degree one and polynomial of degree two when the degree of the divisor does not exceed the degree of the dividend;

D rewrite polynomial expressions of degree one and degree two in equivalent forms using the distributive property;

E factor, if possible, trinomials with real factors in the form ax² + bx + c, including perfect square trinomials of degree two; and

F decide if a binomial can be written as the difference of two squares and, if possible, use the structure of a difference of two squares to rewrite the binomial.

A.11 The student applies the mathematical process standards and algebraic methods to rewrite algebraic expressions into equivalent forms.

A simplify numerical radical expressions involving square roots; and

B simplify numeric and algebraic expressions using the laws of exponents, including integral and rational exponents.

A.12 The student applies the mathematical process standards and algebraic methods to write, solve, analyze, and evaluate equations, relations, and functions.

A decide whether relations represented verbally, tabularly, graphically, and symbolically define a function;

B evaluate functions, expressed in function notation, given one or more elements in their domains;

C identify terms of arithmetic and geometric sequences when the sequences are given in function form using recursive processes;

D write a formula for the nth term of arithmetic and geometric sequences, given the value of several of their terms; and

E solve mathematic and scientific formulas, and other literal equations, for a specified variable.

2 The student will demonstrate an understanding of how to describe and graph linear functions, equations, and inequalities.

A.3 The student applies the mathematical process standards when using graphs of linear functions, key features, and related transformations to represent in multiple ways and solve, with and without technology, equations, inequalities, and systems of equations.

A determine the slope of a line given a table of values, a graph, two points on the line, and an equation written in various forms, including y = mx + b, Ax + By = C, and y - y? = m(x - x?);

B calculate the rate of change of a linear function represented tabularly, graphically, or algebraically in context of mathematical and real-world problems;

C graph linear functions on the coordinate plane and identify key features, including x-intercept, y-intercept, zeros, and slope, in mathematical and real-world problems;

D graph the solution set of linear inequalities in two variables on the coordinate plane;

E determine the effects on the graph of the parent function f(x) = x when f(x) is replaced by af(x), f(x) + d, f(x - c), f(bx) for specific values of a, b, c, and d;

F graph systems of two linear equations in two variables on the coordinate plane and determine the solutions if they exist;

G estimate graphically the solutions to systems of two linear equations with two variables in real-world problems; and

H graph the solution set of systems of two linear inequalities in two variables on the coordinate plane.

A.4 The student applies the mathematical process standards to formulate statistical relationships and evaluate their reasonableness based on real-world data.

A calculate, using technology, the correlation coefficient between two quantitative variables and interpret this quantity as a measure of the strength of the linear association;

B compare and contrast association and causation in real-world problems; and

C write, with and without technology, linear functions that provide a reasonable fit to data to estimate solutions and make predictions for real-world problems.

3 The student will demonstrate an understanding of how to write and solve linear functions, equations, and inequalities.

A.2 The student applies the mathematical process standards when using properties of linear functions to write and represent in multiple ways, with and without technology, linear equations, inequalities, and systems of equations.

A determine the domain and range of a linear function in mathematical problems; determine reasonable domain and range values for real-world situations, both continuous and discrete; and represent domain and range using inequalities;

B write linear equations in two variables in various forms, including y = mx + b, Ax + By = C, and y - y? = m(x - x?), given one point and the slope and given two points;

C write linear equations in two variables given a table of values, a graph, and a verbal description;

D write and solve equations involving direct variation;

E write the equation of a line that contains a given point and is parallel to a given line;

F write the equation of a line that contains a given point and is perpendicular to a given line;

G write an equation of a line that is parallel or perpendicular to the X or Y axis and determine whether the slope of the line is zero or undefined;

H write linear inequalities in two variables given a table of values, a graph, and a verbal description; and

I write systems of two linear equations given a table of values, a graph, and a verbal description.

A.5 The student applies the mathematical process standards to solve, with and without technology, linear equations and evaluate the reasonableness of their solutions.

A solve linear equations in one variable, including those for which the application of the distributive property is necessary and for which variables are included on both sides;

B solve linear inequalities in one variable, including those for which the application of the distributive property is necessary and for which variables are included on both sides; and

C solve systems of two linear equations with two variables for mathematical and real-world problems.

4 The student will demonstrate an understanding of how to describe, write, and solve quadratic functions and equations.

A.6 The student applies the mathematical process standards when using properties of quadratic functions to write and represent in multiple ways, with and without technology, quadratic equations.

A determine the domain and range of quadratic functions and represent the domain and range using inequalities;

B write equations of quadratic functions given the vertex and another point on the graph, write the equation in vertex form (f(x) = a(x - h)²+ k), and rewrite the equation from vertex form to standard form (f(x) = ax²+ bx + c); and

C write quadratic functions when given real solutions and graphs of their related equations.

A.7 The student applies the mathematical process standards when using graphs of quadratic functions and their related transformations to represent in multiple ways and determine, with and without technology, the solutions to equations.

A graph quadratic functions on the coordinate plane and use the graph to identify key attributes, if possible, including x-intercept, y-intercept, zeros, maximum value, minimum values, vertex, and the equation of the axis of symmetry;

B describe the relationship between the linear factors of quadratic expressions and the zeros of their associated quadratic functions; and

C determine the effects on the graph of the parent function f(x) = x² when f(x) is replaced by af(x), f(x) + d, f(x - c), f(bx) for specific values of a, b, c, and d.

A.8 The student applies the mathematical process standards to solve, with and without technology, quadratic equations and evaluate the reasonableness of their solutions. The student formulates statistical relationships and evaluates their reasonableness based on real-world data.

A solve quadratic equations having real solutions by factoring, taking square roots, completing the square, and applying the quadratic formula; and

B write, using technology, quadratic functions that provide a reasonable fit to data to estimate solutions and make predictions for real-world problems.

5 The student will demonstrate an understanding of how to describe and write exponential functions and equations.

A determine the domain and range of exponential functions of the form f(x) = ab to the x power and represent the domain and range using inequalities;

B interpret the meaning of the values of a and b in exponential functions of the form f(x) = ab to the x power in real-world problems;

C write exponential functions in the form f(x) = ab to the x power (where b is a rational number) to describe problems arising from mathematical and real-world situations, including growth and decay;

D graph exponential functions that model growth and decay and identify key features, including y-intercept and asymptote, in mathematical and real-world problems; and

E write, using technology, exponential functions that provide a reasonable fit to data and make predictions for real-world problems.

These student expectations will not be listed under a separate reporting category. Instead, they will be incorporated into test questions across reporting categories since the application of mathematical process standards is part of each knowledge statement.

2A.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;

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;