Algebra I (Texas TEKS)

111.39(c)(1) Mathematical process standards

• 111.39(c)(1) Student applies mathematical processes to acquire and demonstrate understanding: real-world application, problem-solving model, tools, representations, communication, and justification.
• 111.39(c)(1)(A) Apply mathematics to problems from everyday life, society, and the workplace.
• 111.39(c)(1)(B) Use a problem-solving model: analyze information, plan, solve, justify, and evaluate reasonableness.
• 111.39(c)(1)(C) Select appropriate tools and techniques, such as technology or mental math, to solve problems.
• 111.39(c)(1)(D) Communicate ideas and reasoning using multiple representations such as symbols, diagrams, graphs, and language.
• 111.39(c)(1)(E) Create and use representations to organize, record, and communicate mathematical ideas.
• 111.39(c)(1)(F) Analyze mathematical relationships to connect and communicate mathematical ideas.
• 111.39(c)(1)(G) Display, explain, and justify ideas and arguments using precise mathematical language.

111.39(c)(2) Linear functions, equations, and inequalities

• 111.39(c)(2) Student uses linear function properties to write and represent linear equations, inequalities, and systems in multiple ways.
• 111.39(c)(2)(A) Determine and represent domain and range of linear functions in math and real-world contexts.
• 111.39(c)(2)(B) Write linear equations in two variables from one point and slope, or from two points, in various forms.
• 111.39(c)(2)(C) Write linear equations from a table, graph, or verbal description.
• 111.39(c)(2)(D) Write and solve direct variation equations.
• 111.39(c)(2)(E) Write the equation of a line through a given point parallel to a given line.
• 111.39(c)(2)(F) Write the equation of a line through a given point perpendicular to a given line.
• 111.39(c)(2)(G) Write equations of lines parallel or perpendicular to an axis and determine if slope is zero or undefined.
• 111.39(c)(2)(H) Write linear inequalities in two variables from a table, graph, or verbal description.
• 111.39(c)(2)(I) Write systems of two linear equations from a table, graph, or verbal description.

111.39(c)(3) Linear functions, equations, and inequalities

• 111.39(c)(3) Student uses graphs of linear functions and transformations to represent and solve equations, inequalities, and systems.
• 111.39(c)(3)(A) Determine slope from a table, graph, two points, or equations in various forms.
• 111.39(c)(3)(B) Calculate the rate of change of a linear function in tabular, graphical, or algebraic form.
• 111.39(c)(3)(C) Graph linear functions and identify key features such as intercepts, zeros, and slope.
• 111.39(c)(3)(D) Graph solution sets of linear inequalities in two variables.
• 111.39(c)(3)(E) Determine effects on the graph of f(x) = x when transformed by af(x), f(x)+d, f(x-c), f(bx).
• 111.39(c)(3)(F) Graph systems of two linear equations and determine solutions if they exist.
• 111.39(c)(3)(G) Estimate graphically the solutions to systems of two linear equations in real-world problems.
• 111.39(c)(3)(H) Graph solution sets of systems of two linear inequalities on the coordinate plane.

111.39(c)(4) Linear functions, equations, and inequalities

• 111.39(c)(4) Student formulates statistical relationships from real-world data and evaluates their reasonableness.
• 111.39(c)(4)(A) Calculate the correlation coefficient with technology and interpret it as strength of linear association.
• 111.39(c)(4)(B) Compare and contrast association and causation in real-world problems.
• 111.39(c)(4)(C) Write linear functions that reasonably fit data to estimate and predict in real-world problems.

111.39(c)(5) Linear functions, equations, and inequalities

• 111.39(c)(5) Student solves linear equations, inequalities, and systems and evaluates the reasonableness of solutions.
• 111.39(c)(5)(A) Solve linear equations in one variable, including distributive property and variables on both sides.
• 111.39(c)(5)(B) Solve linear inequalities in one variable, including distributive property and variables on both sides.
• 111.39(c)(5)(C) Solve systems of two linear equations with two variables for math and real-world problems.

111.39(c)(6) Quadratic functions and equations

• 111.39(c)(6) Student uses properties of quadratic functions to write and represent quadratic equations in multiple ways.
• 111.39(c)(6)(A) Determine and represent the domain and range of quadratic functions using inequalities.
• 111.39(c)(6)(B) Write quadratic equations from a vertex and another point, and convert between vertex and standard forms.
• 111.39(c)(6)(C) Write quadratic functions given real solutions and graphs of related equations.

111.39(c)(7) Quadratic functions and equations

• 111.39(c)(7) Student graphs quadratic functions and transformations to identify key attributes and determine solutions.
• 111.39(c)(7)(A) Graph quadratics and identify intercepts, zeros, maximum or minimum, vertex, and axis of symmetry.
• 111.39(c)(7)(B) Describe the relationship between linear factors of quadratic expressions and zeros of their functions.
• 111.39(c)(7)(C) Determine effects on the graph of f(x) = x² when transformed by af(x), f(x)+d, f(x-c), f(bx).

111.39(c)(8) Quadratic functions and equations

• 111.39(c)(8) Student solves quadratic equations and writes quadratic functions that fit real-world data to make predictions.
• 111.39(c)(8)(A) Solve quadratic equations with real solutions by factoring, square roots, completing the square, or formula.
• 111.39(c)(8)(B) Write quadratic functions with technology that reasonably fit data to estimate and predict.

111.39(c)(9) Exponential functions and equations

• 111.39(c)(9) Student uses exponential functions and transformations to write, graph, and solve models and evaluates solution reasonableness.
• 111.39(c)(9)(A) Determine and represent the domain and range of exponential functions f(x) = abˣ using inequalities.
• 111.39(c)(9)(B) Interpret the meaning of a and b in exponential functions in real-world problems.
• 111.39(c)(9)(C) Write exponential functions, including growth and decay, to describe math and real-world situations.
• 111.39(c)(9)(D) Graph exponential growth and decay functions and identify y-intercept and asymptote.
• 111.39(c)(9)(E) Write exponential functions with technology that reasonably fit data and make predictions.

111.39(c)(10) Number and algebraic methods

• 111.39(c)(10) Student rewrites and performs operations on polynomial expressions of degree one and two using algebraic methods.
• 111.39(c)(10)(A) Add and subtract polynomials of degree one and degree two.
• 111.39(c)(10)(B) Multiply polynomials of degree one and degree two.
• 111.39(c)(10)(C) Divide a degree-one or degree-two polynomial by a lower or equal degree polynomial.
• 111.39(c)(10)(D) Rewrite degree one and two polynomial expressions in equivalent forms using the distributive property.
• 111.39(c)(10)(E) Factor trinomials with real factors, including perfect square trinomials, when possible.
• 111.39(c)(10)(F) Decide if a binomial is a difference of squares and, if so, rewrite it using that structure.

111.39(c)(11) Number and algebraic methods

• 111.39(c)(11) Student rewrites radical and exponent expressions into equivalent forms.
• 111.39(c)(11)(A) Simplify numerical radical expressions involving square roots.
• 111.39(c)(11)(B) Simplify numeric and algebraic expressions using laws of exponents, including integral and rational exponents.

111.39(c)(12) Number and algebraic methods

• 111.39(c)(12) Student writes, solves, analyzes, and evaluates equations, relations, and functions, including sequences and formulas.
• 111.39(c)(12)(A) Decide whether verbal, tabular, graphical, or symbolic relations define a function.
• 111.39(c)(12)(B) Evaluate functions in function notation given one or more elements of their domains.
• 111.39(c)(12)(C) Identify terms of arithmetic and geometric sequences given in recursive function form.
• 111.39(c)(12)(D) Write a formula for the nth term of arithmetic and geometric sequences from several terms.
• 111.39(c)(12)(E) Solve mathematical and scientific formulas and other literal equations for a specified variable.