Algebra II (Texas TEKS)

111.40(c)(1) Mathematical process standards

• 111.40(c)(1) Student applies mathematical processes to build and show understanding: real-world use, problem solving, tools, representations, communication, and justification.
• 111.40(c)(1)(A) Use mathematics to solve problems that come up in daily life, society, and the workplace.
• 111.40(c)(1)(B) Follow a problem-solving model: analyze the information, plan, solve, justify, and check that the answer makes sense.
• 111.40(c)(1)(C) Choose suitable tools, such as technology, paper and pencil, or estimation, and suitable techniques to solve problems.
• 111.40(c)(1)(D) Share mathematical ideas and reasoning through symbols, diagrams, graphs, and words.
• 111.40(c)(1)(E) Build and use representations to organize, record, and communicate mathematical ideas.
• 111.40(c)(1)(F) Look for relationships between mathematical ideas to connect and explain them.
• 111.40(c)(1)(G) Present, explain, and justify mathematical ideas and arguments with precise language, spoken or written.

111.40(c)(2) Attributes of functions and their inverses

• 111.40(c)(2) Student understands that functions have key attributes and how a function relates to its inverse.
• 111.40(c)(2)(A) Graph the listed parent functions and analyze key attributes such as domain, range, intercepts, symmetry, and asymptotes over set intervals.
• 111.40(c)(2)(B) Graph the inverse of a function and write it using inverse function notation.
• 111.40(c)(2)(C) Describe how a function and its inverse are related, including any domain restrictions needed.
• 111.40(c)(2)(D) Use composition, with domain restrictions where needed, to check whether two functions are inverses.

111.40(c)(3) Systems of equations and inequalities

• 111.40(c)(3) Student writes systems, solves them by several methods, and judges whether solutions are reasonable.
• 111.40(c)(3)(A) Set up a system of three linear equations, or of one linear and one quadratic equation, to model a situation.
• 111.40(c)(3)(B) Solve systems of three linear equations in three variables by elimination, matrices with technology, or substitution.
• 111.40(c)(3)(C) Solve a system made of one linear and one quadratic equation in two variables algebraically.
• 111.40(c)(3)(D) Decide whether the solutions of a linear-quadratic system make sense in context.
• 111.40(c)(3)(E) Set up systems of at least two linear inequalities in two variables.
• 111.40(c)(3)(F) Solve systems of two or more linear inequalities in two variables.
• 111.40(c)(3)(G) Find possible solutions that lie in the solution region of a system of linear inequalities.

111.40(c)(4) Quadratic and square root functions, equations, and inequalities

• 111.40(c)(4) Student uses quadratic and square root functions, equations, and inequalities to model situations, solve problems, and predict.
• 111.40(c)(4)(A) Write the quadratic function that passes through three given points.
• 111.40(c)(4)(B) Write the equation of a parabola from its vertex, focus, directrix, axis of symmetry, and direction of opening.
• 111.40(c)(4)(C) Describe how changing parameters, positive and negative, transforms the graph of the square root function.
• 111.40(c)(4)(D) Rewrite a quadratic in vertex form by completing the square and use it to name key attributes.
• 111.40(c)(4)(E) Use technology to write quadratic and square root equations that model data in a table.
• 111.40(c)(4)(F) Solve quadratic equations and square root equations.
• 111.40(c)(4)(G) Spot extraneous solutions when solving square root equations.
• 111.40(c)(4)(H) Solve quadratic inequalities.

111.40(c)(5) Exponential and logarithmic functions and equations

• 111.40(c)(5) Student uses exponential and logarithmic functions and equations to model situations and solve problems.
• 111.40(c)(5)(A) Describe how changing parameters transforms the graphs of exponential and logarithmic parent functions.
• 111.40(c)(5)(B) Write exponential and logarithmic equations, including recursive forms, that model real situations.
• 111.40(c)(5)(C) Rewrite exponential equations as logarithmic equations and the reverse.
• 111.40(c)(5)(D) Solve exponential equations and logarithmic equations with a single log that have real solutions.
• 111.40(c)(5)(E) Judge whether a solution to a logarithmic equation makes sense.

111.40(c)(6) Cubic, cube root, absolute value and rational functions, equations, and inequalities

• 111.40(c)(6) Student uses cubic, cube root, absolute value, and rational functions and equations to model situations, solve problems, and predict.
• 111.40(c)(6)(A) Describe how changing parameters transforms the graphs of the cubic and cube root parent functions.
• 111.40(c)(6)(B) Solve cube root equations with real roots.
• 111.40(c)(6)(C) Describe how changing parameters transforms the graph of the absolute value parent function.
• 111.40(c)(6)(D) Write absolute value linear equations.
• 111.40(c)(6)(E) Solve absolute value linear equations.
• 111.40(c)(6)(F) Solve absolute value linear inequalities.
• 111.40(c)(6)(G) Describe how changing parameters transforms the graph of the reciprocal function f(x) = 1/x.
• 111.40(c)(6)(H) Write rational equations that model real-world situations.
• 111.40(c)(6)(I) Solve rational equations that have real solutions.
• 111.40(c)(6)(J) Judge whether a solution to a rational equation makes sense.
• 111.40(c)(6)(K) Find domain restrictions caused by asymptotes and write domain and range in several notations.
• 111.40(c)(6)(L) Write and solve equations for inverse variation.

111.40(c)(7) Number and algebraic methods

• 111.40(c)(7) Student simplifies and operates on expressions and solves equations using algebraic methods.
• 111.40(c)(7)(A) Add, subtract, and multiply complex numbers.
• 111.40(c)(7)(B) Add, subtract, and multiply polynomials.
• 111.40(c)(7)(C) Divide a degree-three or degree-four polynomial by a polynomial of degree one or two.
• 111.40(c)(7)(D) Find the linear factors of degree-three and degree-four polynomial functions algebraically.
• 111.40(c)(7)(E) Factor degree-three and degree-four expressions into linear and quadratic factors, including sums and differences of cubes and grouping.
• 111.40(c)(7)(F) Add, subtract, multiply, and divide rational expressions with degree-one and degree-two numerators and denominators.
• 111.40(c)(7)(G) Rewrite radical expressions with variables in equivalent forms.
• 111.40(c)(7)(H) Solve equations that contain rational exponents.
• 111.40(c)(7)(I) Write the domain and range of a function in interval, inequality, and set-builder notation.

111.40(c)(8) Data

• 111.40(c)(8) Student analyzes data, chooses a suitable model, writes functions, and makes predictions.
• 111.40(c)(8)(A) Analyze data to decide whether a linear, quadratic, or exponential model fits best.
• 111.40(c)(8)(B) Use regression on technology to write linear, quadratic, and exponential functions from data.
• 111.40(c)(8)(C) Use regression models to predict and make critical judgments in real situations.