Algebra II

Other Texas Mathematics sets

• Grade K
• Grade 1
• Grade 2
• Grade 3
• Grade 4
• Grade 5
• Grade 6
• Grade 7
• Algebra I (2012)
• Grade 8
• Algebraic Reasoning
• Discrete Mathematics
• Grade 9
• Statistics
• Advanced Quantitative Reasoning
• Geometry (2012)
• Grades 10, 11, 12
• Independent Study in Mathematics
• Mathematical Models with Applications
• Precalculus

The student applies mathematical processes to understand that functions have distinct key attributes and understand the relationship between a function and its inverseAII.2

graph the functions f(x)=√x, f(x)=1/x, f(x)=x³, f(x)= ³√x, f(x)=bx, 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 intervalAII.2.A

graph and write the inverse of a function using notation such as f-1 (x)AII.2.B

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 rangeAII.2.C

use the composition of two functions, including the necessary restrictions on the domain, to determine if the functions are inverses of each otherAII.2.D

The student applies mathematical processes to formulate systems of equations and inequalities, use a variety of methods to solve, and analyze reasonableness of solutionsAII.3

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 quadraticAII.3.A

solve systems of three linear equations in three variables by using Gaussian elimination, technology with matrices, and substitutionAII.3.B

solve, algebraically, systems of two equations in two variables consisting of a linear equation and a quadratic equationAII.3.C

determine the reasonableness of solutions to systems of a linear equation and a quadratic equation in two variablesAII.3.D

formulate systems of at least two linear inequalities in two variablesAII.3.E

solve systems of two or more linear inequalities in two variablesAII.3.F

determine possible solutions in the solution set of systems of two or more linear inequalities in two variablesAII.3.G

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 predictionsAII.4

write the quadratic function given three specified points in the planeAII.4.A

write the equation of a parabola using given attributes, including vertex, focus, directrix, axis of symmetry, and direction of openingAII.4.B

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 dAII.4.C

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)AII.4.D

formulate quadratic and square root equations using technology given a table of dataAII.4.E

solve quadratic and square root equationsAII.4.F

identify extraneous solutions of square root equationsAII.4.G

solve quadratic inequalitiesAII.4.H

The student applies mathematical processes to understand that exponential and logarithmic functions can be used to model situations and solve problemsAII.5

determine the effects on the key attributes on the graphs of f(x) = b^x 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 dAII.5.A

formulate exponential and logarithmic equations that model real-world situations, including exponential relationships written in recursive notationAII.5.B

rewrite exponential equations as their corresponding logarithmic equations and logarithmic equations as their corresponding exponential equationsAII.5.C

solve exponential equations of the form y = ab^x where a is a nonzero real number and b is greater than zero and not equal to one and single logarithmic equations having real solutionsAII.5.D

determine the reasonableness of a solution to a logarithmic equationAII.5.E

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 predictionsAII.6

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 dAII.6.A

solve cube root equations that have real rootsAII.6.B

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 dAII.6.C

formulate absolute value linear equationsAII.6.D

solve absolute value linear equationsAII.6.E

solve absolute value linear inequalitiesAII.6.F

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 dAII.6.G

formulate rational equations that model real-world situationsAII.6.H

solve rational equations that have real solutionsAII.6.I

determine the reasonableness of a solution to a rational equationAII.6.J

determine the asymptotic restrictions on the domain of a rational function and represent domain and range using interval notation, inequalities, and set notationAII.6.K

formulate and solve equations involving inverse variationAII.6.L

The student applies mathematical processes to simplify and perform operations on expressions and to solve equationsAII.7

add, subtract, and multiply complex numbersAII.7.A

add, subtract, and multiply polynomialsAII.7.B

determine the quotient of a polynomial of degree three and of degree four when divided by a polynomial of degree one and of degree twoAII.7.C

determine the linear factors of a polynomial function of degree three and of degree four using algebraic methods.7.D

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.7.E

determine the sum, difference, product, and quotient of rational expressions with integral exponents of degree one and of degree two.7.F

rewrite radical expressions that contain variables to equivalent formsAII.7.G

solve equations involving rational exponentsAII.7.H

write the domain and range of a function in interval notation, inequalities, and set notationAII.7.I

The student applies mathematical processes to analyze data, select appropriate models, write corresponding functions, and make predictionsAII.8

analyze data to select the appropriate model from among linear, quadratic, and exponential modelsAII.8.A

use regression methods available through technology to write a linear function, a quadratic function, and an exponential function from a given set of dataAII.8.B

predict and make decisions and critical judgments from a given set of data using linear, quadratic, and exponential modelsAII.8.C