Standardized Test Preparation



TEKS (Texas Essential Knowledge and Skills)


References: Texas Education Agency : STAAR Released Tests |

Algebra II - Grade 11

Assessment Exam - TEKS Algebra II
Mathematical process standards eTAP Lesson
The student uses mathematical processes to acquire and demonstrate mathematical understanding.
Apply mathematics to problems arising in everyday life, society, and the workplace
TX.MATH.111.40.1.A
 
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
TX.MATH.111.40.1.B
 
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
TX.MATH.111.40.1.C
 
Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate
TX.MATH.111.40.1.D
Functions as Graphs in the Coordinate System
Create and use representations to organize, record, and communicate mathematical ideas
TX.MATH.111.40.1.E
Visually Representing Numerical Data
Analyze mathematical relationships to connect and communicate mathematical ideas
TX.MATH.111.40.1.F
Showing the Overlap with Venn Diagrams
Display, explain, or justify mathematical ideas and arguments using precise mathematical language in written or oral communication
TX.MATH.111.40.1.G
 
Attributes of functions and their inverses eTAP Lesson
The student applies mathematical processes to understand that functions have distinct key attributes and understand the relationship between a function and its inverse.
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 interval
TX.MATH.111.40.2.A
Function Notation
Graph and write the inverse of a function using notation such as f -1 (x)
TX.MATH.111.40.2.B
Inverses of Linear Functions
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
TX.MATH.111.40.2.C
Simple Quadratic Functions
Use the composition of two functions, including the necessary restrictions on the domain, to determine if the functions are inverses of each other
TX.MATH.111.40.2.D
Inverse Variation
Systems of equations and inequalities eTAP Lesson
The student applies mathematical processes to formulate systems of equations and inequalities, use a variety of methods to solve, and analyze reasonableness of solutions.
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
TX.MATH.111.40.3.A
Solving Linear Systems with Matrices
Solve systems of three linear equations in three variables by using Gaussian elimination, technology with matrices, and substitution
TX.MATH.111.40.3.B
What are Matrices
Determine the reasonableness of solutions to systems of a linear equation and a quadratic equation in two variables
TX.MATH.111.40.3.D
Factoring Quadratics
Formulate systems of at least two linear inequalities in two variables
TX.MATH.111.40.3.E
Linear Parametric equations
Solve systems of two or more linear inequalities in two variables
TX.MATH.111.40.3.F
Adding Matrices
Determine possible solutions in the solution set of systems of two or more linear inequalities in two variables
TX.MATH.111.40.3.G
Subtracting Matrices
Quadratic and square root functions, equations, and inequalities eTAP Lesson
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.
Write the quadratic function given three specified points in the plane
TX.MATH.111.40.4.A
Factoring Quadratics
Write the equation of a parabola using given attributes, including vertex, focus, directrix, axis of symmetry, and direction of opening
TX.MATH.111.40.4.B
Parabolas
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
TX.MATH.111.40.4.C
Quadratic Functions in Intercept Form
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)
TX.MATH.111.40.4.D
Quadratic Formula
Formulate quadratic and square root equations using technology given a table of data
TX.MATH.111.40.4.E
Square Root Functions

Sum and Product of Roots
Solve quadratic and square root equations
TX.MATH.111.41.4.F
 
Identify extraneous solutions of square root equations
TX.MATH.111.40.4.G
Completing the Square
Solve quadratic inequalities
TX.MATH.111.40.4.H
Solving Quadratic Equations by Graphing
Exponential and logarithmic functions and equations eTAP Lesson
The student applies mathematical processes to understand that exponential and logarithmic functions can be used to model situations and solve problems.
Determine the effects on the key attributes on the graphs of f(x) = bx 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
TX.MATH.111.40.5.A
Negative and Rational Exponents

Inverses of Exponential Functions
Formulate exponential and logarithmic equations that model real-world situations, including exponential relationships written in recursive notation
TX.MATH.111.40.5.B
Exponential and Logarithmic Equations
Rewrite exponential equations as their corresponding logarithmic equations and logarithmic equations as their corresponding exponential equations
TX.MATH.111.40.5.C
The number e
Solve exponential equations of the form y = abx 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
TX.MATH.111.40.5.D
Graphs of Exponential Functions
Determine the reasonableness of a solution to a logarithmic equation
TX.MATH.111.40.5.E
Exponential and Logarithmic Equations
Cubic, cube root, absolute value and rational functions, equations, and inequalities eTAP Lesson
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.
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
TX.MATH.111.40.6.A
Solving Equations Using Several Operations
Solve cube root equations that have real roots
TX.MATH.111.40.6.B
Cubic Equations
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
TX.MATH.111.40.6.C
Graphs of Polynomial Functions
Formulate absolute value linear equations
TX.MATH.111.40.6.D
Absolute Value Inequalities
Solve absolute value linear equations
TX.MATH.111.40.6.E
Adding and Subtracting Integers
Solve absolute value linear inequalities
TX.MATH.111.40.6.F
Inequalities and the Number Line
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
TX.MATH.111.40.6.G
Graphs and Dipgrahs
Formulate rational equations that model real-world situations
TX.MATH.111.40.6.H
Function Notation
Solve rational equations that have real solutions
TX.MATH.111.40.6.I
Solving Rational Equations
Determine the reasonableness of a solution to a rational equation
TX.MATH.111.40.6.J
Solving Rational Equations
Determine the asymptotic restrictions on the domain of a rational function and represent domain and range using interval notation, inequalities, and set notation
TX.MATH.111.40.6.K
 
Formulate and solve equations involving inverse variation
TX.MATH.111.40.6.L
Inverse Variation
Number and algebraic methods eTAP Lesson
The student applies mathematical processes to simplify and perform operations on expressions and to solve equations.
Add, subtract, and multiply complex numbers
TX.MATH.111.40.7.A
Complex Numbers
Add, subtract, and multiply polynomials
TX.MATH.111.40.7.B
Multiplying and Dividing Polynomials
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
TX.MATH.111.40.7.C
Zeros of Polynomial Functions
Determine the linear factors of a polynomial function of degree three and of degree four using algebraic methods
TX.MATH.111.40.7.D
Cubic Equations
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
TX.MATH.111.40.7.E
Polynomials
Determine the sum, difference, product, and quotient of rational expressions with integral exponents of degree one and of degree two
TX.MATH.111.40.7.F
Adding and Subtracting Polynomials
Rewrite radical expressions that contain variables to equivalent forms
TX.MATH.111.40.7.G
Radical Functions
Solve equations involving rational exponents
TX.MATH.111.40.7.H
Negative and Rational Exponents
Write the domain and range of a function in interval notation, inequalities, and set notation
TX.MATH.111.40.7.I
Ordered Pairs
Data eTAP Lesson
The student applies mathematical processes to analyze data, select appropriate models, write corresponding functions, and make predictions.
Analyze data to select the appropriate model from among linear, quadratic, and exponential models
TX.MATH.111.40.8.A
Using Logarithms to Model Data
Use regression methods available through technology to write a linear function, a quadratic function, and an exponential function from a given set of data
TX.MATH.111.40.8.B
Regression Models and Least Square Methods
Predict and make decisions and critical judgments from a given set of data using linear, quadratic, and exponential models
TX.MATH.111.40.8.C
Exponential Functions and Data