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 |
