State of Texas Assessments of Academic Readiness Resources

MP.2A.1.A: The student is expected to: apply mathematics to problems arising in everyday life, society, and the workplace;

Determining a Spring Constant

Estimating Population Size

MP.2A.1.B: The student is expected to: 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;

MP.2A.1.D: The student is expected to: communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate;

Biconditional Statements

Using Algebraic Expressions

MP.2A.1.E: The student is expected to: create and use representations to organize, record, and communicate mathematical ideas;

Describing Data Using Statistics

Stem-and-Leaf Plots

Using Algebraic Expressions

MP.2A.1.G: The student is expected to: display, explain, or justify mathematical ideas and arguments using precise mathematical language in written or oral communication.

1.2A.7.A: The student is expected to: add, subtract, and multiply complex numbers;

1.2A.7.B: The student is expected to: add, subtract, and multiply polynomials;

Addition and Subtraction of Functions

Addition of Polynomials

Modeling the Factorization of *x*^{2}+*bx*+*c*

1.2A.7.C: The student is expected to: 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;

Dividing Polynomials Using Synthetic Division

1.2A.7.D: The student is expected to: determine the linear factors of a polynomial function of degree three and of degree four using algebraic methods;

Factoring Special Products

Modeling the Factorization of *ax*^{2}+*bx*+*c*

Modeling the Factorization of *x*^{2}+*bx*+*c*

1.2A.7.E: The student is expected to: 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;

Factoring Special Products

Modeling the Factorization of *ax*^{2}+*bx*+*c*

Modeling the Factorization of *x*^{2}+*bx*+*c*

1.2A.7.G: The student is expected to: rewrite radical expressions that contain variables to equivalent forms;

Simplifying Radical Expressions

2.2A.2.A: The student is expected to: graph the functions f(x) = the square root of x, f(x) = 1/x, f(x) = x³, f(x) = the cube root of x, f(x) = b to the x power, 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;

Absolute Value with Linear Functions

Compound Interest

Exponential Functions

General Form of a Rational Function

Graphs of Polynomial Functions

Introduction to Exponential Functions

Logarithmic Functions

Radical Functions

Rational Functions

Translating and Scaling Functions

2.2A.2.B: The student is expected to: graph and write the inverse of a function using notation such as f-¹(x);

2.2A.2.C: The student is expected to: 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; and

2.2A.8.B: The student is expected to: use regression methods available through technology to write a linear function, a quadratic function, and an exponential function from a given set of data; and

Least-Squares Best Fit Lines

Solving Using Trend Lines

3.2A.3.A: The student is expected to: 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;

Solving Equations by Graphing Each Side

Solving Linear Systems (Matrices and Special Solutions)

Solving Linear Systems (Standard Form)

3.2A.3.F: The student is expected to: solve systems of two or more linear inequalities in two variables; and

Linear Programming

Systems of Linear Inequalities (Slope-intercept form)

3.2A.3.G: The student is expected to: determine possible solutions in the solution set of systems of two or more linear inequalities in two variables.

Linear Programming

Systems of Linear Inequalities (Slope-intercept form)

4.2A.4.B: The student is expected to: write the equation of a parabola using given attributes, including vertex, focus, directrix, axis of symmetry, and direction of opening;

4.2A.4.C: The student is expected to: determine the effect on the graph of f(x) = the square root of 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;

4.2A.4.D: The student is expected to: 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);

Circles

Exponential Functions

Quadratics in Vertex Form

Translating and Scaling Functions

Zap It! Game

4.2A.4.E: The student is expected to: formulate quadratic and square root equations using technology given a table of data;

4.2A.4.F: The student is expected to: solve quadratic and square root equations;

Radical Functions

Roots of a Quadratic

4.2A.4.G: The student is expected to: identify extraneous solutions of square root equations; and

Operations with Radical Expressions

4.2A.4.H: The student is expected to: solve quadratic inequalities.

5.2A.5.A: The student is expected to: determine the effects on the key attributes on the graphs of f(x) = b to the x power 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;

Exponential Functions

Introduction to Exponential Functions

5.2A.5.B: The student is expected to: formulate exponential and logarithmic equations that model real-world situations, including exponential relationships written in recursive notation;

Arithmetic Sequences

Geometric Sequences

5.2A.5.C: The student is expected to: rewrite exponential equations as their corresponding logarithmic equations and logarithmic equations as their corresponding exponential equations;

5.2A.5.D: The student is expected to: solve exponential equations of the form y = ab to the x power 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; and

6.2A.6.A: The student is expected to: analyze the effect on the graphs of f(x) = x³ and f(x) = the cube root of 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;

Radical Functions

Translating and Scaling Functions

6.2A.6.C: The student is expected to: 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;

Absolute Value with Linear Functions

Translating and Scaling Functions

6.2A.6.D: The student is expected to: formulate absolute value linear equations;

Absolute Value Equations and Inequalities

Absolute Value with Linear Functions

6.2A.6.E: The student is expected to: solve absolute value linear equations;

Absolute Value Equations and Inequalities

Absolute Value with Linear Functions

6.2A.6.F: The student is expected to: solve absolute value linear inequalities;

Absolute Value Equations and Inequalities

Compound Inequalities

6.2A.6.G: The student is expected to: 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;

General Form of a Rational Function

Rational Functions

6.2A.6.H: The student is expected to: formulate rational equations that model real-world situations;

6.2A.6.K: The student is expected to: determine the asymptotic restrictions on the domain of a rational function and represent domain and range using interval notation, inequalities, and set notation; and

General Form of a Rational Function

Rational Functions

Correlation last revised: 4/2/2018

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.