State of Texas Assessments of Academic Readiness Resources

MP.A.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.A.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.A.1.C: The student is expected to: 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;

Estimating Sums and Differences

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

1.A.10.A: The student is expected to: add and subtract polynomials of degree one and degree two;

Addition and Subtraction of Functions

Addition of Polynomials

1.A.10.B: The student is expected to: multiply polynomials of degree one and degree two;

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

1.A.10.C: The student is expected to: determine the quotient of a polynomial of degree one and polynomial of degree two when divided by a polynomial of degree one and polynomial of degree two when the degree of the divisor does not exceed the degree of the dividend;

Dividing Polynomials Using Synthetic Division

1.A.10.D: The student is expected to: rewrite polynomial expressions of degree one and degree two in equivalent forms using the distributive property;

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

Simplifying Algebraic Expressions I

Simplifying Algebraic Expressions II

1.A.10.E: The student is expected to: factor, if possible, trinomials with real factors in the form ax² + bx + c, including perfect square trinomials of degree two; and

Factoring Special Products

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

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

1.A.10.F: The student is expected to: decide if a binomial can be written as the difference of two squares and, if possible, use the structure of a difference of two squares to rewrite the binomial.

1.A.11.A: The student is expected to: simplify numerical radical expressions involving square roots; and

Operations with Radical Expressions

Simplifying Radical Expressions

1.A.11.B: The student is expected to: simplify numeric and algebraic expressions using the laws of exponents, including integral and rational exponents.

Dividing Exponential Expressions

Exponents and Power Rules

Multiplying Exponential Expressions

Simplifying Algebraic Expressions II

1.A.12.A: The student is expected to: decide whether relations represented verbally, tabularly, graphically, and symbolically define a function;

Introduction to Functions

Linear Functions

Points, Lines, and Equations

1.A.12.B: The student is expected to: evaluate functions, expressed in function notation, given one or more elements in their domains;

1.A.12.C: The student is expected to: identify terms of arithmetic and geometric sequences when the sequences are given in function form using recursive processes;

Arithmetic Sequences

Geometric Sequences

1.A.12.D: The student is expected to: write a formula for the nth term of arithmetic and geometric sequences, given the value of several of their terms; and

Arithmetic Sequences

Arithmetic and Geometric Sequences

Geometric Sequences

1.A.12.E: The student is expected to: solve mathematic and scientific formulas, and other literal equations, for a specified variable.

Area of Triangles

Solving Formulas for any Variable

2.A.3.A: The student is expected to: determine the slope of a line given a table of values, a graph, two points on the line, and an equation written in various forms, including y = mx + b, Ax + By = C, and y - y1 = m(x - x1);

Cat and Mouse (Modeling with Linear Systems)

Function Machines 2 (Functions, Tables, and Graphs)

Function Machines 3 (Functions and Problem Solving)

Introduction to Functions

Linear Inequalities in Two Variables

Point-Slope Form of a Line

Slope

Slope-Intercept Form of a Line

Standard Form of a Line

2.A.3.B: The student is expected to: calculate the rate of change of a linear function represented tabularly, graphically, or algebraically in context of mathematical and real-world problems;

Compound Interest

Direct and Inverse Variation

Function Machines 1 (Functions and Tables)

Points, Lines, and Equations

Slope-Intercept Form of a Line

2.A.3.C: The student is expected to: graph linear functions on the coordinate plane and identify key features, including x-intercept, y-intercept, zeros, and slope, in mathematical and real-world problems;

Absolute Value with Linear Functions

Cat and Mouse (Modeling with Linear Systems)

Compound Interest

Exponential Functions

Function Machines 2 (Functions, Tables, and Graphs)

Function Machines 3 (Functions and Problem Solving)

Graphs of Polynomial Functions

Linear Functions

Point-Slope Form of a Line

Points, Lines, and Equations

Slope-Intercept Form of a Line

Standard Form of a Line

2.A.3.D: The student is expected to: graph the solution set of linear inequalities in two variables on the coordinate plane;

Linear Inequalities in Two Variables

Systems of Linear Inequalities (Slope-intercept form)

2.A.3.E: The student is expected to: determine the effects on the graph of the parent function f(x) = x when f(x) is replaced by af(x), f(x) + d, f(x - c), f(bx) for specific values of a, b, c, and d;

Absolute Value with Linear Functions

Exponential Functions

Slope-Intercept Form of a Line

2.A.3.F: The student is expected to: graph systems of two linear equations in two variables on the coordinate plane and determine the solutions if they exist;

Systems of Linear Inequalities (Slope-intercept form)

2.A.3.G: The student is expected to: estimate graphically the solutions to systems of two linear equations with two variables in real-world problems; and

Solving Linear Systems (Slope-Intercept Form)

2.A.3.H: The student is expected to: graph the solution set of systems of two linear inequalities in two variables on the coordinate plane.

Linear Programming

Systems of Linear Inequalities (Slope-intercept form)

2.A.4.A: The student is expected to: calculate, using technology, the correlation coefficient between two quantitative variables and interpret this quantity as a measure of the strength of the linear association;

2.A.4.B: The student is expected to: compare and contrast association and causation in real-world problems; and

2.A.4.C: The student is expected to: write, with and without technology, linear functions that provide a reasonable fit to data to estimate solutions and make predictions for real-world problems.

Correlation

Least-Squares Best Fit Lines

Solving Using Trend Lines

3.A.2.A: The student is expected to: determine the domain and range of a linear function in mathematical problems; determine reasonable domain and range values for real-world situations, both continuous and discrete; and represent domain and range using inequalities;

Function Machines 3 (Functions and Problem Solving)

3.A.2.B: The student is expected to: write linear equations in two variables in various forms, including y = mx + b, Ax + By = C, and y - y1 = m(x - x1), given one point and the slope and given two points;

Point-Slope Form of a Line

Points, Lines, and Equations

Slope-Intercept Form of a Line

Solving Equations by Graphing Each Side

Standard Form of a Line

3.A.2.C: The student is expected to: write linear equations in two variables given a table of values, a graph, and a verbal description;

Point-Slope Form of a Line

Points, Lines, and Equations

Solving Equations by Graphing Each Side

Standard Form of a Line

3.A.2.D: The student is expected to: write and solve equations involving direct variation;

3.A.2.G: The student is expected to: write an equation of a line that is parallel or perpendicular to the x- or y-axis and determine whether the slope of the line is zero or undefined;

Point-Slope Form of a Line

Slope-Intercept Form of a Line

Standard Form of a Line

3.A.2.H: The student is expected to: write linear inequalities in two variables given a table of values, a graph, and a verbal description; and

Linear Inequalities in Two Variables

Systems of Linear Inequalities (Slope-intercept form)

3.A.2.I: The student is expected to: write systems of two linear equations given a table of values, a graph, and a verbal description.

Cat and Mouse (Modeling with Linear Systems)

Solving Equations by Graphing Each Side

Solving Linear Systems (Matrices and Special Solutions)

Solving Linear Systems (Slope-Intercept Form)

Solving Linear Systems (Standard Form)

3.A.5.A: The student is expected to: solve linear equations in one variable, including those for which the application of the distributive property is necessary and for which variables are included on both sides;

Modeling One-Step Equations

Modeling and Solving Two-Step Equations

Solving Algebraic Equations II

Solving Equations on the Number Line

Solving Two-Step Equations

3.A.5.B: The student is expected to: solve linear inequalities in one variable, including those for which the application of the distributive property is necessary and for which variables are included on both sides; and

Exploring Linear Inequalities in One Variable

Linear Inequalities in Two Variables

Solving Linear Inequalities in One Variable

3.A.5.C: The student is expected to: solve systems of two linear equations with two variables for mathematical and real-world problems.

Solving Equations by Graphing Each Side

Solving Linear Systems (Matrices and Special Solutions)

Solving Linear Systems (Standard Form)

4.A.6.C: The student is expected to: write quadratic functions when given real solutions and graphs of their related equations.

4.A.7.A: The student is expected to: graph quadratic functions on the coordinate plane and use the graph to identify key attributes, if possible, including x-intercept, y-intercept, zeros, maximum value, minimum values, vertex, and the equation of the axis of symmetry;

Quadratics in Factored Form

Quadratics in Polynomial Form

Quadratics in Vertex Form

Translating and Scaling Functions

4.A.7.B: The student is expected to: describe the relationship between the linear factors of quadratic expressions and the zeros of their associated quadratic functions; and

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

Quadratics in Factored Form

4.A.7.C: The student is expected to: determine the effects on the graph of the parent function f(x) = x² when f(x) is replaced by af(x), f(x) + d, f(x - c), f(bx) for specific values of a, b, c, and d.

Exponential Functions

Quadratics in Factored Form

Quadratics in Polynomial Form

Quadratics in Vertex Form

Translating and Scaling Functions

Translations

Zap It! Game

4.A.8.A: The student is expected to: solve quadratic equations having real solutions by factoring, taking square roots, completing the square, and applying the quadratic formula; and

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

Roots of a Quadratic

5.A.9.A: The student is expected to: determine the domain and range of exponential functions of the form f(x) = ab to the x power and represent the domain and range using inequalities;

Exponential Functions

Logarithmic Functions

5.A.9.B: The student is expected to: interpret the meaning of the values of a and b in exponential functions of the form f(x) = ab to the x power in real-world problems;

Compound Interest

Introduction to Exponential Functions

5.A.9.C: The student is expected to: write exponential functions in the form f(x) = ab to the x power (where b is a rational number) to describe problems arising from mathematical and real-world situations, including growth and decay;

Compound Interest

Introduction to Exponential Functions

5.A.9.D: The student is expected to: graph exponential functions that model growth and decay and identify key features, including y-intercept and asymptote, in mathematical and real-world problems; and

Compound Interest

Exponential Functions

Introduction to Exponential Functions

Logarithmic Functions

Correlation last revised: 4/2/2018