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 x2+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 ax2+bx+c
Modeling the Factorization of x2+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 ax2+bx+c
Modeling the Factorization of x2+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