Texas · TEASyllabus
Maths syllabus, dot point by dot point
Every dot point in the Texas Mathssyllabus, with a focused answer for each one. Click any dot point for a worked explainer, past exam questions, and links to related dot points. Written by Claude Opus 4.8, Anthropic's latest AI.
Exponential Functions and Equations
Module overview →- How do you solve real-world exponential problems like population, depreciation, and compound interest, and read values from the model?Solve real-world problems modeled by exponential functions, including population growth, depreciation, and compound interest, evaluate the model, and use technology to find an exponential best fit (TEKS A.9B, A.9E).10 min answer →
- How do you write an exponential function in the form f(x) = ab^x, interpret a and b, and tell growth from decay?Write exponential functions of the form to model growth and decay, interpret the meaning of and in context, and determine whether a situation represents exponential growth or decay (TEKS A.9B, A.9C, A.9D).10 min answer →
- How do you graph an exponential function and identify its key features: the y-intercept, the asymptote, and growth or decay?Graph exponential functions that model growth and decay and identify key features, including the y-intercept and the asymptote, and determine the domain and range (TEKS A.3C, A.9A, A.9F).10 min answer →
- How do you solve a simple exponential equation by rewriting with a common base, and how do you distinguish linear from exponential situations?Solve exponential equations using the properties of exponents (rewriting with a common base), and distinguish between situations that can be modeled with linear functions and with exponential functions (TEKS A.9D, A.9G).9 min answer →
Describing and Graphing Linear Functions, Equations, and Inequalities
Module overview →- How do you graph a linear function and identify its key features: the x-intercept, y-intercept, zeros, and slope?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 (TEKS A.3A).10 min answer →
- How do you graph the solution set of a linear inequality in two variables, choosing the boundary line style and the side to shade?Graph the solution set of linear inequalities in two variables on the coordinate plane, using a solid or dashed boundary and shading the correct half-plane (TEKS A.3D).9 min answer →
- How do you write the equation of a line parallel or perpendicular to a given line, and how do you set up and solve direct variation?Write the equation of a line through a given point parallel or perpendicular to a given line, and write and solve equations involving direct variation (TEKS A.2D, A.2E, A.2F).9 min answer →
- How do you analyze a scatterplot, write a trend line, judge correlation, and use the model to make predictions?Use scatterplots to analyze the relationship between two quantitative variables, write a trend-line equation by informal methods, judge its reasonableness, and make predictions, interpreting the correlation (TEKS A.3F, A.3G, A.4A, A.4B, A.4C).10 min answer →
- How do you find the slope and rate of change of a linear function from a table, a graph, two points, or a context, and interpret it?Calculate the rate of change (slope) of a linear function represented tabularly, graphically, or algebraically, and interpret slope and intercepts as rate and initial value in context (TEKS A.3A, A.3B).10 min answer →
- How do you write a linear equation in slope-intercept, point-slope, and standard form from points, a graph, a table, or a description?Write linear equations in two variables in various forms (, , ) given one point and the slope, two points, a table, a graph, or a verbal description (TEKS A.2B, A.2C, A.2G).10 min answer →
Number and Algebraic Methods
Module overview →- How do you identify terms of arithmetic and geometric sequences in recursive form, and write a formula for the nth term?Identify terms of arithmetic and geometric sequences when given in recursive form, and write a formula for the th term of arithmetic and geometric sequences given several of their terms (TEKS A.12C, A.12D).9 min answer →
- How do you divide a polynomial of degree one or two by a polynomial of degree one, and when can you simplify by factoring instead?Determine the quotient of a polynomial of degree one or two divided by a polynomial of degree one when the degree of the divisor does not exceed the degree of the dividend (TEKS A.10C).9 min answer →
- How do you simplify expressions with the laws of exponents, including negative and rational exponents, and simplify numerical square-root radicals?Simplify numerical radical expressions involving square roots, and simplify numeric and algebraic expressions using the laws of exponents, including integral and rational exponents (TEKS A.11A, A.11B).10 min answer →
- How do you factor trinomials and binomials on STAAR, including the GCF, the difference of two squares, and perfect-square trinomials?Factor, if possible, trinomials with real factors in the form , including perfect-square trinomials, and decide if a binomial is a difference of two squares and rewrite it (TEKS A.10E, A.10F).10 min answer →
- How do you add, subtract, and multiply polynomials of degree one and two, and where does the STAAR test reward the structure of the work?Add and subtract polynomials of degree one and degree two, and multiply polynomials of degree one and degree two, writing the result in standard form (TEKS A.10A, A.10B).9 min answer →
- How do you solve simple-interest and compound-interest problems on STAAR, and why is compound interest an exponential model?Solve problems involving the simple interest formula and compound interest (TEKS A.12E).9 min answer →
Quadratic Functions and Equations
Module overview →- How do you solve real-world problems modeled by quadratics, such as projectile motion and area, and interpret the solutions?Solve real-world problems modeled by quadratic equations, including projectile motion and area, and interpret the reasonableness of solutions in context (TEKS A.8A, A.6B).10 min answer →
- How do you use the quadratic formula to solve any quadratic, and what does the discriminant tell you about the number of real solutions?Solve quadratic equations having real solutions by applying the quadratic formula, and use the discriminant to determine the number of real solutions (TEKS A.8A).10 min answer →
- How do you solve a quadratic equation by factoring, using the zero-product property, and how do the solutions relate to the graph?Solve quadratic equations having real solutions by factoring, using the zero-product property, and relate the solutions to the zeros of the related quadratic function (TEKS A.8A).10 min answer →
- How do you solve a quadratic equation by taking square roots and by completing the square?Solve quadratic equations having real solutions by taking square roots and by completing the square (TEKS A.8A).10 min answer →
Quadratic Functions and Equations
Module overview →- How do you determine the domain and range of a quadratic function, and connect its representations to the situation it models?Determine the domain and range of quadratic functions and represent them using inequalities, and describe representations of quadratic functions in relation to their solutions and the real-world situations they model (TEKS A.6A, A.6B).10 min answer →
- How do you graph a quadratic function and identify its key attributes: vertex, axis of symmetry, intercepts, zeros, and maximum or minimum?Graph quadratic functions on the coordinate plane and identify key attributes, including x-intercept, y-intercept, zeros, maximum or minimum value, vertex, and the axis of symmetry (TEKS A.7A, A.3B).11 min answer →
- How do the parameters a, h, and k transform the parent function f(x) = x squared, and how do you write the transformed function?Describe the effect on the graph of the parent function when , , and change in , and transform quadratic functions graphically and algebraically (TEKS A.7B, A.7C).10 min answer →
- How do you write a quadratic function from its real solutions, its graph, or a data set using vertex or standard form?Write quadratic functions when given real solutions and graphs of their related equations, and write quadratic functions that fit data sets using vertex form or standard form (TEKS A.6C, A.8B).10 min answer →
Writing and Solving Linear Functions, Equations, and Inequalities
Module overview →- How do you determine the domain and range of a linear function, including reasonable continuous or discrete values for a real-world situation?Determine the domain and range of a linear function in mathematical problems, and reasonable domain and range values (continuous and discrete) for real-world situations, representing them using inequalities (TEKS A.2A).9 min answer →
- How do you write a system of two linear equations from a real-world situation and interpret the solution in context?Write systems of two linear equations given a table, a graph, a verbal description, or a real-world problem, then solve and interpret the solution in context (TEKS A.2H, A.2I).10 min answer →
- How do you solve a linear equation in one variable, including ones needing the distributive property and variables on both sides?Solve linear equations in one variable, including those requiring the distributive property and those with variables on both sides, and identify equations with one solution, no solution, or infinitely many (TEKS A.5A).10 min answer →
- How do you solve a linear inequality in one variable, when do you flip the sign, and how do you graph and interpret the solution?Solve linear inequalities in one variable, including those requiring the distributive property and those with variables on both sides, graph the solution, and interpret it in context (TEKS A.5B).9 min answer →
- How do you solve a system of two linear equations by graphing, substitution, and elimination, and tell how many solutions it has?Solve systems of two linear equations in two variables by graphing, substitution, and elimination, and determine whether a system has one solution, no solution, or infinitely many (TEKS A.5C, A.3E).10 min answer →
- How do you write a linear function or equation to model a real-world situation, and evaluate it using function notation?Write linear functions that model the relationship between two quantities from a description, table, or graph, write an equation representing a functional relationship, and evaluate functions in function notation (TEKS A.2C, A.2G, A.12B).10 min answer →