MathsQ&A by dot point

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).

Write exponential functions of the form $f(x) = ab^x$ to model growth and decay, interpret the meaning of $a$ and $b$ in context, and determine whether a situation represents exponential growth or decay (TEKS A.9B, A.9C, A.9D).

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).

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).

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).

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).

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).

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).

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).

Write linear equations in two variables in various forms ($y = mx + b$, $Ax + By = C$, $y - y_1 = m(x - x_1)$) given one point and the slope, two points, a table, a graph, or a verbal description (TEKS A.2B, A.2C, A.2G).

Identify terms of arithmetic and geometric sequences when given in recursive form, and write a formula for the $n$th term of arithmetic and geometric sequences given several of their terms (TEKS A.12C, A.12D).

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).

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).

Factor, if possible, trinomials with real factors in the form $ax^2 + bx + c$, including perfect-square trinomials, and decide if a binomial is a difference of two squares and rewrite it (TEKS A.10E, A.10F).

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).

Solve problems involving the simple interest formula $I = Prt$ and compound interest (TEKS A.12E).

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).

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).

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).

Solve quadratic equations having real solutions by taking square roots and by completing the square (TEKS A.8A).

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).

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).

Describe the effect on the graph of the parent function $f(x) = x^2$ when $a$, $h$, and $k$ change in $f(x) = a(x - h)^2 + k$, and transform quadratic functions graphically and algebraically (TEKS A.7B, A.7C).

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).

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).

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).

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).

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).

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).

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).