Algebra 1 TEKS Reference GuideAlgebra 1 TEKS Standards Reference Guide • Texas Essential Knowledge and Skills Mathematics ALGEBRA I Mathematical Process Standards The student uses mathematical processes to acquire and demonstrate mathematical understanding. A.1(A) Apply mathematics to problems arising in everyday life, society, and the workplace A.1(B) 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 A.1(C) 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 A.1(D) Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate A.1(E) Create and use representations to organize, record, and communicate mathematical ideas A.1(F) Analyze mathematical relationships to connect and communicate mathematical ideas A.1(G) Display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication Linear Functions, Equations, & Inequalities A.2(A) Determine domain/range of linear functions; reasonable domain/range for real-world situations; represent using inequalities A.2(B) Write linear equations in various forms (\(y=mx+b, Ax+By=C, y-y_1=m(x-x_1)\)) given point/slope or two points A.2(C) Write linear equations given graph, table, or verbal description A.2(D) Write and solve equations involving direct variation A.2(E) Write equation of a line parallel to a given line through a point A.2(F) Write equation of a line perpendicular to a given line through a point A.2(G) Write equations of lines parallel/perpendicular to X or Y axis; determine if slope is zero or undefined A.2(H) Write linear inequalities in two variables given graph, table, or verbal description A.2(I) Write systems of two linear equations given table, graph, or verbal description A.5(A) Solve linear equations in one variable with variables on both sides A.5(B) Solve linear inequalities in one variable with variables on both sides A.5(C) Solve systems of two linear equations for math and real-world problems Describing & Graphing Linear Functions A.3(A) Determine slope from table, graph, two points, or various equation forms A.3(B) Calculate rate of change in context of math and real-world problems A.3(C) Graph linear functions and identify key features (\(x\)-int, \(y\)-int, zeros, slope) A.3(D) Graph solution set of linear inequalities in two variables A.3(E) Determine effects on parent function \(f(x)=x\) when replaced by \(af(x), f(x)+d, f(x-c), f(bx)\) A.3(F) Graph systems of two linear equations and determine solutions A.3(G) Estimate graphically solutions to systems in real-world problems A.3(H) Graph solution set of systems of two linear inequalities A.4(A) Calculate/interpret correlation coefficient (\(r\)) as measure of linear association strength A.4(B) Compare and contrast association and causation in real-world problems A.4(C) Write linear functions that provide a reasonable fit to data (linear regression) Quadratic Functions and Equations A.6(A) Determine/represent domain and range of quadratic functions A.6(B) Write quadratic equations in vertex form and rewrite to standard form A.6(C) Write quadratic functions given real solutions and graphs A.7(A) Graph quadratic functions; identify intercepts, zeros, vertex, and axis of symmetry A.7(B) Describe relationship between linear factors and zeros of quadratic functions A.7(C) Determine effects on parent function \(f(x)=x^2\) when replaced by \(af(x), f(x)+d, f(x-c), f(bx)\) A.8(A) Solve quadratic equations by factoring, square roots, completing the square, or quadratic formula A.8(B) Write quadratic functions that provide a reasonable fit to data (quadratic regression) Exponential Functions and Equations A.9(A) Determine/represent domain and range of exponential functions \(f(x) = ab^x\) A.9(B) Interpret meaning of \(a\) and \(b\) values in real-world exponential contexts A.9(C) Write exponential functions for growth and decay in math/real-world situations A.9(D) Graph exponential functions; identify \(y\)-intercept and asymptotes A.9(E) Write exponential functions that provide a reasonable fit to data (exponential regression) Number and Algebraic Methods A.10(A) Add and subtract polynomials of degree one and degree two A.10(B) Multiply polynomials of degree one and degree two A.10(C) Divide polynomials of degree one/two by degree one/two A.10(D) Rewrite polynomial expressions using distributive property A.10(E) Factor trinomials (\(ax^2 + bx + c\)), including perfect square trinomials A.10(F) Identify and rewrite difference of two squares A.11(A) Simplify numerical radical expressions involving square roots A.11(B) Simplify numeric/algebraic expressions using laws of exponents A.12(A) Decide if relations are functions (verbal, table, graph, symbolic) A.12(B) Evaluate functions in function notation given domain elements A.12(C) Identify terms of arithmetic/geometric sequences from function form A.12(D) Write formulas for the \(n^{th}\) term of arithmetic/geometric sequences A.12(E) Solve formulas and literal equations for a specified variable Reference Guide: Texas Essential Knowledge and Skills (TEKS) for Mathematics, Chapter 111. Subchapter C. High School Algebra I.
