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College Algebra (MTH 111) Standards Checklist Name:_____________________ Below is a list of the skills you will learn during this course. After each test (or the chapter 9 quiz), check off the ones you have demonstrated with mastery. By keeping your checker sheet up-to-date you will know which topics you have really learned and which need to be studied further. Chapter 7: Systems of Equations and Inequalities □ □ 17% □ □ □ □ □ Solve systems of equations algebraically or graphically Perform matrix operations including addition, subtraction, scalar multiplication, and multiplication Find the determinant of a matrix and use it to compute the inverse Use matrix algebra to solve systems of equations Analyze the solutions for a system of equations in 2 or 3 variables Solve and interpret systems of inequalities and linear programming problems Model and solve word problems using systems of equations Chapter 1: Functions □ □ 17% □ □ □ □ □ □ Convert back and forth between numeric, algebraic, and graphic representations of functions Demonstrate an understanding of the concept of a function, function notation, and evaluating a function Graph and analyze functions, identifying domain, range, continuity, symmetry, asymptotes, extrema, increasing/decreasing regions, or boundedness Create graphic, algebraic, or numeric representations of functions with specific properties Compare and distinguish the 12 basic functions’ characteristics Perform operations on functions including composition Identify the inverse of a function graphically or algebraically Analyze the effect of transformations on a graph Chapter 2: Polynomial and Rational Functions 17% □ □ □ □ □ Analyze linear relationships using equations, graphs, or correlation Graph a parabola and identify its vertex and axis of symmetry Solve and interpret quadratic equations using factoring or the quadratic formula Apply long or synthetic division to test whether an expression is a factor of a polynomial Perform operations on complex numbers and graph them □ □ □ □ □ Analyze the nature of the roots of a polynomial Using the Fundamental Theorem of Algebra, write a polynomial equation in standard or factored form Graph rational functions and identify their asymptotes Solve rational equations and identify any extraneous solutions Solve rational inequalities using sign-charts or graphs Chapter 3: Exponential Functions and Logarithms □ □ 17% □ □ □ □ Graph, evaluate, and analyze exponential, logistic, and logarithmic equations Analyze data to determine the equation for a curve of best fit and use the equation to make a prediction Identify and apply the inverse relationship between logarithms and exponential functions Apply the basic properties of logarithms Solve exponential and logarithmic equations Model exponential situations involving population growth/decline, compound interest, radioactive half-life, or Newton’s Law of Cooling Chapter 9: Sequences and Series □ □ 12% □ □ Define, recognize, and distinguish between arithmetic and geometric sequences Find the explicit or recursive formulas for arithmetic and geometric sequences and use these formulas to determine a specific term or term number Find partial sums of arithmetic and geometric series and find sums of convergent infinite series Solve word problems by modeling the patterns with sequences or series Overall Retention 20% □ □ □ □ □ Demonstrate retention of Chapter 7: Systems of Equations and Inequalities Demonstrate retention of Chapter 1: Functions Demonstrate retention of Chapter 2: Polynomial and Rational Functions Demonstrate retention of Chapter 3: Exponential Functions and Logarithms Demonstrate retention of Chapter 9: Sequences and Series