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Course Content Form PIMA COMMUNITY COLLEGE Effective Term: Fall 2015 MAT 123 Pre-College Algebra Credit Hours: 5.00 Lecture Periods: 5.00 Lab Periods: Description: Basic and intermediate algebra concepts. Includes translating written statements into algebraic expressions, linear equations, linear inequalities, graphing, integer exponents, and polynomials. Also includes factoring, rational and radical expressions and equations, square roots, quadratic equations, functions, exponential and logarithmic expressions. Prerequisite(s): Within the last three years: MAT 086 with a B or better or required score on the mathematics assessment Information: No more than 3 credit hours can be applied toward graduation for MAT 122, 122Z and/or 123. Access to a scanner required for Math classes taken online. Not a university level course. Student Learning Outcomes: Upon successful completion of the course, the student will be able to: 1. Solve linear, absolute value, quadratic, rational, and radical equations, linear and absolute value inequalities, and linear systems in two and three variables. 2. Graph linear, quadratic, and elementary exponential equations, and linear inequalities. 3. Solve problems involving real world applications. Performance Objectives: Upon successful completion of the course, the student will be able to: 1. Find distance and midpoint between two points. 2. Calculate slopes of lines, determine equations of lines and graph lines. 3. Solve and graph linear inequalities and compound linear inequalities and graph in 1-D and 2-D. 4. Solve systems of two and three linear equations and interpret geometrically. 5. Absolute value equations and inequalities. 6. Factor polynomials and solve related equations. 7. Operations on square root expressions. 8. Solve quadratic equations taking roots and quadratic formula, completing the square and interpreting the discriminant and graph parabolas. 9. Combine rational expressions, simplify and solve. Include quadratic rational expressions 10. Laws of exponents including fractional exponents and radical expressions. 11. Define and identify functions, use function notation and determine basic domains. Outline: I. II. Distance and midpoint between two points A. Distance calculations B. Midpoint calculations Lines in the Plane A. Determine slopes of lines B. Write the equation of a line 1. Given two points 2. Given a point and a slope III. IV. V. VI. VII. VIII. IX. X. XI. 3. Give a point and a parallel or perpendicular line C. Graph lines D. Applications Inequalities A. Interval notation B. Compound Inequalities C. Linear inequalities with two variables D. Applications Systems of Linear Equations A. Graphical representation of systems with two variables B. Elimination and substitution methods for two variables C. Geometrical interpretation of consistent, inconsistent and independent systems D. Applications for two variables E. Algebraically solve systems with three variables F. Geometrical interpretation of consistent, inconsistent and independent systems of three variables G. Applications for three variables Absolute Value A. Solve equations B. Solve inequalities Polynomials A. Factoring 1. Grouping 2. Binomials 3. Substitution methods 4. Sum and difference of cubes B. Solve equations by factoring Square roots A. Evaluate B. Simplify C. Perform operations Quadratic equations A. Completing the square B. Quadratic formula and the discriminant C. Graphs of parabolas D. Applications Rational Expressions and Equations A. Reduce and build B. Basic operations (addition, subtraction, multiplication and division) C. Simplify complex rational expressions D. Solve rational equations including those involving quadratic equations E. Applications Radical and Exponential Expressions and Equations A. Apply laws of exponents for integer exponents B. Scientific Notation C. Convert between rational and radical exponent notation D. Apply laws of exponents to rational exponential expressions E. Addition, subtraction, multiplication and division of radical expressions F. Rationalizing denominators G. Radical equations H. Applications Functions A. Definitions B. Identification C. Notation D. Domains