Southwestern Illinois Community College
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COURSE DESCRIPTION The course consists of the following topics: real numbers, linear equations and inequalities, graphs of lines and linear inequalities, functions, systems of linear equations, exponents and polynomials, factoring, rational expressions, roots and radicals, quadratic equations and nonlinear inequalities. This course is designed to prepare students for MATH 105, MATH 107, MATH 111, or MATH 112. PREREQUISITES Math placement test score or MATH 094 (with a grade of “C” or better) or divisional approval; completion of MATH 096 (with a grade of “C” or better) or successful completion of one year of high school geometry; and completion of ENG 001, a Developmental Education Requirement. COURSE OBJECTIVES The Math Department at Southwestern strives to ensure that mathematics students will be able to: a) demonstrate proficiency in basic mathematical skills and computation as identified in the course objectives. b) reason logically about abstract mathematical concepts. c) apply mathematical concepts to authentic situations. d) use current technologies to investigate mathematical concepts. e) communicate mathematics. For the course objectives below, the letters in parentheses following each objective indicate which departmental objective (listed above) that course objective is intended to support. A. Foundational Knowledge The student will be able to: 1. Classify real numbers as natural, whole, integer, rational, or irrational. (a) 2. Represent an interval of real numbers using interval notation. (a) 3. Evaluate expressions using the order of operations. (a) 4. Identify the appropriate use of the identity, commutative, associative, inverse and distributive properties of real numbers. (a) B. Linear Equations and Inequalities The student will be able to: 1. Solve linear equations and classify a linear equation as a conditional equation, an identity or a contradiction. (a) [Note to Instructor: this is a review topic] 2. Solve formulas for specified variables. (c) 3. Find the union and intersection of two sets. (a) [Note to Instructor: focus on sets in interval notation] 4. Solve simple and compound linear inequalities. (a) 5. Solve absolute value equations and inequalities. (a) 6. Solve word problems involving translating skills, percents, mixture, and motion. (c) [Note to Instructor: this is a review topic] C. Equations of Lines The student will be able to: 1. Identify and write equations of horizontal and vertical lines. (a) 2. Find the intercepts of a line. (a) 3. Find the slope of a line given either a graph of the line, two points on the line, or the equation of the line. (a) 4. Graph a line given its equation or given a point on the line and its slope. (a) 5. Determine from the equations of two lines whether they are parallel, perpendicular or neither. (a) 6. Write equations of lines in slope-intercept, point-slope, and standard form. (a) 7. Graph simple and compound linear inequalities. (a) D. Functions The student will be able to: Determine whether a relation is a function given a listing of correspondences, an equation, or a graph. (a) 1. Determine the domain and range of a function from a graph or ordered pairs. (a) 2. Determine the domain of a function from an equation. (a) 3. Evaluate functions for given values of the domain. (a) 4. Perform basic function operations, including addition, subtraction, multiplication, division, and composition. (a) E. Systems of Equations The student will be able to: 1. Solve linear systems of two equations in two variables using the methods of graphing, elimination, and substitution. (a) [Note to Instructor: cover lightly—this is review material] 2. Solve linear systems of three equations in three variables using the elimination method. (a) 3. Solve application problems involving systems of linear equations, including those involving 3 variables. (c) F. Polynomials The student will be able to: 1. Use the rules for integer exponents. (a) 2. Add, subtract, multiply, and divide polynomials. (a) [Note to Instructor: Objectives F1 and F2 are primarily review but should be included; emphasis should be placed on polynomial division (including problems with more than three terms, fractional coefficients, etc.) and on the function concept as it relates to polynomials] G. Factoring The student will be able to: 1. Factor polynomials using the “greatest common factor” and “factoring by grouping” techniques. (a) 2. Factor trinomials of the form ax2 + bx + c. (a) [Note to Instructor: G1 and G2 are review] 3. Factor sums and differences of cubes. (a) 4. Factor expressions using substitution. (a) 5. Solve equations of degree greater than 1 by factoring. (a) H. Rational Functions The student will be able to: 1. Determine the domain of rational functions. (a) 2. Add, subtract, multiply, and divide rational expressions. (a) 3. Simplify complex fractions, including those with negative exponents and negative coefficients. (a) 4. Solve rational equations and word problems involving rational equations. (c) [Note to Instructor: work rate problems should be included and emphasized.] I. Radicals The student will be able to: 1. Convert between radical expressions and expressions with rational exponents. (a) 2. Use the rules of exponents with rational exponents. (a) 3. Use the product and quotient rules for radicals. (a) 4. Simplify radicals. (a) 5. Add, subtract and multiply radicals. (a) 6. Rationalize denominators involving radicals, including those with index greater than two and with binomials involving square roots. (a) 7. Solve radical equations. (a) 8. Add, subtract, multiply, and divide complex numbers. (b) [Note to Instructor: powers of i is an optional topic.] J. Quadratic Equations The student will be able to: 1. Solve quadratic equations with both real and complex solutions using the square root property, completing the square, and the quadratic formula. (a) 2. Solve equations that are quadratic in form. (a) 3. Solve formulas involving squares and square roots for a specified variable. (a) 4. Solve applied problems involving quadratic equations. (a) 5. Graph a quadratic function (from standard form a(x – h)2 + k and general form ax2 + bx + c) and identify the vertex of the parabola. (a) [Note to Instructor: horizontal parabolas are optional.] 6. Predict the shape of a parabola and the direction it opens given its equation. (a) TEXTBOOK & MATERIALS
GRADING PROCEDURE
major exams – 400pts (50%) quizzes – 100pts (12.5%) homework – 100pts (12.5%) final exam – 200pts (25%) Points Percentage Letter Grade 720 – 800 90% and above A 640 – 719 80% and above B 560 – 639 70% and above C 480 – 559 60% and above D ATTENDANCE POLICY You are expected to be present for all assigned classes, lectures or laboratory sessions. If you are absent more times during the semester than the number of times the class meets per week, you may be dropped from the course at the discretion of the instructor. When an instructor drops a student with an effective date before the midterm date of the class a “W” will be recorded. When an instructor drops a student for non-attendance with an effective date after the midterm date, the instructor will have the prerogative to assign a grade of “F” or “W”. ACADEMIC RIGOR You are enrolled in an academically rigorous college course. Your success in this course will require a significant investment of time outside of class. According to the Administrative Rules of the Illinois Community College Board (section 1501.309), it is assumed that the student will invest at least two hours of outside study time for each hour of classroom lecture time. ADDITIONAL INFORMATION
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Revision Date: 9 August, 2013 |