MTH 122W - College AlgebraCredits: 4
Reviews the mechanics of basic Algebra and solidifies understanding by using algebraic techniques, constructing mathematical models, solving problems and interpreting results. Includes: algebraic expressions; equations and inequalities; functions, inverse functions, and graphs; polynomial and rational functions; radical functions; exponential and logarithmic functions; matrices and determinants; systems of equations and inequalities; complex numbers; sequences and series. A GRAPHING CALCULATOR IS REQUIRED.
Prerequisite(s): MATH LEVEL 6
Corequisite(s): None
Lecture Hours: 60 Lab Hours: 0
Meets MTA Requirement: Natural Science
Pass/NoCredit: Yes
Outcomes and Objectives 1. Students will recognize and understand notation describing sets of real numbers.
A. Understand set and interval notation .
B. Apply the operations of intersection and union.
2. Students can perform operations on polynomial functions.
A. Apply properties of positive integral exponents.
B. Perform addition, subtraction, multiplication and division of polynomial functions.
C. Perform synthetic division.
D. Factor polynomials.
E. Reduce rational expression to simplest form.
F. Add, subtract, multiply and divide rational expressions (including complex fractions).
3. Students can perform operations on radical functions.
A. Apply the properties of rational exponents.
B. Add, subtract, multiply and divide radicals, expressing solutions in simplest form.
4. Students can recognize, graph and solve problems relating to linear functions.
A. Graph ordered pairs of any relation and identify whether or not it is a function.
B. Graph any linear function.
C. Find the distance between any two points in the plane.
D. Find the slope of a line.
E. Find the equation of a line, given information.
F. Solve and graph a linear inequality.
G. Solve absolute value equations and inequalities.
5. Students will be able to graph any polynomial function
A. Determine intercepts, axis of symmetry and maximum or minimum of a quadratic.
B. Graph any quadratic function.
C. Use synthetic division to identify zeros and graph any polynomial function.
6: Students can solve nonlinear equations and inequalities involving a function of one variable.
A. Solve quadratic equations by factoring, the quadratic formula, and graphing.
B. Solve equations involving radicals.
C. Solve polynomial equations symbolically (using synthetic division).
D. Solve polynomial equations of degree greater than 2 using tables and graphs.
E. Solve quadratic inequalities.
F. Set up and solve application problems .
7. Students can recognize and understand concepts related to logarithmic and exponential functions.
A. Recognize an exponential or logarithmic function and its graph.
B. Solve exponential or logarithmic equations.
8. Students can solve systems of equations and inequalities.
A. Solve systems of 2 and 3 linear equations.
B. Solve linear programming problems.
C. Solve systems of inequalities graphically.
D. Set up and solve application problems.
9. Students can work with matrices and determinants.
A. Apply basic operations to matrices.
B. Evaluate determinants.
C. Solve systems of equations by matrix methods.
10. Students can work with complex numbers.
A. Define numbers in the form a + bi.
B. Add, subtract, multiply, and divide complex numbers.
C. Solve quadratic equations with complex solutions.
11. Students can work with sequences and series.
A. Find the terms of an arithmetic and geometric sequence.
B. Find the sum of an arithmetic and geometric series.
C. Apply the Binomial Theorem.
12. Students can communicate effectively about mathematics in writing.
A. Provide complete written solutions to problems using appropriate terminology.
B. Articulate important ideas and conclusions in writing.
13. Students will develop their problem-solving and mathematical modeling skills.
A. Solve real world problems involving linear equations, quadratic equations, exponential equations, logarithmic equations, rational equations,
and systems of equations.
B. Use mathematical modeling to solve real world problems.
C. Clarify and analyze the meanings of words, phrases and statements.
D. Learn the meanings of relevant symbols used in the discipline and ways to use them.
E. Transfer problem solving strategies for use in new contexts.
F. Organize and present information or data in tables, charts, and graphs.
G. Use symbol systems to raise questions about models and proposed answers to problems.
H. Identify, state and clarify arguments or reasoning, including those codified by systems of symbols.
I. Generate and assess solutions to problems.
14. Students will use graphing calculator technology to evaluate and analyze solutions to various functions.
A. Graph linear, quadratic, radical, polynomial, exponential, or logarithmic function.
B. Create a table of input/out pairs for any given function.
C. Determine an appropriate window to obtain a complete graph of a linear, quadratic, square root, exponential, or logarithmic function.
D. Find the intersection of any two functions
E. Evaluate any numerical expression involving linear, quadratic, rational, square root, exponential, or logarithmic functions.
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