MATH 098 Intermediate Algebra for Precalculus (5 credits)
Prerequisite Completion of GSP AND concurrent enrollment in MATHC 098 or instructor permission
Course Description
Algebraic skills, concepts, and applications needed for precalculus, including quadratic, polynomial, rational, and radical expressions and equations, and systems of linear equations.
Course Content
1. Functions: Concepts and Graphs
a. Determining whether a relation expressed as a graph, table, formula, or real-world description is a function.
b. Relating tabular, graphical, verbal, and symbolic representations of functions to each other.
c. Stating the domains and ranges of functions represented in each of the above forms, and finding the domains of rational functions.
d. Evaluating functions represented in each of the above forms, particularly using standard function notation.
e. Graphing, identifying the intercepts, and stating the domain and range of basic “toolkit functions”: constant, x, x^2, x^3, |x|, sqrt(x), cube root(x)
2. Algebraic Expressions
a. Simplifying polynomial expressions using addition, subtraction, multiplication, and division by monomials.
b. Factoring polynomial expressions using the techniques of factoring out a greatest common factor, factoring reasonable trinomials of the form ax^2 + bx + c, and factoring the difference of squares.
c. Simplifying reasonable rational expressions, including complex fractions.
d. Multiplying, dividing, adding, and subtracting rational expressions.
e. Converting expressions involving rational exponents to radical expressions and vice-versa.
f. Applying exponent and radical properties to simplify and evaluate expressions involving rational exponents.
g. Simplifying expressions involving radicals.
h. Applying the Pythagorean Theorem, from memory, in a variety of contexts, including the distance formula.
3. Equations
a. Solving 2x2 systems of linear equations in two variables graphically and algebraically using substitution and elimination, and identify cases of no solutions or infinite solutions.
b. Solving rational equations algebraically including those involving extraneous solutions.
c. Solving radical equations algebraically requiring one radical-clearing operation.
d. Solving quadratic equations by factoring, square root principle, and using the quadratic formula.
e. Solving formulas for a specified variable, including solutions requiring multiple algebraic operations.
4. Applications
a. Obtaining and synthesizing relevant information and using appropriate formulas in order to solve a variety of application problems. Finding the solutions may require the use of linear, quadratic, rational, or radical equations.
b. Interpreting solutions of application problems in the context of the problem and evaluate the reasonableness of the solutions.
5. General Content
a. Extracting relevant information from complex scenarios. Obtaining any necessary additional information from outside sources. Synthesizing the information in order to solve problems and make decisions.
b. Identifying which mathematical skills to use and then apply them in diverse scenarios and contexts.
c. Using technology to find decimal approximations of radicals, evaluate exponential expressions, evaluate rational expressions by using the order of operations correctly, evaluate numerical solutions to application problems, verify solutions, and convert solutions from the quadratic formula into decimal form.
d. Using estimation to approximate solutions and to determine the reasonableness of solutions to problems.
Student Outcomes
1. Evaluate and relate functions expressed as graphs, tables, or formulas, including using standard function notation, state the domain and range of these functions, and identify and graph the basic toolkit functions.
2. Manipulate and simplify quadratic, polynomial, radical, and rational expressions, using appropriate properties and algebraic techniques.
3. Solve quadratic, radical, and rational equations, systems of linear equations, and formulas, using appropriate properties and algebraic techniques.
4. Solve application problems, interpret solutions, evaluate their reasonableness and make decisions by extracting relevant information from a scenario, obtaining any necessary additional information from outside sources, identifying and applying the appropriate techniques.
5. Clearly communicate solution processes, including writing solutions in the context of the problem, including units, using mathematical notation and vocabulary correctly, and using complete sentences when appropriate.
Degree Outcomes
1. Quantitative & Symbolic Reasoning: Students utilize mathematical, symbolic, logical, graphical, geometric, or statistical analysis for the interpretation and solution of problems in the natural world and human society.
2. Critical, Creative and Reflective Thinking: Graduates will evaluate, analyze, synthesize, and generate ideas; construct informed, meaningful, and justifiable conclusions; and process feelings, beliefs, biases, strengths, and weaknesses as they relate to their thinking, decisions, and creations.
Lecture Contact Hours 50
Lab Contact Hours 0
Clinical Contact Hours 0
Total Contact Hours 50
Potential Methods
A. TEST - multiple choice, true/false, computational, matching, or short written answers.
B. WRITING ASSIGNMENT - journal, outline, narrative explanation, essay, notebook, portfolio, or projects.
C. GROUPWORK - written group project, group written solution to problems, group assignment, group presentation, group oral solution to problems, or group discussion.
D. INDIVIDUAL WORK - individual presentation, individual written solution to problems, or individual oral solution to problems.
E. INFORMAL ASSESSMENT - self-evaluation, peer evaluation, or teacher observation.
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