MATH 098 - Intermediate Algebra for Calculus
This course will expose students to a variety of algebraic techniques and functions that will prepare them for calculus. Focus will be placed on quadratic, rational, and radical functions with emphasis on algebraic techniques used to combine and simplify them. Techniques will include factoring, simplifying (adding/subtracting/multiplying/dividing) polynomials, rational and radical expressions, and relationships between equations and their respective functions and graphs.
Pre-requisite(s) MATH 091 min 2.0
Placement Eligibility Math 107, 111, 146, 180, 098
Course Note Graphing Calculator Required; TI-84 recommended
Quarters Typically Offered
Summer Day, Evening
Winter Day, Online
Designed to Serve Students who expect to take Math 141, 142 (Pre-Calculus I and II).
Active Date 20170622T08:38:36
Grading System Decimal Grade
Class Limit 32
Contact Hours: Lecture 55 Lab 0 Worksite 0 Clinical 0 Other 0
Total Contact Hours 55
- Factor expressions used in Pre-calculus, including quadratics, trinomials, difference of squares, sums and differences of cubes, and polynomials.
- Combine and simplify expressions using addition, subtraction, multiplication, and division for:
- Rational expressions including complex fractions
- Radical expressions with limited variable radicands
- Expressions with rational exponents
- Rationalize expressions with monomial/binomial denominators involving only square roots
- Solve various types of equations with an emphasis on:
- Quadratic equations involving completing the square, quadratic formula, factoring, and the square root property
- Rational equations
- Radical equations involving a maximum of two square roots
- Solve nonlinear inequalities (polynomial and rational) using sign analysis and express solutions using interval notation and understand the relationship between sign charts and graphs of functions.
- Combine and simplify complex numbers and convert between radical notation and complex numbers.
II. Functions-with an emphasis on quadratics, rational, and radical functions
- For limited types of elementary functions be able to use and interpret functional notation.
- Determine the domain and range of a variety of functions algebraically and graphically.
- Determine the x and y intercepts and extrema for elementary functions.
- Use simple transformations (horizontal, vertical, x-axis rotations) to create graphs of new functions from their basic elementary functions.
- Determine intervals where a function is increasing/decreasing.
- Algebraically construct new functions using addition, subtraction, multiplication, and division.
- Require initial written self-assessment by students, with periodic revision through quarter.
- Summarize and interpret mathematical information from written formats.
- Identify, extract, and organize critical information into mathematical symbols.
- Clearly communicate steps using proper terminology, symbolization, and notation.
- Demonstrate attention to detail-students will be able to analyze written material for errors and explain why they are incorrect.
IV. Problem solving
- Create realistic mathematical models for applied problems involving polynomials.
- Create a suitable quadratic function for modeling a real world situation presented using words, data, or diagram.
- Identify and justify whether a result generated from a model has real world significance.
V. Technology-emphasis on graphing calculator
- Graph functions choosing the appropriate windows for viewing all details.
- Use the calculator to find intercepts, points of intersection, and extrema for functions.
- Use the table feature to determine values for functions.
- Use a graphing calculator for calculating expression containing multiple operations.
- Emphasize quadratic, rational, and radical functions.
Student Learning Outcomes
Apply mathematical operations to simplify a variety of mathematical expressions including polynomials, rational, and radical expressions.
Apply mathematical operations to solve a variety of mathematical equations including polynomials, rational, and radical equations.
Successfully construct a sign chart for a variety of functions, specifically polynomial and rational, and discuss their relationship to inequalities and graphs.
Examine key features of important function families-quadratic, rational, and radical functions.
Recognize, describe, and analyze functional relationships presented symbolically, tabular, graphically and verbally.
Effectively use graphing calculators to describe and model functions.
Model situations and relationships using polynomial functions.
Communicate, summarize, and interpret mathematical ideas in written and verbal form.
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