MAT 110-4822: Applied Mathematics (College Algebra) – Syllabus and Study Guide

Course Overview

Course Description

This course introduces the principles of ratio and proportion, units and conversions, linear equations in two variables, inequalities, graphing and writing equations of a line, percents, interest, descriptive statistics, and logical symbolism. Emphasis is placed on applications in various technologies.

• Key Topics: Ratio and proportion, unit conversions, linear equations, inequalities, graphing, percents, interest, statistics, logic.

• Applications: Real-world problem solving in economics, science, and technology.

Prerequisites

Required Background

• Placement as determined by KCTCS placement examination.

Course Competencies / Student Learning Outcomes

Upon Completion, Students Will Be Able To:

• Interpret and communicate mathematical and/or statistical information in various forms.

• Determine computations needed and execute appropriate calculations.

• Apply an appropriate model to solve problems.

• Make inferences, evaluate assumptions, and assess limitations in estimation, modeling, and/or statistical analysis.

• Graph a line and write linear equations in two variables.

• Solve systems of linear equations in two variables.

• Use and interpret scientific notation.

• Calculate and interpret percents and interest.

• Use logic to determine the validity of arguments.

• Apply application problems involving the above competencies.

Textbook and Supplies

• Textbook: MyMathLab Student Access Kit ISBN 13: 82201088232426

• Calculator: Scientific calculator (TI-30XIIS recommended). No graphing calculators allowed.

• Other Supplies: Windows-based computer, 3-ring binder.

Course Structure, Evaluation, and Grading Methods

Grading Components

• Exams: Four unit exams (proctored) – 20% each

• Comprehensive Final Exam: (Proctored) – 40%

• Quizzes: 10%

• Homework: 5%

• Discussion/Class Participation/Assignments/Communication: 5%

Grading Scale:

Grade	Percentage
A	90 or above
B	80-89
C	70-79
D	60-69
E	59 or lower

Assessment Details

• Exams: Timed, proctored, and must be completed by the due date. Extensions require instructor approval and tutoring session.

• Quizzes: Weekly, due Monday night. Extensions require tutoring and instructor approval.

• Homework: Must be completed for quiz eligibility. Score of 90% required to unlock quiz.

• Discussion/Class Participation: Includes assignments, projects, and communication. Worth 5% of grade.

• Redo Tokens: Allow retake of one quiz or test per unit (units 1-3), not for proctored exams or final.

Course Schedule

Chapters/Sections Covered

• 3.1-3.3

• 5.1-5.2, 5.3, 5.5, 5.6

• 6.1-6.8

• 7.1 and 7.2

• Chapter 8

• Chapter 11

• 13.1, 13.4-13.7

Note: Schedule is tentative and may be adjusted as needed.

Calculator Policy

Allowed and Not Allowed Calculators

Allowed	Not Allowed
TI-30XIIS (Scientific Calculator)	TI-83 Plus, TI-Inspire CX (Graphing Calculators)

No graphing calculators are permitted. If unsure, consult the instructor.

Academic Honesty and Policies

Cheating and Plagiarism

• All work must be your own. Sharing answers or using unauthorized resources is prohibited.

• Violations result in academic sanctions, including possible failure of the course.

Class Policies and Procedures

• Review all class policies/procedures on the KCTCS Syllabus Information Webpage.

• Late assignments and makeups require instructor approval and may require tutoring.

• Attendance and engagement are required to avoid being reported as a no-show.

Key Mathematical Concepts

Ratio and Proportion

Ratios compare two quantities, while proportions state that two ratios are equal.

• Definition: A ratio is a comparison of two numbers by division.

• Proportion: An equation stating that two ratios are equal.

• Formula: $\frac{a}{b} = \frac{c}{d}$

• Example: If $\frac{2}{3} = \frac{4}{6}$, then the proportion is true.

Unit Conversions

Unit conversions involve changing a quantity from one unit to another using conversion factors.

• Conversion Factor: A ratio that expresses how many of one unit are equal to another unit.

• Example: To convert 5 feet to inches: $5 \text{ ft} \times \frac{12 \text{ in}}{1 \text{ ft}} = 60 \text{ in}$

Linear Equations in Two Variables

Linear equations describe straight lines in the coordinate plane and can be written in several forms.

• Slope-Intercept Form: $y = mx + b$

• Standard Form: $Ax + By = C$

• Graphing: Plot the y-intercept, use the slope to find another point, and draw the line.

• Example: $y = 2x + 3$ has slope 2 and y-intercept 3.

Systems of Linear Equations

Systems involve solving for variables that satisfy multiple linear equations simultaneously.

• Methods: Substitution, elimination, graphing.

• Example: Solve $x + y = 5$ and $x - y = 1$.

Inequalities

Inequalities compare values and can be solved similarly to equations, with attention to direction when multiplying/dividing by negatives.

• Example: Solve $2x - 3 < 7$.

• Solution: $2x < 10 \Rightarrow x < 5$

Percents and Interest

Percents express ratios out of 100; interest calculations are common in financial mathematics.

• Percent Formula: $\text{Percent} = \frac{\text{Part}}{\text{Whole}} \times 100$

• Simple Interest: $I = Prt$ where $I$ is interest, $P$ is principal, $r$ is rate, $t$ is time.

• Example: $P = 1000$, $r = 0.05$, $t = 2$ years: $I = 1000 \times 0.05 \times 2 = 100$

Descriptive Statistics

Descriptive statistics summarize and describe data sets.

• Mean: $\bar{x} = \frac{\sum x_i}{n}$

• Median: Middle value when data is ordered.

• Mode: Most frequently occurring value.

Logical Symbolism

Logic uses symbols to represent statements and arguments, helping determine validity.

• Common Symbols: $\land$ (and), $\lor$ (or), $\neg$ (not), $\rightarrow$ (implies)

• Example: If $p$ is "It is raining" and $q$ is "I have an umbrella", $p \rightarrow q$ means "If it is raining, then I have an umbrella."

Additional info:

• Some details inferred from standard College Algebra syllabi and course descriptions.

• Calculator policy and redo tokens are specific to this course and may differ from other institutions.