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

Course Overview

Course Description

This course introduces the concepts 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.

• Ratio and Proportion: Understanding relationships between quantities.

• Units and Conversions: Converting between different measurement systems.

• Linear Equations: Solving and graphing equations in two variables.

• Inequalities: Solving and interpreting inequalities.

• Percents and Interest: Calculating percentages and simple/compound interest.

• Descriptive Statistics: Summarizing and interpreting data.

• Logical Symbolism: Using logic and symbols to represent mathematical statements.

Prerequisite: Placement as determined by KCTCS placement examination.

Course Competencies / Student Learning Outcomes

Upon completion of this course, students will be able to:

• Interpret and communicate mathematical and/or statistical information verbally, numerically, and graphically.

• Determine when computations are 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 linear equations in two variables and interpret their solutions.

• Use logic to determine the validity of arguments.

• Apply mathematical reasoning to solve real-world problems.

Textbook and Supplies

• Textbook: MyMathLab Student Access Kit ISBN 13: 8220108823246

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

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

Allowed Calculator	Not Allowed Calculators
TI-30XIIS (Scientific)	TI-83 Plus, TI-Inspire (Graphing)
Basic scientific calculators	Any calculator with graphing capabilities

Course Structure, Evaluation, and Grading Methods

Grading Components

• Exams: Four unit exams (proctored) and one comprehensive final exam (proctored).

• Quizzes: Weekly quizzes based on homework and class material.

• Homework: Regular assignments to reinforce learning.

• Discussion/Class Participation: Engagement in class discussions, assignments, and communication.

Component	Percentage
Average of Unit Exams (Proctored)	20%
Comprehensive Final Exam (Proctored)	40%
Quizzes	20%
Homework	15%
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

Key Mathematical Topics

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.

Units and Conversions

Converting between units is essential for solving real-world problems.

• Definition: Changing a measurement from one unit to another.

• Method: Use conversion factors to multiply and change units.

• Example: Convert 5 feet to inches: $5 \times 12 = 60$ inches.

Linear Equations in Two Variables

Linear equations describe straight lines and are fundamental in algebra.

• Standard Form: $Ax + By = C$

• Slope-Intercept Form: $y = mx + b$

• Graphing: Plot points and draw the line through them.

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

Inequalities

Inequalities express relationships where quantities are not equal.

• Definition: Statements using <, >, ≤, or ≥.

• Solving: Similar to equations, but reverse the inequality when multiplying/dividing by a negative.

• Example: Solve $2x + 3 > 7$; $2x > 4$; $x > 2$.

Percents and Interest

Percents are used to describe parts of a whole; interest calculations are common in finance.

• 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.

• Example: Data: 2, 4, 4, 5, 7. Mean = $\frac{2+4+4+5+7}{5} = 4.4$

Logical Symbolism

Logic is used to determine the validity of mathematical arguments.

• 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."

Course Schedule (Tentative)

• Chapters/Sections: 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

• Sections may be omitted or added as needed.

Class Policies and Procedures

• Academic Honesty: Cheating and plagiarism are strictly prohibited.

• Attendance: Participation in assignments and quizzes is required to avoid being reported as a no-show.

• Makeup Policy: No makeup or redo tokens can be used once proctored exams open.

• Communication: Timely response to emails and phone calls is expected.

Additional Info

• Students must activate MyMathLab by the specified date and use a valid email address.

• Temporary access is available for students without financial aid yet.

• Homework must be completed before quizzes can be taken.

• Discussion and class participation are important for success in the course.