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Math 105: Mathematical Reasoning

Course Prerequisites:

One of:

Course Description

This course covers a practical breadth of mathematics, with a focus on math encountered in everyday life. It aims to show the relevancy and usefulness of mathematics and to make it meaningful by putting it in an appropriate context. In this course there is a focus on problem solving with a hands-on and learn-by-doing approach.

Course Topics:

  • Unit I: Geometry, Measurement, and Unit Analysis – Chapters 1 and 2
  • Unit II: Linear Equations – Chapter 3
  • Unit III: Personal Finances – Chapters 4, 5, and 6
  • Unit IV: Statistics – Chapters 10, 11, and 12

Credit Awarded

4 hours of credit (some exceptions noted below)

Credit is not given for MATH 105 if the student has credit in MATH 118 or MATH 121 or MATH 160 or MATH 165 or MATH 170 or MATH 180 or the equivalent. No graduation credit for architecture, business administration, or engineering students. 

Course Materials:


College Mathematics, First Edition, published by Scottsdale Community College. This is an open-source textbook.

Students may access PDF copies through MyOpenMath or on Blackboard. Supplementary notes for the textbook are also available on Blackboard.


This is web-based learning software. This will be used for online homework. In MOM, one has access to an electronic version of a text book. MOM is an open-source platform and is FREE to use.


A scientific calculator is required in each class. Cell phone calculators will not be permitted on the midterm or final exams. Texas Instruments graphing calculator (such as a TI-83/83 or TI-84) is recommended.

List of Topics Heading link

The following topics are covered in MATH 105.
Section Topic(s)
1.1 Geometry Basics
1.2 Perimeter
1.3 Area
1.4 The Pythagorean Theorem
1.5 Circles
1.6 Perimeter and Are of composite Figures
1.7 Volume
2.1 Length (English System)
2.2 Weight (English System)
2.3 Capacity
2.4 Metric System
2.5 Converting Between Systems
2.6 Problem Solving with Rates and Dimensional Analysis
3.1 Functions
3.2 Equations of Lines, Intercepts and Graphing, Rate of Change and Initial value Interpretations, Linear Equation Word Problems, Revenue and Profit Functions
3.3 Linear Regression
3.4 Correlation
4.1 Percentage Basics
4.2 Applications Involving Percentages
4.3 Absolute and Relative Change
4.4 Percent Increase/Decrease
4.5 Exponential Functions
5.1 Simple Interest
5.2 Compound Interest
5.3 Annual Percetage Yield
6.1 Annuities
6.2 Payout Annuities
6.3 Loans
10.1 Population vs. Sample
10.2 Sampling
10.3 Problems
10.4 Expirements
11.1 Describing a Distribution
11.2 Measures of Central Tendency
11.3 Measures of Variation
11.4 Quartiles, 5-Number Summary, Hisograms, Boxplots
12.1 The Normal Distribution
12.2 The Empirical Rule
12.3 Standard Scores (z-scores)
12.4 Finding Percentages with Normally Distributed Variables