Foundations of College Mathematics (MBF3C)

Starting with a focus on trigonometry, this segment of the course immerses learners in the everyday uses of trigonometric principles. Students will gain an essential grasp of core trigonometric ratios, setting the stage for deeper exploration. The journey continues with an in-depth look at the Sine Law, an essential method for solving problems involving non-right triangles. We wrap up the unit with an engaging dive into the Cosine Law, showcasing its real-world applications. This establishes a solid base in trigonometry that will support students throughout the course.

This unit begins by delving into various strategies for conducting surveys in a population. It then shifts to focus on the creation of effective questionnaires to ensure efficient data gathering. Students will learn to use bar graphs, histograms, and circle graphs to visually present their collected data. Additionally, this unit introduces the use of software tools for enhanced data visualization.

After the stage of data collection and visual representation, students will engage in analyzing their results and evaluating the data's reliability. Simultaneously, the unit will introduce concepts of probability and relative frequency. This approach provides students with a comprehensive insight into data analysis and probability, tying these elements seamlessly into the broader course narrative.

Throughout this unit, students will develop their problem-solving abilities with a focus on single-variable data. They will embark on a journey of data management that includes gathering, structuring, examining, and assessing information. As the unit draws to a close, students will have honed their skills in identifying and showcasing probabilities. They will also learn to recognize and explain how probability is applied in different real-world scenarios.

This unit is centered on helping students discover and understand the interplay between numerical, graphical, and algebraic forms of quadratic relationships. The primary objective is to harness these relationships as effective tools for problem solving. Students will dive deep into the core features of quadratic models and investigate their potential transformations. The unit is designed to bolster students' skills in maneuvering through and utilizing quadratic functions in diverse formats to tackle a variety of challenges.

The unit kicks off with an engaging exploration of how parabolas can be approximated in real-world scenarios. Moving forward, students will be introduced to quadratic equations, presented either in the standard format (y = ax^2 + bx + c) or in vertex form (y = a(x-h)^2 + k). With these equations, they'll create value tables and use these to manually sketch out the parabolas. To add a modern twist, students will also use online graphing tools for a more interactive representation.

As students become adept at preparing value tables and drawing functions both manually and digitally, the focus will shift towards understanding how different equation parameters affect the graph. Additionally, they will delve into real-world instances of Quadratic Relationships, analyzing charts and graphs to fully grasp their practical applications and significance.

This unit delves into the art of visualizing three-dimensional objects using diverse techniques such as isometric, perspective, and orthographic views. Students will explore how to unfold solid shapes into their two-dimensional nets, gaining insight into their structural aspects. Furthermore, the unit will cover the real-life uses of geometry in areas like design, art, and architecture. This comprehensive approach will equip students with an understanding of how geometric concepts are applied in various practical scenarios.

This unit starts with a refresher on the laws of exponents, followed by an in-depth examination of negative exponents and their significance. Students will be exposed to real-world scenarios to understand the practical applications of these mathematical concepts. Before delving into exponential relation graphs, there will be a clear differentiation between these and linear (straight line) and quadratic (parabola) relations. In the final stages of the unit, students will engage in practical exercises involving exponential functions, covering instances of exponential growth and decay.

This unit is dedicated to exploring the intricate details of interest, with a special focus on the distinctions and comparisons between simple and compound interest. Students will delve into the relationship between compound interest and exponential growth. Moreover, the unit aims to provide students with the necessary tools and techniques to adeptly handle compound interest-related problems. A significant part of the learning will involve grasping the subtleties of interest computations and their real-world applications in diverse situations.

At the outset of this unit, students will be immersed in practical examples and challenges related to compound interest, using graphing calculators as a key tool for resolution. The unit then progresses into an assignment phase, where students will conduct research on various financial institutions. They will analyze and compare the services, fees, and charges of these institutions to develop a well-rounded understanding of what each offers.

In the concluding section, the focus shifts to the financial considerations involved in major acquisitions, such as purchasing new or used vehicles or opting for vehicle leases. Students will evaluate the financial benefits of each choice, equipping them with real-life knowledge for making informed decisions in significant financial matters.

This crucial task, making up 30% of the final grade, requires students to create a detailed portfolio with three main parts:

1. Quick Reference Guide: A succinct document summarizing key concepts, serving as a handy reference for anyone in the course.
2. Unit-wise Sample Problems: Include one problem with a solution for each unit, demonstrating a broad and deep understanding of the topics.
3. Real-life Application: Present a real-world scenario that applies the course concepts, showcasing practical relevance.

The portfolio should not just display knowledge of each unit but also the students' ability to integrate and apply mathematical concepts in real-life situations.

The ultimate assessment is a supervised two-hour exam, accounting for 30% of the student's overall grade.

• A laptop or personal computer, ideally equipped with Google Chrome or Mozilla Firefox for web browsing.
• A reliable internet connection.
• Means for video recording and scanning handwritten work, such as a mobile phone, tablet, iPad, or webcam.
• A scientific calculator that is non-programmable and non-graphing.

• Provision of Google Suites or Microsoft Education access for word processing and presentation software, with individual accounts for students.
• A selection of supplementary readings to enhance the course content.
• Access to tutorial videos and instructions via Screencast for extra help.
• Solution videos to support comprehension and problem-solving.
• School-facilitated accounts for online tools and platforms like Gizmos, Labster, Mathletics, GeoGebra, and Padlet.

Note: As this course is fully online, there is no requirement for textbooks.