Foundations for College Mathematics, Grade 11, College Preparation
Curriculum Policy
Mathematics, The Ontario Curriculum, Grades 11 and 12, 2007 (Revised)

Course Description:
This course empowers students to deepen their understanding of mathematics as a practical problem-solving tool. Students will explore quadratic relationships, investigate exponential growth, and tackle problems involving compound interest and vehicle ownership finances. They will enhance their reasoning skills by collecting, analyzing, and evaluating one-variable data while making connections between probability and statistics. Additionally, students will engage with geometry and trigonometry to address real-world problems. Throughout the course, students will refine their mathematical skills, fostering effective problem-solving and clear communication of their thought processes.

Chapters and descriptions:

• Review of Mathematical Concepts
  In this unit, students will revisit key mathematical concepts, emphasizing that mathematics is fundamentally about recognizing patterns and forms. The unit begins with a review of polynomials, including operations such as addition, subtraction, multiplication, and division, as well as binomial distribution. Following this, students will explore factoring quadratics, which serves as a precursor to graphing quadratic functions later in the course. The unit will culminate in a review assignment and quiz to reinforce understanding.
• Real-World Mathematical Models
  This unit focuses on real-world applications of parabolic approximations. Students will analyze quadratic equations in both standard form (y = ax² + bx + c) and vertex form (y = a(x-h)² + k). They will create tables of values to graph parabolas by hand and using online graphing tools. As they graph these functions, students will interpret the impact of different parameters and explore examples of quadratic relationships in real-life contexts.
• Understanding Exponential Relations
  In this unit, students will start with a review of exponent laws, progressing to negative exponents and their implications. Real-life applications will be explored to illustrate these concepts. Students will learn to differentiate between the graphs of exponential relations, linear functions, and quadratic functions. The unit will conclude with practical applications of exponential functions, including growth and decay scenarios.
• Personal Finance Fundamentals
  This unit delves into the financial aspects of significant purchases like cars and homes, highlighting the impact of compound interest. Students will investigate compound interest through examples and problems, using graphing calculators for practical solutions. They will conduct research on various financial institutions to compare services and costs, culminating in an analysis of the financial implications of buying new versus used vehicles or leasing options.
• Exploring Data Management
  Students will discover the significance of data management across various fields such as sports, business, and travel. This unit will cover data gathering techniques, questionnaire design, and survey execution. Students will analyze data representation methods using bar graphs, histograms, and circle graphs, and utilize software for data visualization. They will assess the reliability of their findings and begin exploring basic probability and relative frequency.
• Geometry in Three Dimensions
  In this unit, students will examine methods for visualizing solid shapes through isometric, perspective, and orthographic projections. They will explore the nets of various shapes and investigate applications of geometry in design, art, and architecture, enhancing their spatial reasoning skills.
• Introduction to Trigonometry
  The course concludes with an exploration of trigonometry and its real-world applications. Students will learn the foundational trigonometric ratios and how to apply the Sine Law for non-right-angled triangles. The unit will also cover the Cosine Law, equipping students with tools for solving a variety of problems involving triangles.