The importance of mathematics in virtually every university discipline makes it essential that we provide students with a strong foundation and opportunities for success.
Their foundation must be established in algebra, geometry, trigonometry, calculus, and increasingly, probability and statistics. Dedicated to helping our students reach their full potential in mathematics, we provide extensive support for all students: we encourage qualified students to challenge themselves by writing math contests and senior students to pursue AP credits; we enhance our students' learning through the use of technology and collaboration, and we encourage hard work by holding students accountable. In short, we are providing a superior quality of training.
We aim not only to provide students with requisite skillsets for future study but also to offer students an appreciation of the fundamental importance of mathematics in human thought and creativity by demonstrating:
- that a mathematical approach to problem-solving (understanding the problem; considering a variety of possible strategies; carrying out one promising method; evaluating the solution) will serve our graduates in many non-mathematical contexts;
- how mathematics underlies music, poetry, the fine arts, and architecture from the classical to the contemporary;
- that mathematics serves as a tool not only for modelling observations in the physical and biological sciences but as an instrument of imagination for peering beyond the possible; and
- how mathematics leads to unforeseen applications including computer science and game theoretical approaches to economics and politics.
We undertake to offer the resources to help the mathematically challenged overcome the obstacles that impede them; we endeavour to provide stimulating contexts to lead the mathematically gifted to realize their talents; we hope to offer every student an opportunity to appreciate the logic, the beauty and the sheer fun of our discipline.
Head of Mathematics
- Principles of Mathematics, Grade 9, Academic
This course enables students to develop an understanding of mathematical concepts related to algebra, analytic geometry, and measurement and geometry through investigation, the effective use of technology, and abstract reasoning. Students will investigate relationships, which they will then generalize as equations of lines, and will determine the connections between different representations of a linear relation. They will also explore relationships that emerge from the measurement of three-dimensional figures and two-dimensional shapes. Students will reason mathematically and communicate their thinking as they solve multi-step problems.
- Principles of Mathematics, Grade 10, Academic
Prerequisite: Mathematics, Grade 9, Academic or Applied
This course enables students to broaden their understanding of relationships and extend their problem-solving and algebraic skills through investigation, the effective use of technology, and abstract reasoning. Students will explore quadratic relations and their applications; solve and apply linear systems; verify properties of geometric figures using analytic geometry; and investigate the trigonometry of right and acute triangles. Students will reason mathematically and communicate their thinking as they solve multi-step problems.
- Functions and Applications, Grade 11, University/College Preparation
Prerequisite: Principles of Mathematics, Grade 10, Academic, or Foundations of Mathematics Grade 10, Applied
This course introduces the basic features of the function by extending students’ experiences with quadratic relations. It focuses on quadratic, trigonometric, and exponential functions and their use in modelling real-world situations. Students will represent functions numerically, graphically, and algebraically; simplify expressions; solve equations; and solve problems relating to applications. Students will reason mathematically and communicate their thinking as they solve multi-step problems.
Successful completion of MCF3M Functions and Applications will prepare students for, Mathematics of Data Management, MDM4U.
- Functions, Grade 11, University Preparation
Prerequisite: Principles of Mathematics, Grade 10, Academic
This course introduces the mathematical concept of the function by extending students’ experiences with linear and quadratic relations. Students will investigate properties of discrete and continuous functions, including trigonometric and exponential functions; represent functions numerically, algebraically, and graphically; solve problems involving applications of functions; investigate inverse functions; and develop facility in determining equivalent algebraic expressions. Students will reason mathematically and communicate their thinking as they solve multi-step problems.
- Advanced Functions, Grade 12, University Preparation
Prerequisite: Functions, Grade 11, University Preparation, or Mathematics for College Technology, Grade 12, College Preparation
Note: The Advanced Functions course must be taken before or concurrently with Calculus and Vectors (MCV4U).
This course extends students’ experience with functions. Students will investigate the properties of polynomial, rational, logarithmic, and trigonometric functions; develop techniques for combining functions; broaden their understanding of rates of change; and develop facility in applying these concepts and skills. Students will also refine their use of the mathematical processes necessary for success in senior mathematics. This course is intended both for students taking the Calculus and Vectors course as a prerequisite for a university program and for those wishing to consolidate their understanding of mathematics before proceeding to any one of a variety of university programs.
- Calculus and Vectors, Grade 12, University Preparation
Prerequisite: Grade 12 Advanced Functions MHF4U, University Preparation, must be taken before or concurrently with Calculus and Vectors
This course builds on students’ previous experience with functions and their developing understanding of rates of change. Students will solve problems involving geometric and algebraic representations of vectors and representations of lines and planes in three-dimensional space; broaden their understanding of rates of change to include the derivatives of polynomial, sinusoidal, exponential, rational, and radical functions; and apply these concepts and skills to the modelling of real-world relationships. Students will also refine their use of the mathematical processes necessary for success in senior mathematics. This course is intended for students who choose to pursue careers in fields such as science, engineering, economics, and some areas of business, including those students who will be required to take a university-level calculus, linear algebra, or physics course.
- AP Calculus
Recommended preparation: Calculus and Vectors, Grade 12 University Preparation and Advanced Functions, Grade 12, University Preparation
This course will be taught in conjunction with the College Board’s Advanced Placement curriculum
Calculus is an essential tool for advanced study in many disciplines. This interdisciplinary approach to calculus includes applications in physics and economics to illustrate the importance of calculus to the physical and social sciences.
Topics covered by all students include limits and continuity; differential calculus of functions of a single variable including techniques of differentiation; the Mean Value Theorem and determination of extremes; applications of differential calculus with particular emphasis on physics and economics; differential equations and slope fields; integral calculus of functions of a single variable including the Fundamental Theorem of Calculus and techniques of integration; applications of integral calculus.
Students pursuing the BC designation will also study polar coordinates and parametric equations; improper integrals; infinite sequences and series, Taylor Series.
Students will study toward gaining the AP Calculus AB/BC credits in IDC4U.
*St. Andrew’s College entrance requirement:
Students wishing to enroll in this course should have demonstrated a proficiency in previous math courses as well as a sincere desire to work at the accelerated pace required of the Advanced Placement curriculum.
- Mathematics of Data Management, Grade 12, University Preparation
Prerequisite: Functions, Grade 11, University Preparation, or Functions and Applications, Grade 11, University/College Preparation
This course broadens students’ understanding of mathematics as it relates to managing data. Students will apply methods for organizing large amounts of information; solve problems involving probability and statistics; and carry out a culminating investigation that integrates statistical concepts and skills. Students will also refine their use of the mathematical processes necessary for success in senior mathematics. Students planning to enter university programs in business, the social sciences, and the humanities will find this course of particular interest.
Topics to be studied include tools for data management; statistics of one variable; statistics of two variables; permutations and organized counting; combinations and the binomial theorem; introduction to probability; probability distributions; the normal distribution.
- AP Mathematics of Data Management, Grade 12, University Preparation
Prerequisite: Functions, Grade 11, University Preparation
Recommended preparation: Advanced Functions and Calculus and Vectors, Grade 12, University Preparation
This course will be taught in conjunction with the College Board’s Advanced Placement curriculum
AP-Statistics is a university-level course focussing on four main themes:
- Exploring Data (observing patterns and departures from patterns using graphical and numerical techniques)
- Planning a study (deciding what and how to measure: data must be collected according to a well-developed plan if valid information on a conjecture is to be obtained)
- Anticipating patterns (producing models using probability and simulation: anticipating what the distribution of data should look like under a given model)
- Statistical inference (confirming models, including a statement in probability language of how confident one can be about the selection)
Students will employ a variety of resources including TI-83+ programs, Fathom statistical software, a video series entitled Decisions Through Data; review sheets; online applets, online quizzes, Excel, and free-response questions from previous AP-Statistics exams.
OSS Equivalence: This course is cross-listed with MDM4U. Thus, this course will appear as MDM4U on the Ontario Student Transcript. Students must take either MDM4U OR MDM4UP but not both.
The use of laptop technology, as outlined in the Laptop Integration Plan, has given students access to additional and powerful resources. Students can access graphing software that enables two- and three-dimensional objects to be viewed, rotated, and analyzed. Internet links allow the students to view applets that help to demonstrate many difficult to visualize concepts.
Grade 9 through 12 courses require a scientific calculator; Any students in AP courses require at least a TI-84 calculator.
Recommended Scientific Calculators
• TI 30X II
• Casio fx-300MS
• Sharp EL 531X
Throughout the year, St. Andrew’s students participate in various math competitions at both the regional and national levels, including:
- American Mathematics Competition (AMC) (University of Nebraska)
- Canadian Intermediate Math Contest (Grades 9 and 10)
- Fryer, Galois and Hypatia Contests (Grades 9-11)
- The Canadian National Mathematics League Award (Grades 9-12)
- The Cayley Contest (Grade 10)
- The Euclid Contest (Grade 12)
- The Fermat Contest (Grade 11)
- The Pascal Contest (Grade 9)