Grade 12

Advanced Placement(AP) Calculus is taken after MCV4U at Central Toronto Academy and is equivalent to a first semester university calculus course.

The Mathematical Content component of the course prepares students for writing the Advanced Placement(AP) Calculus Exam. This exam is administered by the AP College Board and a course description including topic outline can be found here . 

In many instances it is possible to cover material that exceeds that on the AP Exam, dependent on student interest but may include topics such as Vector Calculus and Complex Analysis.

The Mathematics In The Community component of the course addresses the role of mathematics in society. For AP Calculus this will encompass themes such as:

• application of mathematics in understanding the physical universe

• the nature of knowledge, learning, and understanding in mathematics

• the role of empathy and reflection in mathematical learning and collaboration

Course Outline >

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. Course Outline >

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. Course Outline >

This course broadens students’ understanding of mathematics as it relates to managing data. Students will apply methods for organizing and analysing 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. Course Outline >

This course enables students to broaden their understanding of real-world applications of mathematics. Students will analyse data using statistical methods; solve problems involving applications of geometry and trigonometry; solve financial problems connected with annuities, budgets, and renting or owning accommodation; simplify expressions; and solve equations. Students will reason mathematically and communicate their thinking as they solve multi-step problems. This course prepares students for college programs in areas such as business, health sciences, and human services, and for certain skilled trades. Course Outline >