MCV4U1 (Grade 12 Calculus & Vectors)

About MCV4U1

MCV4U1 is a grade 12 university preparation Math course, "Calculus and Vectors," for students who would like to pursue the fields of science, engineering, economics, and/or some areas of business in university. In this course, students will be introduced to two important branches of Mathematics: Calculus and Vectors.

Calculus is a branch of Mathematics in which students study rates of change, that is, how things change over time. Between the late 17th century and the early 18th century, it was known that Calculus was independently invented by Issac Newton (1643-1727) and Gottfried Wilhelm Leibniz (1646-1716). However, it was also mentioned in the book, "The Secret Lives of Numbers: A Hidden History of Math's Unsung Trailblazers," by Kate Kitagawa and Timothy Revell that the Indian mathematicians such as Mādhava from the Kerala school in the south of India had an understanding of Calculus in the fourteenth century, which was before Newton's and Leibniz's times. However, more research needs to be conducted to find out exactly how much Mādhava and Indian mathematicians in the Kerala school knew about Calculus and when. A summary of the history of Calculus can be read from below:

01c - Supplementary Reading 1.1 (Pioneers of Calculus).docx

In the Calculus portion of this MCV4U1 course, students will learn how to calculate the rates of change of algebraic functions (e.g., polynomial, rational, and piecewise functions) and transcendental functions (e.g., trigonometric, exponential, and logarithmic functions) using the concepts of limits and derivatives. The students will also learn strategies to sketch a curve and solve optimization problems.

After that, students will learn Vectors, another branch of Mathematics. In the Vector portion of this MCV4U1 course, students will study geometric and algebraic quantities that have both magnitudes and directions. They will then learn how to solve 2D and 3D real-world applications using the concepts of geometric and algebraic vectors and their operations, such as the dot product, cross product, and scalar and vector projections. They will also learn different representations of lines and planes (e.g., vector, parametric, Cartesian, and symmetrical forms) and their intersections and distances.