本課程是以學生先前的函數的經驗和對變化率認識為基礎的。學生將解決涉及到向量的幾何和代數表示以及在三維空間內線和平面的表示的問題；擴寬了學生對變化率的理解，包括對多項式的導數，正弦函數，指數函數，有理數函數以及根函數理解；運用對真實世界關係的建模的概念和技巧。學生也完善了高中數學成功所需的數學過程的使用。該課程是為那些選擇在科學，工程，經濟學領域，及商業的一些領域追求事業的學生，同時包括那些要求學習大學水平的微積分，線性代數，或物理課程的學生開設的。
A. RATE OF CHANGE
OVERALL EXPECTATIONS
By the end of this course, students will:
- demonstrate an understanding of rate of change by making connections between average rate of change over an interval and instantaneous rate of change at a point, using the slopes of secants and tangents and the concept of the limit;
- graph the derivatives of polynomial, sinusoidal, and exponential functions, and make connections between the numeric, graphical, and algebraic representations of a function and its derivative;
- verify graphically and algebraically the rules for determining derivatives; apply these rules to determine the derivatives of polynomial, sinusoidal, exponential, rational, and radical functions, and simple combinations of functions; and solve related problems.
B. DERIVATIVES AND THEIR APPLICATIONS
OVERALL EXPECTATIONS
By the end of this course, students will:
- make connections, graphically and algebraically, between the key features of a function and its first and second derivatives, and use the connections in curve sketching;
- solve problems, including optimization problems, that require the use of the concepts and procedures associated with the derivative, including problems arising from real-world applications and involving the development of mathematical models.
C. GEOMETRY AND ALGEBRA OF VECTORS
OVERALL EXPECTATIONS
By the end of this course, students will:
- demonstrate an understanding of vectors in two-space and three-space by representing them algebraically and geometrically and by recognizing their applications;
- perform operations on vectors in two-space and three-space, and use the properties of these operations to solve problems, including those arising from real-world applications;
- distinguish between the geometric representations of a single linear equation or a system of two linear equations in two-space and three-space, and determine different geometric configurations of lines and planes in three-space;
- represent lines and planes using scalar, vector, and parametric equations, and solve problems involving distances and intersections.
More please click : MCV4U - Calculus and Vectors
