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Grade 12 Calculus & Vectors (MCV4U) 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.
12 年级微积分与向量 (MCV4U) 以学生以前的函数经验和他们对变化率的发展理解为基础。 学生将解决涉及向量的几何和代数表示以及三维空间中线和平面的表示的问题; 扩大他们对变化率的理解,包括多项式、正弦、指数、有理和根函数的导数; 并将这些概念和技能应用于现实世界关系的建模。 学生还将改进他们对成功学好高中数学所必需的数学过程的使用。 本课程面向选择在科学、工程、经济学和某些商业领域等领域从事职业的学生,包括需要修读大学级微积分、线性代数或物理课程的学生。

This course builds on your previous experience with functions and your developing understanding of rates of change. You will solve problems involving geometric and algebraic representations of vectors and representations of lines and planes in three-dimensional space; broaden your 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.nnYou will also refine your use of the mathematical processes necessary for success in senior mathematics. This course prepares you for careers in fields such as science, engineering, economics, and some areas of business. It will prepare you for university-level calculus, linear algebra, or physics courses.

课程体系

Unit 1 : Rates of change
1.1: Reviewing prerequisite skills 自由访问 00:00:00
Action 自由访问 00:00:00
Consolidation 自由访问 00:00:00
1.2: Determining rates of change 自由访问 00:00:00
Action 自由访问 00:00:00
Consolidation 自由访问 00:00:00
1.3: Determining limits 自由访问 00:00:00
Action 自由访问 00:00:00
Consolidation 自由访问 00:00:00
1.4: Using first principles to determine the equation of a tangent 自由访问 00:00:00
Action 自由访问 00:00:00
Consolidation 自由访问 00:00:00
Unit 2 : Derivatives
2.1: Finding derivatives (part A) 自由访问 00:00:00
Action 自由访问 00:00:00
Consolidation 自由访问 00:00:00
2.2: Finding derivatives (part B) 自由访问 00:00:00
Action 自由访问 00:00:00
Consolidation 自由访问 00:00:00
2.3: Solving related rates problems 自由访问 00:00:00
Action 自由访问 00:00:00
Consolidation 自由访问 00:00:00
2.4: Investigating velocity, acceleration and second derivatives 自由访问 00:00:00
Action 自由访问 00:00:00
Consolidation 自由访问 00:00:00
Unit 3 : Curve Sketching
3.1: Exploring the first derivative 自由访问 00:00:00
Action 自由访问 00:00:00
Consolidation 自由访问 00:00:00
3.2: Exploring the second derivative 自由访问 00:00:00
Action 自由访问 00:00:00
Consolidation 自由访问 00:00:00
3.3: Sketching curves: part A 自由访问 00:00:00
Action 自由访问 00:00:00
Consolidation 自由访问 00:00:00
3.4: Sketching curves: part B 自由访问 00:00:00
Action 自由访问 00:00:00
Consolidation 自由访问 00:00:00
Unit 4 : Extensions
4.1: Solving optimization problems 自由访问 00:00:00
Action 自由访问 00:00:00
Consolidation 自由访问 00:00:00
4.2: Working with sinusoidal functions 自由访问 00:00:00
Action 自由访问 00:00:00
Consolidation 自由访问 00:00:00
4.3: Working with exponential and logarithmic functions 自由访问 00:00:00
Action 自由访问 00:00:00
Consolidation 自由访问 00:00:00
Unit 5 : Vectors
5.1: Using geometric vectors 自由访问 00:00:00
Action 自由访问 00:00:00
Consolidation 自由访问 00:00:00
5.2: Investigating Cartesian vectors 自由访问 00:00:00
Action 自由访问 00:00:00
Consolidation 自由访问 00:00:00
5.3: Exploring vectors in 3-space 自由访问 00:00:00
Action 自由访问 00:00:00
Consolidation 自由访问 00:00:00
5.4: Creating equations of vectors 自由访问 00:00:00
Action 自由访问 00:00:00
Consolidation 自由访问 00:00:00
5.5: Investigating lines and planes 自由访问 00:00:00
Action 自由访问 00:00:00
Consolidation 自由访问 00:00:00

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