Course information
Students will extend their understanding of rates of change to include the derivatives of polynomial, rational, exponential, logarithmic, and trigonometric functions; and they will apply these to the modelling of real-world relationships. Integral calculus and its applications will be introduced. Students will solve problems involving vectors and lines and planes in three-dimensional space.
The following units are covered in this course.
- Functions, Graphs, and Limits
- The Derivative
- Applications of Derivatives
- Curve Sketching
- Optimization and Related Rates
- Derivatives of Exponential, Logarithmic, and Trigonometric Functions
- Applications of Exponential, Logarithmic, and Trigonometric Functions
- Integral Calculus
- Applications of Integral Calculus
- Introduction to Vectors
- Algebraic Vectors and Applications
- Equations and Intersections of Lines in ℝ2 and ℝ3
- Equations and Intersections of Planes
This course is intended for students who have studied or are currently studying the Advanced Functions and pre-Calculus Courseware.
Typical lesson structure
Each Courseware lesson normally corresponds to between one and three classroom lessons and consists of the sections below.
In this section, the information is presented using narrated slideshows. Key features throughout include the following interactive elements and learning aids:
- Investigation: A guided exploration to create or manipulate mathematical objects.
- Check Your Understanding: Practice questions for students to answer online. Feedback is provided, and students can keep trying variations of the same question until they have mastered the concept.
- Alternative Format: This page is a text version of the narrated slideshows and interactive elements.
Some of the questions and interactive explorations from the Watch section are reproduced here for quick access and to help reinforce the lesson goals.
This final section includes a set of extra problems for students to solve on paper. Answers are provided for all problems, and full solutions are provided for only the even-numbered problems. All the exercises, answers, and solutions in a unit are reproduced as the second-last item in the list of lessons for each unit.
A set of more challenging problems that extend the material, connect different lessons, and explore additional applications is provided as the last item in the list of lessons for each unit.