Course Description:

This course builds on student’s previous experience with functions and their developing understanding of rates of change. Students will solve problems involving geometric and algebraic representations of vectors, 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 knowledge in order to make 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. This course will include those students who are required to take a university-level calculus, linear algebra, or physics course.

 

Aims and Objectives:

• Demonstrate an understanding of the rate of change by making connections between the 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 limit.
• Graph the derivatives of polynomial, sinusoidal, and exponential functions.
• Make connections between the numeric, graphical and algebraic representations of a function and its derivative.
• Verify graphically and algebraically the rules for determining derivatives.
• Determine the derivatives of polynomial, sinusoidal, exponential, rational, and radical functions, and simple combinations of functions by applying these rules and solve related problems.
• Make connections, graphically and algebraically, between the key features of a function and its first and second derivatives and use the connections in the 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.
• Involving the development of mathematical models.
• 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.
• Determine different geometric configurations of lines and planes in three-space.
• Represent lines and planes using scalar, vector, and parametric equations.
• Solve problems involving distances and intersections.

 

Expectations:

• Rate of Change

 

By the end of this course, students will:

 

1. Understand the real-world applications of rates of change used as the average rate of change of a function, representation as a slope corresponding to the secant, an approximate value of the instantaneous rate of change at a given point and over intervals containing that point.
2. Understand and visualize connections between technical terms like slope, tangent, secant, dependent/independent variables, average and instantaneous change.
3. Investigate, a function “f(x)” that is smooth over the interval “a <= x <= (a + h)”, to find tangent to a curve and the connection between the average rate of change and the instantaneous rate of change of the function “f(x)”.
4. Get familiarized with a function “y = f(x)” and technical terms as represented on a Cartesian Graph.

 

• Derivatives

 

By the end of this course, students will:

 

1. Learn a set of rules to quickly determine the instantaneous rate of change.

 

• Curve Sketching

 

By the end of this course, students will:

 

1. Use concepts of derivatives to determine key features of a graph.

 

• Derivatives of Sinusoidal Functions

 

By the end of this course, students will:

 

1. Explore the instantaneous rates of change of sinusoidal functions and apply the rules of differentiation from earlier chapters to model and solve a variety of problems involving periodicity.
2. The numeric, graphical, and algebraic representations of exponential functions.

 

• Exponential and Logarithmic Functions

 

By the end of this course, students will:

 

1. Extend your understanding of differential calculus by exploring and applying the derivatives of exponential functions.

 

• Geometric Vectors

 

By the end of this course, students will:

 

1. Investigate vectors, which are quantities with both magnitude and direction.

 

• Cartesian Vectors

 

By the end of this course, students will:

 

1. Express vectors in Cartesian coordinates and develop a three-dimensional coordinate system.

 

• Lines and Planes

 

By the end of this course, students will:

 

1. Revisit your knowledge of intersecting lines in two dimensions and extend those ideas into three dimensions.
2. Investigate the nature of planes and intersections of planes and lines.
3. Develop tools and methods to describe the intersections of planes and lines.

 

Unit-wise Progression:

Unit	Title and Subtopics
Unit 1	Rate of Change   Rate of Change Limits and Continuity Introductions to Derivatives   -Hours: 10
Unit 2	Derivatives   Derivatives of Polynomial Functions Product Rule, Velocity and Acceleration Chain Rule and Derivatives of Quotients Rate of Change Problems   - Hours:12
Unit 3	Curve Sketching   Increasing and Decreasing Functions, Maxima and Minima Concavity and the Second Derivative Simple Rational Functions and Optimization Problems   - Hours: 13
Unit 4	Derivatives of Sinusoidal Functions   Instantaneous Rate of Change of Sinusoidal Functions Derivatives of Sinusoidal Functions and Differentiation Rules Applications of Sinusoidal Functions and Their Derivatives   - Hours: 14
Mid term - Hours 2:
Unit 5	Exponential and Logarithmic Functions   Rates of Change, The Number 'e', and The Natural Logarithm Derivatives of Exponential Functions and Differentiation Rules Exponential Models   - Hours: 14
Unit 6	Geometric Vectors   Vectors and their Addition, Subtraction and Multiples Applications of Vector Addition and Resolution Into Rectangular Components   - Hours: 10
Unit 7	Cartesian Vectors   Cartesian Vector and The Dot Product Vectors in Three Dimensional Space The Cross Product and it's Properties Geometric Series + Financial Applications   - Hours: 15
Unit 8	Lines and Planes   Equations of Lines in Two-Space and Three-Space Equations of Planes And It's Properties Intersection of Lines and Planes   - Hours: 12
Culminating Activity ­– 5Hours
Final Term – 3Hours
Total –Hours 110

 

 

Teaching/Learning Methodologies:

This course supports learning by providing students with opportunities to review and activate prior knowledge (e.g. reviewing concepts related to trigonometry and geometry from prior mathematics courses) in order to gain new skills. The course further leads students toward recognizing opportunities to apply the knowledge they have gained to solve problems. This course models the use of spreadsheet software, TVM spreadsheet, and additional software like Demos which will allow students to investigate the key concepts of the course Outside the Box. This course connects the concepts taught to real-world applications, such as exponential decay, simple harmonic motion and The Golden Ratio. With the help of examples, practice problems, and solution videos, the course models various ways to demonstrate understanding poses questions that require students to use different representations as they are working at each level of conceptual development - concrete, visual, or symbolic, and allows individual students the time they need to solidify their understanding at each conceptual stage. Through the use of interactive activities (e.g. multiple choice quizzes, and drag-and-drop activities) students receive instantaneous feedback and are able to self-assess their understanding of concepts. A few of the things students will be provided are the following:

• Lesson plans
• PowerPoint presentations
• Videos
• Reading Packs
• Assignment for Learning
• Assessment of Learning
• Quiz   

All of these are a cluster of downloadable and embedded files that will be provided to each candidate with the progression of the course.

 

E-Learning Approach:

E-learning is not only a training method but it is a learning method that is tailored to individuals. It is found that different terminologies have been used to define learning that takes place online which actually makes difficult to develop a generic definition.

E-learning includes the delivery of content via Internet, Intranet, and Extranet, satellite broadcast, audio-video tape, interactive TV and CD-ROM. The term implies that the learner is at a distance from the tutor or instructor, that the learner uses some form of technology.

With attention to this new system of education that is spreading across the globe its imperative that the content of such study programs are enhanced and modified to serve both the learner and the instructor well whilst dealing with the gap of conventional studying methodologies. Thus the courses promise its reader an experience full of engagement, student-concentric approach, personalization and Interaction.  Using a wide array of multimedia tools, cloud based LMS and diverse repository of subject tailored audio-visual material that student can utilize and learn in a stimulated work environment where he’s in charge of his work hours.

Our e-learners paddle through these courses in the mediation of skilled mentors to the finish line with understanding of their subject’s application into real world problems following a futuristic model of education.

 

Strategies for Assessment and Evaluation of Student Performance:

Assessment is the ongoing gathering of information related to the individual student’s progress in achieving the curriculum expectations of the course. To guide the student to his/her optimum level of achievement, the teacher provides consistent and detailed feedback and guidance leading to improvement. Strategies may include:

• Diagnostic assessment
• Formative assessment
• Summative assessment
• Performance assessment
• Portfolio assessment
• Rubrics
• Checklists

The final grade will be based on:

Weightage in Percentage	Categorical Marking Breakdown
35%	Course Work
20%	Mid Term
15%	Culminating Activity
30%	Final Exam

 

Assessment of Learning
Student Product	Observation	Conversation
Learning Logs (anecdotal) Assignment Pre-tests (scale/rubric) Quizzes (scale/rubric) Rough drafts (rubric) Graphic organizers (scale) Peer feedback (anecdotal/checklist) Reports (rubric) Essays (rubric) Webbing/Mapping (rubric/scale) Vocabulary notebooks (anecdotal) Visual Thinking Networks (rubric) Tests (scale/rubric) Exams	Self-proofreading (checklist) Class discussions (anecdotal) Debate (rubric) PowerPoint presentations (rubric) Performance tasks (anecdotal/scale)	Student teacher conferences (checklist) Debate (rubric) Peer-feedback (anecdotal) Peer-editing (anecdotal) Oral pre-tests (scale/rubric) Oral quizzes (scale/rubric) Oral tests (scale/rubric) Question and Answer Session (checklist)

 

Resources Required by the Student:

• Microsoft Suite (Word, Excel, Power-point etc.)
• A laptop, or Mac, or Android, or any other operating system functional enough to use the web browser and use online software.
• Curriculum Reference: The Ontario Curriculum, Maths