Available courses

Course Description

This course enables students to deepen their understanding of physics concepts and theories. Students will continue their exploration of energy transformations and the forces that affect motion, and will investigate electrical, gravitational, and magnetic fields and electromagnetic radiation. Students will also explore the wave nature of light, quantum mechanics, and special relativity. They will further develop their scientific investigation skills, learning, for example, how to analyse, qualitatively and quantitatively, data related to a variety of physics concepts and principles. Students will also consider the impact of technological applications of physics on society and the environment.


 

Unit Titles and DescriptionsTime Allocated

Dynamics

Students will review concepts essential to their success in the course: scientific notation, significant digits, vector operations, and fundamental mathematical tools. Principles of kinematics and free body diagrams will also be reviewed and extended. By the end of the unit, students will demonstrate and understanding of the forces involved in uniform circular motion and motion in a plane. They will have investigated forces involved in these modes of motion and have solved related problems. They will analyse technological devices that apply the principles of dynamics of motion, with particular respect to the effect of g-forces on the human body.

22 hours

Energy and Momentum

Students will demonstrate an understanding of work, energy, momentum. Drawing from Grade 10 concepts of the laws of conservation of energy, they will extend these ideas to conservation of momentum in one and two dimensions. Through computer simulation and other modes of inquiry they will investigate these phenomena and solve related problems. They will conduct analyses and propose improvements to technologies and procedures that apply principles related to energy and momentum, and assess the social and environmental impact of these.

20 hours

Gravitational, Electric and Magnetic Fields

By the end of this unit, students will demonstrate an understanding of the concepts, properties, principles and laws related to gravitational, electric and magnetic fields, particularly with respect to their interactions with matter. They will investigate these phenomena graphically and through use of other electronic models. They will analyse the operation of technologies that use these fields, and discuss the social and environmental impact of these technologies.

22 hours

The Wave Nature of Light

Building upon concepts developed during Grade 10, students will study light with particular respect to its wave nature. Properties of waves will be discussed in a general sense, and the principles of diffraction, refraction, interference and polarization will be investigated theoretically and through simulation. Technologies that make use of the knowledge of the wave nature of light, and their social and environmental impacts, will be discussed.

22 hours

Revolutions in Modern Physics: Quantum Mechanics and Special Relativity

In this unit, some of the most exciting and counterintuitive concepts in physics, including Einstein's ideas about relativity, photoelectric effect, and particle physics, will be examined. Quantum mechanics and special relativity will be investigated mathematically and related problems will be solved. In light of the revolutionary ideas studied in this unit, students will discuss how the introduction of new conceptual models can influence and change scientific thought, and lead to the development of new technologies.

21 hours
Final Assessment

Exam

This is a proctored exam worth 30% of your final grade.

3 hours
Total110 hours 

This course 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.



Unit Titles and DescriptionsTime Allocated

Vectors

There are four main topics pursued in this initial unit of the course. These topics are: an introduction to vectors and scalars, vector properties, vector operations and plane figure properties. Students will tell the difference between a scalar and vector quantity, they will represent vectors as directed line segments and perform the operations of addition, subtraction, and scalar multiplication on geometric vectors with and without dynamic geometry software. Students will conclude the first half of the unit by proving some properties of plane figures, using vector methods and by modeling and solving problems involving force and velocity. Next students learn to represent vectors as directed line segments and to perform the operations of addition, subtraction, and scalar multiplication on geometric vectors with and without dynamic geometry software. The final topic involves students in proving some properties of plane figures using vector methods.

12 hours

Linear Dependence and Coplanarity

Cartesian vectors are represented in two-space and three-space as ordered pairs and triples, respectively. The addition, subtraction, and scalar multiplication of Cartesian vectors are all investigated in this unit. Students investigate the concepts of linear dependence and independence, and collinearity and coplanarity of vectors.

10 hours

Vector Applications

Applications involving work and torque are used to introduce and lend context to the dot and cross products of Cartesian vectors. The vector and scalar projections of Cartesian vectors are written in terms of the dot product. The properties of vector products are investigated and proven. These vector products will be revisited to predict characteristics of the solutions of systems of lines and planes in the intersections of lines and planes.

10 hours

Intersection of Lines and Planes

This unit begins with students determining the vector, parametric and symmetric equations of lines in R2 and R3. Students will go on to determine the vector, parametric, symmetric and scalar equations of planes in 3-space. The intersections of lines in 3-space and the intersections of a line and a plane in 3-space are then taught. Students will learn to determine the intersections of two or three planes by setting up and solving a system of linear equations in three unknowns. Students will interpret a system of two linear equations in two unknowns geometrically, and relate the geometrical properties to the type of solution set the system of equations possesses. Solving problems involving the intersections of lines and planes, and presenting the solutions with clarity and justification forms the next challenge. As work with matrices continues students will define the terms related to matrices while adding, subtracting, and multiplying them. Students will solve systems of linear equations involving up to three unknowns, using row reduction of matrices, with and without the aid of technology and interpreting row reduction of matrices as the creation of new linear systems equivalent to the original constitute the final two new topics of this important unit.

12 hours

Concepts of Calculus

A variety of mathematical operations with functions are needed in order to do the calculus of this course. This unit begins with students developing a better understanding of these essential concepts. Students will then deal with rates of change problems and the limit concept. While the concept of a limit involves getting close to a value but never getting to the value, often the limit of a function can be determined by substituting the value of interest for the variable in the function. Students will work with several examples of this concept. The indeterminate form of a limit involving factoring, rationalization, change of variables and one sided limits are all included in the exercises undertaken next in this unit. To further investigate the concept of a limit, the unit briefly looks at the relationship between a secant line and a tangent line to a curve. To this point in the course students have been given a fixed point and have been asked to find the tangent slope at that value, in this section of the unit students will determine a tangent slope function similar to what they had done with a secant slope function. Sketching the graph of a derivative function is the final skill and topic.

12 hours

Derivatives

The concept of a derivative is, in essence, a way of creating a short cut to determine the tangent line slope function that would normally require the concept of a limit. Once patterns are seen from the evaluation of limits, rules can be established to simplify what must be done to determine this slope function. This unit begins by examining those rules including: the power rule, the product rule, the quotient rule and the chain rule followed by a study of the derivatives of composite functions. The next section is dedicated to finding the derivative of relations that cannot be written explicitly in terms of one variable. Next students will simply apply the rules they have already developed to find higher order derivatives. As students saw earlier, if given a position function, they can find the associated velocity function by determining the derivative of the position function. They can also take the second derivative of the position function and create a rate of change of velocity function that is more commonly referred to as the acceleration function which is where this unit ends.

13 hours

Curve Sketching

In previous math courses, functions were graphed by developing a table of values and smooth sketching between the values generated. This technique often hides key detail of the graph and produces a dramatically incorrect picture of the function. These missing pieces of the puzzle can be found by the techniques of calculus learned thus far in this course. The key features of a properly sketched curve are all reviewed separately before putting them all together into a full sketch of a curve.

12 hours

Derivative Applications and Related Rates

A variety of types of problems exist in this unit and are generally grouped into the following categories: Pythagorean Theorem Problems (these include ladder and intersection problems), Volume Problems (these usually involve a 3-D shape being filled or emptied), Trough Problems, Shadow problems and General Rate Problems. During this unit students will look at each of these types of problems individually.

9 hours

Derivatives of Exponents and Log Functions-Exponential Functions

This unit begins with examples and exercises involving exponential and logarithmic functions using Euler's number (e). But as students have already seen, many other bases exist for exponential and logarithmic functions. Students will now look at how they can use their established rules to find the derivatives of such functions. The next topic should be familiar as the steps involved in sketching a curve that contains an exponential or logarithmic function are identical to those taken in the curve sketching unit studied earlier in the course. Because the derivatives of some functions cannot be determined using the rules established so far in the course, students will need to use a technique called logarithmic differentiation which is introduced next.

9 hours

Trig Differentiation and Application

A brief trigonometry review kicks off this unit. Then students turn their attention to special angles and the CAST rule which has been developed to identify which of the basic trigonometric ratios is positive and negative in the four quadrants. Students will then solve trigonometry equations using the CAST rule to locate other solutions. Two fundamental trigonometric limits are investigated for the concepts of trigonometric calculus to be fully understood. The unit ends, as in all other units in the course, with an assignment and a unit quiz.

9 hours
Final Assessment

Exam

This is a proctored exam worth 30% of your final grade.

2 hours
Total110 hours 

This course extends students’ experience with functions. Students will investigate the properties of polynomial, rational, logarithmic, and trigonometric functions; develop techniques for combining functions; broaden their understanding of rates of change; and develop facility in applying these concepts and skills. Students will also refine their use of the mathematical processes necessary for success in senior mathematics. This course is intended both for students taking the Calculus and Vectors course as a prerequisite for a university program and for those wishing to consolidate their understanding of mathematics before proceeding to any one of a variety of university programs.

MHF4U - Advanced Functions (University Preparation)

 

This course extends students' experience with functions. Students will investigate the properties of polynomial, rational, logarithmic, and trigonometric functions; develop techniques for combining functions; broaden their understanding of rates of change; and develop facility in applying these concepts and skills. Students will also refine their use of the mathematical processes necessary for success in senior mathematics. This course is intended both for students taking the Calculus and Vectors course as a prerequisite for a university program and for those wishing to consolidate their understanding of mathematics before proceeding to any one of a variety of university programs.

Prerequisites:

Functions, Grade 11, University Preparation; or Mathematics for College Technology, Grade 12, College Preparation


Course Break Down 

Unit 1- Statistics of One Variable

Unit 2-Statistics of Two Variables

Unit 3-Permutations and Pascal’s Triangle

Unit 4-Combinations

Unit 5- Introduction to Probability

Unit 6- Probability Distributions and the Normal Distribution

Unit 7- Simulations & Games Fair