MHF4U Advanced Functions: Online Tutoring in Ontario

1. 01
   Functions (characteristics and properties)

   • Functions
   • Absolute value
   • Properties of graphs of functions
   • Sketching graphs of functions
   • Inverse relations
   • Piecewise functions
   • Exploring operations with functions
2. 02
   Functions (understanding rates of change)

   • Average rate of change
   • Estimating instantaneous rates of change from tables and equations
   • Instantaneous rates of change from graphs
   • Creating graphical models
   • Solving rate-of-change problems
3. 03
   Polynomial functions

   • Exploring polynomial functions
   • Characteristics of polynomial functions
   • Factored form
   • Transformations of cubic and quartic functions
   • Dividing polynomials
   • Factoring polynomials
   • Sum and difference of cubes
4. 04
   Polynomial equations and inequalities

   • Solving polynomial equations
   • Solving linear inequalities
   • Solving polynomial inequalities
   • Rates of change in polynomial functions
5. 05
   Rational functions, equations and inequalities

   • Graphs of reciprocal functions
   • Quotients of polynomial functions
   • Graphs of rational functions
   • Solving rational equations
   • Solving rational inequalities
   • Rates of change in rational functions
6. 06
   Trigonometric functions

   • Radian measure
   • Radian measure and angles on the Cartesian plane
   • Graphs of the primary trigonometric functions
   • Transformations of trigonometric functions
   • Reciprocal trigonometric functions
   • Modelling with trigonometric functions
   • Rates of change in trigonometric functions
7. 07
   Trigonometric identities and equations

   • Equivalent trigonometric functions
   • Compound angle formulas
   • Double angle formulas
   • Proving trigonometric identities
   • Solving linear trigonometric equations
   • Solving quadratic trigonometric equations
8. 08
   Exponential and logarithmic functions

   • The logarithmic function
   • Transformations of logarithmic functions
   • Evaluating logarithms
   • Laws of logarithms
   • Solving exponential equations
   • Solving logarithmic equations
   • Problems with exponential and logarithmic functions
   • Rates of change
9. 09
   Combinations of functions

   • Exploring combinations of functions
   • Sums and differences
   • Products
   • Quotients
   • Composition of functions
   • Techniques for solving equations and inequalities
   • Modelling with functions

Best for: Grade 12 students in university-stream maths, science and engineering programmes.

What is MHF4U?

MHF4U is the Ontario Grade 12 University Preparation course Advanced Functions. It covers polynomial, rational, trigonometric, exponential and logarithmic functions, rates of change, and combinations of functions.

What do I need before taking MHF4U?

The usual prerequisite is MCR3U (Functions, Grade 11, University Preparation). Strong algebra and graphing skills from Grade 10 and 11 help a lot.

Are the online MHF4U classes one-to-one, or do I have to join a group?

Classes are live and one-to-one with Janvi Mam, Ph.D., on Zoom or Google Meet, so you never have to join a group or share the class with other students. If you prefer to study with a friend, small-group sessions of 2-3 students in the same course are available at a reduced per-student rate.

What are the benefits of one-to-one MHF4U tutoring?

The lesson follows your own pace and gaps instead of a class average. Every minute goes to your questions, so you can ask anything without worrying about others. Weak topics are spotted and fixed quickly, and the plan can be matched to your school tests and exams.

Can classes fit Canadian time zones?

Yes. Timings are arranged to suit students in Canada, so you can ask for a slot that works after school hours.

Can I try a class before I commit?

Yes. You can book a free demo class, meet the teacher and see how the class runs before deciding.