MHF4U Advanced Functions tutoring, 1-on-1 and online

Grade 12 Advanced Functions moves fast: radians, identities, logarithms and rational functions in one semester. We work through the problems with your child, live and online, one student and one teacher.

Book a free trial lesson

Who this is for

Grade 12 students taking MHF4U this semester, in school or online
Students who finished MCR3U and want a head start before September
Students planning on Calculus and Vectors (MCV4U), which leans on these skills
Parents who want to know, after every lesson, what was covered and how it went

Advanced Functions (MHF4U)

Grade 12 · Prerequisite: MCR3U (Functions) or MCT4C

Exponential and Logarithmic Functions

Logarithms as inverses of exponential functions
Graphs and transformations of logarithmic functions
Laws of logarithms
Solving exponential and logarithmic equations
Exponential and logarithmic models

Trigonometric Functions

Radian measure and the unit circle
Graphs of sine, cosine and tangent, and their reciprocals
Compound angle formulas
Proving trigonometric identities
Solving trigonometric equations in a given interval

Polynomial and Rational Functions

Characteristics of polynomial functions
The factor and remainder theorems
Rational functions and their asymptotes
Solving polynomial and rational inequalities

Characteristics of Functions

Average and instantaneous rates of change
Combining functions by sum, difference, product and quotient
Composition of functions
Choosing a function to model a situation

Coming from MCR3U

Advanced Functions assumes the grade 11 Functions course is solid: transformations, exponent laws, sine and cosine in degrees, and factoring. Most trouble in the first month of MHF4U is a gap from grade 11, not a new idea.

Our first lessons check those foundations with problems and close any gap before the new material builds on it.

Where students get stuck in Advanced Functions

Radian measure and the unit circle
Students who learned trigonometry in degrees have to rebuild their sense of angle. Until special angles in radians are automatic, every later trigonometry question takes twice as long.
Proving trigonometric identities
There is no single procedure, so students stall on where to start. Knowing which identity to reach for, and working one side at a time, is a skill built by doing many of them.
Solving logarithmic and exponential equations
Choosing when to take a logarithm of both sides, applying the laws correctly, and rejecting solutions outside the domain are three separate places to lose marks on one question.
Polynomial and rational inequalities
Factoring is only the start: students need sign charts or interval tests, and must handle the points where a rational expression is undefined.
Composition and combinations of functions
Reading f(g(x)) in the right order, finding the domain of a composite, and sketching a sum or product of two graphs all trip up students who are comfortable with single functions.
Average versus instantaneous rate of change
The secant slope and the tangent slope look similar on paper. Students mix them up on word problems, which also makes the move to MCV4U harder.

How we teach Advanced Functions

Every lesson is MHF4U problems worked with a teacher beside the student, and a unit is done when the student finishes a set on their own.
We keep a mistakes blueprint for Advanced Functions, from radian slips to rejected log solutions, and aim practice at the ones your child has not cleared.
After each lesson the teacher logs the topics covered, the latest test score and where the next lesson starts, within 24 hours.
Students who start in the summer run the whole course before September, so the school semester is their second pass.

How we teach

The method behind the marks

Four things every lesson is built on.

01
Run the course before the course
A grade 12 course taught front to back the summer before, so the school year is the student's second pass, not their first. Four courses in one summer is possible; one is the usual.
02
Lessons are problems, not lectures
Every lesson is the student doing questions with a teacher beside them. A topic is finished when the student completes the set without instruction, not when it has been explained.
03
The mistakes blueprint
For each course we keep a map of every mistake a student can make on it. Practice targets the ones the student has not cleared yet, before one of them costs a mark that stays on the transcript.
04
Logged within 24 hours
After every lesson the teacher logs what was covered, the latest test score, a confidence rating out of five, and where the next lesson starts. Written the same day, while it is still fresh.

The roster

From the lesson log

Students with a logged test in this subject, read straight off the lesson log. Every lesson is logged within 24 hours, in the teachers' own words. Students are shown by number and initials only.

Student 10
H.
Advanced Functions (MHF4U) · Calculus and Vectors (MCV4U) · Grade 12 Physics (SPH4U) · Grade 12 Chemistry (SCH4U)
Grade 12
95%
MHF4U · Nov 5
Ran all four grade 12 courses over the summer. In the school year, chemistry went from 82% on the energy changes test to 89% on the next one, and his latest Advanced Functions test is 95%. Chemistry is now on reaction rates ahead of a test, with calorimetry setup, signs and energy-profile labels still being practised.
Logged Nov 9, 2026
52 lessons logged · since July 2026
Student 15
A.
Grade 12 Chemistry (SCH4U) · Advanced Functions (MHF4U)
Grade 12
91.3%
MHF4U · Oct 31
Scored 90.4% and 92.1% on his first two Advanced Functions assessments (91.3% combined). The marks lost were in checking every condition a question sets, not in the methods, so each answer now ends with a self-audit. Now reviewing that test and moving through trigonometry ahead of the next assessment on Nov 16.
Logged Nov 7, 2026
14 lessons logged · since September 2026

Updated November 10, 2026

Offers

Two ways to work with us

During the school year

1-on-1 tutoring

$60 / hour

Your first lesson is free.

One student, one instructor, one plan. Grade 11 and 12 math, physics, chemistry and biology, online and live.

Weekly, twice weekly, or ahead of a test
Every lesson logged within 24 hours
Stop any time, no packages

Book a free trial lesson

Before the school year

The course intensive

$600 / subject

Start with lesson 1 for $70.

One grade 12 course front to back in 10 lessons, Monday to Friday over two weeks, before the student takes it for marks.

10 lessons, 1 hour each, same time daily
95+ on our final, or we keep teaching free
Advanced Functions, Calculus, Physics, Chemistry

See the intensive

FAQ

Frequently Asked Questions

What parents ask about Advanced Functions tutoring before booking.

My child passed MCR3U but is struggling in MHF4U. Where do you start?

With a short set of grade 11 problems on transformations, exponent laws and trigonometry in degrees. Most early MHF4U trouble traces back to one of those, and we close that gap before moving on.

Should my child take Advanced Functions before Calculus and Vectors?

Most Ontario schools expect MHF4U before or alongside MCV4U, because calculus uses rates of change, logarithms and trigonometric functions from Advanced Functions. We can tutor both in the same semester.

What happens in a first Advanced Functions lesson?

Your child works through problems from the unit they are on at school while the teacher watches how they approach each one. You get a written log the same day with what was covered and where the next lesson starts.

Can lessons follow my child's school MHF4U course?

Yes. Lessons follow the unit and pace of your child's class, and before a test they focus on the question types that unit's test is likely to include.

Start with a free trial lesson

One lesson, one teacher, on the unit your child is on now. You get the lesson log the same day.

Book a free trial lesson

MHF4U Advanced Functions tutoring, 1-on-1 and online

Who this is for

Advanced Functions (MHF4U)

Exponential and Logarithmic Functions

Trigonometric Functions

Polynomial and Rational Functions

Characteristics of Functions

Coming from MCR3U

Where students get stuck in Advanced Functions

Radian measure and the unit circle

Proving trigonometric identities

Solving logarithmic and exponential equations

Polynomial and rational inequalities

Composition and combinations of functions

Average versus instantaneous rate of change

How we teach Advanced Functions

The method behind the marks

Run the course before the course

Lessons are problems, not lectures

The mistakes blueprint

Logged within 24 hours

From the lesson log

Two ways to work with us

1-on-1 tutoring

The course intensive

Frequently Asked Questions

Related

Start with a free trial lesson