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French Baccalaureate, Terminale, Montreal

Maths Expertes in Terminale, in Montreal

Tutor for the Maths Expertes option in Montreal, the most demanding mathematics course of Terminale. Complex numbers, number theory, matrices and graphs: I prepare students aiming at a classe preparatoire or an engineering school, at Lycee Marie de France, College Stanislas and elsewhere. Sessions in English or in French.

Maths Expertes Complex numbers & number theory For prepa and engineering ★ 5.0 · 11 Google reviews
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The closest thing to AP Calculus BC, and then some

If you are trying to place this against a North American frame: the Mathematics speciality alone already covers more than AP Calculus AB and much of BC. Maths Expertes sits on top of that, three extra hours a week, and it goes somewhere AP does not go at all: complex numbers as a working tool, and genuine number theory with proofs.

A student who does Maths Expertes well arrives at a McGill or Concordia first-year mathematics course having already met the level of formalism, which is usually the thing that catches out first-year students rather than the content.

What the Maths Expertes option is

Maths Expertes is a three hour per week option, offered only in Terminale, and reserved for students who keep the Mathematics speciality. It sits on top of the speciality, for students who want to go further and prepare for highly mathematical studies.

Unlike the speciality, Maths Expertes has no dedicated final examination: it is assessed through continuous assessment, on the year's marks. Those marks count toward the Baccalaureat and, more to the point, the option appears in the Parcoursup application, where it is a strong signal for selective courses.

Its value goes beyond the points. Maths Expertes introduces a level of abstraction and formalism close to that of a classe preparatoire. Followed properly, it makes entry into scientific higher education substantially easier.

The Maths Expertes syllabus

Complex numbers

Algebraic form, trigonometric and exponential forms, modulus and argument, equations over the complex numbers, and geometric applications through transformations of the plane. This is usually the first big jump in abstraction of the year.

Number theory

Divisibility and Euclidean division, congruences, greatest common divisor, the theorems of Bezout and Gauss, prime numbers. A chapter where proof and rigorous reasoning are the whole of the work rather than a formality.

Matrices and graphs

Matrix calculation, powers of matrices, coupled sequences, graphs and Markov chains. Powerful tools for modelling evolving systems, and heavily used in higher education.

In French

Free corrected exercises for Maths Expertes

One exercise set per theme of the option, in the format of a class test: 10 questions marked out of 100, a first part on the fundamentals and a second at Baccalaureat level, with a full worked solution for every question. Three sets cover the whole option, and each has a revision sheet giving the results to know by heart, the write-up expected in a number theory proof, and the classic traps starting with a badly determined argument and a rushed induction. Free, no sign-up, written in French.

Corrected exercise sets → Revision sheets → English exercises →

Who should take Maths Expertes?

The option is for students aiming at a French scientific classe preparatoire (MPSI, PCSI, MP2I), an engineering school, degrees in mathematics, computer science or physics, or certain demanding double degrees. For those paths, taking Maths Expertes is often expected and always valued.

It asks for a taste for abstraction and some fluency with proof. That is precisely what we work on together: turning that demand into a strength rather than something to endure.

How I work on Maths Expertes

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Building the abstraction step by step

Complex numbers and number theory are understood by starting from concrete examples, then rising to generality and formalism, not the other way round.

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Mastering proof

We work on writing proofs rigorously, the central skill of the option and an indispensable one in a classe preparatoire.

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Coordinating with the Mathematics speciality

The option and the speciality feed each other, so we coordinate the two rather than treating them as separate workloads.

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Support between sessions, included

The student can message me about a proof they are stuck on or an idea to clarify, at no extra charge.

I hold a French Baccalaureat with the Mathematics speciality, a B.Sc. from McGill and an M.Sc. from Concordia, and have worked with Montreal's most demanding students for more than 10 years. More about the tutor.

Frequently asked questions

What is the Maths Expertes option?

A Terminale option open only to students keeping the Mathematics speciality. It adds complex numbers, number theory and matrices with graphs, and is assessed through continuous assessment.

What is on the syllabus?

Complex numbers (algebraic, trigonometric, exponential forms, equations, geometry), number theory (divisibility, congruences, gcd, Bezout, Gauss, primes) and matrices and graphs (matrix calculation, coupled sequences, Markov chains).

Who should take it?

Students aiming at a scientific classe preparatoire, an engineering school, or degrees in mathematics or computer science. It is a strong signal in the Parcoursup application and excellent preparation for higher education.

Is it harder than the speciality?

More abstract rather than simply harder: complex numbers and number theory bring a new kind of reasoning and formalism, close to a classe preparatoire. With solid method and regular practice it is entirely accessible.

See also

Mathematics speciality Maths Complementaires Terminale Baccalaureate preparation

Succeed in Maths Expertes, in Montreal

Get in touch for a first session, in person or online. Built for students aiming at a classe preparatoire or an engineering school.

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