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Montreal, Quebec CEGEP

CEGEP Tutor in Montreal: NYA, NYB, NYC and Sciences de la nature

Private CEGEP tutoring in Montreal for Differential Calculus (NYA), Integral Calculus (NYB) and Linear Algebra (NYC), plus physics, chemistry and programming in the Sciences de la nature program. Every CEGEP in Montreal is covered, in person and online, in English or in French. Mathematics is the core of the demand: see also my math tutoring page, from secondary school to university.

Calculus I, NYA Calculus II, NYB Linear Algebra, NYC CEGEP physics CEGEP chemistry Sciences de la nature ★ 5.0 · 11 Google reviews
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What CEGEP is, if you did not grow up here

CEGEP is the two year stage between secondary school and university, unique to Quebec. Students finish secondary school after Secondary 5, at about 17, then spend two years in a pre-university program before entering university directly in their major, with no freshman year. Sciences de la nature is the pre-university program that leads to science, engineering, medicine and architecture.

Two consequences catch families off guard. First, the CEGEP grade average, the cote R, is what university admission is decided on, so first term marks matter immediately rather than being a soft landing. Second, the pace is roughly double what students are used to: a chapter that took two weeks in secondary school takes three lectures here. Students who coasted through Secondary 5 mathematics often meet their first real difficulty in the fourth week of NYA.

The three mathematics courses in Sciences de la nature

NYA, NYB and NYC are the three mandatory mathematics courses for Sciences de la nature students at Quebec CEGEPs. They are, reliably, the hardest obstacles of the program.

Differential Calculus, NYA

Term 1 or 2

Differential calculus is usually the first real shock of CEGEP. The pace is far faster than secondary school and the ideas are more abstract. In a few weeks students go from the familiar functions of Secondary 5 to limits, continuity and derivatives. Many students who did well in secondary find themselves in difficulty within the first month.

Topics covered

  • Limits and continuity
  • Definition of the derivative
  • Differentiation rules (product, quotient, chain)
  • Derivatives of trigonometric, exponential and log functions
  • Optimisation and extremum problems
  • Related rates
  • Complete curve sketching

Where students get stuck

  • Indeterminate limit forms
  • Nested chain rule
  • Setting up the optimisation equation
  • Reading the sign of f' and f''
  • Time management under exam conditions

Integral Calculus, NYB

Term 2 or 3

Integral calculus follows NYA. Students who never fully absorbed derivatives run into trouble quickly, because integration requires recognising a form and choosing the right technique from several candidates. It is also the course with the richest applications: areas, volumes, differential equations.

Topics covered

  • Antiderivatives and the indefinite integral
  • Definite integral, fundamental theorem
  • Algebraic and trigonometric substitution
  • Integration by parts
  • Partial fractions
  • Areas between curves, volumes of revolution
  • Improper integrals, sequences and series

Where students get stuck

  • Choosing the right integration technique
  • Repeated integration by parts
  • Setting up volumes of revolution
  • Convergence of improper integrals
  • Convergence tests for series

Linear Algebra and Vector Geometry, NYC

Term 2, 3 or 4

NYC is the course least like the other two. It combines the geometry of vectors in space with the algebra of matrices and systems of equations. The main challenge is visualising geometry in three dimensions and becoming fluent with row reduction. It is essential for university study in science, engineering and computer science.

Topics covered

  • Vectors in two and three dimensions, norm, angle
  • Dot product and cross product
  • Equations of lines and planes in space
  • Systems of equations, Gauss-Jordan elimination
  • Matrices, operations, determinants
  • Eigenvalues and eigenvectors
  • Linear transformations

Where students get stuck

  • Visualising plane intersections in space
  • Choosing the right representation of a line
  • Reduced row echelon form
  • Computing and interpreting eigenvalues
  • Writing proofs rigorously

Physics and chemistry in Sciences de la nature

Physics: Mechanics

The first physics course in Sciences de la nature. Kinematics, Newtonian dynamics, work, energy, momentum and rotation. It demands real fluency with vectors and with the differential calculus tools from NYA, which is why students who are behind in NYA are usually behind here too.

  • Kinematics in one and two dimensions, projectile motion
  • Newton's laws, friction forces
  • Kinetic and potential energy, conservation
  • Momentum, elastic and inelastic collisions
  • Rotation, torque, moment of inertia
See the physics page →

Physics: Electricity and Magnetism

The second physics course. Electrostatics, circuits, magnetic fields, induction, waves and optics. More abstract than mechanics, it asks students to picture phenomena they cannot see, which is a different skill from solving for a number.

  • Coulomb's law, electric field and potential
  • Series and parallel circuits, Kirchhoff's laws
  • Magnetic field, Lorentz force
  • Electromagnetic induction, Faraday's law
  • Waves, light, geometric optics

General Chemistry

The first chemistry course in Sciences de la nature. Atomic structure, the periodic table, bonding, reactions, stoichiometry, gases and solutions. The sheer volume of material in a short term makes it hard to follow without regular support.

  • Atomic model, electron configuration
  • Ionic and covalent bonding, molecular geometry
  • Chemical equations, stoichiometry
  • Ideal gas laws, Dalton's law
  • Solutions, concentration, dilution
See the chemistry page →

Chemistry of Solutions

The second chemistry course. Equilibrium, acids and bases, oxidation-reduction, electrochemistry, kinetics and thermochemistry. pH calculations and equilibrium problems are the usual sticking points.

  • Chemical equilibrium, Kc and Kp
  • Acids and bases, pH calculations, buffers
  • Redox reactions, electrochemical cells
  • Kinetics, rate law, reaction order
  • Thermochemistry, enthalpy, entropy, Gibbs energy

Social Science: the quantitative block

Sciences humaines, Social Science, is the most attended pre-university program in the CEGEP network, and its quantitative half is what discourages most students in it. It comes down to three courses: Quantitative Methods, mandatory for every profile, its advanced sequel that serves the end-of-program research project, and the differential calculus of the "with mathematics" profile.

Quantitative Methods, 360-300

Measurement scales and operationalisation, sampling plans and questionnaires, tables and graphs, Z score and cote R, index numbers and constant dollars, cross tabulation and chi-square, margin of error in a survey, research design. Nine exercise sets and a mock exam.

Chapters of 360-300, in French →

Advanced Quantitative Methods, 360-301

Comparing two groups and effect size, analysis of variance and multiple comparisons, multiple regression and model diagnostics, non-parametric tests, time series and forecasting. Five exercise sets and a mock exam.

Chapters of 360-301, in French →

Differential Calculus, 201-103

The calculus of the "with mathematics" profile follows the same progression as the Sciences de la nature course, from limits to optimisation, but it lands on economics: marginal analysis, elasticity of demand, related rates applied to profit.

Chapters of 201-103, in French →

Linear Algebra, 201-105

The linear algebra of the "with mathematics" profile shares its chapters with the Sciences de la nature course. On top of them sit the matrix models of social science: Markov chains, the Leontief model, population matrices.

Chapters of 201-105, in French →

The statistics of 201-337 (in French) remain a separate course, more mathematical and without an imposed disciplinary context. A Social Science student gains from reading both: quantitative methods give the vocabulary of research, 201-337 gives the statistical machinery.

Computer science at CEGEP and university

I also work with computer science students at CEGEP and university. Programming courses are hard for students without solid foundations, and the same recurring mistakes slow progress far more than the syllabus does.

Computer science programs also have their own mathematics course, distinct from the Sciences de la nature calculus sequence: see the page on mathematics for computer science, 201-N11, covering boolean logic, binary arithmetic, sets and relations, graphs and matrices.

Java, object oriented programming

Classes, objects, inheritance, polymorphism, interfaces. ArrayList and HashMap collections. Exceptions and error handling. Frequent mistakes: confusing reference and value, NullPointerException, misusing inheritance where composition was called for.

C++ and memory management

Pointers, dynamic allocation, destructors and RAII. Hand-built data structures (linked lists, trees). Classic difficulties: memory leaks, double free, pointer arithmetic, segmentation faults.

Data structures and algorithms

Arrays, stacks, queues, binary search trees, hash tables, graphs. Sorting and searching algorithms. Big O complexity. Recursion and memoisation.

Linux and the command line

Navigating the filesystem, permissions, bash scripts. Compiling with gcc and g++, Makefiles, debugging with gdb. Git from the command line. Indispensable for the systems courses at McGill and Concordia.

In French

Free corrected exercises for every CEGEP chapter

One exercise set per chapter of the ministerial course description, built like a real exam: 10 questions marked out of 100, a first part on the fundamentals and a second at final exam level, with a full worked solution for every question. The three calculus courses, linear algebra, statistics, the quantitative methods of Social Science, both chemistry courses, organic chemistry and all three physics courses are covered, and each course has a complete mock exam. Free, no sign-up, written in French.

Corrected exercise sets → Revision sheets → Chapter list by course → English exercises →

Why Sciences de la nature courses are hard

CEGEP is a genuine break from secondary school. Several factors explain why students who did well before find themselves in trouble in the first term.

The pace is much faster. In secondary school a chapter might be spread over two weeks. At CEGEP the same volume can be covered in a handful of lectures. Students who do not review regularly build a backlog that is very hard to clear.

The level of abstraction is higher. Limits, derivatives, integrals, vectors in three dimensions: these ask for a more formal kind of mathematical thinking than secondary school requires. Many students simply do not have the foundations to meet those ideas head on.

The exams give less scaffolding. In secondary school questions are usually broken into progressive parts. At CEGEP an optimisation problem may ask the student to build the entire model themselves. That independence is learned through guided practice, not by reading the textbook again.

Every CEGEP in Montreal, French and English

I adapt to the lecture notes and the exam style of each institution. The NYA, NYB and NYC course description is the same across the network, but the way concepts are presented and the kind of problems set on exams vary noticeably from one college to the next. English-language CEGEPs are covered on the same terms.

Dawson College Marianopolis College Vanier College John Abbott College College Ahuntsic Bois-de-Boulogne College de Maisonneuve Andre-Grasset Cegep du Vieux Montreal Cegep de Saint-Laurent College Lionel-Groulx Montmorency

How I work with CEGEP students

The first session is always a diagnostic. I ask about what has been covered in class, set a few problems to locate the difficulty precisely, and we build a work plan for the coming weeks together.

Each session then follows the same three beats: revisit what was not clear from last time, work through the new material from class, then progressive problems from straightforward to hard. I do not move on while the previous idea is still shaky, because at CEGEP pace an unfixed gap compounds within a fortnight.

Close to exams we switch to complete papers under real conditions: time management, presentation of solutions, and the specific traps each course sets. The point is not to do extra problems at random, but to target what is actually assessed at that particular CEGEP.

Frequently asked questions

What is the NYA course at CEGEP?

NYA is Differential Calculus, the first of the three mandatory mathematics courses in Sciences de la nature. It covers limits, continuity, derivatives and their applications: optimisation, related rates and curve sketching. It is usually the hardest course of the first term for students arriving from secondary school.

What is the difference between NYA, NYB and NYC?

NYA is Differential Calculus, NYB is Integral Calculus, NYC is Linear Algebra and Vector Geometry. They are the three mandatory mathematics courses in Sciences de la nature. The order varies by college, but NYA is normally taken in the first or second term.

Do you tutor students at every CEGEP in Montreal?

Yes: Ahuntsic, Bois-de-Boulogne, Maisonneuve, Andre-Grasset, Vieux Montreal, Saint-Laurent, Dawson, Marianopolis, Vanier, John Abbott and others. I adapt to the lecture notes and exam style of each institution, which differ even though the ministerial course description does not.

Can you tutor CEGEP courses in English?

Yes. I tutor in English for students at Dawson, Marianopolis, Vanier and John Abbott, and for students at French-language CEGEPs who prefer to think in English. The mathematics is identical in both networks; only the vocabulary changes, and I keep both sets of terms in play so the student can read their own exam paper.

Does online tutoring work well for CEGEP?

Yes, very well. Mathematics and science at this level suit the online format. I use Microsoft Teams with a digital whiteboard to work problems in real time. Students share their screen to show their attempt and we correct it together. It is as effective as working in the same room.

See also

Secondary school tutoring Mathematics Physics Chemistry Computer science COMP 202 at McGill About the tutor FAQ

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