Secondary 4 and 5 math tutor in Montreal: CST, TS and SN

CST, TS or SN: what the choice means

Secondary 3 is the last year everyone takes the same math. From Secondary 4, the ministry's program offers three options, and its own descriptions are the clearest guide:

• Cultural, Social and Technical (CST) makes “a greater use of statistics and discrete mathematics” and prepares students “for studies in the arts, communications, the humanities and the social sciences.”
• Technical and Scientific (TS) puts the emphasis on case studies and on identifying “errors and anomalies in processes or solutions,” with an eye to technical fields.
• Science (SN) asks for formal proofs and “more complex algebraic operations,” and leads toward studies in the sciences.

The program says all three prepare students for postsecondary studies, and that TS and SN “are equally demanding, and both provide equal access to higher education.” One admission rule is worth knowing early: the CEGEP Science program lists Secondary 5 Mathematics in the TS or Science option among its conditions for admission. A switch between options at the end of Secondary 4 is possible “only in certain specific cases,” and moving from CST to SN may require a compensatory measure set by the school, so the school is the one to confirm a particular case.

What Secondary 4 and 5 math demand

The three options share some ground in Secondary 4: systems of first-degree equations, trigonometry in triangles, the analytic geometry of lines, and correlation with the regression line. Beyond that they move at different speeds. From the ministry's program:

• SN, Secondary 4: algebraic identities, second-degree equations and inequalities, the quadratic function in standard, general and factored forms, the step (greatest integer) function, systems pairing a first-degree with a second-degree equation, the sine and cosine laws, and equivalent figures.
• SN, Secondary 5: absolute value, square root, rational, exponential, logarithmic, sinusoidal and tangent functions, operations on functions, systems of inequalities and optimization, the unit circle and trigonometric identities, vectors, and the conics.
• TS spreads much of the same algebra over two years: a function's multiplicative parameters in Secondary 4 and its additive parameters in Secondary 5, with rational, sinusoidal and tangent functions, vectors and conics by the end.
• CST works with fewer function families and adds applied branches in Secondary 5: financial mathematics, graph theory, conditional probability and mathematical expectation, and optimization.

Where the marks go. The Secondary 4 exam gives 60 of its 100 marks to six situations involving applications, marked on a rubric that asks whether the student chose suitable concepts, applied them without error, organized the steps clearly and used “appropriate arguments to justify or support the statements, conclusions or results.” A correct number with no visible reasoning does not reach the top of that rubric. The other usual losses are algebraic: a restriction forgotten after simplifying a rational expression, a sign lost while completing the square, an inequality solved without checking which side of the boundary holds.

The June exam is in Secondary 4

The ministry's uniform mathematics exam is written in Secondary 4 only. Each option has its own paper, and all three evaluate the same competency, Uses mathematical reasoning. From the ministry's own documents:

• Weight: the Secondary 4 and 5 ministerial exams “count for 50% of the final mark for the competency or competencies evaluated.”
• Format: 3 hours and 16 questions in three parts: 6 multiple-choice questions (24 marks), 4 short-answer questions (16 marks) and 6 situations involving applications (60 marks).
• Allowed: a calculator with or without a graphing display (any computer algebra system disabled, memory cleared beforehand), and one handwritten memory aid on a letter-size sheet, both sides, prepared the week before.
• Balance: on the 2025-2026 papers, SN was 48% to 54% algebra and only 4% to 10% statistics and probability, CST was 46% to 54% geometry, and TS carried the most statistics and probability, 16% to 28%.
• When: there are sessions in January, June and August. In June 2027 the TS and SN papers are scheduled for June 11 and the CST paper for June 18.

There is no ministry math exam in Secondary 5. The ministry's Secondary 5 exams are language exams. Secondary 5 math is evaluated by the school, and any end-of-year exam is set by the school, its school board or its school service centre.

How sessions prepare for it

• A written diagnostic first. In Secondary 4 a gap is often older than the topic that exposed it: a quadratic problem lost to factoring, a trigonometry problem lost to proportions. The diagnostic finds which, so sessions aim at the cause.
• Exam-style practice. We work through past-exam-style problems until the method is second nature, including the multi-step situations where the reasoning has to be written out, not just the answer.
• Practice between sessions if you want it, marked before the next one, with each error read for what caused it.
• A recap after every session to whoever books, and a standing record with a dated plan through the course and a short list of recurring slips to catch.
• Materials included: practice problems, summaries and formula sheets for the course and the exam.

One Secondary 4 student booked three sessions on a tight schedule before the 2026 ministerial exam and scored 82%: “You were very helpful, especially since I was on a tight schedule.”

Sessions are one-on-one, in person in Montreal (downtown and at public libraries such as the Grande Bibliothèque) for families in Westmount, Outremont, Town of Mount Royal, Hampstead, Côte-Saint-Luc, NDG, Nuns' Island and the West Island, or online on Zoom with a shared whiteboard.

When families usually get in touch

• After the first Secondary 4 report card, when the step up from Secondary 3 shows in the mark. It leaves the whole year to work with.
• Before a unit test on quadratics, trigonometry or, in Secondary 5, the function families.
• In the spring before the June exam, when the remaining weeks are best spent on exam-style situations and on whatever the diagnostic flags.
• In Secondary 5 TS or SN, when the function families become the groundwork for CEGEP calculus.

For gaps that go further back, the high school math page covers Secondary 1 to 3. The free worksheets listed below follow the SN program topic by topic, so a TS or CST student will find some topics that are not in their course.

Free practice worksheets

Every practice sheet is free to print, with no sign-up.

• Secondary 4 Math worksheets: 17 sets
• Secondary 5 Math worksheets: 21 sets

For parents

• CST, TS or SN: what each Sec 4 math sequence keeps open
• Seven signs your teen is falling behind in Sec 4 math

Topics explained, with a self-check

• General, standard or factored: which form of a quadratic function answers what
• How to complete the square: from general form to standard form
• How to find the rule of a quadratic function
• How to find the rule of a step function from its graph
• How to find the rule of an exponential function from two points and an asymptote
• Solving a second degree inequality with a quick sketch
• Square root equations: solve, then catch the extraneous solution
• The greatest integer function, explained from scratch
• The product-sum method for factoring ax² + bx + c
• What is a logarithm? The exponent you’re looking for

Common questions

Tutoring at other levels

• High school math tutoring in Montreal
• CEGEP Science calculus and linear algebra tutoring in Montreal
• AP Calculus AB tutoring and exam preparation in Montreal
• University math and science courses