Montreal, Quebec curriculum, Secondary 5

CST 5 Math Tutor in Montreal

Q: What is studied in CST mathematics in Secondary 5?

CST 5 opens chapters that exist nowhere else in the Quebec curriculum: graph theory, financial mathematics, voting procedures from social choice theory, optimisation by linear programming, probability with expected value, and a geometry block on equivalent figures and solids. It is a more concrete syllabus than Secondary 4, and many students feel markedly more at ease in it.

Q: Is CST 5 required to enter CEGEP?

A great many programs require it, notably social science without mathematics and many technical programs, while other programs require no Secondary 5 mathematics prerequisite at all. The exact prerequisite varies by CEGEP and by program and must be checked in the admission guide of the program concerned, never by hearsay. The secondary school diploma itself is satisfied by Secondary 4 mathematics.

Q: Why are graph theory and voting procedures on the syllabus?

Because the Culture, societe et technique sequence aims to equip a citizen rather than prepare for pure science. A graph models a snow clearing route, a conflict-free exam timetable or the critical path of a construction project. Voting procedures show that six counting methods applied to the same ballot can elect three different people. This is directly applicable mathematics, which is why students often find it more motivating than Secondary 4 algebra.

Tutor in Culture, societe et technique (CST) mathematics for Secondary 5 in Montreal, with more than 10 years of experience. CST 5 is the most disorienting syllabus of the Quebec secondary curriculum: graph theory, financial mathematics, voting procedures, optimisation. Chapters the student has never seen, that no Secondary 4 textbook announces, and on which almost no serious free resource exists. I cover the whole of it. Sessions in English or in French.

CST sequence, Secondary 5 Graph theory Financial mathematics Optimisation and probability Free corrected exercises ★ 5.0 · 11 Google reviews

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This is the year a struggling student can turn things around

Worth knowing if your child has carried a "not good at maths" label since Secondary 3: CST 5 breaks with everything before it. Graph theory, compound interest and voting procedures are new to everybody in the room. Nobody has a head start, the vocabulary is fresh for all, and reasoning counts for more than algebraic technique.

I have seen students who never got past 65 percent make dramatic recoveries on the graphs and financial mathematics blocks. The flip side: because the chapters are new, there is nothing familiar to fall back on, and a two week absence is genuinely hard to recover.

CST mathematics in Secondary 5: a syllabus apart

In the Sciences naturelles sequence, Secondary 5 continues Secondary 4: more functions, harder algebra, obvious continuity. In CST, the break is sharp. The student arrives in September and meets subjects unlike anything since primary school: colouring a graph to build an exam timetable, working out what a credit card balance actually costs, comparing six ways of counting the same ballot.

That break is good news for many students. A student carrying a reputation for being bad at mathematics since Secondary 3 finds themselves in front of a chapter where nobody has an advantage, where the vocabulary is new for everyone, and where reasoning matters more than algebraic technique.

It has a downside too. Because the chapters are new, there is nothing known to lean on, and a two week absence is hard to make up. And because CST 5 is barely taught outside Quebec, there is almost nothing available online: the corrected exercises listed below fill exactly that gap.

The CST 5 syllabus

Optimisation

Systems of inequalities and half-planes
The feasible region polygon and its vertices
The objective function and the vertex table
Minimum and maximum constraints
Production and workshop problems

Graph theory

Order, degrees, connectivity, cut vertices
Eulerian paths and circuits, the degree criterion
Hamiltonian paths and circuits
Chromatic number and colouring
Minimum spanning tree and critical path

Financial mathematics

Simple and compound interest
Periodic rate and compounding frequency
Effective annual rate and comparing offers
Future value, present value, depreciation
Finding an investment period using logarithms

Probability and social choice

Odds for and odds against
Compatible, complementary and independent events
Conditional probability and weighted trees
Expected value and the fair game
Voting procedures: Borda, Condorcet, approval

A geometry block is added: the cosine law, solving general triangles, equivalent figures and solids. Coverage varies slightly from school to school.

In French

Corrected exercises and revision sheets, chapter by chapter

All 7 chapters of the Secondary 5 CST syllabus have their own corrected exercise set and revision sheet, free and with no sign-up. Each set is in the format of an evaluation, ten questions marked out of 100, a first part on the fundamentals and a second at year-end examination level, with the full reasoning for every question. The revision sheet puts a number of marks on each mistake and gives the exact sentence to write. Written in French, which is the language of your child's exam.

L'optimisation par programmation linéaire Exercises Revision sheet
Les mathématiques financières Exercises Revision sheet
La théorie des graphes Exercises Revision sheet
Probabilités, chances et espérance Exercises Revision sheet
Les procédures de vote Exercises Revision sheet
La loi des cosinus Exercises Revision sheet
Les figures et les solides équivalents Exercises Revision sheet

The geometry and optimisation chapters are shared between CST and the Sciences naturelles sequence: the set is then the same one, and it suits both.

What actually loses marks in CST 5

The errors in this syllabus are almost never arithmetic. They come from the question asking one thing and the student solving another, very close to it.

Graphs: treating a route as a vertex problem

A snow clearing route covers every street, therefore every edge: that is an Eulerian problem. A delivery route visits every customer, therefore every vertex: that is a Hamiltonian problem. The two questions read alike, the two methods have nothing in common, and picking the wrong family costs the whole question.

Finance: taking the quoted rate for the period rate

A rate of 6 percent compounded monthly is not 6 percent per month. You must divide the rate by the number of periods and multiply the duration by the same number. Forgetting either half is the most common error of the chapter, and it produces a plausible answer, so it survives a re-read.

Probability: confusing odds with probability

A probability compares favourable cases to the total; odds in favour compare favourable cases to unfavourable ones. Three to one on and a probability of three quarters do not describe the same situation. Exam questions cheerfully use both phrasings in the same problem.

Voting: naming a winner without naming the procedure

The same ballot elects three different people depending on whether it is counted by plurality, by elimination or by the Borda method. An answer that announces a winner without saying which procedure produced them is worth nothing, even when the name is the right one.

Each of these traps is priced in marks, with the sentence to write instead, in the revision sheet of the corresponding chapter.

See all revision sheets, in French →

After CST 5: what the grade commits to

There is no Ministry examination in Secondary 5 mathematics: the provincial paper is written in Secondary 4, one version per sequence. In Secondary 5 the grade comes entirely from the school, which does not make it less important, quite the reverse: it rests on local assessments, therefore on genuine command of the chapters across the year rather than on one day's performance.

A great many CEGEP programs require Secondary 5 CST mathematics as a prerequisite, notably social science without mathematics and many technical programs. Others require no Secondary 5 mathematics at all. The exact prerequisite varies by CEGEP and by program, and it must be checked in the admission guide of the program concerned, never by hearsay or by what a friend heard.

Concretely: a student aiming at a specific technical program should verify the prerequisite in the autumn of Secondary 5, not when filling in the application in March. It is one of the first things I check with families once the CEGEP goal is known.

How the sessions work in CST 5

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First, identifying the type of problem

This is the move that decides the grade in CST 5. Eulerian or Hamiltonian, simple or compound interest, probability or odds: once the family is recognised, the method follows by itself.

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The new chapters are taken from the beginning

Nobody has a head start on graphs or voting procedures. A student who has struggled for years starts level with everyone else, and that is often where confidence comes back.

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Using the calculator properly

Financial mathematics needs powers and logarithms, and rounding too early in the calculation throws the answer out by several dollars. We work exact handling on the student's own calculator, TI or Casio.

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Writing the justification, not only the result

Naming the voting procedure used, citing the degree criterion, announcing the optimal vertex of the feasible region: short sentences that earn marks and that students systematically forget unless they have written them once in a session.

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Support between sessions, included

The student can message me between sessions with any question. It is part of the rate, at no extra charge.

Frequently asked questions

What is studied in CST mathematics in Secondary 5?

Chapters that exist nowhere else in the Quebec curriculum: graph theory, financial mathematics, voting procedures from social choice theory, optimisation by linear programming, probability with expected value, and a geometry block on equivalent figures and solids. It is more concrete than Secondary 4, and many students feel markedly more at ease.

Is there a Ministry examination in Secondary 5?

No. The Ministry mathematics examination is written in Secondary 4, one version per sequence. In Secondary 5 the grade comes entirely from the school. That does not make the year less important: it is the grade several CEGEPs read at admission.

Is CST 5 required to enter CEGEP?

Many programs require it, notably social science without mathematics and many technical programs, while others require no Secondary 5 mathematics at all. The exact prerequisite varies by CEGEP and by program and must be checked in the admission guide. The secondary school diploma itself is satisfied by Secondary 4 mathematics.

Why are graph theory and voting procedures on the syllabus?

Because the CST sequence aims to equip a citizen rather than prepare for pure science. A graph models a snow clearing route, a conflict-free exam timetable or the critical path of a project. Voting procedures show that six counting methods on the same ballot can elect three different people. Directly applicable mathematics, which many students find more motivating than Secondary 4 algebra.

Are there free corrected CST 5 exercises?

Yes, free and complete, solutions included, listed above. Graph theory, financial mathematics, probability and expected value, voting procedures, linear programming, solving triangles and equivalent solids all have their set and their revision sheet. They are written in French.