(1) When do students in Canada learn about the four triangle centres (centers), circumcenter, incenter, orthocenter, and centroid? In the USA (more precisely, Indiana), the math curriculums are by topics and the 9th grade students who completed Algebra 1 can take Geometry in which they learn about them. I looked up some textbooks for Grade 9 to 12 in Canada and couldn't find about them.

(2) How could students in Canada (Ontario) take both MCV4U Calculus and Vectors and MDM4U Math for Data Management in their 12th grade? MHF4U Advanced functions should be taken before MCV4U. MCF3M Functions and applications should be taken before MDM4U. It seems that the 12th graders should take all three MHF4U, MCV4U, and MDM4U in their last year in high school. I think in USA (Indiana) students take Algebra 2 in Grade 10, Precalculus in Grade 11, and both Calculus and Statistics in Grade 12. In Algebra 2 students are introduced to the early part of Precalculus including the essential functions. It seems that MHF4U still covers Precalculus that is offered in the 12th grade at the same time with MCV4U Calculus.

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    $\begingroup$ Odd I am a maths graduate in the UK and I do not remember ever been taught what circumcenter, and orthocenter are. Either my memory has completely gone or syllabuses really differ. I suspect I have not done any real geometry. you can't assume that what you teach is taught everywhere else. $\endgroup$
    – mmmmmm
    Jun 3, 2020 at 11:57
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    $\begingroup$ I have an undergraduate degree in math and physics and a PhD in physics, and I couldn't define any of these terms off the top of my head. $\endgroup$
    – user507
    Jun 3, 2020 at 13:34
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    $\begingroup$ You seem to have edited the question to introduce a second question. That's discouraged; instead you should just ask the second question separately. $\endgroup$
    – dbmag9
    Jun 3, 2020 at 14:36

2 Answers 2


To answer (2): MHF4U is a co-requisite of MCV4U so there nothing stopping a student taking all 3 courses at the same time. Further more, many Ontario high school operate on semester bases - a student could take MHF4U in first semester and MCV4U in second semester in Grade 12.


The centroid, circumcenter, and orthocenter are concepts that I teach in Grade 10. It is part of the analytic geometry unit, and is where we relate knowledge on slope and distance formulas to geometric concepts.

A textbook that includes this topic is Principles of Mathematics 10 by Nelson. Here is a set of sample teaching notes.

Reference: Grade 10 math curriculum (Ontario, Canada).

  • $\begingroup$ Thank you. I noticed that the edition for 2010 added many more sections to the edition for 2007 which I looked up initially. $\endgroup$
    – Jessie
    Jun 3, 2020 at 13:54

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