Cambridge Interview Problem - A triangle's maximum area

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  • Опубліковано 23 гру 2024

КОМЕНТАРІ • 10

  • @amansparekh
    @amansparekh 4 дні тому +2

    For the first one, an alternative argument: Let’s say you fix two vertices of a triangle. The loci of points that will form a triangle with perimeter 12 is an ellipse. Clearly an ellipse has maximum ‘height’ at the centre between two foci, so we know to maximise the area, the triangle should be isosceles. By symmetry, the triangle must be equilateral.

    • @JPiMaths
      @JPiMaths  4 дні тому

      @@amansparekh that's a cool argument I'd not considered, nice!

  • @wjeksababakqabzzhzaab873
    @wjeksababakqabzzhzaab873 5 днів тому

    hello jpi , im in y12 and have a few questions. When do u think is good time to start practicing for the mat, and do you think bmo problems will help with it or anything else for that matter? Because even though my school doesnt compete , ive been doing bmo problems in my spare time (very inconsisitently) for over a year and have gotten quite good at them. I think if i dedicate myself to them i can get to point where i can do some bmo2 problems, which is why im wondering if that will help with anything? Will the problem solving carry over into uni as ive heard oxbridge maths is very problem solvy like bmo problems. Is there anyhting else i can do currently to help with the mat? Ive done a few long form questions from recent papers and found them quie straight forward so thats probably a good sign. So yeah, when to start with mat practice, and do bmo problems help with much outside of competition maths? Thanks!!

    • @voicutudor7331
      @voicutudor7331 5 днів тому

      if you are y12 you probably should have already taken the mat and applied to uni

    • @wjeksababakqabzzhzaab873
      @wjeksababakqabzzhzaab873 4 дні тому

      Year 13s would have taken the mat and applied , year 12s only started college 3 months ago

    • @JPiMaths
      @JPiMaths  4 дні тому +1

      BMO problems are good, but definitely not the best way to prepare. For the time being it's better than nothing. Your focus should be to try and learn the Y12 content well (e.g. make sure you fully understand why/where each formula is derived from, even if this isn't required as per the A-Level syllabus). Then, you maybe want to look at some past papers such as MAT, TMUA, STEP1. Don't worry about doing them under timed conditions just yet, focus on really understanding the solution and ensuring you can explain it to someone else.

    • @JPiMaths
      @JPiMaths  4 дні тому +1

      You don't really do problem solving in the same way at uni, it's more learning concepts and then tackling problems about these concepts

    • @voicutudor7331
      @voicutudor7331 4 дні тому

      @@wjeksababakqabzzhzaab873 ok, the uk system is pretty weird then 😂