Points of inflexion

I learnt something new today! I always believed that equating the first derivative and zero would find you all the stationary points, including points of inflexion, however, today I found out it is the solution of the second derivative that will find you the points of inflexion on a curve. This might be useful in the Higher Maths course. I would never learn so much if it weren't for Mathletics!

Tomorrow I return to school for another year of unknowns, although I know one thing: I will be starting topic 11 in Higher Maths! I am now two thirds of the way through unit 2. Topic 11 is more trigonometry, identities like in Int 2 (though much harder), and equations like in unit 1.

I may be doing the Senior Maths Challenge this November, although I don't know yet, I will post back if I find out.

3 d trig

I finished 3 d trigonometry today, I'm so pleased! It is still pretty difficult, as I haven't become accustomed to it yet. But I've done it, and I can progress now, so that's what matters. I can start the next topic, addition formulae, but first, I will revise topic 5, so I don't have too much work to do at prelim time (January), as I also have another 4 subjects!

I haven't done too much on Mathletics this week, as I've been to busy with the textbook work, but I did manage the co ordinate geometry test. I plan to do a little more work on the differentiation unit next week, and also integration if I have time. I will then get my gold certificate the week after that, and I'll be near the end of my course!

Trigonometry

This update is about my progress on the higher maths course:

I have managed to complete (or rather struggle through) one more exercise on 3 d trigonometry, which was very difficult. Instead of finishing that unit, I decided to revise topic 4 today instead. That was fairly easy, apart from 2 questions, one of which was crazily hard and made no sense to me, and one of which was just very difficult. Now that is done, I only have 2 more topics from unit 1 to revise. And once I finally finish 3 d trig, I'll be two thirds of the way through unit 2! I'm still hoping to sit the NAB sometime in October, after the holiday. I then only have a little bit of work to do before I'm ready for the prelim!

Normals

I have just got 100% on my equations of normals activity, I'm pleased about that! I knew what a normal is from Standard Grade Physics, but I never knew how to find the equation of one, until yesterday. It's similar to finding the equation of a tangent: you differentiate the given curve's equation, then substitute in the associated x value to find the gradient of the tangent, then take the negative reciprocal, to find the normal's gradient (it is perpendicular to the tangent). You then substitute the x value into the original equation to find a y value, then use y-b=m(x-a) and rearrange for the equation of the normal. It sounds complicated, but it's multiple choice, and on at least 4 questions out of 10 today, Mathletics didn't find the perpendicular gradient and used the tangent's gradient in the equation instead. So that's that finished, and I only need to do the co ordinate geometry test now!

Problems!

Sorry for the lack of updates to this blog, but I had some major problems last week! On August 1st, Mathletics reset all school accounts, in preparation for the new school year, but it also deleted all my work, on my personal account! I was quite upset about this, as I was faced with having to redo about a year's worth of work all over again. I struggled to regain as many gold bars as I could, when, after I'd reached 50, all of them were reinstated, but I also got to keep all the points and credits I earned the second time round, meaning I have over 50,000 credits. I have now been buying a lot for my Mathlete! I am presently at 140 gold bars and am working on the co ordinate geometry unit. I have the equations of normals topic to do (complicated), and then the test, before I finish. I will then work on the calculus activities.

I have also looked at the 3 D trigonometry in my Higher maths textbook, as I finally finished Integration on July 31st, but I haven't made any progress on it as I found it overwhelmingly difficult. I will have another look at it tomorrow to see if I can do it, although it is very abstract so I may need to wait until I go back to school and ask the teacher about it, as I just can't visualise the three dimensional objects necessary to understand it. But I will have to do something with the rest of this summer, even if it's just more revision.