The HARDEST EVER de Moivre's Theorem Question | A Level Further Maths

[@DarkPlaysThings]

Wow it's crazy to see someone answering the questions from my A level paper! It's funny, at the time I don't actually remember finding this to be the worst question and answered it pretty well. In hindsight, it was definitely the toughest one on the paper

[@shazuu]

which exam board?

[@H786...]

one thing i noticed about the graph of x^4 -x^2 is that it is an even function with symmetry, meaning root alpha will have another root of -alpha so you can basically just do it from there.

[@ohisko9004]

This is probably the best explanation I have seen, do you think you could upload videos of topic explanations for further math or maybe stream it?

[@Henry.Bt17]

I just found this question in the aqa year 2 further pure book back on Thursday and thought it seemed tricky. Glad to have gotten it correct though

[@NeilDoesMaths]

Koioioioidoesmaths

[@akfti]

Further maths!!! Thank the lords, im dying in school

[@NeilDoesMaths]

I got'chu bruh

[@H786...]

this q is actually from IAL 2017 FP2 (P48259A0128) , is it possible that they reused the same question in a recent A level exam?

[@scollyer.tuition]

For the final part, the identity: tan(pi-x) = -tan(x) is useful. It can be derived from the formula for tan(A+B). From that, we have: tan(3pi/5) = tan(pi-2pi/5) = -tan(2pi/5) tan(4pi/5) = tan(pi-pi/5) = -tan(pi/5) Certainly a fairly challenging question.

[@NeilDoesMaths]

Can be derived in a couple ways which is super cool

[@sdmnreacts1843]

@@NeilDoesMathssince tan is an odd function, tan(-x)=-tan(x). Adding the pi doesn’t alter the value of tan(x)

[@scollyer.tuition]

@@NeilDoesMaths Right. It's very useful to be able to derive a result in as many ways as possible. And, of course, being able to deduce results from e.g. graphical symmetry, as you did, is a very useful skill for the aspiring mathematician.

[@justdeclang3071]

what was the range for part b??

[@terrifier1536]

do u do further maths ? since when? thought u only do videos on a level math, u should def do more further maths

[@NeilDoesMaths]

FM is my favourite thing to teach. I just tailor to the masses mostly. DW more videos coming soon

[@samuellacobbinah]

I wish i could do this schmancy theorem question?

[@sdmnreacts1843]

I just don’t get how u deduce all the roots. Once you have the quadratic are I saying that equals tan5theta which equals zero. Then what?

[@NeilDoesMaths]

Remember the roots repeat themselves so we stop at 4

[@adw1z]

It really isn’t too hard if you actually understand what you are studying

[@NeilDoesMaths]

Benching 140kg isn't actually hard if you're just really really strong

[@adw1z]

@ that’s a completely wrong analogy. Everyone is “really strong” given that they are doing further maths A level and have gotten this far without dropping out. More like “understanding the perfect technique” will make it much easier for some than others, even if everyone is strong. That’s to say, understand WHY the method works instead of just blindly following the method, which is why so many struggle with A level (and any other level of) math

[@iJxcobi]

@@NeilDoesMaths It's a matter of the difference between relational and instrumental understanding. Someone understanding a mathematical concept relationally would be able to apply it to a question easily as they have a grasp of all the mathematical concepts required. It's why Maths and Further Maths can be one of the easiest papers to sit as long as the student has understood everything (You probably know this if you look at the average attainment of students who sit A level further maths, In 2024, 58.4% of students achieved A*-A grades in Further Maths, which is a higher proportion than all other A-Level subjects)

[@Sanatan_saarthi_1729]

I don't know what in the paper made you write the toughest question on de moivre's theorem. Like all these are standard questions 😅 nothing out of the box . Anyways nice 👍 video 😊

[@tomwoods5104]

DeMonford is cold

[@noaht2]

Simon de Montford

[@NeilDoesMaths]

He was a cool guy tbf

[@haulidayz302]

if you take a look at HSC extension 2 demoivre questions i can guarantee they get harder than this.

[@NeilDoesMaths]

never heard of HSC... might check it out

[@BP-gn2cl]

It takes 30 sec to solve

[@DanielTeachesMaths]

yeah right! 😊

[@dayingale3231]

I mean, it is just computations, don't think it is difficult at all.

[@loafee]

yoo ur a goat

[@NeilDoesMaths]

thanks boss