HARDEST A Level Maths Tricky Question #16

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[JettixX]

The circle has centre O, so its equation is x^2 + y^2 = r^2
The curves meet so you can square the x and y values of the parametric curve and put them in the circle equation for an equation in r (make the double angle trig function a single angle one first)
Then you can use b^2-4ac = 0 since the points only touch to find r

[trilltochill]

For part b you can achieve the answer by differentiating both equations and equating them so that you get -2x=18x^2-9x^3 solving gives you correct x and correct y which you can use Pythagoras for to find radius

[MintyMit]

For part b I used the discriminant = 0 for the quadratic (well quartic, hidden quadratic) to get 10/3

[MorgKev]

r^2 = x^2 + y^2 ... rewrite y^2 in terms of x^2... then get d(r^2)/dx and set to zero to find x (at max r^2). Then y^2 follows by substitution... and hence r^2.

[kausarlolz]

hi sir! i was able to do part a very easily using the trig trianlge we often do in mechanics questions (slope inclined at sinx = 4/5 etc) i set sint = x/2. made a trig triangle and subbed in cost into y = 3(2sintcost) and squared both sides :)

[AITunesUK]

at first sight, I thought this was easy enough and just found the stationary point and got distance to that which is sqrt(11) and thought it was easy enough lol, because it looks like the circle just touches the maxima on the diagram. I could not have been more wrong, this is slightly trickier than I anticipated.

[stan]

7:50 Why is r maximised at dr/dx = 0 ? Thanks!

[AG-qlsy]

Any chance jack k is heading to oxford or Cambridge?😂

[theupson]

good lord, it wants to be easy, you just have to let it.
a: the objective becomes
1 double angle identity, 1 pythagorean identity and cancel.

b: max x^2+y^2 subject to y^2 = 9x^2 - 9/4x^4
just freaking substitute. its conspicuously easy, closest thing to tricky is remembering that x has a range

literally five lines start to finish

[onaopemipoadeniyi]

Hi Sir, why is dr/dx = 0 when for max r at 7:39?

[rheajohri]

Hello, thank you so much for this video. I also fell into the trap of parametric differentiation in part b. I wanted to ask at 11:15 why the discriminant = 0 is used? Wouldn't it be discriminant > 0 as there are 4 solutions (not one)?

[Lexler]

Great explanation, i was able to part a) but part b) i forgot about doing Rmax as a derivitive ❤

[billyunited]

As a year 13 student I got part a correct and part b as root 11 so correct to 2 sig figs lol. Very tricky

[AlevelStudent-cy]

Hi Sir, For the 2023 maths papers, should we expect 16+ questions. Over the years Edexcel have put more and more questions in the papers., so I’m a little anxious about timing

[sulamakamyon]

when you do b squared- 4ac, =0 doesnt that only refer to equations where its tangent ( one intersection point), however for the circle there are multiple intersections.

[AlevelStudent-cy]

Hi Sir, wouldn’t you make the discriminant greater than 0 since C1 and C2 are intersecting multiple times ?

[adrianhall]

I was also thinking of using the discriminate however why did you have to let u=x^2 to do this does the discriminate only work on highest power 2?

[uvwv]

Very interesting question… dare I say even enjoyable lol

[RingsideReels]

I did it throught modelling it as a quadratic, knowing it as 1 solution and got 10/3

[BBK]

which paper is this from?? great video btw