NO ONE gets this right first time! | Super tricky A-Level Maths question

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[ASC]

Nah this brother is saving so many individual's grades!

[reload]

I had this in a test recently and managed to get it right, I made a cubic in terms of t then drew a sketch with 4 roots.I then differentiated to find the maximum and minimum values. Then used those to find the upper limit for k. Then as it was a quartic I used the discriminant to find the lower limit for k. Pretty tough question honestly

[theupson]

the radius of circle c1 has to be greater than the minimum distance between the center of C1 and parabola C2. it's objectively ludicrous to frame the question this way, but for many students the constrained optimization problem will feel more familiar, and when you're under pressure that counts.

[otherthings]

Pls make many more videos like this, they are super helpful and help understand maths easy . Keep it up

[akhilms]

Excellent content !!!! KEEP MAKING MORE FOR EVERYTHING A STAR QUESTIONS NEEDED THANK YOU SO MUCH

[infintysolar]

icl i wouda never spotted that i wouldve just looked at a quartic graph and see t^4+t^2-(k), and see the possible values when theres 4 sols but this is good algebraically

[limegagliano]

Nice problem! My solution was for the lower bound was similar. For the upper bound, perhaps a graphical approach is easier to intuit.

First i let k+25=r for simplicity. By completing the square, I turned the equations into (x-5)^2 + y^2 = r^2 ==> y=sqrt[r^2-(x-5)^2] and y=±2sqrt(x) then solved for positive discriminant to get k>-9.

On the graph, which looks like a sideways parabola intersecting a circle centered at (5, 0), I noticed that there are :
1. no intersections when the circle is "inside" the parabola (this is when k<-9).
2. two intersections when k=-9 (tangent on the inside)
3. four intersections when the circle does not go past the origin, but is past the tangent state.
4. three intersections when the curves are tangent at the origin
5. two intersections when the radius is bigger than in part 3

So for the upper bound, we just need to find when the curves are tangent at the origin, then all the radii between that and k=-9 are the solution.
It's clear that when the curves are tangent at the origin, the radius of the circle is 5 ==> r^2 = k+25 = 5^2 = 25 ==> k=0.

so the solutions is k ∈ (-9, 0)

[thanoschin]

Hello sir, can you please make videos about IAL pure maths 2 and Statistics 1?

[idk.igcse_]

Hey sir when are you going to make predictions for mathematics IGCSE edexcel. Please can you nmake them ASAP. And your channel is literally saving my grades!!

[parveshfilms]

hello sir, can you make a video about May/June igsce edexcel predicted paper 1h? My exam is in 2 months.Thank you

[zxin]

at 3:51 how did you know it already had 2 distinct real roots

[T-ch]

Brother, can you make videos on igcse edexcel science?

[Josama]

This is wrong, k can be greater than 0