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Year 13 Maths Help Thread

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Original post by RDKGames
Not quite sure where I'm going wrong.

dudx+2ux=1x2\frac{du}{dx}+\frac{2u}{x}=\frac{1}{x^2}

PI=e∫2x.dx=x2PI=e^{\int \frac{2}{x} .dx}=x^2

but that doesn't seem right as I wouldn't get the left side from ddx(ux2)\frac{d}{dx}(ux^2)


The derivative of ux2ux^2 is x2dudx+2uxx^2 \frac{du}{dx} + 2ux which is what you would have on the left side if you multiplied everything by the PI.
Original post by kiiten
??? I have no idea what you're talking about.
What is 2n and is arcsin inverse of sin?


These will give you all the solutions you need in the question. These are called general solutions to sine.
If you think about it graphically, sine has a period of 2pi so it will repeat itself every 2 pi hence the n to reach any interval of it. Arcsin is indeed inverse sine.

If you want to learn about general solutions to make our life easier; you can learn them here: https://www.desmos.com/calculator/r7dmaljcom

I'd recommend it as you wouldn't be messing around with anything you don't understand. I was never taught the cast circle but if you use these you will get the questions of that type right 24/7.
Original post by RDKGames
Not quite sure where I'm going wrong.

dudx+2ux=1x2\frac{du}{dx}+\frac{2u}{x}=\frac{1}{x^2}

PI=e∫2x.dx=x2PI=e^{\int \frac{2}{x} .dx}=x^2

but that doesn't seem right as I wouldn't get the left side from ddx(ux2)\frac{d}{dx}(ux^2)


LHS becomes x2du/dx+2ux x^2du/dx +2ux which is d/dx(x2u) d/dx(x^2u) . You have to multiply everything through by your integrating factor.
Original post by NeverLucky
The derivative of ux2ux^2 is x2dudx+2uxx^2 \frac{du}{dx} + 2ux which is what you would have on the left side if you multiplied everything by the PI.


OH OF COURSE! Completely forgot to multiply through, thank you! xD
Original post by kiiten
Am i doing this wrong?

Solve: 5+2sin(2x+1)=6 for 0<=x<=720

rearranged to sin(2x+1)= 1/2

let u = 2x+1
sinu=1/2
u=1/6 pi

change the bounds to 1 <=u<=4pi +1
using a cast circle i got the first answer to be 2.05 but it should be 0.81 ???

*sorry if this doesnt make sense - let me know and ill post the full working

The 0.81 solution comes from 2x+1=5π/6 2x+1=5\pi /6 which gives x=5π/12−1/2. x=5\pi /12 -1/2. You are forgetting the symmetry of the sine curve about the line x=π/2 x=\pi /2 .
Original post by NeverLucky
The derivative of ux2ux^2 is x2dudx+2uxx^2 \frac{du}{dx} + 2ux which is what you would have on the left side if you multiplied everything by the PI.

PI?
Original post by B_9710
The 0.81 solution comes from 2x+1=5π/6 2x+1=5\pi /6 which gives x=5π/12−1/2. x=5\pi /12 -1/2. You are forgetting the symmetry of the sine curve about the line x=π/2 x=\pi /2 .


How did you get that first part????
Original post by B_9710
PI?


Ooops I meant IF :redface: I always say the wrong thing when I'm talking about integrating factors, particular integrals etc...
Original post by kiiten
How did you get that first part????


If 2x+1=π/6 2x+1=\pi /6 , then by symmetry of the curve 2x+1=5π/6 2x+1=5\pi /6 as well.
Original post by NeverLucky
Ooops I meant IF :redface: I always say the wrong thing when I'm talking about integrating factors, particular integrals etc...

It happens to the best of us.
Original post by kiiten
How did you get that first part????


Refer back to my post and look at where you add on pi and take away arcsine(alpha). Alpha = 1/2. That's where it comes from with n=0.
Original post by NeverLucky
Ooops I meant IF :redface: I always say the wrong thing when I'm talking about integrating factors, particular integrals etc...


Trust me I'm learning all of these at the moment and my head is getting confused between all of them when it comes to what to use, what to do, when and why. A mess.
hey guys, I've just finished year12 maths. I'm hoping for an A in my as, would you say A2 is much much harder than AS? and if so, do you have any tips/advice that you don't mind sharing? Thanks:biggrin:
Original post by OGFakiie
hey guys, I've just finished year12 maths. I'm hoping for an A in my as, would you say A2 is much much harder than AS? and if so, do you have any tips/advice that you don't mind sharing? Thanks:biggrin:


Practice questions and understand the topics, though I'm sure you learnt that in AS. It isn't much harder if you know AS inside out.
Original post by RDKGames
Practice questions and understand the topics, though I'm sure you learnt that in AS. It isn't much harder if you know AS inside out.


Any textbook recommendations?
Original post by RDKGames
Practice questions and understand the topics, though I'm sure you learnt that in AS. It isn't much harder if you know AS inside out.

Any textbook recommendations?
Original post by OGFakiie
Any textbook recommendations?


Yeah. The ones from your exam board concerning your modules.
Original post by RDKGames
Yeah. The ones from your exam board concerning your modules.


Publishers you donut
Original post by RDKGames
Trust me I'm learning all of these at the moment and my head is getting confused between all of them when it comes to what to use, what to do, when and why. A mess.


You learning FP2 right now? It is a bit of work to get your head round everything but it'll be easier once you do. A fair bit of FP2 is just memorising things.
Original post by kiiten
Am i doing this wrong?Solve: 5+2sin(2x+1)=6 for 0<=x<=720rearranged to sin(2x+1)= 1/2let u = 2x+1sinu=1/2u=1/6 pichange the bounds to 1 <=u<=4pi +1using a cast circle i got the first answer to be 2.05 but it should be 0.81 ???*sorry if this doesnt make sense - let me know and ill post the full working
Anyone know how to answer this using a CAST circle (i dont understand the graph method so i stick to CAST circles :smile:)

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