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Year 12 Maths Help Thread

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Original post by Palette
Having done the question, you'll never get anything like that unless it's

a) International paper
b) Siklos having a go at making A Level questions.

There is a bit of C3 which is rare for an M2 question. Draw a line from the center of mass (call it G) to D and mark the angle GDA as 'a'. See what you can do. Remember the moment formula Fd*sin X.

Really appreciate you taking your time to do this, I'll be sure to ask again if I need a little more assistance.
Reply 2341
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Palette
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14
Original post by Vanilla Poison
Really appreciate you taking your time to do this, I'll be sure to ask again if I need a little more assistance.


No problem. I just stepped in as it's my aim to have every question answered on here.
Original post by Zacken
Not x= 99, but yeah, it's just 99. Good job!! :biggrin:


Thanks for all the help! Thats all the maths im doing today, i have a tonne of english homework, but ill be back tomorrow! :smile:
Original post by It's Me!
Thanks for all the help! Thats all the maths im doing today, i have a tonne of english homework, but ill be back tomorrow! :smile:


Sure thing, quote/tag me.
Reply 2344
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Palette
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Original post by Zacken
Sure thing, quote/tag me.


Do you have any tips for revising for A Level Physics?
Reply 2345
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RosaA
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Hi!

My exam board/subject is: AQA-Level 2 Further Mathematics

I am currently trying to learn the Matrices topic :biggrin: (Reflection, Rotation and transformations by matrices)

Does anyone have any good websites/resources that could help me?
Original post by RosaA
Hi!

My exam board/subject is: AQA-Level 2 Further Mathematics

I am currently trying to learn the Matrices topic :biggrin: (Reflection, Rotation and transformations by matrices)

Does anyone have any good websites/resources that could help me?


I found the examsolutions video on that quite helpful and intuitive. :-)
Reply 2347
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RosaA
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Original post by Zacken
I found the examsolutions video on that quite helpful and intuitive. :-)


Where can I find that? :biggrin:
Original post by RosaA
Where can I find that? :biggrin:


http://www.examsolutions.net/maths-revision/syllabuses/Edexcel/period-1/FP1/module.php

The "Matrix Algebra" part?
Reply 2349
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RosaA
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Original post by Zacken


Yes, thank you so much! :biggrin:
@Zacken Hey, I hope you've had a nice day. ^-^

Well, I know this is a year 12 thread but is it possible to ask for help on C3 too? I don't think there's a year 13 version of this. :s-smilie:
Original post by Anon_98
@Zacken Hey, I hope you've had a nice day. ^-^

Well, I know this is a year 12 thread but is it possible to ask for help on C3 too? I don't think there's a year 13 version of this. :s-smilie:


Hope you had a good one yourself!

Sure thing, go for it! We'd be more than happy to help. :smile:
Oh yay thank you v much! - it's appreciated. :h: The user I've tagged below is stuck on a few questions and so I thought it was best that I directed her here since you perfectly explained stuff to me last time + will therefore most likely do a better job of it than if I tried.

Edexcel board.

- June 2005 Q5
- January 2006 Q6

@Carolinec1206 - Ask/Explain about it here! :smile:

Edit: Here is the Jan 2006 link:

https://07a69ccf283966549a9350d1a66951a7bc96e2dc.googledrive.com/host/0B1ZiqBksUHNYZ0JQM1NRcmdHdXM/January%202006%20QP%20-%20C3%20Edexcel.pdf

I can't find the June 2005 one, but hopefully she'll be able to provide it soon to make it easier. :colondollar:
(edited 8 years ago)
Original post by Anon_98
Oh yay thank you v much! - it's appreciated. :h: The user I've tagged below is stuck on a few questions and so I thought it was best that I directed her here since you perfectly explained stuff to me last time + will therefore most likely do a better job of it than if I tried.


It's nice that you remember! :h:

Okay, cool - Caroline, can you tell me precisely what you're not understanding or what's troubling you so I can address that?
Original post by Anon_98
Oh yay thank you v much! - it's appreciated. :h: The user I've tagged below is stuck on a few questions and so I thought it was best that I directed her here since you perfectly explained stuff to me last time + will therefore most likely do a better job of it than if I tried.

Edexcel board.

- June 2005 Q5
- January 2006 Q6

@Carolinec1206 - Ask/Explain about it here! :smile:

Edit: Here is the Jan 2006 link:

https://07a69ccf283966549a9350d1a66951a7bc96e2dc.googledrive.com/host/0B1ZiqBksUHNYZ0JQM1NRcmdHdXM/January%202006%20QP%20-%20C3%20Edexcel.pdf

I can't find the June 2005 one, but hopefully she'll be able to provide it soon to make it easier. :colondollar:

Thank you guys for helping me out. Truly appreciate that :smile:
Question 1 :
Using the identity cos(A + B) ≡ cosA cosB – sinA sinB, prove that cos 2A ≡ 1 – 2 sin2A.
I know how to do first step but then I don't know why and how they get that answer.
Link to the paper. Question 5
07a69ccf283966549a9350d1a66951a7bc96e2dc.googledrive.com/host/0B1ZiqBksUHNYZ0JQM1NRcmdHdXM/June%202005%20QP%20-%20C3%20Edexcel.pdf

Question 2:
Express 4 cos θ + 6 sin θ in the form R sin(θ + α), where R > 0 and 0 < α < π.
I know how to do it and get full marks but in sample answers people tend to write the formula for it which is :R sin θ cos α + R sin θ cos α and I'm wondering whether you have to write it or not ,I couldn't find it in markscheme or exam report whether you loose mark if you don't write it

Question 3: f(x) = 12 cos x – 4 sin x.
Given that f(x) = R cos(x + α), where R . 0 and 0 - α - 90°,
(a) find the value of R and the value of α.
12 cos x – 4 sin x = 7
(b) Hence solve the equation for 0 - x < 360°, giving your answers to one decimal place.
(c) (i) Write down the minimum value of 12 cos x – 4 sin x.
(ii) Find, to 2 decimal places, the smallest positive value of x for which this minimum value occurs.
I know how to work it out beside c) ii). I don't understand where they take that info from and the answer
Paper. January 2006,Q6
07a69ccf283966549a9350d1a66951a7bc96e2dc.googledrive.com/host/0B1ZiqBksUHNYZ0JQM1NRcmdHdXM/January%202006%20QP%20-%20C3%20Edexcel.pdf
Original post by Carolinec1206

Question 2:
Express 4 cos θ + 6 sin θ in the form R sin(θ + α), where R > 0 and 0 < α < π.
I know how to do it and get full marks but in sample answers people tend to write the formula for it which is :R sin θ cos α + R sin θ cos α and I'm wondering whether you have to write it or not ,I couldn't find it in markscheme or exam report whether you loose mark if you don't write it


Okay, I'll answer this first because it's the easiest. You won't lose marks for it, no. I would recommend writing it down anyway because it might help you spot silly mistakes or such. I certainly make sure to do that - it helped in a year where they switched the terms around and students got confused because they were so used to doing it directly. So you won't lose marks, but do it anyway - it's good form.
Original post by Carolinec1206

Question 3: f(x) = 12 cos x – 4 sin x.
Given that f(x) = R cos(x + α), where R . 0 and 0 - α - 90°,
(a) find the value of R and the value of α.
12 cos x – 4 sin x = 7
(b) Hence solve the equation for 0 - x < 360°, giving your answers to one decimal place.
(c) (i) Write down the minimum value of 12 cos x – 4 sin x.
(ii) Find, to 2 decimal places, the smallest positive value of x for which this minimum value occurs.
I know how to work it out beside c) ii). I don't understand where they take that info from and the answer
Paper. January 2006,Q6
07a69ccf283966549a9350d1a66951a7bc96e2dc.googledrive.com/host/0B1ZiqBksUHNYZ0JQM1NRcmdHdXM/January%202006%20QP%20-%20C3%20Edexcel.pdf


Okay - so, you've written 12cos⁡x−4sin⁡x≡160cos⁡(x+18.4∘)12 \cos x - 4 \sin x \equiv \sqrt{160}\cos (x + 18.4^{\circ}), right?

Then - because you know that cos⁡(x+18.4∘)\cos (x + 18.4^{\circ}) oscillates between −1-1 and 1, you rightly said that the minimum value of the entire expression occurs when cos⁡(x+18.4∘)=−1\cos (x + 18.4^{\circ}) = -1 so that the total minimum value is −160-\sqrt{160}.

Now, to find the value of xx for which this minimum occurs, you want to know which xx makes cos⁡(x+18.4∘)=−1\cos (x + 18.4^{\circ}) = -1. Now you can solve this equation by taking the inverse cosine of both sides, etc...

Do you understand or does that need more explanation?
Original post by Zacken
Okay - so, you've written 12cos⁡x−4sin⁡x≡160cos⁡(x+18.4∘)12 \cos x - 4 \sin x \equiv \sqrt{160}\cos (x + 18.4^{\circ}), right?

Then - because you know that cos⁡(x+18.4∘)\cos (x + 18.4^{\circ}) oscillates between −1-1 and 1, you rightly said that the minimum value of the entire expression occurs when cos⁡(x+18.4∘)=−1\cos (x + 18.4^{\circ}) = -1 so that the total minimum value is −160-\sqrt{160}.

Now, to find the value of xx for which this minimum occurs, you want to know which xx makes cos⁡(x+18.4∘)=−1\cos (x + 18.4^{\circ}) = -1. Now you can solve this equation by taking the inverse cosine of both sides, etc...

Do you understand or does that need more explanation?


I understand this but how do you know its between -1 and 1 is it because of graph of cos ? Would the same case be with sin ?
Original post by Carolinec1206
Thank you guys for helping me out. Truly appreciate that :smile:
Question 1 :
Using the identity cos(A + B) ≡ cosA cosB – sinA sinB, prove that cos 2A ≡ 1 – 2 sin2A.
I know how to do first step but then I don't know why and how they get that answer.
Link to the paper. Question 5
07a69ccf283966549a9350d1a66951a7bc96e2dc.googledrive.com/host/0B1ZiqBksUHNYZ0JQM1NRcmdHdXM/June%202005%20QP%20-%20C3%20Edexcel.pdf


Your link doesn't work, so I'll work through the question a bit and you tell me if you understand it all:

cos⁡2A=cos⁡(A+A)=cos⁡Acos⁡A−sin⁡Asin⁡A=cos⁡2A−sin⁡2A\cos 2A = \cos (A+A) = \cos A \cos A - \sin A \sin A = \cos^2 A - \sin^2 A, by letting B=AB=A in the formula given, you okay with that?

Now, use the fact that cos⁡2A+sin⁡2A=1  ⟺  cos⁡2A=1−sin⁡2A\cos^2 A + \sin^2 A = 1 \iff \cos^2 A = 1 - \sin^2 A. So you can replace this into the above equation, to get:

cos⁡2A−sin⁡2A=(1−sin⁡2A)−sin⁡2A\cos^2 A - \sin^2 A = (1 - \sin^2 A) - \sin^2 A, can you see why this is so? I'm sure you can finish off from here.
Original post by Carolinec1206
I understand this but how do you know its between -1 and 1 is it because of graph of cos ? Would the same case be with sin ?


Yes, you need to know that cos⁡\cos and sin⁡\sin is bounded between −1-1 and 11. It's a property that you will need to use over and over again in questions of this type in nearly every C3 paper.

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