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Mega A Level Maths Thread MK II

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Reply 100

ThePersian

Original post by justinawe

Seems like a fairly simple induction proof, what exactly are you having trouble with?

What I don't get is what is all that '2n+1' and '2n' about when trying to prove something is even or odd?

Reply 101

Adam_Pritchard

Original post by priyashah95

So scared for tomorrow :frown:

wanna cry

Posted from TSR Mobile

dont worry

Reply 102

justinawe

Original post by ThePersian

What I don't get is what is all that '2n+1' and '2n' about when trying to prove something is even or odd?

Oh, I see.

2n means you have an integer n multiplied by two... which means it is divisible by two. By definition, an even number has to be divisible by two, and therefore an even number can always be represented by "2n".

Now, we know that an even number+1=an odd number, so an odd number can be represented by 2n+1.

Reply 103

Felix Felicis

Original post by ThePersian

Hello,

Could someone help me out here, I never understand proof questions.

If you know, can you also explain this whole idea behind '2n+1' and '2n' I don't understand it.

Thank you.

You don't need to write it in the form of 2n+1/ 2n/ whatever.

n^{3} + 3n^{2} + 2n = n(n+1)(n+2), n \in \mathbb{Z^{+}}

As 'n' is a positive integer, the expression is the product of 3 consecutive integers - so you have factors of 2 and 3 in there, thus it is divisible by 6 for all n.

Reply 104

justinawe

Original post by Felix Felicis

You don't need to write it in the form of 2n+1/ 2n/ whatever.

n^{3} + 3n^{2} + 2n = n(n+1)(n+2), n \in \mathbb{Z^{+}}

As 'n' is a positive integer, the expression is the product of 3 consecutive integers - so you have factors of 2 and 3 in there, thus it is divisible by 6 for all n.

I think he was asking about 2n/2n+1 thing was a side question rather than as part of that question :redface:

Reply 105

Felix Felicis

Original post by justinawe

I think he was asking about 2n/2n+1 thing was a side question rather than as part of that question :redface:

Oh! I see, my bad :redface:

Reply 106

upthegunners

Is it just me or is no one else in the mood to revise for m1 tomorrow?

Reply 107

ThePersian

Original post by Felix Felicis

You don't need to write it in the form of 2n+1/ 2n/ whatever.

n^{3} + 3n^{2} + 2n = n(n+1)(n+2), n \in \mathbb{Z^{+}}

As 'n' is a positive integer, the expression is the product of 3 consecutive integers - so you have factors of 2 and 3 in there, thus it is divisible by 6 for all n.

Thank you!

Reply 108

Kvothe the Arcane

Original post by DJMayes

Double quoted!

Firstly, Edexcel are notoriously bad at exam timetabling, for no conceivable reason other than to finish AS Level exams before A2 level exams. For example, I have the following clashes in my Maths exams this summer:

18th June - C4/M4
21st June - FP2/S4
24th June - FP3/M5

So many clashes could be avoided just by, for example, sitting M5 with M1 instead of with FP3, as M5 and FP3 are basically always sat together. But Edexcel never do this.

And you'll find calculus comes up in all modules past M1. M2 has basic differentiation and integration to solve kinematics problems. M3 contains more advanced differentiation and integration in kinematics, including acceleration as a function of displacement, integration to find work done and impulse, and integration to find centres of mass. M4 contains first and second order differential equations, along with calculus to find positions of stability. M5 contains first and second order vector differential equations, differential equations on varying mass (Where you have to derive the equations yourself using limits), integration to find moments of inertia and a bit of calculus in rotational motion.

Thanks for the reply. It was very informative! Can I post the post in the M1 thread the post you made a few days ago on M1 in this thread for the benefit of M1 candidates who don't follow this thread?

(edited 10 years ago)

Reply 109

username937760

Original post by reubenkinara

Thanks for the reply. It was very informative! Can I post the post you made a few days ago on M1 in the M1 thread for the benefit of M1 candidates who don't follow this thread?

I haven't posted in the M1 thread... :confused:

EDIT: This has now been explained to me by the mysterious forces watching over this thread. Yeah, go ahead, the post is meant to be helping people. I couldn't really care less if someone posted it there claiming it as their own to be quite honest, so long as someone gets something out of it.

(edited 10 years ago)

Reply 110

Ateo

Original post by Ursin

Yo, I wonder if anyone can answer this S1 question? I can't do it, my teachers can't do it, my friend who got 100 in S1 the first time we took it can't.
Eight cards are selected with replacement from a standard pack of 52 playing cards, with 12 picture cards, 20 odd cards and 20 even cards.
a) How many different sequences of 8 cards are possible?
For this I did 52^8, which is correct.
b) How many of the sequences in part a) will contain 3 picture cards, 3 odd-numbered cards and 2 even-numbered cards?
The answer in the back of the book says 3.097 x 10^12. I have tried a multitude of methods and cannot for the life of me obtain this answer.
Thanks :smile:

I can't get that answer either. Are you sure it is correct?

Perhaps the man himself may shed a light on this.

ghostwalker

...

Reply 111

Felix Felicis

Original post by Ateo

I can't get that answer either. Are you sure it is correct?

Perhaps the man himself may shed a light on this.

Original post by Ursin

Yo, I wonder if anyone can answer this S1 question?...

Ok, call the sequence of picture cards, odd cards and even cards: PPPOOOEE
As there are 12 picture cards, 20 odd cards, 20 even cards, then the number of ways this specific sequence can be made is:

12^{3} \times 20^{3} \times 20^{2}

But this is simply one of the ways we can arrange this sequence; we could have POPOPOEE for example as well, this still counts as 3 pictures, 3 odds, 2 evens. There are 8 items, so the total number of ways we can arrange this sequence is:

12^{3} \times 20^{3} \times 20^{2} \times 8!

But we've over-counted here - for example, the sequence of say PPP and PPP are the exact same. Since there are 3 Ps, 3 Os, 2 Es, we've over counted by

3! \times 3! \times 2!

Hence, the total number of ways this sequence can be made is

\dfrac{12^{3} \times 20^{3} \times 20^{2} \times 8!}{3! \times 3! \times 2!} = 3.096576 \times 10^{12}

(edited 10 years ago)

Reply 112

Bixel

Hey guys, I've got two questions on M1.

1) When the question asks you to "write an equation for motion" of something, what's the best way to go about this? Do they care about how you write it? i.e. Resolving a particle of mass 4m hanging off of a string in the downards direction in equilibrium, including tension, could it be 4m - T = 0 or does it have to be 4m = T?

2) Can you use Fmax = uR? This was the way I was taught friction in school, but as soon as I saw DJ's post, this confused me a bit.

Thanks!

Reply 113

joostan

Original post by Bixel

If something is in motion then

\ F_{Max} = \mu R

I think either's satisfactory for your first q, though I don't actually know.

(edited 10 years ago)

Reply 114

Luxlo

Y'all recon we will get a long question on connected particles?

Reply 115

Zaphod77

Original post by Bixel

1) I shouldn't have thought it matters, but someone else might be able to shed light - I think so long as the content is right, it should be fine, unless they've asked for a certain form!
2) Fmax=uR when a particle (or whatever) is moving or on the point of moving (limiting equilibrium). In M1 the majority of questions do say that, but if the object/particle is stationary and the question doesn't say it's on the point of moving then that isn't the maximum value of Friction necessarily, which is where the inequality Fr<=uR comes into play.

Reply 116

Ateo

Original post by Felix Felicis

...

What puzzles me is why does the answer of the book for the first part include various arrangements of the same sequence and we take into account the fact that the same sequence could be arranged in different ways in the second part?