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Mega A Level Maths Thread MK II

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I'm sorry to say that the two forms you've given me are not equivalent. Check the bold.
The inductive proof was so much tidier :tongue:

Original post by DJMayes

As said, it cost me 5 UMS - I don't know exactly how many raw marks that is though, and I'm fairly sure I got the rest of the paper right.

You're not allowed to just quote the summation formula, so there are a few things you could do. Firstly, you could prove the summation formula

S_n = \frac{1}{2}n(2a+(n-1)d)

(I think that's the formula) but in my opinion a better way would be to simply prove the given summation using induction.

(You could also prove the result for the sum from one to n of r, and then use this and series methods to derive the result. The problem is that I'm not familiar with the WJEC syllabus so I don't know what method is going to be expected.)

Wait what?

I can get the summation from first principles...

But then what do I do with that?

( 4n^2 - 2n ) / 2 = 2n^2 - n

= n(2n-1)

Reply 861

justinawe

Original post by L'Evil Fish

Wait what?

I can get the summation from first principles...

But then what do I do with that?

( 4n^2 - 2n ) / 2 = 2n^2 - n

= n(2n-1)

You ask a question, then proceed to solve it... so are you really asking a question at all? :curious:

Reply 862

L'Evil Fish

Original post by justinawe

You ask a question, then proceed to solve it... so are you really asking a question at all? :curious:

So my two choices are:

Prove general summation and sub in values.

Prove summation using the values there (as Llewellyn showed me from the mark scheme)

Reply 863

justinawe

Original post by L'Evil Fish

So my two choices are:

Prove general summation and sub in values.

Prove summation using the values there (as Llewellyn showed me from the mark scheme)

I honestly have no clue what is meant by proving "from first principles" here, so I'd just go with what they put in the markscheme.

Reply 864

L'Evil Fish

Original post by justinawe

I honestly have no clue what is meant by proving "from first principles" here, so I'd just go with what they put in the markscheme.

Okay that's fine then...

What else... There was this too, maybe I'm just finding manipulation difficult, it was last night though...

I'll post them in a few minutes if you don't mind?

Reply 865

justinawe

Original post by L'Evil Fish

Okay that's fine then...

What else... There was this too, maybe I'm just finding manipulation difficult, it was last night though...

I'll post them in a few minutes if you don't mind?

Sure, go ahead.

Reply 866

L'Evil Fish

Original post by justinawe

Sure, go ahead.

Really simple method I guess... Just don't know where I went wrong.

AP:
55 = Sum of first ten
4th + 7th + 9th = 27

55 = 5(a+9d)
11 = a + 9d
a = 11 - 9d

(a+3d)+(a+6d)+(a+8d)=27
(11-9d+3d)+(11-9d+6d)+(11-9d+8d)=27

33 - 10d = 27
d = 6/10
a = 5.6

(edited 10 years ago)

Reply 867

Fuzzy12345

Original post by joostan

On second thoughts I suppose you're right. :smile:

Btw I proved the summation formula on the previous page :tongue:

Ahh, fair do's, fair do's ^^

Original post by L'Evil Fish

So my two choices are:

Prove general summation and sub in values.

Prove summation using the values there (as Llewellyn showed me from the mark scheme)

Or, choice number 3... :tongue:

Reply 868

justinawe

Original post by L'Evil Fish

Reply 869

L'Evil Fish

Original post by justinawe

Damn, okay, that's sorted then...

Last one before it should be full marks in my knowledge (like I could now)

I think it was a circle one...

Area of Sector OAB = 43.56

Arc BC is 13cm shorter than CD.

Radius is 11cm.

I need to find theta and the other one.

I got

Theta = 0.72
The other one = 1.80 (this is wrong I think)

Forgot to post a diagram... *walks upstairs*

And now it wont upload :mad:

(edited 10 years ago)

Reply 870

justinawe

Original post by L'Evil Fish

Your value for theta is right.

What's this "other one" you speak of, though? :colonhash:

Reply 871

L'Evil Fish

Original post by justinawe

Your value for theta is right.

What's this "other one" you speak of, though? :colonhash:

Call it angle x.

Basically:

11x + 13 = 11(pi-x)

In my opinion, because it's the diameter, split up into two sectors, with one labelled x. And one arc is 13cm less than the other arc.

Reply 872

joostan

Original post by L'Evil Fish

Wait what?

I can get the summation from first principles...

But then what do I do with that?

( 4n^2 - 2n ) / 2 = 2n^2 - n

= n(2n-1)

Precisely

Reply 873

L'Evil Fish

Original post by joostan

Precisely

Sn = 1 + 5 + . . . + (4n – 7) + (4n – 3)
Sn = (4n – 3) + (4n – 7) + . . . + 5 + 1
Reversing and adding
Either:
2Sn = (4n – 2) + (4n – 2) + . . . + (4n – 2) + (4n – 2)
Or:
2Sn = (4n – 2) + . . . (n times)
2Sn = n(4n – 2)
Sn = n(2n – 1)