Math Is Fun Forum

I need some advice in what to take next year for AS level.

Im doing my GCSEs right now, and i should be getting a minimum of 9A*s and 2As (in RS and Food Tech).

Im definitely going to take maths, but i dont know whethere to do maths with mechanics, maths with statistics, or even further maths?

The other subjects im thinking of taking include physics, english, german and history.

I can only pick 4.

Advice will be greatly appreciated.

Im doing past gcse papers, and I came across this question:

Prove algebraically that the sum of the squares of any two odd numbers leaves a remainder of 2 when divided by 4.

I have tried this, and i think i am on the right lines, but i have two problems with it. My workings so far:

An odd number can be represented by 2r+1, and 2r-1 etc.

This has not left a remainder of 2, but a remainder of 1/2 instead. However, I thought that when dividing by 4, a remainder of 2 would mean a remainder of 2/4 = 1/2, so the 1/2 is a remainder of 2.

But if this remainder is correct, Im still not sure I have proved it. (2r+1) and (2r-1) are both odd numbers, but they are consecutive odd numbers - so would using them be the same as using non-consecutive odd numbers? So have i only proved that that the sum of the square of two consecutive odd numbers gives a remainder of 2 when divided by 4? If so how would i go about doing the question?

Thanks.

I am having trouble understanding how x°=1, for any value of x.

I can understand it algebraically:

x^m ÷ x^m = 1

x^m ÷ x^m = x^m-m = x°

∴ x° = 1

But I cannot understand how any number multiplied by itself 0 times would give 1? It doesn't make much sense logically to me. Can anyone explain how this works (bearing in mind i am 15 - so not too complicated please)?

Thank you.

I heard this on the radio a while ago, but i did not hear who discovered it - i would like to know who did discover it before applying it to anything.

The area of a right-angled triangle and a circle will be equal if:

i) the height of the triangle is equal to the radius of the circle

and

ii) the base of the triangle is equal to the circumference of the circle

I have looked on the internet but cant find anything on it.
A little explanation about it would be nice too:).. but im only 15 so it needs to be kept fairly simple.

Thanks.