Planetarion Forums

Phang · 5 Jan 2005, 21:56

Today's delightful AS Maths mock:

"Express √75 in the form (a + √b)/c, where a, b and c are integers."

Please, someone, a hand? It'd be staggeringly easy as (a√b)/c but that, alas, is not the question.

queball · 5 Jan 2005, 22:22

a=0
b=75
c=1

Phang · 5 Jan 2005, 22:24

Quote:

Originally Posted by queball

a=0
b=75
c=1

ah.

good grief, that's cheap

Deepflow · 5 Jan 2005, 22:28

that doesnt really seem AS level to me...

the answer i mean, not the question.

Tomkat · 5 Jan 2005, 22:56

It's not the right answer, is it?

0 isn't an integer.

MrL_JaKiri · 5 Jan 2005, 22:57

Quote:

Originally Posted by Tomkat

It's not the right answer, is it?

0 isn't an integer.

Yes it is.

Inferno · 5 Jan 2005, 23:03

I do AS Maths and that is not a AS Maths question. You dont do edexcel do you?

Androme · 5 Jan 2005, 23:14

I'm doing Further Maths

Inferno · 5 Jan 2005, 23:17

So am I. It sucks!

Deepflow · 5 Jan 2005, 23:22

you fools!

Inferno · 5 Jan 2005, 23:24

An ignorant man is in eternal bliss!

Androme · 5 Jan 2005, 23:34

Quote:

Originally Posted by Inferno

So am I. It sucks!

Aye. We've finished C1, C2, S1 & M1 - now that's left for the rest of the year is to study C3 & C4. C1, C2 & S1 are all easy - M1 is something I don't ****ing get. C3 has been fine so far - we started on the differentiation chapter which is piss-easy bar the quoitent rule will takes forever to work out - am getting used to how to derive to cot, cosec and sec - don't remember the exact methods but I'll learn the outcomes eventually. Moving onto the trig chapter & graphs chapters now - don't really understand the whole modulus crap and we were asked to look over some exam q's @ end of book - no-where in the book does it say anything about what g(x) is and yet there's a question on it - woo!

Also, in the last lesson, the teacher spent it teaching DeMoivre's theorem and spending the double lesson explaining imaginary no's in preperation for C4 or P4 or something. I missed the lesson before it so don't know where and why it came up

SYMM · 5 Jan 2005, 23:40

g(x) is just a function of x, like f(x) but with a different letter.
I'm sure I knew that at GCSE...

Tomkat · 5 Jan 2005, 23:46

Quote:

Originally Posted by MrL_JaKiri

Yes it is.

My mistake then. It's a long time since I did A-level Maths

Inferno · 5 Jan 2005, 23:50

SYMM is right about the g(x).

But imaginary numbers suck. Some clever clog came up with the idea that you cant get √-1 so you replace it with i or j. j² is equal to -1 and that helps with solving certain equations and is vital in an engineer's work. Nothing much to it, just know what it is and how to solve it and you are sorted.

Someone answer Phang's question since we have totally derailed from his question/thread.

MrL_JaKiri · 6 Jan 2005, 02:31

Quote:

Originally Posted by Inferno

But imaginary numbers suck. Some clever clog came up with the idea that you cant get ?-1 so you replace it with i or j. j² is equal to -1 and that helps with solving certain equations and is vital in an engineer's work. Nothing much to it, just know what it is and how to solve it and you are sorted.

Just i, actually. i and j are only used together in the context of unit vectors.

Imaginary numebrs are also a fine area of mathematics.

mist · 6 Jan 2005, 02:50

i thought 'i' was the maths version and 'j' the engineering version?

queball · 6 Jan 2005, 03:00

Quote:

Originally Posted by MrL_JaKiri

Just i, actually. i and j are only used together in the context of unit vectors.

Imaginary numebrs are also a fine area of mathematics.

What mist said. Also, quarternions.

Nusselt · 6 Jan 2005, 10:16

Quote:

Originally Posted by mist

i thought 'i' was the maths version and 'j' the engineering version?

it is (to avoid confusion with current), but like jakiri said when dealing with vectors you use i and j.

Androme · 6 Jan 2005, 10:27

Good riddance.

LHC · 6 Jan 2005, 11:16

M1 is really stupid and crap and I hate it

Flayer · 6 Jan 2005, 11:35

Hey guys I'm wondering over the original question too, I tried so hard and got so far. But in the end it didn't even matter! Anyone know how to solve it? please post solution ta

Nodrog · 6 Jan 2005, 11:46

Quote:

Originally Posted by Flayer

Hey guys I'm wondering over the original question too, I tried so hard and got so far. But in the end it didn't even matter! Anyone know how to solve it? please post solution ta

queball answered it in the 2nd post in this thread...

Flayer · 6 Jan 2005, 11:47

Quote:

Originally Posted by Nodrog

queball answered it in the 2nd post in this thread...

Yes, but do other solutions exist? I think not!

MrL_JaKiri · 6 Jan 2005, 11:56

Hmmm.

Ragnarak · 6 Jan 2005, 12:56

16
3
2

MrL_JaKiri · 6 Jan 2005, 12:59

Quote:

Originally Posted by Ragnarak

16
3
2

SQRT 78.6?

To put it another way, I don't think that 8 is equal to 9 SQRT3 / 2

Ragnarak · 6 Jan 2005, 12:59

Am i wrong? Cos i got that as soon as i typed in root 75 to my calculator and recognised that after the decimal was (root 3)/2 (which i guess they think is probably a number you should be able to recognise)

ps. i suck at maths

Ragnarak · 6 Jan 2005, 13:01

Quote:

Originally Posted by MrL_JaKiri

SQRT 78.6?

I didn't bother to check it properly

I just recognised the root3/2 part and guessed at the rest.

Oh well, i suck at maths

MrL_JaKiri · 6 Jan 2005, 13:02

Quote:

Originally Posted by Ragnarak

Am i wrong? Cos i got that as soon as i typed in root 75 to my calculator and recognised that after the decimal was (root 3)/2 (which i guess they think is probably a number you should be able to recognise)

ps. i suck at maths

SQRT 75 = SQRT 25 * SQRT 3 = 5 SQRT 3. You've accounted for 0.5 of the SQRT 3's.

It's also a good idea to 'test' the numbers you come up with.

Anyway, this is all pointless. It's fairly obvious that there's only one form of solution, where a = 0. c works for any natural number, you just have to multiply b by c^2 to get the ratio correct.

Nadval · 6 Jan 2005, 13:39

Maths/Further maths AS is piss easy

infact AS levels are piss easy.

MrL_JaKiri · 6 Jan 2005, 13:40

Quote:

Originally Posted by mist

i thought 'i' was the maths version and 'j' the engineering version?

**** engineering!

Proteus · 6 Jan 2005, 13:51

I'm so glad after reading this thread that A-Level Further Maths is behind me. (Although P4 and P6 were quite fun.)

Stew · 6 Jan 2005, 13:59

Quote:

Originally Posted by Proteus

(Although P4 and P6 were quite fun.)

No they ****ing wern't.
Ragnarak - back me up on this.

P4, (P5) and P6 were bastards if you were a work shy individual like I.
Because one had never seen anything like the majority of stuff on there before (and thankfully not since, vectors floating in 3d my arse), it was rather difficult to do well without exerting any effort.

Ragnarak · 6 Jan 2005, 14:15

Quote:

Originally Posted by Stew

No they ****ing wern't.
Ragnarak - back me up on this.

P4, (P5) and P6 were bastards if you were a work shy individual like I.
Because one had never seen anything like the majority of stuff on there before (and thankfully not since, vectors floating in 3d my arse), it was rather difficult to do well without exerting any effort.

At the time they were hard to do unless you just 'got' it naturally. Looking back they were pretty simple but i don't know about fun.

MrL_JaKiri · 6 Jan 2005, 15:13

P4 and P6 (at least on my board) were immensely trivial, relatively more so than P1, 2 or 3.

Flayer · 6 Jan 2005, 15:22

I am waiting for someone to give proof that there is no solution with a != 0

MrL_JaKiri · 6 Jan 2005, 15:34

Quote:

Originally Posted by Flayer

I am waiting for someone to give proof that there is no solution with a != 0

If a =! 0, then b has to be a perfect square (75c^2 = a^2 + b + 2aSQRT b*), otherwise the LHS would be integral, and the RHS wouldn't.

If b is a perfect square, then you have 5 SQRT 3 = (Integer + integer) / integer, and root 3 is irrational.

*squaring, and rearranging

Deepflow · 6 Jan 2005, 15:43

Quote:

Originally Posted by MrL_JaKiri

If a =! 0, then b has to be a perfect square (75c^2 = a^2 + b + 2aSQRT b*), otherwise the LHS would be integral, and the RHS wouldn't.

If b is a perfect square, then you have 5 SQRT 3 = (Integer + integer) / integer, and root 3 is irrational.

*squaring, and rearranging

i was about to say that

Boogster · 6 Jan 2005, 17:49

Not too many English students on here, then?

MrL_JaKiri · 6 Jan 2005, 18:02

Quote:

Originally Posted by Boogster

Not too many English students on here, then?

All of the Arts students I know did maths to at least AS.

Boogster · 6 Jan 2005, 18:28

Ergh. I did not.

Phang · 6 Jan 2005, 18:41

Quote:

Originally Posted by MrL_JaKiri

All of the Arts students I know did maths to at least AS.

yes, but isn't AS Maths pretty much a requirement at Cambridge?

Structural Integrity · 6 Jan 2005, 19:11

Quote:

Originally Posted by queball

a=0
b=75
c=1

First thing that popped in my head too... I laughed out loud when I read your post.

Stew · 6 Jan 2005, 19:49

Quote:

Originally Posted by Structural Integrity

I laughed out loud when I read your [queball's] post.

Then you dear sir need to get yourself a life

Structural Integrity · 6 Jan 2005, 20:20

Quote:

Originally Posted by Stew

Then you dear sir need to get yourself a life

I was waiting for someone to mention that. But I guess you're kind of right.

Still, it's an incredibly simple solution for a seemingly difficult question. I suspect this to be somesort of trick question.

Boogster · 6 Jan 2005, 21:07

Quote:

Originally Posted by Phang

yes, but isn't AS Maths pretty much a requirement at Cambridge?

Cambridge is the more science based of Oxbridge, or so I always thought.

Phang · 6 Jan 2005, 21:13

Quote:

Originally Posted by Boogster

Cambridge is the more science based of Oxbridge, or so I always thought.

exactly my point.

MrL_JaKiri · 6 Jan 2005, 23:01

Quote:

Originally Posted by Phang

yes, but isn't AS Maths pretty much a requirement at Cambridge?

Nothing like a small sample size to guarantee overall trends!

Phang · 7 Jan 2005, 10:38

Quote:

Originally Posted by MrL_JaKiri

Nothing like a small sample size to guarantee overall trends!

1)i know a dozen or so people (not online) who go to or went to cambridge and did maths at AS.

2)i know half a dozen more who tried to go to cambridge, had excellent but non-maths a-levels, but failed.

3)i don't know anyone who tried to get into cambridge with good grades including maths that didn't get in, barring a couple who instead went to oxford.

it's a small sample size, certainly, but there's certainly a trend there.