Solutions to Paper 1 Higher Level Maths 2004 Qs 1,2,3,5,6,7,8.

mat

These are just my results, not the actual ones, but i checked them with a friend and we got the same...so it's likely that they're right.

1. (a) root3 - 2
(b) (i) k=3
(ii) constant = 3
(c) (i) -3pq(p+q)
(ii) x = a, b, (a+b)/2

2. (a) x= 1, y= -2, z= -1
(b) (ii) x(squared) + pqx + q(cubed)
(c) (i) 3f(x)

3. (a) p = 3, q = -1
(b) (i) 1/2 - (root3)/2 i
(c) (i) 1 0
0 1024
(ii) 3070 3069
-2046 -2045

5. (a) 15 (answer rectified thanks 2 PrecariousNuts, cheers!)
(b) a = 16/3 r=3/2

6. (a) -5 / (2+5x)(squared)
(b) (i) 1/3
(ii) -sin x
(c) 3[(x + 2)(squared) + 1]

7. (a) 6 m/s
(b) (i) 2sin2O / 2-2cos2O
(ii) root3 and -1/(root3)
(c) 1/(1-x(squared))

8. (a) (i) - 1/x + C
(ii) 1/6 sin6x + C
(b) (i) pie/3
(ii) 15/64
(c) (ii) h/3[(y1) + (y3) + 4(y2)]

PrecariousNuts

1a says in the form a root 3 minus b, you have it the wrong way round

Isn't 5a +15?

all the others get my seal of approval

DS

5a is +15, other than that, identical to mine.
Here's Q4:

b(ii) 1 - 1/(2n-1)
(iii) 1
c(i) root(2)
(ii) 2d^2 >= d^2

PrecariousNuts

8a (i) should just be -1/x + C

Mutant_Fruit

(b) (i) 2sin2O / 2-2cos2O

I think it was asked for simplest terms... so you should have cancelled out the 2, i know i did. But i doubt they'd be that stingy with marks...

PrecariousNuts

Nope only dy/dx I cancelled anyway, I couldn't resist

claire h

Originally posted by PrecariousNuts
Nope only dy/dx I cancelled anyway, I couldn't resist

It simplifies down to cosO/sinO or 1/tanO, lovely altogether...

subway_ie

Originally posted by claire h
It simplifies down to cosO/sinO or 1/tanO, lovely altogether...

Bit of a waste of time though... all though it does look quite sexy.

The Shol'va

Originally posted by subway_ie
Bit of a waste of time though... all though it does look quite sexy.

Oh God yes, those precious 5 seconds! :P

Even sexier when you make it Cot

subway_ie

Originally posted by The Shol'va
Even sexier when you make it Cot

I dunno if I'd be able to handle Cot. Cot's just so intense. And sexy. In fact, Pg.9 is the new Pg.3.

Mutant_Fruit

i got a huge Page 9 stuck up on my wall. It helps get me going when the (imaginary) girlfriend bores me

PrecariousNuts

Isn't Cot counterproductive? You can't exactly look it up in the tables without transforming it back into one of the three

subway_ie

Originally posted by Mutant_Fruit
i got a huge Page 9 stuck up on my wall. It helps get me going when the (imaginary) girlfriend bores me

Oh my god. You can get those??? I tried to blow one up to A4 using my scanner, but it' just lost some of its appeal. I think the whole cheapness of the paper and small size just makes it all the more appealing. I hear they're going to bring out a new. You know you can get loads of websites with trigonometric identities? They can be a bit hardcore though... This is my personal favourite.

PrecariousNuts

Oh man they use 'u' instead of A. HARDCORE TO THE EXTREME!!!!!!!!!!!!!!111

I'm actually going to print that one and prove them, thats exactly the sort of stuff that comes up on paper 2

The Shol'va

Originally posted by Mutant_Fruit
i got a huge Page 9 stuck up on my wall. It helps get me going when the (imaginary) girlfriend bores me

I thought you were just humouring Colin when you said that :eek:

Mutant_Fruit

Ssshh, people think i'm joking. **looks around nervously** i don't what them to know the secert to my mathematical powers...

wow, mere days after i sit my engrish (sic) exam, my spelling goes through the floor. that is so cool!

penguincakes

Answers for 4:

(a) 3*nC3 n*(n-1)C3 (ie proved)

(b) (i) 2/(2r-1)*(2r+1) = 1/(2r-1) - 1/(2r+1) (ie proved)

(ii) 1 - 1/(2n+1)

(iii) 1

(c) (i) 2^(1/2) ( = root2)

(ii) p^2 + r^2 >= 2(q^2) (ie proved)

God damn it I just noticed I took "second term" in 5 (b) (i) to mean ar^2 rather than ar :mad: Ah well I did 7 questions anyway

I was finished at 10 to 11. Did anyone else think it was extremely short?

Mutant_Fruit

I tihnk i made a boo boo too, but i'm not certain...

Q 2 (C) (i)

It asked us to show there was a value K that made f(x + f(x)) = kf(x) for all X.

Is this telling us that it is true for all X, or are we supposed to prove it for all X? I belive that it is telling us that it is true for all X, and all we have to show is that there is a Value K that makes the thing equal?

So what i did was set x=1, and then i worked out f(x + f(x)) to be 9 and f(x) to be 3.

I then said, f(x + f(x)) has to be kf(x)
Therefore 9 = 3k, therefore k = 3. Q.E.D.

But was i supposed to leave it in the more general form of the X's, and not select the value? I'm still not sure...

I thought it was quite short too, i had finished 7 questions by 11:00, and took my time with the 8th, and rechecked everything. I learned from experience that rushing isn't worth the effort it takes to right fast. You are a lot more likely to drop signs if you rush, so i take it at a nice slow pace.

penguincakes

Unfortunately I think you shoulda left it in Xs, as it works out nicely as (6x+3)/(2x+1) = k = 3. You've only proved it for x = 1.

subway_ie

The setting x=1 one thing does seem a bit dodgy, but you did end up with the right answer, so at the very least you'd get an attempt mark. I didn't think it was very short... I just took my time on everything. As usual, I fecked up the matrices and triple simultaneous. Luckily my (ever so slightly illegal) calculator told me I was wrong so I could go back and change it. Did 6 questions and made a start on a 7th, then I ran out of time. I think if I didn't bother with the 7th I would definetly have gotten out the more retarded feck ups.

CuTeAnGeL

well thanx 4 that....and until i saw this, i thought i did really well!!! lol

Mutant_Fruit

Hmmm. i'm hoping that i'll lose only a max of 3 marks, considaring i did everything right, and then subbed in 1.

But i still ahve 6 other questions which i thnik are perfect, so it shou;dn't affect me at all.

If it does turn out to be grade-threatening mistake i'll try and convince the examiner that it was badly worded

DS

Looks fairly black and white to me. They said to prove it (show) for all x. You only proved it for one value of x. I hate to be a negative bastard, but I know how strict they are about subbing in numbers for proofs (for inequalities anyway). I'm not even sure if you get the attempt mark. It's only 10 marks anyway, don't get hung up about it.

subway_ie

Need to do some paper twos... even holding a pen right now is sore. Think I grip my biro too hard. Any recommendations for a challenging past paper 2?

Mutant_Fruit

can't remember if it was applied maths or normal maths... but wasn't 99 supposed to be hard? I;ve done all the papers from 94-03 (and paper1 04 ). Nothing seems hard to me anymore

penguincakes

Goddddamn it, I was just trying to write out my proof for 2^n >= n^2 & I realised I had a sign mistake somewhere. Still proved it "true" anyway, hopefully the corrector won't notice...

PrecariousNuts

I did the same thing, it was an accident on the last line so... slip?

PrecariousNuts

What happened to 2b i?

DS

x > 5/3, x < 1