C2 Maths AS aqa 2016 (unofficial mark scheme new)

Hmm for 9a I got y=1/2m-6n... I'm pretty sure you had a negative indice on the bottom so it would become positive when you bring it to the top???

I'm still confused as to why it was 5+3cosx and not 3+5cosx also as to why the min value was -2, cheers tho

Gotta love AQA
Thanks for the clarification though, that was annoying me. Awful lot of work for 2 marks (never seen anything like it before either)

The question was show that (16 + 9sin^2x)/(5-3cosx) can be written in the form p + qcosx and state the minim value, and the exact value of x for this point.

Here's the method:

(16 + 9(1 - cos^2x))/(5 - 3cosx)

(25 - 9cos^2x)/(5 - 3cosx) then difference of two squares

(5 + 3cosx)(5 - 3cosx)/(5 - 3cosx)

The (5 - 3cosx) cancel to give 5 + 3 cosx
Minimum value of cosx is -1 so minimum value is 5 + 3(-1) = 5 - 3 = 2 when x = pi

Hmm for 9a I got y=1/2m-6n... I'm pretty sure you had a negative indice on the bottom so it would become positive when you bring it to the top???

I find it hilarious that the value for x was pi, it felt like they were trying to trick us and it ended with a simple answer. :P

And for 2c divided 5 by 0.2 and got a stretch of sf 25 in the y axis. Why isnt this correct?

+1 OP pls fix

Another thing - 6c is confusing the hell out of me

y=\sqrt{x^2+9}
onto
y=3\sqrt{x^2+1}

Let f(x) = \sqrt{x^2+9}

f(x) --> 3f(x) = Stretch in y direction SF 3
However, your mark scheme says "Stretch in x direction SF 1/3"
For that to be the case, wouldn't the equation have to be the following:
f(x) --> f(3x) = Your answer
Which would lead to the "original equation" having to be:
y=\sqrt{3x^2+1}

My logic was that the 3 is multiplying the entirety of the sqrt function.
For example:
5^x --> 3 * 5^x = Stretch in y direction SF 3
5^x --> 5^3x = Stretch in x direction SF 1/3
This would be the case because the number 3 is only multiplying the x by 3, not the entire function (which in this case is 5^x)

You said you proved it was x direction SF 1/3 using differentiation, could you show this please? Using methods and formulae that I'd been taught, I got to a y stretch SF 3.

Forgive me if I'm talking out my ass too

Got the same.
Question was:

log3(c) = m
log27(d) = n

log3(sqrt(c)) = log3(3^1/2m)
log3(d^2) = log3(3^6n)

It wanted sqrt(c)/d^2 which is:
log3(sqrt(c)) - log3(d^2) = log3(3^1/2m) - log3(3^6n)

sqrt(c)/d^2 = (3^1/2m)/(3^6n)
= 3^1/2m-6n

...right? I've already lost enough marks on this paper

Better than -1648x^10 making you doubt yourself for the remainder of the paper :P

Got the same.
Question was:

log3(c) = m
log27(d) = n

log3(sqrt(c)) = log3(3^1/2m)
log3(d^2) = log3(3^6n)

It wanted sqrt(c)/d^2 which is:
log3(sqrt(c)) - log3(d^2) = log3(3^1/2m) - log3(3^6n)

sqrt(c)/d^2 = (3^1/2m)/(3^6n)
= 3^1/2m-6n

...right? I've already lost enough marks on this paper

Better than -1648x^10 making you doubt yourself for the remainder of the paper :P

6c) Is that not a stretch along the y-axis SF 3?

Yes this is correct

I got the coefficient for the power of ten wrong; just because I messed up the addition of the coefficients at the end; even though I expanded both of them correctly. :C

Could you have done sum of 3 terms?

+1 OP pls fix

Another thing - 6c is confusing the hell out of me

y=\sqrt{x^2+9}
onto
y=3\sqrt{x^2+1}

Let f(x) = \sqrt{x^2+9}

f(x) --> 3f(x) = Stretch in y direction SF 3
However, your mark scheme says "Stretch in x direction SF 1/3"
For that to be the case, wouldn't the equation have to be the following:
f(x) --> f(3x) = Your answer
Which would lead to the "original equation" having to be:
y=\sqrt{3x^2+1}

My logic was that the 3 is multiplying the entirety of the sqrt function.
For example:
5^x --> 3 * 5^x = Stretch in y direction SF 3
5^x --> 5^3x = Stretch in x direction SF 1/3
This would be the case because the number 3 is only multiplying the x by 3, not the entire function (which in this case is 5^x)

You said you proved it was x direction SF 1/3 using differentiation, could you show this please? Using methods and formulae that I'd been taught, I got to a y stretch SF 3.

Forgive me if I'm talking out my ass too

Like using a sledgehammer to crack a nut :P

I don't think the test was that bad, pretty decent; but it was very hard, I know I lost a few marks. For the trapezium rule question I even checked it with my calculator and it said 65.3 or something so I was like phew I got the answer correct. (Answer was 65.6 but calculator can do integration to more precision).

Ummmm... Do you know what question I'm talking about?