STEP 2013 Solutions

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Reply 100

MathsNerd1

Original post by cpdavis

Oh, that was what a user gave. If I get a better copy I will link it (and will also link STEP II this evening).

I can take a photo of each question individually if that would help?

Reply 101

MathsNerd1

Original post by Appeal to reason

I got c=6 as well. If I can be bothered later I'll have a look at writing up a solution. Firstly though, it is time to enjoy some halo now that exams are done.

Very nice! That's the two full solutions for me in the bag, now just got to see about the integral one, the 2nd one and the last function one really :tongue:

Reply 102

Appeal to reason

Original post by Pyoro

STEP I Q4 looks like a gift so I'll type up a solution to practise my LaTeX skills. I've literally used it 3 times so far so good luck to me :rolleyes:

.

DJMayes stacked up solutions to Q9, 10, 11 in that one post. :tongue:

I loved doing 4. Didn't quite manage it as fast as you, I felt the need to repeat the first two integrals every time I needed to use their results. Still didn't really trouble me for time, I doubt 10 minutes saved on 4 would've allowed me to finish off 5.

Reply 103

Pyoro

Original post by cpdavis

I've just finished the first two integrals :ahee:

If anything, I could just put both solutions up (I've it in the past :wink:

)

If there was ever a question where one approach was more than enough... :wink:

But do post yours, else I will mourn all the labour lost over this ridiculous typesetting process...

Reply 104

Appeal to reason

I'd really love for someone to get a solution to Q8 done so I can check that - I'm worried I'll have accidentally got domains/ranges wrong. Horizontal asymptote of y=0 for the final sketch? (As

\sqrt{x^2-1}<x

, and they're going to get closer in value to each other, so as

lim_{x\to\infty}(x-\sqrt{x^2-1})=0

)? TBH, I could be talking out my arse.

(edited 10 years ago)

Reply 105

metaltron

I 8:

i)

Spoiler

ii)

Spoiler

iii)

Spoiler

(edited 10 years ago)

Reply 106

Appeal to reason

Original post by metaltron

I 8:

i)

Spoiler

ii)

Spoiler

iii)

Spoiler

Shouldn't some of those xs be |x|? Can't remember the individual functions.

Missed out on the y=2x asymptotes for h(x) and k(x), and I can't remember my domain and range for kh(x).

Reply 107

metaltron

Original post by Appeal to reason

Shouldn't some of those xs be |x|? Can't remember the individual functions.

Missed out on the y=2x asymptotes for h(x) and k(x), and I can't remember my domain and range for kh(x).

Damn, I left the mods out but covered myself with the ranges, hope I won't be penalised too heavily.

Reply 108

Slowbro93

Q4

The first integral that we get given is:

\displaystyle\int^{\frac{\pi}{4}}_0 tan^n (x) sec^2(x) dx

Note that we have the differential of

tan(x)

within our integral.

\therefore \displaystyle\int^{\frac{\pi}{4}}_0 tan^n (x) sec^2(x) dx = \left[ \dfrac{tan^{n+1}(x)}{n+1}\right]_0^{\frac{\pi}{4}}=\dfrac{1}{n+1}

2 Integral

3 Integral

4 Integral

Reply 109

msmith2512

Original post by cpdavis

Oh, that was what a user gave. If I get a better copy I will link it (and will also link STEP II this evening).

And much appreciated - its just I'm on an iPad and it is difficult to increase the resolution on images without them closing.

Reply 110

Slowbro93

Original post by DJMayes

Hey, could I suggest spoilering each separate answer to make it easier to tell what questions what? :tongue:

Reply 111

username937760

Original post by cpdavis

Hey, could I suggest spoilering each separate answer to make it easier to tell what questions what? :tongue:

Will do, sorry.

Reply 112

Appeal to reason

How many marks would you lose in I, Q1 for not ignoring the negative y values? :s-smilie:

Reply 113

Slowbro93

Original post by DJMayes

Will do, sorry.

No need to apologise, you've done a brill job :biggrin:

Reply 114

FJacob

Original post by Appeal to reason

How many marks would you lose in I, Q1 for not ignoring the negative y values? :s-smilie:

Hard to know, but that's usually the point of these square root questions right? Knowing when to square, which solutions to take, etc...
I myself messed up the ending while substituting things back and ended up with x=12 even though the methods were correct...=p

(edited 10 years ago)

Reply 115

username937760

Original post by cpdavis

No need to apologise, you've done a brill job :biggrin:

Well, I enjoyed the Mechanics on the STEP I paper and assumed other people would rather be left with the Pure so decided to write up the whole Mechanics section. :lol:

Reply 116

Math-Magician

Original post by Mastermind2

STEP I 2013 Question 7:

Spoiler

Please let me know if I've made any mistakes.

As other people have said I also used y=ux^2 for the last one but I can't remember what my final solution was.

Reply 117

atsruser

Original post by Smaug123

Question 2:

Spoiler

Unless I'm missing it somehow, you don't seem to have given working for the final part of i) i.e. showing:

I_n=\frac{n}{2(2n+1)}I_{n-1}

Spoiler

Reply 118

Pyoro

Glad to see this thread resurface.. losing all that typesetting, I don't even... :coma:

Original post by Appeal to reason

Even 20mins odd is still impressive during an actual exam; quality over speed is generally the right policy IMO. Disregard my hurried attempt that involved two massive errors and led to much more time spent in the end correcting all that code :colondollar: