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# STEP 2016 Solutions

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1. Also, for STEP1 question 10, upon successfully reaching lambda * e = 1 (I think it's towards the end) then going wrong after that, how many marks should I approximately get? I continued with the wrong answers after that for part (ii) in an attempt to scrape some method marks and I ended up with a value of lambda and e but it's wrong.

15-16/20? or less
2. (Original post by kelvin1338)
A bit late for this post,

But for STEP 1's question 2, if I differentiate the given giant equation correctly, and manage to solve part (ii) correctly using an FP3 substitution (let x=sinhu) is that acceptable?

I failed to solve part (i) and part (iii) completely. How many marks should I get out of 20 for that, you guys think, approximately?
The question specifically says "hence" which means you must use the previous result so I'm not sure if they'd give you any marks. You definitely wouldn't get full marks for that part since it doesn't state "hence, or otherwise"

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3. (Original post by kelvin1338)
A bit late for this post,

But for STEP 1's question 2, if I differentiate the given giant equation correctly, and manage to solve part (ii) correctly using an FP3 substitution (let x=sinhu) is that acceptable?

I failed to solve part (i) and part (iii) completely. How many marks should I get out of 20 for that, you guys think, approximately?
Sorry mate, about 4-5/20 just for the differentiation.

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4. (Original post by IrrationalRoot)
Alternate one which I'm surprised no one else did:
IBP with x and 1/cosx(cosx+sinx), antiderivative of 1/cosx(cosx+sinx) is ln(1+tanx), result follows.
Alternately divide both sides with cos^2 x gives sec^2 x / (1 + tan x).
This is in the form of f'(x) / f(x) so integration is ln (1+ tan x).

Edit: I just realised that I got the sketch of the curve in Q1 incorrect for t < 0, reflecting the curve into the y-axis instead of the x-axis. This caused me to miss the 2nd intersection point too. How many marks will be gone? I got everything else in that question correct by the way.
5. (Original post by physicsmaths)
sorry i had not asked, how did the exam go for you? hope it went well.
Oh thanks, it went ok. Zacken said my scores added up to about 90, which is good (but not an S I don't think). I only got one full though, but hopefully I've scraped as many marks as possible in my partials.

6. (Original post by IrrationalRoot)
Oh thanks, it went ok. Zacken said my scores added up to about 90, which is good (but not an S I don't think). I only got one full though, but hopefully I've scraped as many marks as possible in my partials.

Yeh S perhaps. Got 4 fulls and a few partials hoping it adds to 95 but most likely on the lower side of 90 which probably won't be an S.

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7. (Original post by physicsmaths)
Yeh S perhaps. Got 4 fulls and a few partials hoping it adds to 95 but most likely on the lower side of 90 which probably won't be an S.

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Was the offer S,1? Either way I think if you get a 1 in III they'd probably accept you, I mean they're unlikely to accept a 2,1 or a 1,2 as opposed to a 1,1 from you even if your offer was S,1.
8. (Original post by IrrationalRoot)
Was the offer S,1? Either way I think if you get a 1 in III they'd probably accept you, I mean they're unlikely to accept a 2,1 or a 1,2 as opposed to a 1,1 from you even if your offer was S,1.
It is S,1 in any order. Yes, I think they will accept if I only get 1,1.

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9. (Original post by IrrationalRoot)
Oh thanks, it went ok. Zacken said my scores added up to about 90, which is good (but not an S I don't think). I only got one full though, but hopefully I've scraped as many marks as possible in my partials.

I also have the habit of not finishing last parts of questions due to timing myself to spend max 30 minutes on each question. I am thinking of changing my exam technique for STEP III though, or at least making sure I do last parts in 30-35 minutes. I feel like getting 6 solutions down is more beneficial than not finishing last parts of the questions, as long as last parts are not worth as much, so not gonna go my way to spending more than 35 minutes on each question otherwise I would risk getting only 5 solutions on my script. What do you think?

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10. (Original post by Insight314)
I also have the habit of not finishing last parts of questions due to timing myself to spend max 30 minutes on each question. I am thinking of changing my exam technique for STEP III though, or at least making sure I do last parts in 30-35 minutes. I feel like getting 6 solutions down is more beneficial than not finishing last parts of the questions, as long as last parts are not worth as much, so not gonna go my way to spending more than 35 minutes on each question otherwise I would risk getting only 5 solutions on my script. What do you think?

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I did this whole 'attempt 6 but unable to complete many questions' thing for both I and II this year, which is strange because in basically all of my (25 ish?) mocks I get mostly fulls but not 6 Qs. Not sure if this is because of my psychology for the actual exams or that these ones are just harder to complete.
So yeah basically I think my mindset changed to the one you've mentioned here just for these exams lol, I never usually attempt 6 Qs.

STEP III however the absolute priority is to get a 1, so certainly not going to 'restrict' myself to 30 mins per Q, I managed to get a very good 1 in last years paper from spending 45 mins on the first Q and 45 mins on the second, but they were 39 marks in total which was worth it.
If I for some reason could attempt 6 that would be ideal, but not aiming for it.

Honestly I don't know how hard these questions are gonna be, so I would recommend just using your own judgement in the exam and decide whether or not it's worth trying to finish a question or move on (which is where experience from mocks comes in).
11. (Original post by IrrationalRoot)
I did this whole 'attempt 6 but unable to complete many questions' thing for both I and II this year, which is strange because in basically all of my (25 ish?) mocks I get mostly fulls but not 6 Qs. Not sure if this is because of my psychology for the actual exams or that these ones are just harder to complete.
So yeah basically I think my mindset changed to the one you've mentioned here just for these exams lol, I never usually attempt 6 Qs.

STEP III however the absolute priority is to get a 1, so certainly not going to 'restrict' myself to 30 mins per Q, I managed to get a very good 1 in last years paper from spending 45 mins on the first Q and 45 mins on the second, but they were 39 marks in total which was worth it.
If I for some reason could attempt 6 that would be ideal, but not aiming for it.

Honestly I don't know how hard these questions are gonna be, so I would recommend just using your own judgement in the exam and decide whether or not it's worth trying to finish a question or move on (which is where experience from mocks comes in).
Yeah, I used my '30 minutes per question' strategy for STEP I and II as well. I have about 7 minutes of looking through the questions at the start, ranking them and finding out which ones I am gonna do, so if it happens that STEP III has more of my favourite questions then I am probably gonna continue this strategy so I can get 6 potentially good solutions on the script for a potential S grade. However, if I do not like most of the questions, I would probably try to give more fully complete solutions so I can at least get a solid/high Grade 1. I feel like my usual strategy is a bit more risky, but if last parts are worth less or I just really like the questions, then it is more beneficial.

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12. (Original post by kelvin1338)
A bit late for this post,

But for STEP 1's question 2, if I differentiate the given giant equation correctly, and manage to solve part (ii) correctly using an FP3 substitution (let x=sinhu) is that acceptable?
Unfortunately not. The question specified "hence".

I failed to solve part (i) and part (iii) completely. How many marks should I get out of 20 for that, you guys think, approximately?
Depending on what exactly you've done, you could get anywhere between 5 and 12?
13. (Original post by Insight314)
Yeah, I used my '30 minutes per question' strategy for STEP I and II as well. I have about 7 minutes of looking through the questions at the start, ranking them and finding out which ones I am gonna do, so if it happens that STEP III has more of my favourite questions then I am probably gonna continue this strategy so I can get 6 potentially good solutions on the script for a potential S grade. However, if I do not like most of the questions, I would probably try to give more fully complete solutions so I can at least get a solid/high Grade 1. I feel like my usual strategy is a bit more risky, but if last parts are worth less or I just really like the questions, then it is more beneficial.

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Yeah this seems like a logical strategy. Unfortunately in my situation it's almost guaranteed I will have very little choice so it'll probably be going for full solutions for me.
14. My strategy is to solve questions I like at the beginning (Questions involving vectors, (coordinate) geometry or number theory) and I usually do them under 20 mins, so it is a good start. After I try to solve other questions and with the time boost I try to keep the 30 min boundaries for each question. It is regular that I solve 5/6 questions.
15. https://www.desmos.com/calculator/muiga0eqk4

Slightly better framing, more zoomed in:

This relates to STEP II Q1.
Press the play button next to the t slider.
16. (Original post by EricPiphany)
https://www.desmos.com/calculator/muiga0eqk4

Slightly better framing, more zoomed in:

This relates to STEP II Q1.
Press the play button next to the t slider.
17. (Original post by Zacken)
18. In a simultaneous effort to learn a bit of LaTeX and to rub in my own face just how stupid I was to miss out some of the questions, I've typed up the questions and solutions for STEP II (credit is given, even if I've extended, abridged, corrected, or tweaked solutions).

I figured you guys may as well have it. Give me a shout if I've messed something up.
Attached Images
19. STEP II 2016.pdf (357.5 KB, 44 views)
20. (Original post by farryharnworth)
In a simultaneous effort to learn a bit of LaTeX and to rub in my own face just how stupid I was to miss out some of the questions, I've typed up the questions and solutions for STEP II (credit is given, even if I've extended, abridged, corrected, or tweaked solutions).

I figured you guys may as well have it. Give me a shout if I've messed something up.
Were you at the STEP Easter School this year?

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21. (Original post by Insight314)
Were you at the STEP Easter School this year?

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I was not. Was there another farry there?

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