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# STEP Maths I,II,III 1987 Solutions

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1. Just started looking at some of these and not really up to standard. Can anyone just explain on STEP I question 2 the first part, why the angle is pi/n ?
2. (Original post by thestudent)
Just started looking at some of these and not really up to standard. Can anyone just explain on STEP I question 2 the first part, why the angle is pi/n ?
As DFranklin said, you take a right angled triangle, hypotenuse R, small side r consider the angle of this triangle theta such that sin(theta)=r/R.

Now if you think of it like this, there are 2 'thetas' for every smaller circle and there are n smaller circles, so n=2pi/2theta so theta=pi/n.

It's kinda hard to explain without a diagram.
3. thanks for the help and thanks for the thread, a great help
4. Here is my attempt at Paper 1 number 6. Does anyone agree with it?
Attached Images
5. 1987PAPER1.6pdf.pdf (28.5 KB, 353 views)
6. (Original post by Dystopia)
STEP II, Q5.

i)

This is an infinite geometric series with . Since , it converges to .

As expected.

ii) Let

But , so

Note that when n=0.

iii) Let

But y = 0, so

Edit: Fixed. Didn't realise it was actually posting last night...
Been wondering what was wrong with this. Finally realised that in first part you have lower limit of sum as n=0 when it should be n=1
7. Here are my attempts at numbers 9-12 on 1987 STEP Paper I
I would be grateful for any confirmation or reports of errors.

Some errors have been discopvered. For revised solutions
see post no.237 for question 10
Post 238 for question 11 and post 239 for question 13
Attached Images
8. 1987PAPER1.9.pdf (32.2 KB, 318 views)
9. 1987PAPER1.10.pdf (40.6 KB, 247 views)
10. 1987PAPER1.11.pdf (41.1 KB, 270 views)
11. 1987PAPER1.12.pdf (26.2 KB, 288 views)
12. STEP I numbers 13-16
Again if anyone could check them I would be most grateful.
Attached Images
13. 1987PAPER1.13.pdf (43.1 KB, 254 views)
14. 1987PAPER1.14.pdf (25.2 KB, 185 views)
15. 1987PAPER1.15.pdf (45.6 KB, 244 views)
16. 1987PAPER1.16.pdf (35.5 KB, 237 views)
17. I think you need to update the links to the papers on the front page, as when I click on them I get sent to some random advertising webiste and am bombarded by pop-ups for 5 minutes.
18. (Original post by brianeverit)
Been wondering what was wrong with this. Finally realised that in first part you have lower limit of sum as n=0 when it should be n=1
Thank you for pointing that out; is it correct now?

Are you also in Y13 btw?
19. The links for the papers don't work.
20. Still not working...
21. (Original post by DaveSimpson)
Still not working...
That site no longer "works", it hasn't for several months. Shame, it was really good.

That should work.
23. lol it's no good, just gives me Page cannot be displayed
24. STYEP 1987 Fma
Questions 2,3 and 4
Attached Images
25. 1987PAPER fma.2.pdf (35.1 KB, 475 views)
26. 1987PAPER fma.3.pdf (28.9 KB, 380 views)
27. 1987PAPER fma.4.pdf (30.7 KB, 287 views)
28. 198987 STEP Fma numbers 8,9 and 10
Attached Images
29. 1987PAPER fma.8.pdf (43.7 KB, 258 views)
30. 1987PAPER fma.9.pdf (21.9 KB, 181 views)
31. 1987PAPER fma.10.pdf (35.5 KB, 183 views)
32. 1987 STEP Fma numbers 12 -16
Attached Images
33. 1987PAPER fma.12.pdf (51.6 KB, 218 views)
34. 1987PAPER fma.13.pdf (29.0 KB, 178 views)
35. 1987PAPER fma.14.pdf (41.1 KB, 177 views)
36. 1987PAPER fma.15.pdf (22.9 KB, 168 views)
37. 1987PAPER fma.16.pdf (15.4 KB, 224 views)
38. Those are the answers not the questions.
39. (Original post by DaveSimpson)
Those are the answers not the questions.
The purpose of this thead is to provide answers to the 1987 paper questions .
40. Yeah but what's the point of answers if no one has the questions?

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