# STEP 2017 Solutions

Watch
Announcements
#1
4
#2
STEP I, Question 1:

Let so that . Hence the integral is

Let so that . Hence the integral is

Let so that . Hence the integral is

Let so that . Hence the integral is

This was embarrassingly easy for a STEP question, so it's hard to predict the spread of marks but something like: 3/4/5/8 or 3/4/6/7 is what I'd guess.
0
3 years ago
#3
1. STEP IV (paper here):
1:
2:
3:
4:
5:
6:
7:
8:
9:
10:
11:
12:
13:
10
3 years ago
#4
(Original post by Zacken)
Question 1:

Let so that . Hence the integral is

Let so that . Hence the integral is

Let so that . Hence the integral is

Let so that . Hence the integral is

This was embarrassingly easy for a STEP question, so it's hard to predict the spread of marks but something like: 3/4/5/8 or 3/4/6/7 is what I'd guess.
zain set me link for good copy for the paper
0
3 years ago
#5
Question 3
0
3 years ago
#6
Do you have the paper?
0
3 years ago
#7
(Original post by A Slice of Pi)
Do you have the paper?
No but i remember this question, it was pretty standard. If you happened to study parabola then its a piece of cake else I would rate it moderate.
0
#8
Question 2:

Note that, since integration preserves rank, we have for all . This gives

for all . If then replace the above with to get

by multiplying both sides by . This completes (i) and (ii). Again. Integration preserves rank so for all we have

Hence

so that from above and from below by some trivial rearranging. Hence we get

for all . For simply invert and you get the same thing after some trivial rearranging, completing (iii).

I'd predict a split of about 5/7/8.
0
#9
(Original post by solC)
Question 11: (Credit to JohnCraig)
The attachment doesn't seem to be working for me - could you try uploading it so something like imgur and then inject the image here using the "insert image via URL"?

(Original post by A Slice of Pi)
Do you have the paper?
Yep, but just a bunch of badly taken pictures - I'll rotate/crop and pdf them at some point today.

(Original post by Rishabh_01)
...
If anybody is willing to LaTeX this up, please do!
0
3 years ago
#10
(Original post by Zacken)
The attachment doesn't seem to be working for me - could you try uploading it so something like imgur and then inject the image here using the "insert image via URL"?

Yep, but just a bunch of badly taken pictures - I'll rotate/crop and pdf them at some point today.

If anybody is willing to LaTeX this up, please do!
dished why u blanking me
0
3 years ago
#11
(Original post by Zacken)
The attachment doesn't seem to be working for me - could you try uploading it so something like imgur and then inject the image here using the "insert image via URL"?
Oh right, sorry. I'll try to fix it now.

What are your opinions on the paper thus far, from the questions you've seen?
0
3 years ago
#12
Question 5
0
3 years ago
#13
What do you thing you be the marks boundries for grade 1 and grade S
0
3 years ago
#14
Question 11: (credit to JohnCraig)

If this doesn't work I give up
0
#15
STEP I, Question 8:

Base case is trivial. Assume then

(i) Assume that and . Then and

Now let so that , so that as we have unbounded above so and assuming that gives , i.e since .

(ii) Assume that , then since we have so .

Hence since we have giving as required.

Now note that from the recurrence for we can compute so .
1
3 years ago
#16
If anyone has a copy of the paper can you send it to me? I could write up a few solutions.
0
#17
0
#18
STEP I, Question 6:

(i) Assume that takes only (wlog) non-negative values in the interval . Let be such that . Then by continuity we have an interval where . But then . Contradiction. (really contraposition)

(ii) We have . Hence must take both positive and negative values on (or identically and we are done anyway). But since squares are non-negative this means that must take positive and negative values on hence must hit at some point.

We get and so two possible solutions are . Both of which hit 0 at some point in (0,1) which you can check using obvious inequalities. e.g .

(iii) Set then . Also . And finally .

So apply (ii) with and get somewhere in .
2
3 years ago
#19
0
#20
(Original post by Rishabh_01)
0
X

new posts
Back
to top
Latest
My Feed

### Oops, nobody has postedin the last few hours.

Why not re-start the conversation?

see more

### See more of what you like onThe Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

### Poll

Join the discussion

#### Current uni students - are you thinking of dropping out of university?

Yes, I'm seriously considering dropping out (181)
14.31%
I'm not sure (59)
4.66%
No, I'm going to stick it out for now (371)
29.33%
I have already dropped out (37)
2.92%
I'm not a current university student (617)
48.77%