The Student Room Group
Uni students - Complete our survey >>
Uni students - Complete our survey >>
Uni students - Complete our survey >>

STEP 2005 Solutions Thread

You can let someone else take control of the OP whenever.

STEP I:
1: Solution by nuodai
2: Solution by Unbounded
3: Solution by Unbounded
4: Solution by Unbounded
5: Solution by Unbounded
6: Solution by Unbounded
7: Solution by Unbounded
8: Solution by Unbounded
9: Solution by nuodai
10: Solution by Sk1lz
11: Solution by nuodai
12: Solution by darkness9999
13: Solution by brianeverit
14: Solution Farhan.Hanif93

STEP II:
1: Solution by SimonM
2: Solution by Daniel Freedman
3: Solution by SimonM
4: Solution by Glutamic Acid
5: Solution by SimonM
6: Solution by Daniel Freedman
7: Solution by SimonM
8: Solution by sonofdot
9: Solution by Farhan.Hanif93
10: Solution by Glutamic Acid
11: Solution by Farhan.Hanif93
12: Solution by nuodai
13: Solution by brianeverit
14: Solution by brianeverit

STEP III:
1: Solution by DeanK22
2: Solution by Adje
3: Solution by SimonM
4: Solution by SimonM
5: Solution by Daniel Freedman
6: Solution by sonofdot
7: Solution by sonofdot
8: Solution by SimonM
9: Solution by sonofdot
10: Solution by brianeverit
11: Solution by brianeverit
12: Solution by sweeneyrod
13: Solution by brianeverit
14: Solution by sonofdot

Solutions written by TSR members:
1987 - 1988 - 1989 - 1990 - 1991 - 1992 - 1993 - 1994 - 1995 - 1996 - 1997 - 1998 - 1999 - 2000 - 2001 - 2002 - 2003 - 2004 - 2005 - 2006 - 2007
(edited 7 years ago)

Scroll to see replies

Reply 1
Avatar for SimonM
SimonM
18
I'm not going to type it up, but STEP III Question 7 is one of my favourite STEP questions
Reply 2
Avatar for sonofdot
sonofdot
8
STEP III 2005 Question 7

This is one of my favourites too

We have ∫1uf(u) du=F(u)+c\displaystyle\int \frac{1}{u f(u)} \, du = F(u) +c

Making a substitution u=xm⇒du=mxm−1dxu=x^m \Rightarrow du = mx^{m-1} dx

∴∫mxm−1xmf(xm) dx=F(xm)+c  ⟺  ∫mxf(xm) dx=F(xm)+c\displaystyle\therefore \int \frac{mx^{m-1}}{x^m f(x^m)} \, dx = F(x^m) + c \iff \int \frac{m}{x f(x^m)} \, dx = F(x^m) + c

(i)

(ii)

STEP II 2005, Question 6

Spoiler

sonofdot
.

What happens when n = 2 in part ii)?
STEP II 2005, Question 2

Spoiler

Reply 6
Avatar for sonofdot
sonofdot
8
Daniel Freedman
What happens when n = 2 in part ii)?

Good point, edited
STEP I: Question 12
Part 1

Spoiler


Part 2

Spoiler

Reply 8
Avatar for sonofdot
sonofdot
8
STEP III 2005 Question 14

:eek: that was a long one...

Spoiler

Spoiler

Spoiler

Spoiler

Spoiler

II/4:

1st part



2nd part



3rd part

STEP III

Question 1

1st part



2nd part



Cheating with the graphs.
stthrthsrtrhrsth.jpg28.6KB
Reply 11
Avatar for sonofdot
sonofdot
8
STEP III 2005 Question 6

Spoiler

Spoiler

Spoiler

Spoiler

III/2 - with the proviso that I think I may have missed something somewhere.

Solution of Differential Equation



d/dx and d²/dx² of (x² + y²)



Graph


0 Point of minimum distance to origin with < c a^2



If c > a²

step052.jpg10.8KB
For this part, is it not far simpler to note that as the gradient of PR is 1p\frac{1}{p} and the gradient of SQ is −q-q, and as pq=−1pq = -1 it's clear that p=−1qp = -\frac{1}{q} and therefore PR and SQ are parallel?

The same method works to show QR and PS are parallel, and as PR and PS are definition perpendicular, as are QR and QS, therefore PSQR is a rectangle.

The saves a fair bit of algebra, and as far as I can see there's no flawed reasoning.
Reply 14
Avatar for SimonM
SimonM
18
STEP III, Question 3

Spoiler

Reply 15
Avatar for SimonM
SimonM
18
STEP III, Question 4

Spoiler

Reply 16
Avatar for SimonM
SimonM
18
STEP II, Question 1

Spoiler

Reply 17
Avatar for SimonM
SimonM
18
STEP II, Question 3

Spoiler

GHOSH gave all the solutions I have for 1 2005:Q2,3,4,7
I'll try another one
Reply 19
Avatar for sonofdot
sonofdot
8
STEP III 2005 Question 9

Hopefully my diagram makes it clear what all the symbols I use mean

Diagram

First Part

Second Part

Third Part

Quick Reply

Related discussions

Latest

Trending

Trending

Articles for you