STEP Prep Thread 2015

Original post by DomStaff

That is Q1 2001, right? Already done it, I'm afraid. Any others?!

This exact same question has come up twice in STEP I

Reply 382

Original post by newblood

This exact same question has come up twice in STEP I

What was the other year?

Reply 383

Original post by DomStaff

What was the other year?

I think it was actually the year after it was first written. Let me have a look

EDIT: It was 1988 and 2001. Exact same question (wording and all)

(edited 9 years ago)

Reply 384

Original post by newblood

I think it was actually the year after it was first written. Let me have a look

EDIT: It was 1988 and 2001. Exact same question (wording and all)

No way! Does this happen often?

Reply 385

Original post by DomStaff

No way! Does this happen often?

not often, but it has happened occasionally. i think thats the only step i question its happened in though. 2006 STEP III for example had about 3 questions from the older STEP II/III papers

Reply 386

Original post by newblood

not often, but it has happened occasionally. i think thats the only step i question its happened in though. 2006 STEP III for example had about 3 questions from the older STEP II/III papers

Oh, I see. That provides motivation to do as many papers as possible.

Reply 387

Original post by DomStaff

Oh, I see. That provides motivation to do as many papers as possible.

Certainly do lots of papers: but i wouldnt do it in hope of remembering certain solutions as the chances of a repeated question coming up are still very small...i doubt its happened in any paper in the last 5 years or so at least.

Reply 388

Original post by newblood

Certainly do lots of papers: but i wouldnt do it in hope of remembering certain solutions as the chances of a repeated question coming up are still very small...i doubt its happened in any paper in the last 5 years or so at least.

Good point. Although, you'd kick yourself if a question had came up and that happened to be from the paper you hadn't done!

Reply 389

ThatPerson

18

Original post by shamika

It's a point of principle (and law) - he wrote the book, he's the only one who should be able to publish it and make money from it.

You were right; it's someone else who is selling Siklos' book. He wrote a review.

Reply 390

brianeverit

9

Original post by DomStaff

What was the other year?

This question was quite tricky

Arthur and Bertha stand at a point O on an inclined plane. The steepest line in the plane through O makes an angle

\theta

with the horizpontal. Arthur walks uphill at a steady pace in a straight line which makes an angle

\alpha

with the steepest line. Bertha walks uphill at the same speed in a straight line which makes an angle

\beta

with the steepest line (and is on the same side of the steepest line as Arthur) Show that, when Arthur has walked a distancde

d

, the distance between Arthur and Bertha is

2d|\sin\frac{1}{2}(\alpha-\beta)|

. Show also that, if

\alpha\not=\beta

, the line joining arthur and Bertha makes an angle

\phi\text{ with the vertical, where }\cos\phi=\sin\theta\sin\frac{1}{2}(\alpha+\beta)

Reply 391

Godel_Mark

Can someone explain to me the last part of Question 12, Advanced Problems in Mathematics Siklos Booklet. It's the questions that asks:

Show by means of counterexample or otherwise, that not all cubic equations of the form

x^{3} + \alpha x^{2} + \beta x^{} + \gamma = 0

can be solved by this method

Reply 392

ctrls

9

Original post by Godel_Mark

Can someone explain to me the last part of Question 12, Advanced Problems in Mathematics Siklos Booklet. It's the questions that asks:

Show by means of counterexample or otherwise, that not all cubic equations of the form

x^{3} + \alpha x^{2} + \beta x^{} + \gamma = 0

can be solved by this method

The question is a bit weird, the discussion below does give an example but I'm not how you are expected think of it on your own. Granted the question itself is pretty old (II 1989), so the style is a bit different from the more recent questions - I don't think you'll be asked something like this anymore.

Although it's a lot of work and it's probably not ideal if this question comes up in the actual exam, you can try the method on an arbitrary cubic and see what the requirements are to get it in that form. It's actually pretty interesting, you can express the valid coefficients in the form of an inequality.

Another possibility that just occurred to me is to consider what happens if there are complex roots, looking back at the example cubic you just solved. Still not exactly easy to come up with, but hopefully that also gives you an idea of why the example they listed doesn't work.

Reply 393

username1162972

18

Original post by ThatPerson

You were right; it's someone else who is selling Siklos' book. He wrote a review.

Yes i sent him an e mail alerting him about this earlier on today.

Posted from TSR Mobile

Reply 394

jjpneed1