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STEP Prep Thread 2017

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Original post by Zacken
Cool, cool. That's all sorted; now back to maths and banter. :wink:

since when did you have banter
Original post by Zacken
Excuse me? You should probably stop with your petty childish crap before you ruin the thread anymore.

I can't reply to every single post on here, because (as I have pointed out to you before) Cambridge maths is (surprise!) intensive and eats up my time, I've got 18,000+ posts on here helping people out with maths, I'd rather you didn't tell people that I 'don't give a ****' beause really, you've been far far far far less contructive than anybody else on this thread.

\rant. Sorry for this, but you're really overdoing it now.



I beg you pardon!!
At no stage I expected you to reply to every question on this thread!!!
I am mentioning your name because of your answers to me on the other thread which started with this one:
''

1.

(Original post by Melanie Leconte)
There is one but busy with chatter unrelated to STEP Prep. It is understandable because they have done it, been there so don't care..

2.

Zacken. It's not busy with chatter, it's seriously inactive. We do care, even if we've done STEP. It's just that it's way too early to be starting any serious prep.

3.

M.L. It would be nice to have a serious helpful one.

4.

Zacken. The STEP Prep 2017 is a serious helpful thread.''

and you carried on insisting that no one was ignored.
I understand that you have started this thread but at no stage I took it as you will be the sole provider of wisdom and certainly not jumping at me because I was stating my opinion on another thread.
(edited 7 years ago)
[QUOTE="physicsmaths;68167982"]
Original post by Melanie Leconte

People actually have work to do and not replying to something which had already been answered
Irrationalroot answered that straight away and he is great at step. A great response aswell which i just read. Jst read everything now since i only come on here once or twice every day or 2 days.



@physicsmaths I understand and I was initially just agreeing that we should start a group for a proper revision as it was suggested on the other thread only to be told that it was too early......

Actually one was answered by Irrational but the other one was not until lately by Gregorius.

I hope all is going well for you and as you have hoped for :smile:
(edited 7 years ago)
Original post by Gregorius
@Melanie Leconte - Do keep posting here. The new cohort of steppers hasn't really yet gelled, and last year's cohort are busy beginning the stressful ascent of Mount RealMaths, so you may have to be patient. Us oldies will try to pick things up the loose scraps in the meantime.



@Gregorius Thank you very much for your reassurance, your patience and willingness to go through hand written work :smile: I was encouraged to learn LaTex ''if I wanted to get an answer'' that's why the whole storm.
Reply 344
Avatar for Zacken
Zacken
OP
22
we have a new dalek
Original post by Zacken
we have a new dalek


You might think so and some might follow your lead in this ''banter'' but the only one who has understood the concern is Gregorius so far and has dealt with it and I thanked him for his reassurance.

If you want to tackle the Maths, I am more than happy to carry on posting on this thread but if you want someone to gang on, that won't be me.

I did joke with you before by using :tongue: and talked by PM but I would prefer you stick to the Maths or even ignore my posts.
Original post by Zacken
You should look at the STEP specification (a quick google should turn it up, or I can link it when I get to my room and get on my laptop) and then learn the relevant pure bits from there that are in FP3 using either a textbook or examsolutions. It's all very straightforward! :smile:


I had a quick look through it last night...I don't really know what most of the words mean yet haha, but I'll cross refer with my textbooks and see what's missed out :biggrin: Thank you!
@Lauren-x- Try this link and I hope you find it helpful :smile:

http://drfrostmaths.com/resources/sow.php?year=A%20Level&term=FP3
(edited 7 years ago)
I wonder if we might just try to be a bit more friendly to each other on this thread? It's very easy to get the wrong end of the stick in a written forum like this - and too easy to get worked up about what may be misunderstandings.

So, STEP is hard, let's not make it harder for the youngsters coming up to try it.
Original post by Melanie Leconte
@Lauren-x- Try this link and I hope you find it helpful :smile:

http://drfrostmaths.com/resources/sow.php?year=A%20Level&term=FP3


Thank you!
Reply 350
Avatar for obich
obich
3
Hi, i was trying this question and want to verify my solution, thanks in advance !
Q: If n is a perfect square and its second last digit is 7, what are the possibilities for the last digit of n and can you show this will always be the case?

My solution:
Let n be a perfect square. Perfect squares: 1, 4, 9, 16, 25, 36, 49, ....
Expressing as mod 4 produces a pattern: 1, 0, 1, 0, 1, 0, 1, ....
So if n is a perfect square, n must equal 0 or 1 (mod 4).

Also if n is a number abcde7x, it can expressed as abdce00 + 7x. But we know abcde00 is a multiple of 100 thus a multiple of 4 so it would equal 0 (mod4). This means 7x must be 0 or 1 (mod 4) as well. [a, b, c etc represent digits here]

Numbers between 70 and 79: 70, 71, 72, 73, 74, 75, 76, 77, 78, 79
When expressed as mod 4: 2, 3, 0, 1, 2, 3, 0, 1, 2, 3

The only numbers in the form 7x that are 0 or 1 (mod 4) are 72, 73, 76, 77
So the last digit can be 2, 3, 6 or 7.
Original post by obich
..Inline comments in red...

Q: If n is a perfect square and its second last digit is 7, what are the possibilities for the last digit of n and can you show this will always be the case?

My solution:
Let n be a perfect square. Perfect squares: 1, 4, 9, 16, 25, 36, 49, ....
Expressing as mod 4 produces a pattern: 1, 0, 1, 0, 1, 0, 1, ....
So if n is a perfect square, n must equal 0 or 1 (mod 4). This is not *proof*, it is simply an observation.

Also if n is a number abcde7x, it can expressed as abdce00 + 7x. But we know abcde00 is a multiple of 100 thus a multiple of 4 so it would equal 0 (mod4). This means 7x must be 0 or 1 (mod 4) as well. [a, b, c etc represent digits here]

Numbers between 70 and 79: 70, 71, 72, 73, 74, 75, 76, 77, 78, 79
When expressed as mod 4: 2, 3, 0, 1, 2, 3, 0, 1, 2, 3

The only numbers in the form 7x that are 0 or 1 (mod 4) are 72, 73, 76, 77
So the last digit can be 2, 3, 6 or 7. You have (correctly) observed that a square must = 0 or 1 modulo 4. But this does *not* mean that because you have a number = 0 or 1 modulo 4 that it *must* be a square,

That is, it's fair to say that it's impossible for the last 2 digits to be 71, 74, 75, 78 or 79, but that doesn't mean the other options are actually attainable (and in fact, they are not).


To move this forwards, you need to consider other things than reduction modulo 4.

Spoiler

Once you think you've reduced the options as much as you can, you still need to show that the options you have left *are* attainable.

For example, suppose we had ...3x instead of ...7x; at some point I'll have shown that ..36 is a possibility, but I still need to exhibit a number N s.t. N^2 ends ....36.
Reply 352
Avatar for obich
obich
3
Original post by DFranklin
Inline comments in red...



To move this forwards, you need to consider other things than reduction modulo 4.

Spoiler

Once you think you've reduced the options as much as you can, you still need to show that the options you have left *are* attainable.

For example, suppose we had ...3x instead of ...7x; at some point I'll have shown that ..36 is a possibility, but I still need to exhibit a number N s.t. N^2 ends ....36.

Ah yes of course I haven't proved all squares are 0 or 1 (mod 4). If necessary I should be able to however.
Using mod 5 as recommended, I observed the perfect squares are either 0 or 1 (mod 5).

Applying this to numbers 70 to 79, only 71, 75 and 79 satisfy this.
We can see only 76 satisfies both conditions, thus the square must end in 76 if its penultimate digit is 7.

Now to find such a square. Trying the obvious choice, (76)^2 which equals 5776. Thus we have found a square ending in 76 and hopefully proven the solution. Thank you very much for you help!!
Just being anxious, which is harder?

a) Average MAT vs Average STEP I
b)Most difficult MAT vs Average STEP I
c)Most difficult MAT vs Easiest STEP I
Original post by LaserRanger
Just being anxious, which is harder?

a) Average MAT vs Average STEP I
b)Most difficult MAT vs Average STEP I
c)Most difficult MAT vs Easiest STEP I


Imho, the easiest STEP I is more difficult than the most difficult MAT (excluding the old style MAT which was similar to STEP).

But you have more chance of an offer, more time to prepare, and everyone else also finds it a lot harder.
Original post by Mathemagicien
Imho, the easiest STEP I is more difficult than the most difficult MAT (excluding the old style MAT which was similar to STEP).

But you have more chance of an offer, more time to prepare, and everyone else also finds it a lot harder.


I have only just begun preparing for STEP, with the remaining time I have left, do you think it's still possible to achieve a 1,1 in STEP 2 and 3?
Original post by LaserRanger
Just being anxious, which is harder?

a) Average MAT vs Average STEP I
b)Most difficult MAT vs Average STEP I
c)Most difficult MAT vs Easiest STEP I


STEP is much better preparation for a rigorous degree than MAT for sure.
Reply 357
Avatar for Zacken
Zacken
OP
22
Original post by PumpkinPatrick
I have only just begun preparing for STEP, with the remaining time I have left, do you think it's still possible to achieve a 1,1 in STEP 2 and 3?


Most people start preparing for STEP in late January when they get news about their Cambridge decision; starting from late Jan is more than enough time to prepare to get whatever grade you want. Starting now is a lot earlier than usual and is of course, way more that enough time to prepare.
(edited 7 years ago)
Original post by Zacken
Most people start preparing for STEP in late January when they get news about their Cambridge decision; starting from late Jan is more than enough time to prepare to get whatever grade you want. Starting now is a lot earlier than usual and is of course, way more that enough time to prepare.


Alright cool!

I have a few more questions, if you don't mind.

How many past papers did you do for STEP?

What do you think the key for success in STEP is?
Reply 359
Avatar for Zacken
Zacken
OP
22
Original post by PumpkinPatrick
How many past papers did you do for STEP?


Probably did a bit more than you strictly need to, because I enjoyed the questions, but I probably did about 23 years of past papers and doing ~12 questions on each paper for all three papers. So that's 23 * 3 = 69 past papers? (recall that that's a fair bit more than anybody needs to do)

A normal amount would be doing past papers for STEP II and III from 2000, so 15 * 2 = 30.

What do you think the key for success in STEP is?


Hard work, but not overly hard. At this stage, a question or two a week is a good pace.

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