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STEP 2013 Solutions

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How do you figure out the direction for friction? Sorry if you explained it already, but it is hard to read your attachments.

Sorry about the poor quality. The direction of the friction is always in the opposite direction to where the object would move if there were none. So as the system would just fall down without the friction, friction acts upwards on the top ball and downward (and to the right/left for the left/right ball respectively) for the bottom ones. Always perpendicular to the normal reaction, of course.

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Reply 21

mikelbird

Original post by jack.hadamard

I had to practice some drawing on a software, so enjoy.

Question 4

Preliminary stuff

Spoiler

First part

Spoiler

Second part (a)

Spoiler

Second part (b)

Spoiler

for the prelim stuff why not simply use the sum of the roots and then half it for the x coordinate of M?

In part (ii)(a) the point (a,0) in NOT included!!

In part (ii) (b) the point (0,-1) is not included

(edited 10 years ago)

Reply 22

jack.hadamard

Original post by mikelbird

for the prelim stuff why not simply use the sum of the roots and then half it for the x coordinate of M?

Because STEP II is based on A-level Maths content.

In part (ii)(a) the point (a,0) in NOT included!!

You are right. I forgot to mention it.

In part (ii) (b) the point (0,-1) is not included

I didn't claim it was included.

Reply 23

mikelbird

Because STEP II is based on A-level Maths content.

Playing around with the roots of quadratic equations IS part of A level!

Reply 24

mathsymathsy

Original post by DJMayes

Q7 – STEP II

Part i):

Spoiler

Part ii):

Spoiler

Part iii):

Spoiler

I think part I is incomplete and the solution could be used in part III :tongue:

Reply 25

mathsymathsy

Nobody is writing up a solution for step II Q1?

Reply 26

mikelbird

Original post by mathsymathsy

Nobody is writing up a solution for step II Q1?

OK...If you want one....

Step2013Paper2Question1.pdf140.3KB

Reply 27

mikelbird

Original post by mikelbird

Because STEP II is based on A-level Maths content.

Playing around with the roots of quadratic equations IS part of A level!

And it is in the Step specification!!

Reply 28

metaltron

Original post by mikelbird

And it is in the Step specification!!

For STEP III I would imagine, it is in FP1 on OCR.

Reply 29

mathsymathsy

Original post by mikelbird

OK...If you want one....

Step II is complete now :biggrin:

Reply 30

mikelbird

Original post by metaltron

For STEP III I would imagine, it is in FP1 on OCR.

no..for Step 2...it talks about a cubic and knowing that the constant is the product of the roots....but yes you are right about OCR!

Reply 31

jack.hadamard

Original post by mikelbird

no..for Step 2...it talks about a cubic and knowing that the constant is the product of the roots....but yes you are right about OCR!

What's this rant about? If you don't like the quadratic formula, then don't use it. The specification of STEP I and II is the same and, in particular, you are not required to know the Viète formulae. The example you gave is likely to instead emphasise identities and comparing coefficients. I tried to produce a solution that resembles official solutions, which I recall use the formula.

Reply 32

mikelbird

Oh dear...this was never meaning to be a rant. All I wanted to point out is a quick and easy ( and something well within the capabilities of a good A level student) method of getting a result. The fact that I pointed out the fact seems to have enraged you.. I apologise profusely but still believe that it was a better method... You don't have to. Let's leave it there.

Reply 33

jack.hadamard

Original post by mikelbird

The fact that I pointed out the fact seems to have enraged you.. I apologise profusely but still believe that it was a better method...

I apologise then. :smile:

It is a better method -- there is no question about that. It didn't 'enrage' me, I just didn't see a reason why you would ask.

Reply 34

username937760

Original post by mathsymathsy

I think part I is incomplete and the solution could be used in part III :tongue:

Damn. When I did the question I missed the "hence find". However, I had x as 3 and y=2 as my first solution, so would this likely lose marks?

Reply 35

GG.TintiN

Original post by mathsymathsy

I think part I is incomplete and the solution could be used in part III :tongue:

Although it is incomplete, I think they won't give u the credit for writing down the solution for x^2-2y^2=1...in the previous year there was one question asking you to write down the cube from 1 to 10...the report said no mark is given.

Reply 36

GG.TintiN

Original post by DJMayes

Damn. When I did the question I missed the "hence find". However, I had x as 3 and y=2 as my first solution, so would this likely lose marks?

I missed the writing down part...and used nonsense logic to argue ii)...throw away easy marks sigh...

Reply 37

Jkn

Original post by cpdavis

Question 5:
To see when

f(x)>\frac{343}{36}

, we use our diagram as an aid and you see that

x<-2, -\frac{1}{2}<x<\frac{1}{3}, \frac{2}{3}<x<\frac{3}{2}, x>3

You are forgetting to adjust your ranges such that they do not include the values for which

f(x)

is undefined :tongue:

Reply 38

MW24595

Original post by DJMayes

Damn. When I did the question I missed the "hence find". However, I had x as 3 and y=2 as my first solution, so would this likely lose marks?

Ouch. Perhaps. No more than 1 or 2, though, provided the rest of the question is good. Because, if that's all good, then the last part is just trivial experimentation.
Meh, no issues. From what I see, I reckon you can still gun for a near-perfect score.