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STEP Prep Thread 2016 (Mark. II)

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STEP ii 2014, Q3,

The last part, how does the sketch looks like? This is what the mark scheme says.
Part (iii) then requires combining the two possible cases from part (ii) to construct a curve whichsatisfies the conditions given. This must be an arc of a circle with no vertical tangents, with straightlines at either end of the arc in the direction of the tangents to the circle at that point.


I think that the two lines have the same gradient and different cutting points and hence they are moving to the same direction as the equation of line in part ii indicates.

I don't know why the mark scheme says that, because if it's like that, then the gradient of the lines are different and cutting points are the same which is different to what is supposed to be the lines in part ii?
(edited 7 years ago)
Good luck all for STEP I tomorrow!
Original post by shamika
Good luck all for STEP I tomorrow!


Seconded!
Original post by Zacken

...

7. After the exam

This advice will be updated if the 2016 process if different to 2015.

- Do not register for results until 5 days before the exam. This is due to a quirk in the results page, which has caused issues in the past.

- Some browsers, particularly Chrome, don't work well with the results page. The best browsers seem to be IE and Firefox.

...


I don't know if this has already been answered, but from the original post, what does the bit in Red mean, i.e. what is this about registering? What do I need to do before the exam? (My school confirmed that they've entered me for STEP 2/3)
Reply 944
Avatar for Zacken
Zacken
OP
22
Original post by Miningstew
I don't know if this has already been answered, but from the original post, what does the bit in Red mean, i.e. what is this about registering? What do I need to do before the exam? (My school confirmed that they've entered me for STEP 2/3)


Heh, that's a typo. It should say "Do not register until 5 days before results". Once the exam is over, the examiners will hand you a slip with a password and/or username that you'll use to register on ATS's website for results. There's a quirk with the website that has historically led to students being locked out if they register earlier than 5 days before the results day, so the advice is to wait till then before registering.
Reply 945
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Zacken
OP
22
Original post by shamika
Good luck all for STEP I tomorrow!


Original post by Gregorius
Seconded!


Thank you both very much!
Reply 946
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Zacken
OP
22
Original post by krishdesai7
What do A1, M1, B1 etc. mean in the marking schemes?


Accuracy mark, method mark, independent mark.
Reply 947
Avatar for Zacken
Zacken
OP
22
Original post by ox2015
Hi, I don't know if its just me or is anyone else having this problem. But for the past week or so, the equations across multiple threads are not displaying, they are instead displaying as an text such as

"displaystyle \begin{equation*} \int \frac{x + 1 - 1}{1+x} \, \mathrm{d}x = \int 1 - \frac{1}{x+1} \, \mathrm{d}x = x - \ln |x+1| + \mathcal{C}\end{equation*}"

and a symbol that represents missing image.

Thanks.


The TSR LaTeX compliler hasn't been working intermittently over the past week or so. It'll be fixed in due course, it's linked to some maintenance they're doing.
I have a few things to check if they are correct to do:
1. As in the front of page of STEP does not specify, I guess that diagrams can be drawn with pencil.
2. (sqroot(x^2))=modulus(x) unless we are sure that x>0, in that case we will write =x.
3. Always write ln(modulus(x)) instead of lnx in step?
4. Use the methods that the questions suggest you unless the word 'otherwise' appears, so we can use other methods and gain marks.
5. Shall we know the area and volumes of sphere and cones,etc?
6. And one silly question, the integral of sinx in the limits pi and -pi, without the modulus sign, is it equal to 0 or 4. In other words, shall we split the integrals into 2 halves with limits 0 and -pi, and pi and 0.
:smile:
Reply 949
Avatar for Zacken
Zacken
OP
22
Original post by IrrationalRoot
Guys for STEP III 1991 Q7 (which is an awesome Q btw) last bit of part (c), is this reasoning ok? I'm not sure it's what they wanted or even if it would get full marks.

lim⁡x→0xln⁡(sin⁡x)=lim⁡x→0xln⁡(xsin⁡xx)=lim⁡x→0xln⁡x+lim⁡x→0xln⁡(sin⁡xx)=0\displaystyle\lim_{x \to 0} x\ln(\sin x)=\displaystyle\lim_{x \to 0} x\ln\left(\dfrac{x\sin x}{x}\right)=\displaystyle\lim_{x \to 0} x\ln x +\displaystyle\lim_{x \to 0} x\ln\left(\dfrac{\sin x}{x}\right)=0 since lim⁡x→0sin⁡xx=1\displaystyle\lim_{x \to 0} \dfrac{\sin x}{x}=1


Seems fine, I did it by just saying that sin x approx x as x tends to 0, which is what I think they expected.
Reply 950
Avatar for Zacken
Zacken
OP
22
Original post by Geraer100
I have a few things to check if they are correct to do:
1. As in the front of page of STEP does not specify, I guess that diagrams can be drawn with pencil.
2. (sqroot(x^2))=modulus(x) unless we are sure that x>0, in that case we will write =x.
3. Always write ln(modulus(x)) instead of lnx in step?
4. Use the methods that the questions suggest you unless the word 'otherwise' appears, so we can use other methods and gain marks.
5. Shall we know the area and volumes of sphere and cones,etc?
6. And one silly question, the integral of sinx in the limits pi and -pi, without the modulus sign, is it equal to 0 or 4. In other words, shall we split the integrals into 2 halves with limits 0 and -pi, and pi and 0.
:smile:


1. Yes, you can use pencil to draw diagrams.
2. That's correct.
3. I think in most cases, you write ln x for whatever reason in STEP, the solutions always seem to skim over it. So I wouldn't worry about it too much unless it was obvious that the question was asking about it.
4. That's correct.
5. The basis areas/volumes like triangle/rectangles/trapezium are the only really important ones, maybe volume of a sphere, I've never seen a cone come up (or, I think it has once but they gave the formula for it...? not sure)
6. Well, sin x is an odd function and you're integrating it between an even interval, so it's 0. You should get 0 even if you split it into two integrals.
Reply 951
Avatar for rad058
rad058
STEP 1 2015 Q3

In this answer:
http://www.thestudentroom.co.uk/attachment.php?attachmentid=430125&d=1434482176

Why is tan x = (b-a)/(b+a)?
Original post by Zacken
1. Yes, you can use pencil to draw diagrams.
2. That's correct.
3. I think in most cases, you write ln x for whatever reason in STEP, the solutions always seem to skim over it. So I wouldn't worry about it too much unless it was obvious that the question was asking about it.
4. That's correct.
5. The basis areas/volumes like triangle/rectangles/trapezium are the only really important ones, maybe volume of a sphere, I've never seen a cone come up (or, I think it has once but they gave the formula for it...? not sure)
6. Well, sin x is an odd function and you're integrating it between an even interval, so it's 0. You should get 0 even if you split it into two integrals.


Thanks!
6. Yes my mistakes, one integral - the same integral=0, its because in A level, we used to make that equal to 4 as we are finding the area in C2/C3. So it's confusing. Pd: And by even integral, you mean the the values of limits are a and -a?
(edited 7 years ago)
Reply 953
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Zacken
OP
22
Original post by rad058
STEP 1 2015 Q3

In this answer:
http://www.thestudentroom.co.uk/attachment.php?attachmentid=430125&d=1434482176

Why is tan x = (b-a)/(b+a)?


Opposite/adjacent?
Reply 954
Avatar for Zacken
Zacken
OP
22
Original post by Geraer100
Thanks!
6. Yes my mistakes, one integral - the same integral=0, its because in A level, we used to make that equal to 4 as we are finding the area in C2/C3. So it's confusing.


Well yes, there's a difference between the integral of a function and the (unsigned) area bounded by the axes and the function. At A-Level you're asked to find the latter.
Reply 955
Avatar for rad058
rad058
Original post by Zacken
Opposite/adjacent?


Isn't that x / b?
How do I integrate arcsinh(x)

EDIT: it's okay I'm a genius I got it, how are you supposed to do it though?

EDIT^2: Reality kicked in, I'm not a genius, I didn't get it :frown:
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(edited 7 years ago)
Original post by Zacken
Well yes, there's a difference between the integral of a function and the (unsigned) area bounded by the axes and the function. At A-Level you're asked to find the latter.


Okay, thankks! and before you said even integral for point 6, by even integral do you mean an integral with limits a and -a?
Original post by Geraer100
I have a few things to check if they are correct to do:
[...]
6. And one silly question, the integral of sinx in the limits pi and -pi, without the modulus sign, is it equal to 0 or 4. In other words, shall we split the integrals into 2 halves with limits 0 and -pi, and pi and 0.
:smile:


It depends - if you want to evaluate the integral, you get 0. If you're trying to find the area bounded by the curve and the x-axis, then you split it up, take the absolute values (getting 4) and sum.
Original post by MathHysteria
It depends - if you want to evaluate the integral, you get 0. If you're trying to find the area bounded by the curve and the x-axis, then you split it up, take the absolute values (getting 4) and sum.


Thanks!

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