MAY13 Maths HL TZ2 Paper 2 Discussion

[yii yann]

Good lord I thought this paper was rather tricky compared to paper 1, which was a breeze. The differential eqn question in section B slipped me up (especially the first part), and I made a horrible mistake on qn 13 (I put tan instead of tan inverse for the angles), resulting in somewhat weird answers.

Did anyone get a really really tiny value for the final part of qn thirteen? I think it was the rate of change of theta with respect to x.

Overall felt the paper was harder than other years. What do you guys think the boundary will be?

[Garmr]

Good lord I thought this paper was rather tricky compared to paper 1, which was a breeze. The differential eqn question in section B slipped me up (especially the first part), and I made a horrible mistake on qn 13 (I put tan instead of tan inverse for the angles), resulting in somewhat weird answers.

Did anyone get a really really tiny value for the final part of qn thirteen? I think it was the rate of change of theta with respect to x.

Overall felt the paper was harder than other years. What do you guys think the boundary will be?

haha I'm the opposite of you, I think paper 1 was slightly harder but overall these papers were relatively easier than past years (except maybe M12).

Yeah I got something like 2.27 x 10^-4 rad s^-1 (although I got the units wrong in the exam since I put degrees, but hopefully I won't get penalized lol)

Given that last year's boundaries were around 91~ and these papers were harder (I think), I would hope that 7 will be around the mid-80s.

[Zuler]

Sweet! I can't remember what the second part asked but I think it was something standard/basic so no problems there. Also, I noticed you were asking about the velocity question, maybe I can explain why the only value is indeed 30.8 or whatever it was.

So, let's take an example of the differential equation dy/dx = y. Let's say when x =0, y =3.

dy/y = 1dx

ln |y| = x + c

|y| = e^(x+c)

y = +-e^c * e^x

y = Ae^x (where A = +-e^c)

So substituting our points,

3 = A(1)

A=3

So y = 3e^x

The point I'm trying to make is, the +- gets 'absorbed' by the constant, and the initial values given will determine whether the function is the + variant or the - variant. If I said when x=0, y = -3, our function would be -3e^x. Our initial condition leads to one function as desired.

In the case of our velocity function, the values made our equation the positive variant, so indeed we're all right and there's only one answer. Hope that makes sense

Hey, thanks for trying to explain it, i really appreciate you taking your time. It makes quite some sense, but still seems kind of vague, since I still didn't really understand how my method gave me two different results and how to decide between them ^^ I spent some serious in depth thoughts about it and if you're interested then have a read:

The differential equation is called "autonomous", because it does not explicitly contain the independent variable t (time).  Theinstantaneous time rate of change of v, acceleration, depends only upon the value of v.  If we have two objects moving according to this law of motion, one having velocity 0 at t=0, and the second having v=0 at t=10, then whatever the velocity of the first object is at time t, the second object will have the same velocity at  time t+10. The time-velocity graph of the second object will just be the graph of the first object shifted 10 units to the right (i.e. 10 seconds later). Note that v=60 is an "equilibrium solution".  If v = 0, then the acceleration is 0, so the object will neither speed up nor slow down, so it will continue moving at exactly velocity v.  If v < 60, then dv/dt > 0 so the object will speed up, and if dv/dt > 0, it will slow down, so in both situations, the velocity will move toward the equilibrium velocity, v = 60.  This is often represented by a phase space (or for a single dependent variable, a phase line):      |     |     v   v > 60     |     |     +----------- v = 60     |     |          ^   v < 60     | which shows that if v < 60, then the DE says that velocity will increase toward 60, while if v > 60, velocity will decrease toward 60. In solving the DE, when you reach     ln |60-v| = -(t/40) - c and exponentiate to get    |60-v| = e^((-t/40)-c)          = e^(-t/40) * e^(-c)          = C*e^(-t/40)          (where C = e^(-c)) The left side is either 60-v, if v < 60, or it is v-60, if v > 60, so we can write    60-v = C1 * e^(-t/40)     where C1 = -C if v > 60, and C1 = C if v < 60.  In this form, setting t=40 gives C1 = 60, and    60 - v = 60*e^(-t/40) ,   or  v = 60(1-e^(-t/40))  . The last formula shows that v < 60 for all t, so 31.7 must be the answer. We don't ignore or absorb the absolute value, we have to use what the DE tells you about the problem, which is this caseis the qualitative behavior of the object we see in the phase plane.

In some way that is what I meant, especially the part where you say "we have to use what the DE tells you about the problem". It's the initial values that definitely decide which function we're using

@JohnSmith: I wasn't talking about that question, that one itself is a different problem all on its own I was talking about question 10 in Paper 2, the velocity one?

[Zuler]

Good lord I thought this paper was rather tricky compared to paper 1, which was a breeze. The differential eqn question in section B slipped me up (especially the first part), and I made a horrible mistake on qn 13 (I put tan instead of tan inverse for the angles), resulting in somewhat weird answers.

Did anyone get a really really tiny value for the final part of qn thirteen? I think it was the rate of change of theta with respect to x.

Overall felt the paper was harder than other years. What do you guys think the boundary will be?

haha I'm the opposite of you, I think paper 1 was slightly harder but overall these papers were relatively easier than past years (except maybe M12).

Yeah I got something like 2.27 x 10^-4 rad s^-1 (although I got the units wrong in the exam since I put degrees, but hopefully I won't get penalized lol)

Given that last year's boundaries were around 91~ and these papers were harder (I think), I would hope that 7 will be around the mid-80s.

I was going back through my calculator and I realised I entered the expression wrong and didn't get your answer How many marks would you lose for that?

[Garmr]

I believe it was a 3-mark question, so if you still wrote something like "d0/dt = d0/dx * dx/dt" or the actual derived function you'll probably still get 1/2 marks

[NikY]

Hey guys,

about 12, there were no restrictions on the function, so the answer is f(x)= +-sqrroot

I answered all the question but I think I might have skipped the binomial one...I dont even remember what question was it. I am guessing 11, part b? how many marks was it worth?

[Garmr]

In functions one input must relate to exactly one output, so +/- should not be a function since one input relates to two outputs, right? o_o

I don't think the binomial question was worth that many marks, it was a small two-part subquestion probably worth 5-6 marks overall.

[NikY]

exactly, but the didnt say the word function...it was just: "express in form of y=f(x)", and y can equal to +- f(x). And besides, there were no restrictions on either domain nor the range of the function...so when you get y^(2)= sin2x + c, it is clear that y=+-sqrt(sin(2x)+3).

That is why when they ask you to find the area you have to find the integral from 0 to pi/2 of +f(x) and the integral from 0 to pi/2 of -f(x) (or 2* the integral of the positive function)

So about Binomial, it was question 11, right? and it was after we had to prove that n*(n-3)/2 is the number of the diagonals, right?

[Giveme45]

Hey guys,

about 12, there were no restrictions on the function, so the answer is f(x)= +-sqrroot

I answered all the question but I think I might have skipped the binomial one...I dont even remember what question was it. I am guessing 11, part b? how many marks was it worth?

No, they asked to express in the form of y=f(x) and f(x) is a function. They wanted one in particular, and y cannot equal to +- f(x). Because y=+-sqrt(sin(2x)+c) is not a function. Besides it wasnt sin(2x)+3 but just sin(2x)+c. I asked one of the moderators and he said that they only wanted one of them, and both were fine.

And no they did not want twice the integral since the function was either + or -, not both.

Yes, the binomial was question 11.

Edited May 12, 2013 by Giveme45

[MylakIB]

Guys, was variance 9.5 or 9.5² in that question with cats?

Edited May 12, 2013 by MylakIB

[difiCa]

Guys, was variance 9.5 or 9.5² in that question with cats?

IIRC it was 9.5 and SD was sqrt(9.5).

Oh, and I'd say the binomial question was definitely on 16 trials, as one experiment (say, in physics) can very well contain 16 trials of the same dependent variable, and having a trick question like that would, in my opinion at least, be too stupid for it to actually appear on a paper. I mean, does anyone have any knowledge of a question that actually cannot be answered to its fullest appearing on a paper?

[Giveme45]

Guys, was variance 9.5 or 9.5² in that question with cats?

IIRC it was 9.5 and SD was sqrt(9.5).

Oh, and I'd say the binomial question was definitely on 16 trials, as one experiment (say, in physics) can very well contain 16 trials of the same dependent variable, and having a trick question like that would, in my opinion at least, be too stupid for it to actually appear on a paper. I mean, does anyone have any knowledge of a question that actually cannot be answered to its fullest appearing on a paper?

Yes the velocity question required a complex understanding of phase planes since v had two solutions (thought this is not necessary to require full marks), and the ydy/dx=cos2x in the general form of y=f(x) was extremely badly phrased. Since the differential equation gave y=+-sqrt(sin2x+k). And this is not a function so it was unclear what to proceed with.

Edited May 12, 2013 by Giveme45

[MylakIB]

Well, the equation has a solution +-sqrt indeed, but later on, they wanted a specific solution for y>0 (it was y=1 or 2 i dont remember), and the whole thing was then about working on the region above the y axis (because of this fact)

[Giveme45]

Well, the equation has a solution +-sqrt indeed, but later on, they wanted a specific solution for y>0 (it was y=1 or 2 i dont remember), and the whole thing was then about working on the region above the y axis (because of this fact)

Yes that's what i did as well. Still bit confused whether they expected the answer y=+-sqrt(sin2x+k), or wehterh just y=sqrt(sin2x+k), since the former is not a function, though they wanted it in the form fo y=f(x).

[MylakIB]

Well, they are notorious of forgetting about pluses and minuses, and we can't do anything. I think that theyll accept both solutions...

[Giveme45]

Well, they are notorious of forgetting about pluses and minuses, and we can't do anything. I think that theyll accept both solutions...

Yes it's kind of ridiculous that this occurs in a HIGHER LEVEL MATHS paper... I hope I won't punished for only writing y=sqrt(sin2x+k), because of this ambiguity. They can't expect to write down both solutions if they only ask for one.

How did you do for the rest of the paper? I was expecting a full 120, until I realized that apparently the standart deviation was root9.5 instead of 9.5, making me lose 1 or 2 marks, and also I made a mistype for the expected income giving me a false solution making me lose anotehr A1 mark... I don't understand why I keep doing such careless mistakes!

[MylakIB]

Up to now, nobody has pointed me any fault, but I always lose 1 or 2 points for some unnecessary things. I really liked the questions on P2 (they seemed difficult, but as u started doing it, they turned out to be eaaasy). (AND I DIDNT DO ANY STUPID MISTAKES LIKE IN P1 where I messed up the first question with stupid intergal lol)

EDIT: so i hope to get a 7, since it's vital for fulfilling my university offer...

Edited May 12, 2013 by MylakIB

[Giveme45]

Up to now, nobody has pointed me any fault, but I always lose 1 or 2 points for some unnecessary things. I really liked the questions on P2 (they seemed difficult, but as u started doing it, they turned out to be eaaasy). (AND I DIDNT DO ANY STUPID MISTAKES LIKE IN P1 where I messed up the first question with stupid intergal lol)

EDIT: so i hope to get a 7, since it's vital for fulfilling my university offer...

Yeah same feeling. It's just so frustrating if you know everything and then notice how you lost marks due to some small careless error

[MylakIB]

But actually, Maths was (and is) the subject I am really confident of. I'm really scared of Polish since my results are always fluctuating, and geography (didnt start studying)

[Garmr]

Up to now, nobody has pointed me any fault, but I always lose 1 or 2 points for some unnecessary things. I really liked the questions on P2 (they seemed difficult, but as u started doing it, they turned out to be eaaasy). (AND I DIDNT DO ANY STUPID MISTAKES LIKE IN P1 where I messed up the first question with stupid intergal lol)

EDIT: so i hope to get a 7, since it's vital for fulfilling my university offer...

Yeah same feeling. It's just so frustrating if you know everything and then notice how you lost marks due to some small careless error

Same here, I always overthink papers after I do them and realize I made a bunch of mistakes, but oh well.

I'm actually pleasantly surprised with the difficulty of this years' papers. I got a 5 in my mocks but right now I'm fairly confident for a 6, and 7 if I'm really lucky. It could also be the fact that I did papers day and night between then and now but I'm hoping I get a 7 since Math is my most important subject (both for uni and because for some reason I really got to love math after I started HL... baffling) and it would be a good compensation for Physics.

I have a whole free week before paper 3 so I guess I should study that wisely.