Mistake in exam question!! (1 Viewer)

[SamFramcisco]

I was just doing a Year 11 AP1 Maths Extension Exam for 2013 (here), when I came across Q1 c).

This question asks you to "evaluate a and b" by "squaring both sides of:"

sqrt(a) + sqrt(b) = sqrt(9 + sqrt(56))​

There's no problem with this question, provided a and b are integers.

However, the exam paper doesn't say anything of the sort, at least that I could see.

This is really important. If a and b aren't required to be integers, then the question cannot be answered: there is no way to "evaluate" a and b, because there are an infinite number of (a, b) pairs that satisfy the given equation.

It seems possible to me that the Cherrybrook Technology High School might owe some students a new exam result!

Does anyone have any thoughts about this, or have I fucked up?

 

[Carrotsticks]

You are correct that there exist infinitely many solutions if we drop A and B being integers (for example A=0 and B=9+sqrt(56) works too).

However, I doubt many students would have thought of that. It is pretty much assumed at that level that A and B are integers.

 

[SamFramcisco]

Thanks for your reply.

However, I've never heard of the convention that variables at the beginning of the alphabet (a, b, etc.) are implicitly regarded as integers -- assuming that's the rule being used. (This makes maths sound like that ancient version of Fortran -- Fortran77 ? -- which automatically assumed that the variables I and J were declared, and had the type INTEGER.)

Shouldn't maths be a bit more precise than this? If the question had some context that suggested a and b should be integers then I'd say fair enough, but as it stands it seems a bit random.

I'm probably getting more worked up about this than I should. In my defence, this was the first test exam that I've tried, so I was pretty shaken when I found what seemed to be a mistake.

 

[anomalousdecay]

You are right in that sense as there are many solutions.

It seems possible to me that the Cherrybrook Technology High School might owe some students a new exam result!

Lol how is that even possible if it was done and dusted last year. All (or most) of the students are in uni now

 

[Carrotsticks]

It is Year 11 Mathematics Extension 1, most students at that level don't know better.

 

[anomalousdecay]

Shouldn't maths be a bit more precise than this? If the question had some context that suggested a and b should be integers then I'd say fair enough, but as it stands it seems a bit random.

You are correct in this sense, however you will be surprised how there are many more unnoticeable loopholes in many school maths papers compared to uni maths or even the HSC.

Like there are cases in exams where they will forget to say one word that could possibly end up putting people in your situation.

With HSC they refine the exam many times and make sure there are absolutely no errors outside of knowledge to a HSC student. However, dare I say that to a uni student there are a few assumptions you would have to make clear to the marker because of some missing information (like saying a function is continuous and differentiable, MVT, etc).

So take this as a lesson. WHENEVER you find such a question, state at the top of your answer "Assume that a and b are integers" or "Assume that a and b are real", etc to make it clear to the marker that you may have misread something (if you do) or that its not clear in the question (in that case you should get full marks).

Also, if you are ever in such a situation, read the question at least 3 times (preferably 5 if you have extra time) and do a sanity check, because you don't want to assume something then realise at the end that you didn't read a piece of information.

 

[SamFramcisco]

What of the students who, for some strange reason, find themselves doing this subject and who do know better?

What if they really did try thinking through the problem carefully, and through some miracle noticed a = 0, sqrt(b) = sqrt(9 + sqrt(56)) was a solution? They'd be caught between the obvious (their solution) and a reason that precluded the obvious (e.g. something on the exam paper that excluded their answer)?

I guess we could dismiss these hypothetical students as collateral damage, in a lazy, under-equipped education system. Somehow that doesn't seem good enough to me, bleeding heart that I am.

 

[SamFramcisco]

Anomalousdecay, I've gotta say that I'm more worried about the screamingly obvious loopholes: I can live with the unnoticeable ones. OK, enough smart-arsing around from me.

Thank's for a genuinely positive and helpful reply.

 

[anomalousdecay]

What of the students who, for some strange reason, find themselves doing this subject and who do know better?

What if they really did try thinking through the problem carefully, and through some miracle noticed a = 0, sqrt(b) = sqrt(9 + sqrt(56)) was a solution? They'd be caught between the obvious (their solution) and a reason that precluded the obvious (e.g. something on the exam paper that excluded their answer)?

I guess we could dismiss these hypothetical students as collateral damage, in a lazy, under-equipped education system. Somehow that doesn't seem good enough to me, bleeding heart that I am.

Calm down you did a practice paper.

As I said, state your assumptions above.....

If you just look at it and say a = 0, b = 9 + sqrt(56) and vice versa, then you would have completely missed the point of what the question asked of "by squaring both sides".

It asks to evaluate using that, so if you can't do what the question blatantly asked for, then obviously you missed the point and will most likely lose the 2 marks.

I would not be surprised if 1 mark was attempting to or actually squaring both sides, and the other mark is for writing down a = 2, b = 7 or a = 7, b = 2.

If you arrived at the conclusion above in any other way without squaring both sides then you would probably only get 1/2 for using trial and error method which is not what you wanted.

And also I just realised after reading the question for the first time, the question is not incorrect. It just asked to find the solutions when you square both sides. So there is nothing by HSC standards that is completely wrong with the question as HSC standards will indeed be made so that you might have to do a question in a sequential order that is specific to what they want.

Anomalousdecay, I've gotta say that I'm more worried about the screamingly obvious loopholes: I can live with the unnoticeable ones. OK, enough smart-arsing around from me.

Thank's for a genuinely positive and helpful reply.

Read above. You just didn't read the question properly

 

[Crisium]

LOL that's a past paper from my school

That's the first ever error I've seen them make in a past paper

 

[anomalousdecay]

LOL that's a past paper from my school

That's the first ever error I've seen them make in a past paper

If you arrived at the conclusion above in any other way without squaring both sides then you would probably only get 1/2 for using trial and error method which is not what you wanted.

And also I just realised after reading the question for the first time, the question is not incorrect. It just asked to find the solutions when you square both sides. So there is nothing by HSC standards that is completely wrong with the question as HSC standards will indeed be made so that you might have to do a question in a sequential order that is specific to what they want.

Read above. You just didn't read the question properly

.

 

[RealiseNothing]

Holy shit you need a reality check.

 

[Kiraken]

itt: OP tries to sound smart by reading too much into a question to prove it wrong

 

[dunjaaa]

http://www.youtube.com/user/misterwootube -> file a complaint here lol

 

[SamFramcisco]

Calm down
..
If you just look at it and say a = 0, b = 9 + sqrt(56) and vice versa, then you would have completely missed the point of what the question asked of "by squaring both sides".

I'm so calm that I'm bordering on being comatose, but I'm not pleased by what seems like back-pedalling in your reply: the question is either properly stated or it's not, at least at this level.

Yes, the question asks us to square the expression, giving (for positive a and b):

a + b + 2 sqrt(ab) = 9 + sqrt(56)​

At this stage, a student who doesn't know that "variables with names starting with the letter 'a' are integers" (yes, sarcasm) might reasonably think:

"One solution is a = 0 and b = 9 + sqrt(56). And another is b = 0 and a = 9 + sqrt(56)."

In short, while squaring the expression might be important from a marking point of view, it makes no difference whatsoever to my original point.

And also I just realised after reading the question for the first time, the question is not incorrect. It just asked to find the solutions when you square both sides.

Do you really want to stick with this? Question 1c) (here) asks us to square both sides and "evaluate a and b," but the paper doesn't provide enough information to do the job. As I pointed out before, you can pick out two potential values for a and b - after squaring both sides - just by looking at the equation, but those are just two arbitrary values from an infinity of candidates.

So there is nothing by HSC standards that is completely wrong with the question as HSC standards will indeed be made so that you might have to do a question in a sequential order that is specific to what they want.

There is nothing wrong with a question asking a student to follow a line of reasoning. There is something wrong when the question asks you to do the impossible.

This question is analogous to asking "What is the average petrol consumption of this car?" Well, which car? There are hundreds of millions of cars out there - just as there is an infinity of solutions to problem 1c) - but "by HSC standards" students are somehow meant to know exactly which car the question is referring to.

 

[anomalousdecay]

I said calm down because you were bashing at a practice paper. Imagine what you would do if you came across this in an actual exam....
If this pops up in any of your exams, there is not much you can do. You just have to deal with it. No-one is perfectly clear when expressing something or asking a question. Neither was the person who made the paper, whom forgot one or two things.

The only thing with your reasoning here is that if they wanted the whole set of solutions, then a student can just write "infinitely many sets of solutions", without doing any working out at all.

There is no general answer either for the infinite set within HSC methods (not sure if there is a method to find it though). So if you find the sets of solutions (0 and 9 + sqrt(56)) and (2 and 7), then I'm sure that you would be fine, as long as you showed out the working out of squaring both sides that is.

Your analogy should be something like "Find the average petrol consumption, over a distance of 100 km of this car model and year make" as the question tells you to use a specific method.....
You would still have infinitely many solutions for the average petrol consumption which differ a tiny bit, but who said you couldn't go for the advertised manufacturer, or a specifically tested figure of the average ?

You are given what method to do. By squaring both sides you are being told to do algebraic manipulation.

By using algebraic manipulation then you shouldn't be using a trial and error method here at all in the steps.

If it just asked you to "find the values of a and b for this question" your argument would be valid. All I can say really is this:

itt: OP tries to sound smart by reading too much into a question to prove it wrong

You should just let it go. If it takes me this much explaining to do then obviously the person who made the question was not very clear. In an exam you won't get much of an opportunity to ponder about this for too long. Just state your assumptions and the marker will realise what you did wrong and may give you 1 mark for it. Otherwise, read the question again and do a quick check to make sure that you haven't mis-read or made a mistake.

This happened last year in HSC Physics where they asked for "explain how a photocell works and draw one in the square box space below".

Now a photocell can include many things, including a solar cell, LDR, etc. However what most Physics teachers pointed out is that they were asking for the photocell based on a glass vacuum tube where a stream of cathode rays creates a potential across two electrodes. In the end, because technically you can speak about solar cells, I was told (courtesy of Fizzy_Cyst) that solar cells were accepted for it. Because the question was not 100% clear, they couldn't mark any one down for talking about an actual photocell, but using the wrong example.

And this was a practice paper so I still have no idea why you won't just accept that there was a lack of clarity here, and that really all they wanted was the integer solutions.

 

[Kiraken]

the point is you can argue about this question and even though you're technically right, it's a paper from 2013 you are doing practice on, saying the question could have been phrased better in a paper that is a year old and has no continued relevance in determining anyone's marks on a student website where it doesn't impact anybody literally achieves nothing except giving off the impression you are a pretentious smart alec.

Papers have errors, but finding mistakes in them when they are already old and then talking about them here achieves nothing

Not to mention that often marks are allocated not just for the correct answer but providing the best possible answer. Don't overthink questions and go for the optimal solution. Also keep in mind it's a 2 mark question the a=0 solution is only 1 mark worth of working so clearly there has to be more to it

 

[dunjaaa]

Like I said, if you have a problem with the paper, consort the Cherrybrook Tech head maths teacher -> http://www.youtube.com/user/misterwootube

 

[anomalousdecay]

Like I said, if you have a problem with the paper, consort the Cherrybrook Tech head maths teacher -> http://www.youtube.com/user/misterwootube

Hahaha.

 

[panda15]

If you see a question like this in an actual exam, just make an assumption so that the question makes sense. I mean, for this one, it's pretty obvious they mean integers a and b. You writing "There are infinitely many solutions because it wasn't specified which field a and b belong to" doesn't show any mathematical working, and makes you come off as a douche, so you would most likely get zero for the question.

Also, I don't think the students of Cherrybrook would care about getting a new result. 1. Because most of them would have just assumed a and b were integers. 2. Because it's in the past and it's a year 11 exam, which has no effect on their HSC what so ever. I mean, for you, it's a practice paper. I don't get why you felt the need to make such a big deal out of it.