Tuesday, 22 September 2015

"SQA boss admits new Higher maths exam was too hard". Blogger begs to differ.

According to the BBC, this question was too hard:

No it wasn't. Here are my workings:

Crocodile, river, zebra, SQUA, differentiation, trigonometry, maths.


Random said...

"The time taken, T measured in tenths of a second"
Why tenths? Usually it is hundredths or just secs?

Bayard said...

In maths exams, I was taught to do the easiest bit first. So:

"a) ii) Calculate the time taken if the crocodile swims the shortest distance possible"

The shortest distance possible is straight across the river.
Therefore x = 0

Therefore T(x)= 5 root(36+x2)+4(20-x)=> T(0)= 5 root(36+0)+4(20-0)
=> 0=5(6)+80 => 0=110, which is manifestly wrong.

I suppose what it means is "The time taken, T(x), measured...."

It's always hard when they don't get the question right

DBC Reed said...

A further example of the need to curtail the amount of Maths taught in schools.

Curtis said...

Random: T is in tenths of a second to keep the "formula" simpler, otherwise replace the 5 with 0.5 and the 4 with 0.4. Also to catch people out, such as Bayard.

Bayard: T is in tenths of a second, therefore when x = 0, T = 110 or eleven seconds.

Or, since we already know that the water speed is 2m/s and the land speed is 2.5m/s, 6m in water takes 3 seconds and 20m on land takes 8 seconds, 3+8=11

Bayard said...

DBCR, I'd say it was an example of the need to get less sloppy mathematicians setting the questions in exams.

"T = 110 or eleven seconds."

Not as the formula is given it doesn't; T(x) or T times x, has to equal zero when x equals zero and that is what the formula says, T(x) = 5 root etc. not T = 5 root etc. This is true whether T is in seconds, tenths of a second or nanoseconds.

DBC Reed said...

This kind of thing induces maths phobia, then school phobia in ordinary young people,if reinforced by inability to cope with English spelling system. ( I grant you this is Higher Maths/insanity,not the ordinary vanilla variety).Lets face it, even for a quite complex way of life you are only going to need simple arithmetic in whole numbers.The Maths syllabus has grown to fit the time available to teach it, in classic Parkinson's Law fashion.

Lola said...

Why doesn't the croc just buy a rifle and shoot the prey and then it won't matter how long (within reason) it takes to get to it.

Dinero said...


you say that its not difficult but you left out the difficult bit. Calculating the speed on land and water.

They can be ascertained by logical reasoning but the quantities are presented in the question in an arbitrarily awkward cryptic manner. Arguably its not a maths question ,its a logical reasoning question.

Also if the candidate misses that and it is a timed exam the candidate could waist a lot of time before abandoning it, thus leaving less time for the other questions.

View from the Solent said...

Aah, you're misinterpreting the symbols Bayard.

In mathematics, T(x) means the function T of any value of x. (In this case, x can take any value between 0 and 20). And this function is defined on the RH of the equation. So T(0) means the value of T when x is 0.
Since Highers are the equivalent of A-level, I'd hope that the students would have interpreted it that way.

View from the Solent said...

Mark, I'd argue that your method takes a lot longer. That question is a simple minimum value problem. At the minimum value, the (first) differential of the function T with respect to x = 0.

So you just differentiate the RHS of the equation w.r.t. x, set it = 0, and solve for x.

It was a very long time ago, but I'm sure that this sort of thing came very early in my pure maths A-level. If it was beyond the capability of the complaining students, then there's been some serious dumbing down of the syllabus.

Dinero said...

Considering view from the Solent's comment

it seems then that the candidate doesn't need to work out the two speeds, or the width of the stream.

DBC Reed said...

See above/
Oh my Gawd!

Bayard said...

VFTS, In that case shouldn't the x and brackets be subscript and shouldn't it be "The time taken, T(x),...."

"I'd argue that your method takes a lot longer."

I'd agree. Once you have arrived at point 4, it is fairly easy to calculate that the time saved running along the bank over swimming is x/0.5 (0.5 being the difference between the two speeds and distance upon speed equals time) and therefore the length of the optimum hypoteneuse is 6+x/2. Therefore x²+36=(6+x/2)²=36+6x+x²/4. Subtracting 36 from both sides and dividing both sides by x gives x=6+x/4, i.e. x=8.

No differentiation required, which is good as I've completely forgotten how to do it.

Mark Wadsworth said...

VFTS, thanks for the email explaining how to differentiate multiples of square roots.

B, have you road tested that method with different speeds and river widths? How do you get from "x/0.5" for time saved (which is obvious) to optimum diagonal 6 + x/2 )+(the 6 is obvious, by the way, it is the x/2 which puzzles me)?

If it works, then that is a nice way of doing it. But "flipping the triangle" once you understand the principle is still the quickest - you can basically jump from step 5 all the way to step 13.

DBC Reed said...

All of this obsessiveness with totally imaginary worlds and problems leads ordinary people to believe that simple Economics is not for them
and is best left to a technocratic elite who have imposed far too much
on the school curriculum.I would have thought making solving this kind of problem a matter of personal success or failure in school is not educational but mental abuse and training to be acquiescent.
Then you get the likes of good old Thicky Thatcher with a wartime Chemistry degree from Cambridge (when all the lads were off fighting and highly left-wing)gaining power and she demolishes the carefully balanced Mixed economy post-war state on the There Is No Alternative system borrowed from Science.The genuine popularity of Corbyn is partly because he talks about simple important things and does not believe that figures make things impossible as they are made to appear by ten-a-penny liars and loonies trained in Maths .
Have you read the anti Maths statements of the Sorbonne graduates who mutinied (in 2000?) against the imaginary worlds they had to study on economics courses?

DBC Reed said...

The Sorbonne students can be referenced by researching Post Autistic Economics, the name they gave their movement, which did not do them any favours in the Anglo world by appearing crass and unfeeling.
Their petition however has the following headings: We wish to escape from imaginary worlds; we oppose the uncontrolled use of mathematics;we are for a pluralism of approaches in Economics;and a Call to teachers: wake up before its too late!
Clearly as representatives of the old, now fugitive, tradition of land-value based Economics, we should support all their demands for
changes to the way Economics is studied and applied.We are being sidelined and the economy ruined by experts who are bang to rights guilty of the accusations the Sorbonne and successive waves of students have flung at them.N.B the uncontrolled use of mathematics in imaginary worlds.

Bayard said...

DBCR, why are you conflating maths, where everything is demonstrably true (although I never really got my head round imaginary numbers) with economics, where everything is more or less demonstrably just somebody's theory and most likely to have no bearing in the real world?

Bayard said...

Mark, on reflection, I am not sure I agree with your point 4, which I was taken as a given. For your solution to be valid, it must be valid for all sub-optimal solutions, including x=0. If you take x=0 as the sub-optimal solution, then the extra time the croc spends in the water is the time longer than the 3 seconds it takes it to swim straight across the river, but that then means it would take the same time to reach point P, regardless of whether it swam the whole way or swam the shortest distance and we know that isn't the shortest time, because we are told that it isn't.

Graeme said...

DBCR...still inventing history. Why not read a few books, old chum?

DBC Reed said...

The point the Sorbonne students were making is that the conflation of Maths and Economics was already taking place with weird theories being "proved" by complex mathematical models that had little resemblance to reality. Their protest was in 2000 and the whole financial system hit the buffers in 2007, something the mathematical models had utterly failed to predict,( which they should have done if they embodied scientific and mathematical certainty).
@G What are you on about? I gave independent factual backing, dates ,quotes etc for the history involved.

Bayard said...

It's hardly the fault of mathematics if economists use it to try and achieve the impossible, i.e. making a science out of economics, but otherwise, I see your point.

Nick Simmons said...

The key clue that you are supposed to differentiate here is 'minimum', school mathematics gives points for working using the 'correct' method even if you get the answer wrong.
I bet that a single mark of those 8 can be gained for writing 'differentiation' even if all the rest of your working is wrong.

Using your triangle method would results in a comment like 'correct answer but incorrect method, be careful as you will get no marks if wrong!' from my old teacher