Chinahand Posted October 10, 2015 Share Posted October 10, 2015 The link will show you it is a Scottish Higher Maths paper, which many people complained was too hard. It is an interesting issue to debate how much of a population needs to understand calculus. In the last month I made a significant engineering error due to doing it wrong - I'm very glad we have a two pairs of eyes rule on calculations. If you want to analyse anything remotely complicated - involving volumes, areas, centroids, rates of change etc - calculus is necessary. It's an A level maths type question, so I'm not sure how many people on MF will be able to solve it, but this level is basically necessary for any job which involves modelling the world beyond a basic level. Quote Link to comment Share on other sites More sharing options...
wrighty Posted October 10, 2015 Share Posted October 10, 2015 The problem with school maths, in my increasing experience of coaching kids through GCSE and A levels is that schools don't teach kids how to think mathematically and write 'good' maths. Instead they're given a bag of tricks which gives them the ability to solve a few standard calculations. Calculus in school is presented initially as a formula to differentiate x^n, and in the next chapter how to integrate the same. I'd start with a fundamental definition of a derivative as a gradient, an integral as an area, and then connect the two with the fundamental theorem of calculus. I'm a firm believer that to progress in maths you need a sound grasp of the fundamentals, rather than a knowledge of increasingly complicated rules that help solve increasingly complicated problems. I'm not surprised most adults have forgotten most of the maths they learned at school, as they never understood the principles in the first place. Quote Link to comment Share on other sites More sharing options...
WTF Posted October 10, 2015 Share Posted October 10, 2015 No acceleration or deceleration figures and no turning radius! ! Quote Link to comment Share on other sites More sharing options...
Chinahand Posted October 10, 2015 Share Posted October 10, 2015 WTF - this is a school maths question. It is one that probably 90% of the population wouldn't be able to solve. It is massively simplistic, ignoring multiple issues that in the real world would complicate it even more. Add in all those things and it becomes a far far more difficult problem. When teaching people you start with simple models and concepts and build up - as Wrighty says trying to get them to understand the principles involved. The problem isn't realistic, but it does enable pupils to demonstrate the principles involved in understanding an optimization algorithm. It is meant to be solved in 20minutes in an exam. Later in life it is perfectly possible for people who have these skills to spend years building optimization models involving thousands of differential equations etc. These accurately model all sorts of things - GPS, flight control systems, cutting speeds and wear, turbine performance. The people doing it wouldn't be able to do that without the baby-steps of solving the simple examples when they were 18. Let's not run before we can walk, hey. Can you solve the question? Quote Link to comment Share on other sites More sharing options...
Albert Tatlock Posted October 10, 2015 Share Posted October 10, 2015 I think I've solved it...jeez took a while, maths I'd not used for a long time. Quote Link to comment Share on other sites More sharing options...
dilligaf Posted October 10, 2015 Share Posted October 10, 2015 The link will show you it is a Scottish Higher Maths paper, which many people complained was too hard. It is an interesting issue to debate how much of a population needs to understand calculus. In the last month I made a significant engineering error due to doing it wrong - I'm very glad we have a two pairs of eyes rule on calculations. If you want to analyse anything remotely complicated - involving volumes, areas, centroids, rates of change etc - calculus is necessary. It's an A level maths type question, so I'm not sure how many people on MF will be able to solve it, but this level is basically necessary for any job which involves modelling the world beyond a basic level. Not that you would be condescending in any way. Why post such a comment ? I would guess that like me, many on here are just ordinary folk who would not give two f**** about such things. Are you on the correct forum for your intellect? 1 Quote Link to comment Share on other sites More sharing options...
Chinahand Posted October 10, 2015 Share Posted October 10, 2015 (edited) Only about 5% of the population take A level maths - this is a general forum I was being factual but take it anyway you like. Edited October 10, 2015 by Chinahand Quote Link to comment Share on other sites More sharing options...
Albert Tatlock Posted October 11, 2015 Share Posted October 11, 2015 Mathematician or not...if it wasn't a Zebra...and it was you, I'd expect you would want to know what kind of a headstart you'd got. Quote Link to comment Share on other sites More sharing options...
Chinahand Posted December 8, 2015 Share Posted December 8, 2015 Mice weigh the same as Whales. The weight of a mouse = m The weight of a whale = w The sum of the weights of a mouse and a whale = 2s - humour me with the 2 - it makes the maths easier. so m + w = 2s Rearranging we get 1) w = 2s - m 2) w - 2s = - m Multiply 1) by 2) w2 - 2sw = m2 - 2ms Add s2 to either side of the equation w2 - 2sw + s2 = m2 -2ms + s2 Collect terms and simplify: (w - s)2 = (m - s)2 Take square roots of both sides: w - s = m - s Add s to both sides w = m All whales weigh the same as mice QED Quote Link to comment Share on other sites More sharing options...
the stinking enigma Posted December 8, 2015 Share Posted December 8, 2015 Can you change a wheel on a car or fit a dado rail? 1 Quote Link to comment Share on other sites More sharing options...
Chinahand Posted December 8, 2015 Share Posted December 8, 2015 I certainly can, can you see where the logic is incorrect? Quote Link to comment Share on other sites More sharing options...
the stinking enigma Posted December 8, 2015 Share Posted December 8, 2015 Yup Quote Link to comment Share on other sites More sharing options...
wrighty Posted December 8, 2015 Share Posted December 8, 2015 These things usually have a division by zero in them somewhere. This one however does not. Instead you need to consider functions and their inverses, and the relevant domains and co-domains. Good solid pure maths. (alternatively just realise that if a squared equals b squared, a does not necessarily equal b) 1 Quote Link to comment Share on other sites More sharing options...
Chinahand Posted December 8, 2015 Share Posted December 8, 2015 Exactly - with these things it can often be a good idea to bring them back to the real world from the esoteric-ism of pure maths. If 2s is the total weight of a mouse and a whale, then what is s? Answering that should help to explain what is going on and hence the error. Quote Link to comment Share on other sites More sharing options...
paswt Posted December 8, 2015 Share Posted December 8, 2015 I certainly can, can you see where the logic is incorrect? I would venture to suggest that you don't need 'logic' to know that a whale weighs more than a mouse . just saying 1 Quote Link to comment Share on other sites More sharing options...
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