Is this maths exam too hard?

[shibafu]

Earlier this year there was a hoo-ha in the news here about a Scottish Higher maths exam that students claimed was unfair and too hard.  This is an exam that pupils sit at age 18.

One of the questions from that exam has been published at the bottom of this news article:
http://www.bbc.co.uk/news/uk-scotland-scotland-politics-34318232

If you have Scottish Higher maths, England/Wales A-level maths, or the equivalent in your country (especially if you did it recently and can remember anything from it!), give it a try and see what you think.  Too hard?

[dks]

had a quick read and no, it does not seem too hard - more of a common sense than a maths question, as the formula is given.

[shibafu]

It may be harder than you think... part A is more or less common sense and applying the given formula, but part B has more to it, and is worth 8 of the 10 marks.

[sLaughterMed]

Speaking as an American Engineering student, who took the equivalent class in high school, (but now with more mathing under my belt) its not a super hard problem, but I can see how part two would be difficult to a high schooler.

Having said that, if they missed part one, they need a swift kick out of that class

[Higgins617]

I suck at math so they're all too hard

[Syph007]

That's not harder then we did in school.  I assume they would have been taught calculus in high school and to differentiate to find the extreme values of an equation?

At least its not in N dimensional space!   

[Higgins617]

That's not harder then we did in school.  I assume they would have been taught calculus in high school and to differentiate to find the extreme values of an equation?

At least its not in N dimensional space!   

It sort of depends on what students are being given this test, frankly I didn't do this sort of thing until my senior year. But I also chose to avoid calc like the plague.....

[captain spaulding]

That's not harder then we did in school.  I assume they would have been taught calculus in high school and to differentiate to find the extreme values of an equation?

At least its not in N dimensional space!   

It sort of depends on what students are being given this test, frankly I didn't do this sort of thing until my senior year. But I also chose to avoid calc like the plague.....

This exactly. I graduated with basic math (believe it or not) so this sort of thing really makes me feel like an idiot. 

[detron]

That's not harder then we did in school.  I assume they would have been taught calculus in high school and to differentiate to find the extreme values of an equation?

At least its not in N dimensional space!   

or non-euclidean geometry   

[Higgins617]

That's not harder then we did in school.  I assume they would have been taught calculus in high school and to differentiate to find the extreme values of an equation?

At least its not in N dimensional space!   

or non-euclidean geometry   

 

Detron and the scary math returnsssss

[dks]

As pointed, some people do know a bit more mathematics than the average 17 year old pupil.... and it has been a long time since they were 17, or have been taught different syllabi .

Basically, if that question, or a similar one, was taught then it is fair for it to be in an exam. It examines mathematics and the mathematical/logical way of thinking - the problem solving, as it is usually called. You need to "get" the question first.

There is the need to have some harder questions to enable better pupils to show their work and get higher grades.
Not everybody deserves an A.

In addition, examining boards use normal distribution curves and adjust grades based on the statistical analysis of the higher, lower,average etc. marks in each exam

[shibafu]

The differential calculus part of the syllabus for that exam is:

Calculus skills
The learner will use calculus skills and apply them in context

Differentiating functions

• Differentiating an algebraic function which is, or can be simplified to, an expression in powers of x
• Differentiating k x sin , k x cos
• Differentiating a composite function using the chain rule

Using differentiation to investigate the nature and properties of functions

• Determining the equation of a tangent to a curve at a given point by differentiation
• Determining where a function is strictly increasing/decreasing
• Sketching the graph of an algebraic function by determining stationary points and their nature as well as intersections with the axes and behaviour of f (x) for large positive and negative values of x

Which certainly covers everything required to solve that problem.  When I tried it I couldn't really see any particular trick or difficulty in how the techniques are combined.  However among the complaints about the paper being too hard there was some suggestion that it was the combination of techniques that was unfair.
I'm guessing maybe when they learned about finding stationary points of a function, they didn't do any sample questions where the chain rule was required for the differentiation, and then they learned the chain rule separately.  But having tried the question, that seemed like a specious complaint to me.  Surely if you know you have to differentiate the function to find the minimum, and you know the chain rule, it should be obvious you need to use the chain rule to do the differentiation.  Even if you had not previously seen a question exactly like that.  Reasonable, or not?

[pfrsantos]

Something like this?...

You probably need to derive the function to find the extremes, right?

The 110 and 104,4031 are easy to get.