Who's smart here and understands math? Element? Element?? Maybe we have another real teacher or professor here?

This is about as far as I got in high school with math.  I remembered having to do this but I forgot a lot of it right away after final exams, but I did get all As in high school.  My GPA was 3.95 but I chose to go to work right away after high school instead of going to a university.  I went to a technical college instead to learn how to be a truck driver.  It was a good middle class income and I made twice the median income for women in my area but now I've chosen to be a stay-at-home mom instead.

The test paper is Canadian.  Their phone number's the biggest clue.  It's from Brampton ON.  Canadians have a mix of doing things the way the USA does stuff and the way the rest of the world does stuff.

 Thank you Livvie - I didn't really notice the phone number but would not have known it.

I used to know a woman who became a truck-driver, but in a rather unusual way. Anne was a hospital radiographer who won a chance to try driving a heavy goods vehicle, in a staff-magazine competition. She enjoyed it so much that she took the relevant driving-lessons, gained her HGV licence and drove for a while before eventually moving into haulage management!

Though as I mentioned obliquely, I found some mathematical topics hard because they were so abstract, and taught as abstractions, I found comprehension in some areas, in later life. That was because I now saw the problems from new angles in real-life situations. For example...

Years after leaving school I joined a company making sonar equipment, and took those evening-class courses hoping to improve my prospects there a bit. One result was finally understanding the Logarithms that were still used as an arithmetical-calculation tool when I was at school. However, the logs were not in the Maths courses, but in the work, whose stock-on-trade measurement scale for sound and electrical signals is the decibel (dB), based on Logarithms. 

Further, it was not there that the light dawned, but in an off-shoot - bats! You've probably seen side-scan sonar pictures of things like shipwrecks. Well, familiar with seeing them at work, I pondered the bat's mental version when navigating in the total darkness of a cave, where it can't augment echo-location with sight. (Bats have fairly good eyesight.) So I set out to learn about the animal's voice and hearing; so learnt how the mammal ear works by using the human ear as example - plenty of readily-available information - and to gain a basic understanding of Acoustics, hence the Decibel hence.... Logarithms!

Actually, what I learnt of the human ear's characteristics proved awe-inspiring in itself...

My other dawn light was in Calculus, which defeated me at school. In my 50s I developed an interest in Geology, and joined a geology club. One day it ran a tutorial on numerically analysing a river's gradients, in which sudden but perhaps subtle changes might indicate geological boundaries concealed under the valley-floor deposits and vegetation. Something, I know not what, made write the simple formula in calculus notation, and I realised I had at last twigged Differentiation - effectively, that formula Differentiates the mapped stream channel by altitude loss over distance. dA/dL (If I recall correctly, you then graph the gradient / length, and apart from in upper reaches tumbling off mountains and known waterfalls, look for odd breaks in the generally smooth curve that becomes practically asymptotic to sea-level.) 

' 

In my kitchen is a  coffee-mug someone had abandoned at work, with a design commemorating the (18?)C English mathematician George Green. It bears an equation quoted from his work. I would love to know what it does, and what practical purposes it might serve. It could be that like Matrices, it lay waiting for future mathematicians to give it Something Useful to Do.

I am not sure if I can insert it here or what will happen to the formatting, but I'll try:

ʃdxdydzUδV + ʃdσU dV/dw - 4 πU’’ = ʃdxdydzVδU + ʃdσV dU/dw - 4 πV’ ….. (3’)

Hmmm. Sort of worked, though the integral signs are a bit stunted.

So, what does it do? I will hazard a guess....

Clearly, it equates one sum of two integrals and a negative pi term, to another, with one side sort of mirroring the other.
It uses all three dimensions, shown by (x, y, z).
I guess V and U mean Volume and Area (so why U, not A?), presumably of solids bounded in all directions by regular equations.
I cannot guess what the "w" is - and it may be a lower-case Omega altered by the font.
The 4pi terms do something Very Important, obviously...

So......

I wonder if we are analysing Solids of Revolution here, by reference to the [4.pi], as in the sphere's 1/3(4.pi.R^3).

I do not know what Mr Green was telling us here, and anyway it's just one line (Eqn.3) from a complete study, but it does intrigue me!


Rosie, on her own bit of AnswerMug, asks whence the abilities of orchestral composers. I wonder likewise, on the abilities of mathematicians!     

    

 

(she took the relevant driving-lessons driving lessons her HGV licence license)

All right, I'll accept the deleted hyphen, but the spelling is correct - L-I-C-E-N-C-E - in my country!

The 'S' is used in the verb form - "licensing". 

Anyway the topic is Mathematics (abbr. maths here), not English Language! :-)

 

  Good points, the differences in spelling based on countries. I had not taken into consideration that you are not here in the US. 

  For me, anything written in the English language is always about the English language; the two cannot ever be separated one from the other. 

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Thank you!

I see your point,  but as Livvie was describing a course, I was referring to the academic subject called "English Language" rather than an everyday definition.

 

  You’re welcome. 

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