Current and active math majors: NCEA test

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Batman

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#203146 19-Sep-2016 18:31

Hi i tried to do the questions and couldn't do a single one. Mind you i don't claim to know math.
But i read head of departments couldn't do the paper.

So my question is: can university math majors or lecturers do the paper?
Can't be that hard, just need to know some formulae to apply ... Right?

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#1635992 19-Sep-2016 18:33

http://m.nzherald.co.nz/nz/news/article.cfm?c_id=1&objectid=11712429

DarthKermit

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#1636017 19-Sep-2016 18:44

Algebra. I remember hating that garbage at school.

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#1636041 19-Sep-2016 19:06

I used to love unlocking those stuff. A bit like puzzles for nerds. But I can tell it serves little purpose to me as obviously i haven't retained a single bit of those math stuff.

Finch

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#1636043 19-Sep-2016 19:08

DarthKermit:

Algebra. I remember hating that garbage at school.

Honestly, why do we even learn it at school. What a massive waste of time.

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#1636048 19-Sep-2016 19:11

I remember thinking the same. It was a dry academic exercise for me. If they'd actually made it more interesting by giving some real world uses for it, that might have been better.

MattikusNZ

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#1636067 19-Sep-2016 19:40

I'll post some answers as I get a chance - just in the middle of the kids bedtime routine (bath / book / etc).

Day 1 MCAT 2016

1ai - the area of a rectangle is x²-x-2, if one side has length x+1 meters, give the second side in terms of x

Rectangle area = length * width

x²-x-2 = length * (x+1)

so length = (x²-x-2)/(x+1)

Or you could continue on with a bit of long division and get (x-2) as the other length - I'm not sure where they're expected to stop in Year 11. I did this through long division, but you can check the result with:

area = length * width

area = (x+1)(x-2)

area= x²-2x+x-2

area = x²-x-2 (which is the area given at the start)

[edit - bit of formatting tidy up, use of the superscript 2, etc)

MattikusNZ

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#1636098 19-Sep-2016 20:11

Quick one before the kids bedtime
1aii - what do you know about the value of x for this rectangle

We have the area of the rectangle as:
area = (x+1)(x-2)

So if x = -1 or x = 2 then the rectangle has an area of 0
One could question how often a rectangle has a length of -1 (how often does any shape have a length of -1?), so I think it would be a fair assessment to say that for this rectangle x>2 which would result in rectangle having an area > 0 (so the rectangle actually has an area).
Though this is an assumption and not fact (it is possible that the rectangle could have a negative area)

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mdf

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#1636101 19-Sep-2016 20:21

I got very distracted by these at lunchtime today. I managed to do most of them (I think) and haven't done maths since 7th form. But I can most certainly see the complaint about the questions being cryptic / a bit of a comprehension exercise. The rectangle one (in particular since it was first up) was a trinomial equation (i.e. algebra) but was phrased totally as a geometry query. I spent a minute or two looking at it totally blankly until I twigged what they were asking.

When I was at school, the "smart" kids did maths. I haven't used it in my professional career or at university since. Contrast the kids in the vocational stream (who I am still mates with) who use pythagoras and trigonometry daily in their trades careers.

zenourn

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#1636104 19-Sep-2016 20:24

PDF copies at http://static.stuff.co.nz/files/exam1.pdf and http://static.stuff.co.nz/files/exam2.pdf

I'm a real-life mathematician - BSc (Hons in mathematics, 1st class). Then did a PhD in Medicine but was basically a lot of mathematics.

Questions are classical algebra along with requirements for logical thinking and that you can actually describe what you are doing and the meaning. It looks like it has been put together by a mix of a classical mathematician as well as reflecting the new mathematics curriculum.

These questions are definitely not any more difficult than when I went through school.

I don't actually use this stuff much at all these days, although there is still value in learning it (the process you learn in attacking a problem). Computers trivially solve these equations and most real-world work is such that you can't solve algebraically anyhow. In applied mathematics now it really is a case that you spend most of your time understanding a problem and writing code.

MattikusNZ

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#1636110 19-Sep-2016 20:37

1b - Hone and Ranee
Effectively this is a word problem - so:
If Ranee gives Hone $20, they have the same amount of money -> R - $20 = H + $20
If Hone gave Ranee $22, Ranee would have twice as much as Hone -> H - $22 = 2(R + $22)

So we can solve this with simultaneous equations (or a matrix if they're taught these?)
R - $20 = H + $20
R = H + $20 + $20
R = H + 40

And substituting this into the second equation:
H - $22 = 2(R + $22)
H - $22 = 2(H + 40 + 22)
H - 22 = 2(H + 62)
H - 22 = 2H + 124
H - 2H = 124 + 22
-H = 146
H = -$146 - so Hone is $146 in debt.

Backfilling for Ranee
R = H + 40
R = -146 + 40
R = -106
So Ranee is $106 in debt

Which seems like a nasty question to ask (especially if they're loaning money to each other)
But to check the numbers, Ranee gives Hone $20, they have the same amount of money
R - $20 = H + $20
-106 - 20 = -146 + 20
-126 = -126 (so this checks out)

If Hone gave Ranee $22, Ranee would have twice as much as Hone
H - 22 = 2( R+ 22 )
-146 - 22 = 2( -106 + 22 )
-168 = 2( -84 )
So Hone would have -$168 and Ranee would have -$84.
-$84 * 2 = -$168 - so this works out too

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#1636113 19-Sep-2016 20:41

Finch:

Honestly, why do we even learn it at school. What a massive waste of time.

Saw this online yesterday, seems apt

vexxxboy

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#1636114 19-Sep-2016 20:42

i asked my son about it, who's finishing a Hons in computer science, 1st class, and he said thats a pretty brutal test and its everything they should know but its like they picked the hardest example for every type of question, not really fair

Common sense is not as common as you think.

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#1636122 19-Sep-2016 20:58

MattikusNZ: 1b - Hone and Ranee
If Hone gave Ranee $22, Ranee would have twice as much as Hone -> H - $22 = 2(R + $22)

I think there's a whoopsie here. If Ranee had twice as much as Hone, its 2(H-22)=R+22 isn't it? i.e. Ranee plus 22 is twice Hone less 22. I don't have my working in front of me, but from memory I had Ranee with $146 and Hone with $106.

MattikusNZ

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#1636124 19-Sep-2016 21:07

Yeah you're right on that - sorry, serves me right for answering on the tablet while putting the kid to bed.
No doubt the Mrs will remind me it's why I shouldn't multitask.

mattwnz

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#1636204 19-Sep-2016 21:57

They looked to be the standard type of questions when I did end of year maths exams at school for school C and the like in the 90s. They don't even look you difficult just basic algebra.Many people used to fail maths when I was at school so it makes me wonder if students these days aren't learning how to put real life situation's to maths.

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