Hey guys these are my suggested solutions to the math methods exam 1. I apologize if there are any errors present as I was attempting to finish the paper and upload it before students left the examination room. However, I was delayed in receiving the paper
I'll be checking over my solutions in due time and then heading back to study for my own exams. If you find any errors please post below and I'll fix them and re-upload the file.
Hope you all did well and met your expectations and best of luck for the second exam tomorrow!
p.s. Sorry for shit photos, I'll fix that up and upload a better quality version
Edit: File is too big to attach so;
Download from here: http://www.mediafire.com/?896dl1meygz5yjg*The only error I can find is that I wrote "maxe", I assume I was going for "max"
Summary of answers:1.a)
))
(expanded or factorised is fine)
b)
 = 6e^9)
(
 = 2xe^{x^2})
)
2. An antiderivative is
^4})
(other forms such as
^4})
are also acceptable as is any answer with a constant added to it such as 1, 2, -7, 24, 55, 18905790 etc.)
3.
 = \frac{1}{2\pi}(3 - \cos(2\pi x)))
(expanded or factorised is fine)
4.
5.a)
b)
6.
(I imagine answers such as
will not be accepted, sorry (could be wrong))
7. a) By equating
 = 1)
you should find that
are solutions.
b) i.
 = \sum x \text{Pr}(X=x) = \frac{28}{15})
ii.
) = \frac{8}{15})
8.
 = 2 - \frac{4}{\pi})
9. a)
b) Left end point = (-2,8), right end point = (2,2)
c) i.
ii. Domain = [-3,1]
10. a)
b)
, occurs at
c)
-3\right))
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