2014 Mathematical Methods Exam 1 Paper + Solutions

[chuck981996]

Attached is the 2014 Mathematical Methods Exam 1 Paper and my handwritten solutions. They are error free, in my opinion and the opinion of several of my teachers, except I would note that the graph should go through the point (1,2) (sorry!).

Good luck for tomorrow everyone! Remember, when it gets tough: Pen Down. Breathe. Think.

-Charlie

[Dreamweaver]

Hi, can someone explain why its 12- antidiff please?

[Phy124]

Firstly, form a square bounded by and . Now the area enclosed between the line and the function is equal to the area of this square minus the area between the x axis and the function over the interval . The area of the square is given by 3 x 4 = 12 so we have:



You could otherwise look at by taking the integral of the upper curve (y=4) minus the lower curve (the function f) over the same interval i.e.



Which if you split up straight away would be , the same as the other method!

If instead you were wondering why we bounded it to rather than (and as such had 12 rather than 16) it is because the area in the interval is not bounded as there is no line along .