Please find a sample test here.

Note that question 1 is going to be one of Summer 2011 Question 2(a), Summer 2009 Question 6(b)(i) or 6(b)(ii). Question 2 will be taken from the other exam questions that we have done in class or have set as exercises (The only thing that’ll change is the constants will be different for Tests A and B). Question 3 will be a graph question.

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February 17, 2012 at 3:06 pm

Student 1I’m a little confused about what are the right theorems for question 1. I was just wondering could you clarify if my answers are right. For the question on motivation do you use the theorem on summer 2011 Q.2 (a) from the webpage? For the Q.1 on the sample test do you use the therorm on the bottom of page 12 or the theorem on the top of page 13?

February 17, 2012 at 3:15 pm

J.P. McCarthyYes, http://irishjip.wordpress.com/2012/02/03/ms3011-week-5/ is the best place to look at a motivation for the logistic equation.

Q. 1 on the sample test is the top of page 13.

J.P.

February 17, 2012 at 3:09 pm

Student 2Can you justify why It seems to be a result used on bottom of page 12 in your notes and again at top of page 13.

February 17, 2012 at 3:21 pm

J.P. McCarthymeans that the function is iterated times; e.g. . Therefore is the function iterated times (and applied to ):

.

We get exactly the same thing by iterating the function times:

,

and then iterating another times:

.

In other words iterating times is the same as iterating times, and then times. e.g

.

J.P.