M1M1 Treasure Hunt

The M1M1 treasure hunt, week 2



Welcome to the 2013-14 M1M1 treasure hunt!


This quiz is not for course credit, but I hope it will be fun. Each week I shall produce a page such as this with a number of questions relating to the course. Entering the correct answers (in any order) will automatically decrypt a message giving a clue to the mystery M1M1 treasure.

The treasure hunt should work on most standard browsers, but you will need to have javascript enabled. Please e-mail me if there are any errors. The encryption algorithm is fairly secure - it is certainly MUCH easier just to answer the questions than to crack it.

Note: The Hunt takes the role of the "starred questions" on the problem sheets for M1M1 - it is intended that you might discuss the questions with your Personal Tutor and/or your peer group tutors.

Type the answer to each question in the box below it - you will be told whether each answer is right or not. When all answers are correct, you will receive the first of the treasure clues.

(1) What is the even part of the function log[1-sin(x)] for |x| < π/2? Simplify your answer if possible.


?

(2) For which values of the constant a is the function x3 +(a-1) x2 + 4 invertible for all x?


?

(3) If f(x) = 1/x, g(x)=1+x and h(x)=x-1, then what is the sum of h[f(g[f(x)])] and f[g(x)]?


?