Puzzle 1
Criticise the following statement:

Since ln x2 = 2 ln x,
the graph of y = ln x2
can be found by doubling
all co-ordinates of points
on the graph of y = ln x.

Puzzle 2
As a part of a psychological experiment, a group of students took an exam on material they had studied in a mathematics course. At monthly intervals thereafter they were given equivalent exams. After t month, the average score S of the group was found to be given by S = 78 - 55 log(t + 1). What was the average score (i) when they took the original exam and (ii) 9 month later? (iii) When will the group have forgotten everything they learned?