Hi,
More examples for students' reference :)
Example 6:
Find the set of values of x for which a certain
inequality is to be solved.
The student writes the answer as x > a [not meeting
the question's requirement].
Example 7:
Suppose the result to be shown by induction is
sum {r = 1 to n} (r + 1) / (2^r) = 3 - (n + 3)(1/2)^n
and the student is attempting to prove that a proposition
is true for n = k + 1.
He writes
sum {r = 1 to k + 1} (r + 1)/(2^r)
= 3 - (k + 3)(1/2)^k + (k + 2) / (2^(k + 1))
= 3 - (1/2)^k [ (k + 3) + (k + 2)/2 ],
thereby making the negative sign error.
Example 8:
The function f is defined by f : x -> ..., x <
a.
The student is asked to find the inverse of f in a
similar form and writes his answer as
f(x) = ... [not meeting the question's requirement].
Example 9:
A question about vectors asks the student to find the
coordinates of the point F which is the foot of a perpendicular of
a point to the plane. He writes the answer in column vector form
[not meeting the question's requirement].
Example 10:
Refer to Q8 in 2010 H2 Maths exam paper 2. The student
goes on to find the number of ways, rather than giving the answer
as a probability.
Thanks.
Cheers,
Wen Shih