Standard +0.3 This is a straightforward C1 question requiring factorisation by taking out common factors, then recognising the product of three consecutive integers. The divisibility proof follows immediately from the factorisation. Slightly above average difficulty due to the proof element, but the reasoning is direct once factorised.
an induction approach using the factors may also be
used eg by those doing paper FP1 as well;
A0 for just substituting numbers for n and stating
results;
allow SC2 for a correct induction approach using the
original cubic (SC1 for each of showing even and
showing divisible by 3)
Question 4:
4 | n (n + 1)(n + 2)
argument from general consecutive
numbers leading to:
at least one must be even
[exactly] one must be multiple of 3 | M1
A1
A1 | condone division by n and then
(n + 1)(n + 2) seen, or separate factors
shown after factor theorem used;
or divisible by 2;
if M0:
allow SC1 for showing given
expression always even | ignore ‘ = 0’;
an induction approach using the factors may also be
used eg by those doing paper FP1 as well;
A0 for just substituting numbers for n and stating
results;
allow SC2 for a correct induction approach using the
original cubic (SC1 for each of showing even and
showing divisible by 3)