Easy -1.8 This is a straightforward question requiring only substitution of small integer values (n=2,3,4,5,6) into the expression and checking if any result is composite. Finding that n=5 gives 25=5² is immediate and requires no problem-solving insight, just basic arithmetic and recognition of what 'prime' means.
\(n = 5\) is a counterexample: \(5^2 - 5 + 5 = 25\) which is not prime
M1, A1
Tries at least one value in the interval; States that when \(n = 5\) it is false and provides evidence
$n = 5$ is a counterexample: $5^2 - 5 + 5 = 25$ which is not prime | M1, A1 | Tries at least one value in the interval; States that when $n = 5$ it is false and provides evidence
Use a counter example to show that the following statement is false.
"$n^2 - n + 5$ is a prime number, for $2 \leq n \leq 6$"
\hfill \mbox{\textit{Edexcel AS Paper 1 Q2}}