Edexcel AS Paper 1 — Question 2

Exam BoardEdexcel
ModuleAS Paper 1 (AS Paper 1)
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicProof
TypeCounter example to disprove statement
DifficultyEasy -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.
Spec1.01c Disproof by counter example

Use a counter example to show that the following statement is false. "\(n^2 - n + 5\) is a prime number, for \(2 \leq n \leq 6\)"

AnswerMarks Guidance
\(n = 5\) is a counterexample: \(5^2 - 5 + 5 = 25\) which is not primeM1, 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}}