OCR MEI C1 — Question 9 2 marks

Exam BoardOCR MEI
ModuleC1 (Core Mathematics 1)
Marks2
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicProof
TypeParity and evenness proofs
DifficultyModerate -0.8 This is a straightforward proof requiring students to factor n² + n = n(n+1) and recognize that consecutive integers always include one even number. It's simpler than average A-level questions as it only requires basic algebraic manipulation and a single conceptual insight about parity, typical of early proof questions in C1.
Spec1.01a Proof: structure of mathematical proof and logical steps

\(n\) is a positive integer. Show that \(n^2 + n\) is always even. [2]

Question 9:
AnswerMarks
9n (n + 1) seen
= odd × even and/or even × odd
AnswerMarks
= evenM1
A1or B1 for n odd ⇒ n2 odd, and
comment eg odd + odd = even
B1 for n even⇒ n2 even, and
comment eg even + even = even
allow A1 for ‘any number
multiplied by the consecutive
AnswerMarks
number is even’2
Question 9:
9 | n (n + 1) seen
= odd × even and/or even × odd
= even | M1
A1 | or B1 for n odd ⇒ n2 odd, and
comment eg odd + odd = even
B1 for n even⇒ n2 even, and
comment eg even + even = even
allow A1 for ‘any number
multiplied by the consecutive
number is even’ | 2
$n$ is a positive integer. Show that $n^2 + n$ is always even. [2]

\hfill \mbox{\textit{OCR MEI C1  Q9 [2]}}