| Exam Board | OCR MEI |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Indices and Surds |
| Type | Expand and simplify surd expressions |
| Difficulty | Easy -1.2 This is a straightforward algebraic manipulation question requiring basic expansion and simplification, followed by simple reasoning about odd/even properties. Part (i) involves routine algebraic skills (expanding brackets, collecting like terms) that are fundamental to C1. Part (ii) requires only elementary number theory reasoning about parity. Both parts are more mechanical than problem-solving oriented, making this easier than a typical A-level question. |
| Spec | 1.02j Manipulate polynomials: expanding, factorising, division, factor theorem |
| Answer | Marks | Guidance |
|---|---|---|
| 3 | (i) | 3n2 + 6n + 5 isw |
| [2] | M1 for a correct expansion of at least one of |
| Answer | Marks | Guidance |
|---|---|---|
| 3 | (ii) | odd numbers with valid explanation |
| [2] | marks dep on 9(i) correct or starting again |
| Answer | Marks |
|---|---|
| B0 for just a few trials and conclusion | accept a full valid argument using odd |
Question 3:
3 | (i) | 3n2 + 6n + 5 isw | B2
[2] | M1 for a correct expansion of at least one of
(n + 1)2 and (n + 2)2
3 | (ii) | odd numbers with valid explanation | B2
[2] | marks dep on 9(i) correct or starting again
for B2 must see at least odd × odd = odd
[for 3n2] (or when n is odd, [3]n2 is odd) and
odd [+ even] + odd = even soi,
condone lack of odd × even = even for 6n;
condone no consideration of n being even
or B2 for deductive argument such as: 6n is
always even [and 5 is odd] so 3n2 must be
odd so n is odd
B1 for odd numbers with a correct partial
explanation or a partially correct
explanation
or B1 for an otherwise fully correct
argument for odd numbers but with
conclusion positive odd numbers or
conclusion negative odd numbers
B0 for just a few trials and conclusion | accept a full valid argument using odd
and even from starting again
Ignore numerical trials or examples in
this part – only a generalised argument
can gain creditYou are given that $n$, $n + 1$ and $n + 2$ are three consecutive integers.
\begin{enumerate}[label=(\roman*)]
\item Expand and simplify $n^2 + (n + 1)^2 + (n + 2)^2$. [2]
\item For what values of $n$ will the sum of the squares of these three consecutive integers be an even number? Give a reason for your answer. [2]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI C1 Q3 [4]}}