| Exam Board | OCR |
|---|---|
| Module | AS Pure (AS Pure Mathematics) |
| Year | 2017 |
| Session | Specimen |
| Marks | 5 |
| Topic | Proof |
| Type | Counter example to disprove statement |
| Difficulty | Standard +0.3 Part (a) requires listing primes 20-40 and testing a simple arithmetic pattern—straightforward but requires systematic checking. Part (b) is a basic proof by cases (mod 3) with algebraic manipulation, a standard technique at AS level. Both parts are accessible with routine methods, making this slightly easier than average. |
| Spec | 1.01c Disproof by counter example1.01d Proof by contradiction |
\begin{enumerate}[label=(\alph*)]
\item A student suggests that, for any prime number between 20 and 40, when its digits are squared and then added, the sum is an odd number.
For example, 23 has digits 2 and 3 which gives $2^2 + 3^2 = 13$, which is odd.
Show by counter example that this suggestion is false. [2]
\item Prove that the sum of the squares of any three consecutive positive integers cannot be divided by 3. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR AS Pure 2017 Q6 [5]}}