| Exam Board | SPS |
|---|---|
| Module | SPS SM Pure (SPS SM Pure) |
| Year | 2023 |
| Session | June |
| Marks | 6 |
| Topic | Proof |
| Type | Contradiction proof of irrationality |
| Difficulty | Standard +0.3 This is a two-part proof question with standard techniques. Part (i) is straightforward algebra using (2n+1)² + (2n+3)² representation. Part (ii) is a textbook proof by contradiction following the standard template for irrationality proofs. Both parts require clear logical reasoning but use well-rehearsed methods with no novel insight needed, making this slightly easier than average. |
| Spec | 1.01a Proof: structure of mathematical proof and logical steps1.01d Proof by contradiction |
\begin{enumerate}[label=(\roman*)]
\item Prove that the sum of the squares of 2 consecutive odd integers is always 2 more than a multiple of 8 [3]
\item Use proof by contradiction to show that $\log_2 5$ is irrational. [3]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM Pure 2023 Q14 [6]}}