| Exam Board | OCR |
|---|---|
| Module | FP3 (Further Pure Mathematics 3) |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Groups |
| Type | Non-group structures |
| Difficulty | Standard +0.8 This is an FP3 group theory question requiring understanding of group axioms (closure, associativity, identity, inverses) and counterexample construction. While showing non-commutativity is straightforward, proving associativity requires careful algebraic manipulation with absolute values and cases, and systematically checking all group properties demands mathematical maturity beyond standard A-level. The multi-part structure and abstract algebra content place it moderately above average difficulty. |
| Spec | 8.03a Binary operations: and their properties on given sets |
The operation $\circ$ on real numbers is defined by $a \circ b = a|b|$.
\begin{enumerate}[label=(\roman*)]
\item Show that $\circ$ is not commutative. [2]
\item Prove that $\circ$ is associative. [4]
\item Determine whether the set of real numbers, under the operation $\circ$, forms a group. [4]
\end{enumerate}
\hfill \mbox{\textit{OCR FP3 Q6 [10]}}