Moderate -0.5 This is a straightforward application of Euler's formula (V - E + F = 2) with simple algebraic substitution. While it's a Further Maths topic, the question requires only direct recall and one-step rearrangement: F = 2 - V + E = 2 - x + (2x - 4) = x - 2. The multiple-choice format further reduces difficulty by eliminating the need to verify the answer independently.
2 A connected planar graph has \(x\) vertices and \(2 x - 4\) edges.
Find the number of faces of the planar graph in terms of \(x\).
Circle your answer.
\(x - 6\)
\(x - 2\)
\(6 - x\)
\(2 - x\)
2 A connected planar graph has $x$ vertices and $2 x - 4$ edges.\\
Find the number of faces of the planar graph in terms of $x$.\\
Circle your answer.\\
$x - 6$\\
$x - 2$\\
$6 - x$\\
$2 - x$
\hfill \mbox{\textit{AQA Further AS Paper 2 Discrete Q2 [1]}}