QP-202010-Further Mathematics-UFD2-Local · Question 4

Question Text:
4 The connected planar graph P is Eulerian and has at least one vertex of degree x. Some of the properties of P are shown in the table below. Number of vertices Number of edges Number of faces 3x þ 6 x2 þ 8x 2x2 þ 2 Deduce the value of x. Fully justify your answer. [4 marks] _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ box Jun20/7366/2D (06) DO NOT WRITE ON THIS PAGE ANSWER IN THE SPACES PROVIDED 7 Turn over for the next question Do not write outside the box Jun20/7366/2D Turn over s (07) 8 Do not write outside the