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1 of 8 0-day streak

A full network investigation

DIFFICULTYstandardchallenge
QUESTION TYPEMix of allChange
Five-part investigation; all-even six-vertex networkFive-part investigation; two-odd six-vertex networkNOWMix of allRecommended
Question 1 of 8

Calculator allowed

Consider this plan of water lines between community facilities. The graph is connected and can be drawn in planar form. Each edge label gives the installation cost in dollars

Weighted investigation network. Vertices in listed order: [Garden | Depot | Station | Clinic | School | Pool]. Full edge list: Depot–Garden ($451); Depot–Station ($475); Station–School ($741); Clinic–School ($445); Pool–Station ($493); Garden–Station ($601); Depot–Clinic ($235).$451$475$741$445$493$601$235GardenDepotStationClinicSchoolPool
(a)3 marks

Count the vertices and edges, then use Euler's formula to find the number of faces

(b)1 mark

How many vertices have odd degree?

(c)1 mark

Can every connection be traversed exactly once while returning to the starting vertex? Select the correct verdict and reason

(d)1 mark

Find the shortest total installation cost from Garden to School

(e)1 mark

Find the minimum total installation cost for a set of water lines that reaches every vertex