By Malcom Swan
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Content material: bankruptcy 1 easy ideas (pages 21–43): bankruptcy 2 timber (pages 45–69): bankruptcy three colours (pages 71–82): bankruptcy four Directed Graphs (pages 83–96): bankruptcy five seek Algorithms (pages 97–118): bankruptcy 6 optimum Paths (pages 119–147): bankruptcy 7 Matchings (pages 149–172): bankruptcy eight Flows (pages 173–195): bankruptcy nine Euler excursions (pages 197–213): bankruptcy 10 Hamilton Cycles (pages 26–236): bankruptcy eleven Planar Representations (pages 237–245): bankruptcy 12 issues of reviews (pages 247–259): bankruptcy A Expression of Algorithms (pages 261–265): bankruptcy B Bases of Complexity idea (pages 267–276):
Within the spectrum of arithmetic, graph conception which reports a mathe matical constitution on a suite of parts with a binary relation, as a famous self-discipline, is a relative newcomer. In contemporary 3 many years the interesting and speedily starting to be region of the topic abounds with new mathematical devel opments and important purposes to real-world difficulties.
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Extra resources for The Language of Functions and Graphs An Examination Module for Secondary Schools
Who was making a local call? Again, explain. • Which people were dialling roughly the same distance? Explain. • Copy the graph and mark other point which how people making local calls of different durations. • If you made a similar graph showing every phone call made in Britain during one particular week-end, what would it look like? Draw a ketch, and clearly state any assumptions you make. • Copy the graph below. On each graph, mark and label two points to represent A and B. A"LS;"L Crui ing peed 3.
5) and ending at (45,1). However, since it is not "concave downwards", she was awarded 2 marks out of the possible 3. Mark 3 Radius of tape on left hand spool (em) 2 1 o 10 20 30 40 50 Time (minutes) Mark's sketch is a "concave downwards" curve, but does not end at (45,1). He was also awarded 2 marks for this section. he. /) O--A? ~ ~ v... - ~iv-':> t;ba. con SI-CLfl CJ' \rlcJ'd spool. J ~ tA- ~; II 5~ ~s ~~~C-~ ~ s~ t- . Julie /he r-I'§I-Y h=nd at: h:9 h 0. hOU3 h +-h
She was awarded 3 marks for these. Wendy does not, however, obtain any "commentary" marks, since she has described each athlete's run separately, rather than giving a commentary on the race as a whole. 45 THE CASSETTE TAPE r::71 I;: H >1 This diagram represents a cassette recorder just as it is beginning to playa tape. The tape passes the "head" (Labelled H) at a constant speed and the tape is wound from the left hand spool on to the right hand spool. 5 cm. The tape lasts 45 minutes. (i) Sketch a graph to show how the length of the tape on the left hand spool changes with time.
The Language of Functions and Graphs An Examination Module for Secondary Schools by Malcom Swan