BACCALAURÉAT GÉNÉRAL ET TECHNOLOGIQUE SESSION 2009 ÉPREUVE SPÉCIFIQUE MENTION « SECTION EUROPÉENNE OU DE LANGUE ORIENTALE »
Académies de Paris-Créteil-Versailles
Binôme : Anglais / Mathématiques Sujet n° 13 SEQUENCES
The first three diagrams in a sequence are shown above. The diagrams are made up of dots and lines. Each line between two consecutives dots is one centimetre long. (a) Make a sketch of the next diagram in the sequence. (b) The table below shows some information about the diagrams. Diagram n Area (x) Number of dots (y) Number of one centimetre lines (z)
1 1 4 4
2 4 9 12
3 9 …. ….
4 …. …. ….
…. …. …. ….
(i) Complete the empty squares in the table for diagrams 3 and 4. (ii) Write down x and y in terms of n. (iii) Explain why z = 2 n (n + 1) . (c) The total number of one centimetre lines in the first n diagrams is given by the expression 2 3 n + fn 2 + gn . 3 10 (i) Use n = 1 in this expression to show that f + g = . 3 32 (ii) Use n = 2 in this expression to show that 4 f + 2g = . 3 (iii) Find the values of f and g. (iv) Find the total number of one centimetre lines in the first 10 diagrams. Adapted from IGCSE exam, Cambridge University, 2007
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