OJM SIBIU, 6 martie 2004

Inspectoratul colar Judeean

Sibiu

Olimpiada de Matematic

Faza judeean, 6 martie 2004

Clasa a VI-a

Barem de corectare:1. i)

ii)

2. (1p)

(1p) (1p)

x, y, zN

(2p)

Numai tripletul (1,2,3) verific toate egalitile (2p)

3. i) Fie i (1p)

i sunt prime ntre ele (2p)

ii) (1p)

+

(1p)

(1p)

(1p)

4. Figura (1p)

i) DBE PBE, PBE PBM, PBM PCM (2p)

ii) n perimetrul poligonului sunt cuprinse 2 ipotenuze, 2 catete mici, 2 catete mari, deci (2p)

iii) 1punct pentru urmtoarele observaii :

Traseul C M P E D cost (4 + 3 + 3 + 3) 4 = 9

Traseul C P B D cost (5 + 5 + 5) 5 = 10

Traseul C M B E D cost (4 + 4 + 4 + 3) 4 = 11

Traseul C P E D cost 5 + 3 + 3 = 11

Deci, cel mai ieftin este C M P E D cu 90000 lei (1p)

M

C

B

D

A

P

P

E

_1139914410.unknown

_1139914814.unknown

_1139917425.unknown

_1139997068.unknown

_1139917512.unknown

_1139916724.unknown

_1139917408.unknown

_1139914715.unknown

_1139914774.unknown

_1139914545.unknown

_1139598201.unknown

_1139601316.unknown

_1139602776.unknown

_1139603022.unknown

_1139755332.unknown

_1139757798.unknown

_1139602917.unknown

_1139602073.unknown

_1139602506.unknown

_1139601703.unknown

_1139601895.unknown

_1139598270.unknown

_1139598296.unknown

_1139598228.unknown

_1139597797.unknown

_1139597922.unknown

_1139597611.unknown

_1139597762.unknown