Variables

Ejercicios.

1) A game is played with tokens according to the following rules. In each round, the player with the most tokens gives one tokento each of the other players and also places one token into a discard pile. The game ends wend some player runs out of tokens. Players A, B, and Cstart with 15, 14 and 13 tokens respectively. How many rounds will there be in the game?

A) 36 (B) 37 (C) 38 (D) 39 (E) 402) A sequence of three real numbers forms an arithmetic progression with a first term of 9. If 2 is added to the second term and 20 is addedto the third term, the three resulting numbers form a geometric progression. What is the possible value for the third term in the geometricprogression?

A) 1 (B) 4 (C) 36 (D) 49 (E) 81

3) A plane contains points A and B with AB=1. Let S be the union of all disksof radius 1 in the plane that cover AB. What is the area of S?

(A) [pic] (B) [pic] (C) [pic] (D)[pic] (E) [pic]4) In ∆ABC, let D, E, and F be points on sides BC, CA and AB respectively, so that the segments AD, BE and CF are concurrent at point P. If AF: FB= 4 : 5 and the ratio of the area of ∆ APB to that of ∆ APC is 1 : 2, determine AE : AC.

Respuesta: 2 : 7

5) The perimeter of aright triangle is 90 cm. The squares of the lengths of its sides sum up to 3362 [pic]. What is the area of the triangle?

Respuesta: 180[pic]