Math Kangaroo 2012 Sample Questions - Levels 9 & 10

1. The diagram shows an isosceles triangle; M and N are the midpoints of the equal sides. The triangle has been divided into four regions by two straight lines. Three of the regions have areas of 3, 3 and 6, as shown. What is the area of the fourth region?


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A) 3                 B) 4                 C) 5                 D) 6                 E) 7


6. The sum of the digits of a seven-digit number is 6. What is the product of these digits?

 

A) 0                 B) 6                 C) 7                 D) 1 x 2 x 3 x 4 x 5 x 6 x 7              E) 5

 

11. If Adam stands on the table and Mike stands on the floor, then Adam is 80 cm taller than Mike. If Mike stands on the same table and Adam stands on the floor, then Mike is one meter taller than Adam. How high is the table?

 

A) 20 cm         B) 80 cm         C) 90 cm         D) 100 cm       E) 120 cm

 

15. The diagram shows a right triangle with sides 5, 12 and 13. What is the radius of the inscribed semicircle?


Picture 15

 

A) 7/3              B) 10/3            C) 12/3            D) 13/3            E) 17/3

 

24. The last non-zero digit of the number K = 259 x 34 x 553 is

 

A) 1                 B) 2                 C) 4                 D) 6                 E) 9

 

25. Peter creates a Kangaroo game. The diagram shows the board for the game. At the start, the Kangaroo is at the School S. According to the rules of the game, from any position except Home H the Kangaroo can jump to either of the two neighboring positions. When the Kangaroo lands on H the game is over. In how many ways can the Kangaroo move from S to H in exactly 13 jumps?

 

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A) 12               B) 32               C) 64               D) 144             E) 1024