IKMC 2005 - Grades 9-10 - Self-study

Question 1

1. 22
2. 28
3. 24
4. 32
5. 13

Question 2

1. 50
2. 75
3. 99
4. 100
5. 101

Question 3

There are eight kangaroos in the cells of the table. Any kangaroo can jump into any free cell. Find the least number which have to jump into another cell so that exactly two kangaroos remain in every row and column.

1. 0
2. 1
3. 2
4. 3
5. 4

Question 4

1. 10
2. 12
3. 14
4. 11
5. 18

Question 5

1. 160
2. 216
3. 240
4. 288
5. 320

Question 6

The five circles have the same radius and touch as shown. The small square joins the centres of the four outer circles. What is the ratio of the area of the shaded parts of the five circles to their unshaded parts?

1. 1 : 3
2. 1 : 4
3. 2 : 5
4. 2 : 3
5. 5 : 4

Question 7

1. 20%
2. 30%
3. 40%
4. 50%
5. 60%

Question 8

There are seven squares in the picture, including small and big. How many more triangles than squares are there?

1. 1
2. 2
3. 3
4. 4
5. The same quantity

Question 9

Which of the following cubes could be made from the net shown?

Question 10

A mother kangaroo and her baby Jumpy go around a stadium of perimeter 330 m. Both make one jump per second; the mother jumps 5 m and Jumpy 2 m. They start at the same point in the same direction. After 25 seconds Jumpy stops while his mother continues. How long is it until she is next to Jumpy again?

1. 15 sec
2. 24 sec
3. 51 sec
4. 66 sec
5. 76 sec

Question 11

Three semicircles have radius 2 cm. Points A and B lie directly above the centres E and F of the two lower semicircles. What is the area of the shaded region, in square centimetres?

1. $2\pi$
2. 7
3. $2\pi+1$
4. 8
5. $2\pi+2$

Question 12

1. 3 : 1
2. 6 : 1
3. 11 : 4
4. 5 : 1
5. 8 : 1

Question 13

What is the sum of the ten angles marked in the picture?

1. $300^\circ$
2. $450^\circ$
3. $360^\circ$
4. $600^\circ$
5. $720^\circ$

Question 14

1. 16
2. 23
3. 136
4. 156
5. 256

Question 15

Each of the two pieces of wire consists of eight segments of length 1. One is placed over the other so that they partly coincide. What is the largest possible length of their common part?

1. 1
2. 3
3. 4
4. 5
5. 7

Question 16

A 24 m by 1 m rectangle is cut into seven rectangles of width 1 m: four of length 4 m, two of length 3 m, and one of length 2 m. They are reassembled into another rectangle. What is its smallest possible perimeter?

1. 14 m
2. 20 m
3. 22 m
4. 25 m
5. 28 m

Question 17

1. 21:30
2. 21:50
3. 22:00
4. 22:10
5. 22:30

Question 18

What is the diameter of the circle in the picture?

1. 18 cm
2. 12 cm
3. 10 cm
4. 12.5 cm
5. 14 cm

Question 19

What is the starting number (?) in the displayed calculation chain?

1. 18
2. 24
3. 30
4. 40
5. 42

Question 20

1. 1
2. 2
3. 3
4. 4
5. 5