IKMC 2010 - Grades 5-6 - Self-study

Question 1

1. 2
2. 3
3. 4
4. 6

Question 2

The number 4 is next to two mirrors, so it reflects twice as shown. When the same thing happens to 5, what replaces the question mark?

Question 3

Kalim goes directly from Zoo to School and counts every flower on his way. Which number cannot be his result?

“Directly” means choosing a forward branch at each fork, without turning back.

1. 9
2. 10
3. 11
4. 12

Question 4

1. 13
2. 11
3. 12
4. 10

Question 5

Adil has connected every upper point to every lower point. How many lines has he drawn?

1. 20
2. 25
3. 30
4. 35

Question 6

1. 3 cats
2. 4 cats
3. 5 cats
4. 6 cats

Question 7

Seven bars lie in the box. By sliding the bars, space can be made for one more identical bar. At least how many bars must be moved?

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

Question 8

A square sheet has a grey upper side and a white lower side. Sadia divides it into nine little squares. Along which numbered lines should she cut?

The required folded result is the second original diagram.

1. 1,3,5 and 7
2. 2,4,6 and 8
3. 2,3,5 and 6
4. 3,4,6 and 7

Question 9

What is the perimeter of the figure, whose angles are all right angles?

1. $3\times5+8\times2$
2. $6\times5+4\times2$
3. $6\times5+6\times2$
4. $6\times5+8\times2$

Question 10

1. $20\div10\times20\times10$
2. $20\times10\times20\div10$
3. $20\times10+10\times20$
4. $20\div10\times20+10$

Question 11

If the given figure is rotated half a turn (180°) about F, the result is:

Question 12

1. 111
2. 722
3. 567
4. 728

Question 13

Write 1,4,7,10,13 in the cross so that the three-number row and three-number column have equal sums. What is the greatest possible sum?

1. 20
2. 21
3. 22
4. 24

Question 14

The picture illustrates $1+3+5+7=4\times4$. What is $1+3+5+7+\cdots+17+19+21$?

1. $10\times10$
2. $11\times11$
3. $12\times12$
4. $13\times13$

Question 15

Esha draws a flower with 5 petals and colours every petal either red or yellow. How many different flowers can she get?

The equality in the source picture shows that flowers related by a rotation count as the same.

1. 7
2. 8
3. 9
4. 10

Question 16

What fraction of the square is shaded?

1. $\frac13$
2. $\frac14$
3. $\frac15$
4. $\frac38$

Question 17

The picture shows a balanced mobile. Neglect the weights of horizontal bars and vertical strings. Its total weight is 112 grams. What is the star’s weight?

1. 7
2. 12
3. 16
4. We cannot know

Question 18

1. 30
2. 12
3. 18
4. 48

Question 19

A jeweller connects identical grommets as in picture 1. Their dimensions are shown in picture 2. How long is a chain of 5 grommets?

1. 20 mm
2. 19 mm
3. 17.5 mm
4. 16 mm

Question 20

Zoha winds some rope around a piece of wood. She rotates the wood as shown by the arrow. Which is the correct back side?

Source note: the original linework is very faint. It is retained; the worked solution includes a labeled connection diagram for clarity.