IKMC 2012 - Grades 5-6 - Self-study

Question 1

1. 7
2. 8
3. 9
4. 10
5. 13

Question 2

A blackboard is 6 m wide. The width of the middle part is 3 m. The two other parts have equal width. How wide is the right-hand part?

1. 1 m
2. 1,25 m
3. 1,5 m
4. 1,75 m
5. 2 m

Question 3

Sally can put 4 coins in a square built with 4 matches (see picture). At least how many matches will she need in order to build a square containing 16 coins that do not overlap?

1. 8
2. 10
3. 12
4. 15
5. 16

Question 4

1. 120
2. 138
3. 142
4. 144
5. 150

Question 5

1. 6 o’clock yesterday morning
2. 6 o’clock yesterday evening
3. 12 o’clock yesterday afternoon
4. 12 o’clock midnight
5. 6 o’clock this morning

Question 6

The picture shows a pattern of hexagons. We draw a new pattern by connecting all the midpoints of any neighbouring hexagons. What pattern do we get?

Question 7

1. $(6+3\cdot2)+1$
2. $6+3\cdot2+1$
3. $(6+3)\cdot(2+1)$
4. $(6+3)\cdot2+1$
5. $6+3\cdot(2+1)$

Question 8

The upper coin is rotated without slipping around the fixed lower coin to a position shown on the picture. Which is the resulting relative position of kangaroos?

1. 
2. 
3. 
4. 
5. depends on the rotation speed

Question 9

One balloon can lift a basket containing items weighing at most 80 kg. Two such balloons can lift the same basket containing items weighing at most 180 kg. What is the weight of the basket?

1. 10 kg
2. 20 kg
3. 30 kg
4. 40 kg
5. 50 kg

Question 10

1. 12
2. 13
3. 16
4. 20
5. 21

Question 11

Which three of the numbered puzzle pieces should you add to the picture to complete the square?

1. 1, 3, 4
2. 1, 3, 6
3. 2, 3, 5
4. 2, 3, 6
5. 2, 5, 6

Question 12

Lisa has 8 dice with the letters A, B, C and D, the same letter on all sides of each die. She builds a block with them. Two adjacent dice always have different letters. What letter is on the die that cannot be seen on the picture?

1. A
2. B
3. C
4. D
5. Impossible to say

Question 13

There are five cities in Wonderland. Each pair of cities is connected by one road, either visible or invisible. On the map of Wonderland, there are only seven visible roads, as shown. Alice has magical glasses: when she looks at the map through these glasses she only sees the roads that are otherwise invisible. How many invisible roads can she see?

1. 9
2. 8
3. 7
4. 3
5. 2

Question 14

1. impossible to say
2. red or blue
3. only green
4. only red
5. only blue

Question 15

The perimeter of the figure below, built up of identical squares, is equal to 42 cm. What is the area of the figure?

1. 8 cm²
2. 9 cm²
3. 24 cm²
4. 72 cm²
5. 128 cm²

Question 16

Look at the pictures. Both shapes are formed from the same five pieces. The rectangle measures 5 cm × 10 cm, and the other parts are quarters of two different circles. The difference between the perimeter lengths of the two shapes is

1. 2.5 cm
2. 5 cm
3. 10 cm
4. 20 cm
5. 30 cm

Question 17

Place the numbers from 1 to 7 in the circles, so that the sum of the numbers on each of the indicated lines of three circles is the same. What is the number at the top of the triangle?

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

Question 18

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

Question 19

There are 4 gearwheels on fixed axles next to each other, as shown. The first one has 30 gears, the second one 15, the third one 60 and the last one 10. How many revolutions does the last gearwheel make, when the first one turns through one revolution?

1. 3
2. 4
3. 6
4. 8
5. 9

Question 20

A regular octagon is folded in half exactly three times until a triangle is obtained, as shown. Then the apex is cut off at right angles, as shown in the picture. If the paper is unfolded what will it look like?