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IKMC 2019 - Grades 5-6 - Self-study

Question 1

Carrie has started to draw a cat. She finishes her drawing by adding more colour. Which of the figures below can be her drawing?

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Question 2

The Mayan people wrote numbers with dots and bars. A dot is written for 1 and a bar for 5. How did they write 17?
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Question 3

A digital clock shows the time 20:19. What will the clock show the next time it uses the same digits?

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Question 4

There are 14 girls and 12 boys in a kindergarten. If half of the children go for a walk, at least how many of them are girls?
  1. 5
  2. 4
  3. 3
  4. 2
  5. 1

Question 5

The sum of the dots on opposite faces of an ordinary dice is equal to 7. Which of the following shows the ordinary one?
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Question 6

Which of the following geometric figures is not in this design?

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    triangle
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    square
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    regular hexagon
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    regular octagon
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    regular dodecagon

Question 7

Laura wants to colour a 2 × 2 square of this figure. How many possibilities are there?

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  1. 5
  2. 6
  3. 7
  4. 8
  5. 9

Question 8

The 6 smallest odd natural numbers are written on the faces of a dice. Toni throws it three times and adds the results. Which of the following numbers cannot be the sum?
  1. 21
  2. 3
  3. 20
  4. 19
  5. 29

Question 9

The sum of the ages of a group of kangaroos is 36 years. In two years time the sum of their ages will be 60 years. How many kangaroos are in that group?
  1. 10
  2. 12
  3. 15
  4. 20
  5. 24

Question 10

Michael paints the following buildings made up of identical cubes. Their bases are made of 8 cubes. Which building needs the most paint?
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Question 11

On each of three pieces of paper a three digit number is written. Two of the digits are covered. The sum of the three numbers is 826. What is the sum of the two covered digits?

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  1. 7
  2. 8
  3. 9
  4. 10
  5. 11

Question 12

Riri the frog usually eats 5 spiders a day. When Riri is very hungry, she eats 10 spiders a day. She ate 60 spiders in 9 days. How many days was she very hungry?
  1. 1
  2. 2
  3. 3
  4. 6
  5. 9

Question 13

Ria plays with a yardstick consisting of 10 sticks (see picture). Which of the following figures cannot be formed with this yardstick?

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Question 14

Five equal squares are divided into smaller squares. Which square has the largest black area?
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Question 15

A big triangle is divided into equilateral triangles as in the figure. The side of the small gray triangle is 1 m. What is the perimeter of the big triangle?

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  1. 15 m
  2. 17 m
  3. 18 m
  4. 20 m
  5. 21 m

Question 16

In the garden of a witch there are 30 animals: dogs, cats and mice. The witch turns 6 dogs into cats. Then she turns 5 cats into mice. Now her garden has the same number of dogs, cats and mice. How many cats were there at the beginning?
  1. 4
  2. 5
  3. 9
  4. 10
  5. 11

Question 17

With blocks of dimension 1 cm × 1 cm × 2 cm, you can build towers as shown in the picture. How high is a tower that is built in the same way with 28 blocks?

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  1. 9 cm
  2. 11 cm
  3. 12 cm
  4. 14 cm
  5. 17 cm

Question 18

Ali Baba and 40 thieves equally divided 42 identical bags of gold coins. Each of them got one full bag and 2 coins. How many coins did a bag contain?
  1. 42
  2. 81
  3. 82
  4. 84
  5. 41

Question 19

Alex, Bob and Carl go for a walk every day. If Alex doesn't wear a hat, then Bob wears a hat. If Bob doesn't wear a hat, then Carl wears a hat. Today Bob is not wearing a hat. Who is wearing a hat?
  1. Both Alex and Carl
  2. Only Alex
  3. Only Carl
  4. Neither Alex, nor Carl
  5. It is not possible to determine.

Question 20

The cardboard is folded into a 2 × 1 × 1 box. Which picture does NOT show this box?

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