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IKMC 2025 - Grades 5-6 - Set 2 - Self-study

Question 1

Which of the pieces shown completes the pattern?

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Question 2

Anna has built a wall displaying the year 2025. Bella stands on the other side of the wall. What does Bella see?

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Question 3

Mike has a leaflet with numbers and holes in the flaps on both sides, as shown. He folds the right flap along the dotted line and sees 2, 3, 5 and 6 through the holes. He then folds the left flap along the other dotted line. What is the sum of the numbers he can now see?

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  1. 10
  2. 12
  3. 14
  4. 9
  5. 8

Question 4

A cube is decorated by gluing identical grey squares onto it. All faces look the same. How many grey squares are there altogether?

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  1. 30
  2. 18
  3. 16
  4. 15
  5. 14

Question 5

Emil put tomato slices, black olives, chillies, mushrooms and onion rings on a pizza, one topping type at a time. The finished pizza is shown. Which topping did he put on third?

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  1. Tomato slices
  2. Black olives
  3. Chillies
  4. Mushrooms
  5. Onion rings

Question 6

Container A contains 10 litres of water. Its five bottom plugs are removed at the same time, and the water flows out through the illustrated channels. What volume flows into container B?

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

Question 7

Thea rotates a paper hexagon divided into six equal parts. Each rotation moves it clockwise by one part. The starting position and the result of one rotation are shown. What does it look like after eight rotations in total?

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Question 8

Rain has erased some numbers on a burger menu. The burgers are listed in increasing order of price. Which of the following is the price of one of the burgers?

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  1. 4.10
  2. 5.50
  3. 5.60
  4. 6.30
  5. 6.60

Question 9

Six children ran a race. Ariadne finished third. Biel finished sixth, just behind Ernest. Fatima finished between Ariadne and Ernest. Diana overtook Charles just before the finish line. Who won?
  1. Ariadne
  2. Charles
  3. Diana
  4. Ernest
  5. Fatima

Question 10

A bookcase has 17 books on its top shelf, 15 on the middle shelf and 7 on the bottom shelf. Monika wants equal numbers on all three shelves while moving as few books as possible. How many books should she move from the middle shelf to the bottom shelf?

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

Question 11

Three turtles race over 10 kilometres at constant speeds. When the first finishes, the second has covered one quarter of the distance and the third one fifth. How far from the finish will the third turtle be when the second finishes?
  1. 1 km
  2. 2 km
  3. 3 km
  4. 4 km
  5. 5 km

Question 12

Vera replaces the two question-mark blocks with numbered blocks. She wants the number on every block to be at least 2 greater than the number immediately below it. In how many ways can she choose the two numbers?

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

Question 13

Each wheel of fortune is divided into equal sectors. You win if the pointer stops on a shaded sector. Which wheel offers the greatest chance of winning?

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

Question 14

Which shape cannot be placed entirely on the white cells of the large square, even after rotating it?

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Question 15

Five swimmers complete equal relay legs one after another. The stopwatches show the cumulative time after each swimmer finishes. The first swimmer took 2 minutes 8 seconds. Which swimmer took the least time?

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  1. First
  2. Second
  3. Third
  4. Fourth
  5. Fifth

Question 16

Janaína cuts four identical squares from the corners of a square sheet. The removed area totals 16 square centimetres and the remaining cross has area 9 square centimetres. What is the perimeter of the cross, in centimetres?

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  1. 9
  2. 16
  3. 20
  4. 25
  5. 32

Question 17

Each card contains two three-digit numbers, with some digits hidden by ink. Exactly one card can have the same digit sum for its two numbers. Which card is it?
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Question 18

The diagram consists of identical squares. B is halfway between A and C; D is halfway between C and E. Maria wants to split the shape into two equal areas with one straight segment from S. To which point should she join S?

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  1. A
  2. B
  3. C
  4. D
  5. E

Question 19

Hasan fills every cell with 0 or 1 so that each row, each column and each of the two main diagonals has sum 3. One 0 is already given. What is the sum in the four question-mark cells?

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  1. 1
  2. 2
  3. 3
  4. 4
  5. Cannot be determined

Question 20

Mary and Paul each form three three-digit numbers using the digits 1 to 9 exactly once. Each orders the numbers from smallest to largest. Mary makes the middle number as large as possible; Paul makes it as small as possible. What is the difference between their middle numbers?

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  1. 642
  2. 684
  3. 864
  4. 888
  5. None of these