IKMC 2024 - Grades 5-6 - Self-study

Question 1

Kangaroo Joey starts in the bottom-left square of the maze. The number of arrows gives the length of the jump in their direction: three arrows mean jumping over two squares and landing in the third. Where will Joey leave the maze?

1. A
2. B
3. C
4. D
5. Joey cannot leave anywhere.

Question 2

The footprints show the first jumps of a hopscotch pattern: left foot, right foot or both feet as drawn. Mia starts with both feet in square 1 and repeats the pattern in the arrow direction. In which listed square may she land with her right foot only?

1. Square 10
2. Square 1
3. Square 20
4. Square 22
5. Square 23

Question 3

Dina has placed three building blocks behind a wall. The front view is shown. What does the arrangement look like from behind?

Question 4

Mona wants to draw the figure without lifting her pen. The segment lengths are given. She may start anywhere and retrace segments. What is the minimum distance her pen must travel?

1. 6 cm
2. 7 cm
3. 8 cm
4. 9 cm
5. 10 cm

Question 5

Pieter has a 445 g parcel and the eight weights shown. He puts the parcel on the right pan. Weights may go on either pan. What is the minimum number of weights needed to balance the scale?

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

Question 6

Werner has a transparent circular sheet with holes and lines. He folds it along the dashed line. What does the folded sheet look like?

Question 7

Two children are flying their kites. Which picture fits the gap so that each child is holding one kite?

Question 8

There are eight boxes on a lorry (see picture). A worker cannot pick up a box with another box lying on top. He puts each box on the floor or on another box and touches each box only once. Which tower cannot he build?

Source note: the printed sentence says “eight”, but the diagram and options show the six labelled boxes A–F. Use the illustrated boxes.

Question 9

Pia writes a number in each of the 16 circles. Neighbouring numbers differ by 1. One number is 5 and another is 13. How many different numbers does she write?

1. 9
2. 10
3. 13
4. 14
5. 16

Question 10

The picture is 45 cm wide and 30 cm high and consists of identical rectangles. What is the area of one rectangle?

1. 24 cm²
2. 27 cm²
3. 30 cm²
4. 33 cm²
5. 36 cm²

Question 11

1. 25
2. 26
3. 34
4. 35
5. 41

Question 12

Christian cuts four grey corner squares out of a large square. The remaining white shape has half the area of the large square. The small-square side lengths are shown. What is the perimeter of the white shape?

1. 36
2. 40
3. 44
4. 48
5. 52

Question 13

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

Question 14

Simon has four cups with matching saucers. He puts a randomly chosen cup on each saucer. Which statement is definitely true?

1. Certainly no cup matches.
2. Certainly exactly one cup matches.
3. Exactly two matches are impossible.
4. Exactly three matches are impossible.
5. Four matches are impossible.

Question 15

Four rectangles touch as shown. What is the area of the rectangle with the question mark?

1. 12 cm²
2. 14 cm²
3. 16 cm²
4. 18 cm²
5. 20 cm²

Question 16

Braille represents numbers and letters with up to six tactile dots, shown black. The codes for digits 0–9 are shown. How many two-digit numbers have exactly four black dots?

1. 11
2. 12
3. 21
4. 22
5. 23

Question 17

The two large squares have equal area. In the left square the dots bisect the sides; in the right they divide the sides into thirds. The four grey parts on the left total 9 cm². What is the total grey area on the right?

1. 4 cm²
2. 8 cm²
3. 9 cm²
4. 10 cm²
5. 12 cm²

Question 18

Annie puts the numbers 1 to 10 in the ten circles, each once. Each line of four circles must sum to 23. Which number must go in the question-mark circle?

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

Question 19

The map shows seven subway lines; circles are stations. Lines with a common station need different colours. What is the minimum number of colours?

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

Question 20

Dimitri folds the net into a cube. At each shared edge, the triangles next to one another must have the same colour. How must he colour the white square?