IKMC 2022 - Grades 5-6 - Self-study

Question 1

Six points are numbered as shown. Kirsten draws one triangle joining the even-numbered points and another joining the odd-numbered points. She colours one red and the other green. Which option shows her picture?

Question 2

Eileen rowed around five buoys, as shown. Which buoys did she row around in an anticlockwise direction?

1. 1 and 4
2. 2, 3 and 5
3. 2 and 3
4. 1, 4 and 5
5. 1 and 3

Question 3

Laser beams reflect in mirrors as shown in the example. At which letter will the laser beam in the larger picture end?

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

Question 4

Cistercian numerals were used in the early thirteenth century. Any integer from 1 to 99 can be represented by a single glyph combining the shown units and tens glyphs. The examples show 24, 81 and 93. What does the glyph for 45 look like?

Question 5

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

Question 6

ABCD is a square with side-length 10 cm. What is the area of the shaded part?

1. $40\text{ cm}^2$
2. $45\text{ cm}^2$
3. $50\text{ cm}^2$
4. $55\text{ cm}^2$
5. $60\text{ cm}^2$

Question 7

In the garage shown, vehicles can only move forward or backward and cannot turn. What is the smallest number of vehicles that have to move for the black car to be able to exit?

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

Question 8

Giulia has one long string of spaghetti. Every time she breaks one piece, it becomes three pieces as shown. Which number of pieces could she not get?

1. 13
2. 17
3. 20
4. 23
5. 25

Question 9

Bodil rearranges the seven pieces shown to make the smallest possible 12-digit number. What are the last three digits of this number?

1. 699
2. 113
3. 551
4. 967
5. 459

Question 10

Which of the following fractions of a whole turn should the Ferris wheel turn to bring a white pod to the top?

1. $\frac12$
2. $\frac13$
3. $\frac16$
4. $\frac1{12}$
5. $\frac56$

Question 11

Five big elephants and four small ones walk along a path as shown. At the junction, each turns left or right. Which option cannot show the situation after all have passed the junction?

Question 12

Clara starts with 12 and follows the arrows using the rules shown on the left. What number will she finish with? Rules: left ÷2, right ×2, down ×4, up ÷4.

1. 3
2. 6
3. 12
4. 24
5. 48

Question 13

Masoud and his friends built the number 2022 from 66 cubes, as shown. They painted the whole surface of the structure yellow. How many cubes have exactly four faces painted?

1. 16
2. 30
3. 46
4. 54
5. 60

Question 14

A rectangular water tank measures 1 m × 2 m × 4 m. The water is initially 25 cm deep, as in the left picture. The tank is turned so that a 1 m × 2 m face becomes its base. What is the new water depth?

1. 25 cm
2. 50 cm
3. 75 cm
4. 1 m
5. 1.25 m

Question 15

The picture shows transparent paper with a design. It is folded twice, as shown. What will be seen on the folded paper?

Question 16

The square has area 100 square centimetres. What is the area of the shaded figure?

1. $20\text{ cm}^2$
2. $25\text{ cm}^2$
3. $30\text{ cm}^2$
4. $35\text{ cm}^2$
5. $40\text{ cm}^2$

Question 17

1. 18
2. 20
3. 22
4. 23
5. 134

Question 18

Andrew wants each row, each column and each set of four circles connected by line segments to contain 1, 2, 3 and 4. What number belongs in the circle with the question mark?

1. 1
2. 2
3. 3
4. 4
5. It cannot be determined

Question 19

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

Question 20

Jessi writes 3, 4, 5, 6, 7, 8 and 9 in the seven circles so that the three numbers on each line have the same sum. What is the largest possible sum on a line?

1. 28
2. 18
3. 22
4. 16
5. 20