IKMC 2022 - Grades 5-6 - Set 2 - Self-study

Question 1

Kirsten joins the even-numbered points to make one triangle and the odd-numbered points to make another. She colours one triangle red and the other green. Which option shows her picture?

Question 2

Eileen rows around the five buoys along the shown path, following the arrows. Which buoys does she go around anticlockwise?

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 from mirrors as in the small example. At which letter will the beam in the larger diagram end?

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

Question 4

Cistercian numerals were used in the early thirteenth century. A number from 1 to 99 is written by combining the appropriate unit and tens glyphs shown. Examples for 24, 81 and 93 are also shown. Which glyph represents 45?

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

Vehicles in the garage may move forward or backward but cannot turn. What is the smallest number of vehicles that must move to make it possible for the black car to leave?

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

Question 8

Giulia starts with one long piece of spaghetti. Whenever she breaks a piece, it becomes three pieces. Which number of pieces can she not obtain?

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 its last three digits?

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

Question 10

What fraction 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 elephants walk along the path in the order shown. At the junction each turns left or right. Which situation cannot occur after all have passed?

Question 12

Clara starts with 12 and follows the arrow path, applying the direction rules shown on the left. What number does she finish with?

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

Question 13

Masoud and his friends use 66 cubes to build 2022 as shown. They paint the entire surface yellow. How many cubes have exactly four painted faces?

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

Question 14

A rectangular tank measures 1 m by 2 m by 4 m. Initially its base is 4 m by 2 m and the water is 25 cm deep. It is turned so the 1 m by 2 m face is the base. What is the new water depth?

1. $25\text{ cm}$
2. $50\text{ cm}$
3. $75\text{ cm}$
4. $1\text{ m}$
5. $1.25\text{ m}$

Question 15

The transparent paper has the design shown. It is folded twice along the dashed lines in the indicated directions. 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

Fill the circles so each row, each column and each connected group of four circles contains 1, 2, 3 and 4. What number belongs at the question mark?

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

Question 19

1. $2\text{ kg}$
2. $3\text{ kg}$
3. $4\text{ kg}$
4. $5\text{ kg}$
5. $6\text{ kg}$

Question 20

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

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