IKMC 2025 - Grades 7-8 - Set 2 - Self-study

Question 1

Lisa has four wooden digits. She can use them to form the number 2025. Which of the following numbers is the largest she can form with these digits?

1. 2502
2. 5202
3. 5220
4. 5502
5. 5520

Question 2

Isabelle rotates the hexagonal sheet of paper, as shown. Each rotation turns the hexagon through the same angle in the same direction. The figure shows the result of one rotation. Which of these numbers of rotations would leave the sheet looking the same as it did at the start?

1. 7
2. 8
3. 9
4. 10
5. 12

Question 3

Question 4

The regular hexagon shown is divided into many triangles of equal area. Which fraction of the hexagon is shaded?

1. $\frac12$
2. $\frac13$
3. $\frac14$
4. $\frac15$
5. $\frac16$

Question 5

1. 60
2. 24
3. 12
4. 10
5. 6

Question 6

1. 26
2. 27
3. 28
4. 29
5. 30

Question 7

Ohad wants to write the four digits 2, 0, 2 and 5 in the four boxes of the calculation shown. What is the smallest result that Ohad could get?

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

Question 8

1. 0
2. 5
3. 15
4. 20
5. 25

Question 9

Five circles, each with an area of $8\,\mathrm{cm}^2$, overlap to form the figure shown. The area of each section where two circles overlap is $1\,\mathrm{cm}^2$. What is the total area covered by the figure?

1. $32\,\mathrm{cm}^2$
2. $36\,\mathrm{cm}^2$
3. $38\,\mathrm{cm}^2$
4. $39\,\mathrm{cm}^2$
5. $42\,\mathrm{cm}^2$

Question 10

The real combination for the bicycle lock shown in the picture is 0000. However, when someone looks at it from the side, they see 8888. When Paul looks at the combination of his friend’s lock from the side, he sees 2815. What is the real combination of his friend’s lock?

1. 4037
2. 4693
3. 0639
4. 0693
5. 9603

Question 11

Matjaz the mouse wants to get to a piece of cheese. He can only move horizontally or vertically between any two cells in the directions shown by the arrows. How many different routes can Matjaz take to reach a piece of cheese?

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

Question 12

1. 16 m
2. 14 m
3. 12 m
4. 10 m
5. 8 m

Question 13

Edgar wants to write a number in each circle in the diagram. He wants each number to be equal to the sum of the numbers in the two adjacent circles. He has already written two numbers, as shown. What number should he write in the grey circle?

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

Question 14

Louise places three rectangular pictures in the way shown. What is the value of $x$?

1. 64
2. 70
3. 72
4. 76
5. 80

Question 15

Werner is on a treadmill in the gym. He keeps looking at two stopwatches. The first shows the time elapsed since he started his session and the second the time remaining until the end of his session. At some point the two stopwatches show the same reading. What do they show at that point?

1. 17:50
2. 18:00
3. 18:12
4. 18:15
5. 18:20

Question 16

Julia wants to fill each box with a different prime number less than 20 so that the value of $A$ is an integer. What is the maximum value of $A$?

1. 20
2. 14
3. 10
4. 8
5. 6

Question 17

Morten wants to fill in the cells on the diagram shown so that each cell contains either a cross or a circle. He also wants to ensure there is no line of four consecutive identical symbols in any column, row or diagonal. When he has completed the diagram, what will the column coloured grey contain?

1. 3 circles and 3 crosses
2. 2 circles and 4 crosses
3. 4 circles and 2 crosses
4. 5 circles and 1 cross
5. 1 circle and 5 crosses

Question 18

In rectangle $ABCD$, the points $E$ and $F$ are marked on side $DC$, as shown, so that $\angle EBA=\angle DFA=45^\circ$ and $AB+EF=20$ cm. What is the length of $BC$?

1. 4 cm
2. 6 cm
3. 8 cm
4. 10 cm
5. 12 cm

Question 19

1. 6
2. 7
3. 10
4. 11
5. 12

Question 20

Peter has drawn a quarter circle with centre at each corner of a flag with dimensions 12 cm by 9 cm and coloured the region formed, as shown. What is the length indicated by the question mark?

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