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IKMC 2021 Grade 5-6

Total questions: 24

Worksheet time: 1hrs 10mins

Name
Class
Date
1.

Sofie wants to write the word KENGU by using letters from the boxes. She can only take one letter from each box. What letter must Sofie take from box 4?

a)

K

b)

E

c)

N

d)

G

e)

U

2.

In how many places in the picture are two children holding each other with their left hands?

a)

1

b)

2

c)

3

d)

4

e)

5

3.
a)
b)
c)
d)
e)
4.

Which of the following solid shapes can be made with these 6 bricks?

a)
b)
c)
d)
e)
5.

When the 5 pieces shown are fitted together correctly, the result is a rectangle with a calculation written on it. What is the answer to this calculation?

a)

22

b)

32

c)

41

d)

122

e)

203

6.

A measuring tape is wound around a cylinder. What is the number at the question mark?

a)

53

b)

60

c)

69

d)

77

e)

81

7.

The 5 figures on the grid can only move in the directions indicated by the black arrows. Which figure can leave through gate G?

a)

A

b)

B

c)

C

d)

D

e)

E

8.
a)

Only P

b)

Only Q

c)

Only R

d)

Only P or Q

e)

Any of P, Q and R

9.

Carin is going to paint the walls in her room green. The green paint is too dark so she mixes it with white paint. She tries different mixtures. Which of the following mixtures will give the darkest green color?

a)

1 part green + 3 parts white

b)

2 parts green + 6 parts white

c)

3 parts green + 9 parts white

d)

4 parts green + 12 parts white

e)

They will all be equally dark

10.

There is a square with line segments drawn inside it. The line segments are drawn either from the vertices or the midpoints of other line segments. We colored 18\frac{1}{8}  of the large square. Which one is our coloring?

a)
b)
c)
d)
e)
11.

The number 5021972970 is written on a sheet of paper. Julian cuts the sheet twice so he gets three numbers. What is the smallest sum he can get by adding these three numbers?

a)

3244

b)

3444

c)

5172

d)

5217

e)

5444

12.

The map shows three bus stations at points A, B and C. A tour from station A to the Zoo and Port and back to A is 10 km long. A tour from station B to the Park and Zoo and back to B is 12 km. A tour from station C to the Port and Park and back to C is 13 km long. Also a tour from the Zoo to the Park and Port and back to the Zoo is 15 km long. How long is the shortest tour from A to B and C and back to A?

a)

18 km

b)

20 km

c)

25 km

d)

35 km

e)

50 km

13.

Rosa wants to start at the arrow, follow the line and get out at the other arrow. Which piece is NOT possible to put in the middle to obtain that?

a)
b)
c)
d)
e)
14.

The diagram shows three hexagons with numbers at their vertices, but some numbers are invisible. The sum of the six numbers of each hexagon is 30. What is the number on the vertex marked with a question mark?

a)

3

b)

4

c)

5

d)

6

e)

7

15.

Three rectangles of the same height are positioned as shown. The numbers within the rectangles indicate their areas in cm2cm^2  . If AB=6 cmAB=6\ cm  , how long is CD?

a)

7 cm

b)

7.5 cm

c)

8 cm

d)

8.2 cm

e)

8.5 cm

16.

A triangular pyramid is built with 10 identical balls, as shown. Each ball has one of the letters A, B, C, D and E on it. There are 2 balls marked with each letter. The picture shows three side views of the pyramid. What is the letter on the ball with the question mark?

a)

A

b)

B

c)

C

d)

D

e)

E

17.

Ronja had four white tokens and Wanja had four grey tokens. They played a game in which they took turns to place one of their tokens to create two piles. Ronja placed her first token first. Which pair of piles could they NOT create?

a)
b)
c)
d)
e)
18.

My little brother has a 4-digit bike lock with the digits 0 to 9 on each part of the lock as shown. He started on the correct combination and turned each part the same amount in the same direction and now the lock shows the combination 6348. Which of the following CANNOT be the correct combination of my brother's lock?

a)
b)
c)
d)
e)
19.

There were 20 apples and 20 pears in a box. Carl randomly took 20 pieces of fruit from the box and Luca took the rest. Which of the following statements is always true?

a)

Carl got at least one pear.

b)

Carl got as many apples as pears.

c)

Carl got as many apples as Luca.

d)

Carl got as many pears as Luca got apples.

e)

Carl got as many pears as Luca.

20.
a)
b)
c)
d)
e)
21.

Ann, Bob, Carina, Dan and Ed are sitting at a round table. Ann is not next to Bob, Dan is next to Ed and Bob is not next to Dan. Which two people are sitting next to Carina?

a)

Ann and Bob

b)

Bob and Dan

c)

Dan and Ed

d)

Ed and Ann

e)

It is not possible to be certain

22.

Maurice asked the canteen chef for the recipe for his pancakes. Maurice has 6 eggs, 400 g flour, 0.5 liters of milk and 200 g butter. What is the largest number of pancakes he can make using this recipe?

a)

6

b)

8

c)

10

d)

12

e)

15

23.

The picture shows three gears with a black gear tooth on each. Which picture shows the correct position of the black teeth after the small gear has turned a full turn clockwise?

a)
b)
c)
d)
e)
24.

Three pirates were asked how many coins and how many diamonds their friend Graybeard had. Each of the three told the truth to one question but told a lie to the other. Their answers are written on the piece of paper pictured. What is the total number of coins and diamonds that Graybeard has?

a)

11

b)

12

c)

13

d)

14

e)

15