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IKMC 2010 - Grades 5-6

Question 1

Given that:

Question illustration

Which number should replace Question illustration?
  1. 2
  2. 3
  3. 4
  4. 5
  5. 6

Question 2

The number 4 is reflected twice in the picture. What appears in the field with the question mark if we do the same with the number 5?

Question illustration
  1. Question illustration
  2. Question illustration
  3. Question illustration
  4. Question illustration
  5. Question illustration

Question 3

Kangi goes directly from the zoo to school and counts the flowers along the way. Which of the following numbers can he not obtain this way?

Question illustration
  1. 9
  2. 10
  3. 11
  4. 12
  5. 13

Question 4

The figure illustrates a staircase which has 2 steps.

Question illustration

A staircase that Nick and Mike are playing has 21 steps. They count the steps; one from bottom to top and the other from top to bottom. They meet at one step which Nick indicates as the 10th. As which number does Mike indicate this step?
  1. The 13th
  2. The 14th
  3. The 11th
  4. The 12th
  5. The 10th

Question 5

Anna has connected all the upper and lower points with straight lines. How many lines has she drawn?

Question illustration
  1. 20
  2. 25
  3. 30
  4. 35
  5. 40

Question 6

A fly has 6 legs and a spider has 8. Together, 2 flies and 3 spiders have as many legs as 10 birds and ...
  1. 2 cats
  2. 3 cats
  3. 4 cats
  4. 5 cats
  5. 6 cats

Question 7

In the box are seven blocks. It is possible to slide the blocks around so that another block can be added to the box. What is the minimum number of blocks that must be moved?

Question illustration
  1. 1
  2. 2
  3. 3
  4. 4
  5. 5

Question 8

Lines are drawn on a piece of paper and some of the lines are given numbers. The paper is cut along some of these lines and then folded as shown in the picture. Along which lines were the cuts made?

Question illustration
  1. 1, 3, 5, 7
  2. 2, 4, 6, 8
  3. 2, 3, 5, 6
  4. 3, 4, 6, 7
  5. 1, 4, 5, 8

Question 9

What is the perimeter of the figure shown (all angles are right angles)?

Question illustration
  1. 23
  2. 31
  3. 38
  4. 42
  5. 46

Question 10

In the following figures you see five elastic bands, only one of which is tied in a knot. Which one is it?
  1. Question illustration
  2. Question illustration
  3. Question illustration
  4. Question illustration
  5. Question illustration

Question 11

Which of the following expressions has a value that differs from the others?
  1. $20\times10+20\times10$
  2. $(2010)\times20\times10$
  3. $20\times10\times(2010)$
  4. $20\times10+10\times20$
  5. $(2010)\times20+10$

Question 12

The figure should be rotated $180^\circ$ around point $F$. What is the result?

Question illustration
  1. Question illustration
  2. Question illustration
  3. Question illustration
  4. Question illustration
  5. Question illustration

Question 13

Benjamin chooses a number, divides it by 7, adds 7 to the result and multiplies that result with 7. He obtains the number 777. Which number did he start with?
  1. 7
  2. 111
  3. 722
  4. 567
  5. 728

Question 14

The numbers 1, 4, 7, 10 and 13 should be written into the squares so that the sum of the three numbers in the horizontal row is equal to the sum of the three numbers in the vertical column. What is the largest possible value of these sums?

Question illustration
  1. 18
  2. 20
  3. 21
  4. 22
  5. 24

Question 15

In order to produce a newspaper with 60 pages, you need 15 sheets that are bound together. In one such newspaper, page 7 is missing. Which other pages are also missing from this newspaper?
  1. 8, 9 and 10
  2. 8, 42 and 43
  3. 8, 48 and 49
  4. 8, 52 and 53
  5. 8, 53 and 54

Question 16

With what expression can Question illustration be replaced to have an equality?

Question illustration
  1. $2$
  2. $3$
  3. $2\times3$
  4. $2\times2$
  5. $3\times3$

Question 17

In the picture, we see that $1+3+5+7=4\times4$. Then, $1+3+5+7+\cdots+17+19$ is equal to...?

Question illustration
  1. $10\times10$
  2. $11\times11$
  3. $12\times12$
  4. $13\times13$
  5. $14\times14$

Question 18

Lydia draws flowers with 5 petals. She wants to colour each petal in either white or black. How many different flowers can she draw this way? (A flower can be totally white or totally black. Two flowers which differ by a rotation are consider the same.)

Question illustration
  1. 6
  2. 7
  3. 8
  4. 9
  5. 10

Question 19

What fraction of the square is grey?

Question illustration
  1. $\frac13$
  2. $\frac14$
  3. $\frac15$
  4. $\frac38$
  5. $\frac29$

Question 20

Three identical dice are glued together as shown. The sum of dots on two opposite sides of a die is always 7. What is the sum of dots on the sides which are glued together?

Question illustration
  1. 12
  2. 13
  3. 14
  4. 15
  5. 16