Skip to content / Đến nội dung
ThichHocToan.com

IKMC 2015 - Grades 5-6 - Self-study

Question 2

My umbrella has KANGAROO written on top. It is shown in the picture. Which of the following pictures does not show my umbrella?

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

Question 3

Sam painted the 9 squares with the colours black, white and grey as shown. At least how many squares does he need to repaint so that no two squares with a common side have the same colour?

Question illustration
  1. 2
  2. 3
  3. 4
  4. 5
  5. 6

Question 4

There are 10 ducks. 5 of these ducks lay an egg every day. The other 5 lay an egg every second day. How many eggs do the 10 ducks lay in a period of 10 days?
  1. 75
  2. 60
  3. 50
  4. 25
  5. 10

Question 5

The figure shows a board where each small square has an area of 4 cm². What is the length of the thick black line?

Question illustration
  1. 16 cm
  2. 18 cm
  3. 20 cm
  4. 21 cm
  5. 23 cm

Question 6

Which of the following fractions is smaller than 2?
  1. $\frac{19}{8}$
  2. $\frac{20}{9}$
  3. $\frac{21}{10}$
  4. $\frac{22}{11}$
  5. $\frac{23}{12}$

Question 7

How much does Dita weigh?

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

Question 8

Peter looks through a magnifying glass at different parts of a drawing on a wall. Which is the picture that he cannot see?

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

Question 9

Each plant in John's garden has either 5 leaves, or 2 leaves and 1 flower. In total, the plants have 6 flowers and 32 leaves. How many plants are there?

Question illustration
  1. 10
  2. 12
  3. 13
  4. 15
  5. 16

Question 10

Alva has 4 paper strips of the same length. She glues 2 of them together with a 10 cm overlap, and gets a strip 50 cm long. With the other two paper strips, she wants to make a strip 56 cm long. How long should the overlap be?

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

Question 11

Tom used 6 squares with side 1 to form the shape in the picture. What is the perimeter of the shape?

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

Question 12

Every day Mary writes down the date and calculates the sum of the digits written. For example, on March 19 she writes 19.03 and calculates 1 + 9 + 0 + 3 = 13. What is the largest sum that she calculates during a year?
  1. 7
  2. 13
  3. 14
  4. 16
  5. 20

Question 13

The rectangle ABCD in the picture consists of 4 equal rectangles. If BC has length 1 cm, what is the length of AB?

Question illustration
  1. 4 cm
  2. 3 cm
  3. 2 cm
  4. 1 cm
  5. 0.5 cm

Question 14

Which of these five nets cannot be the net of a pyramid?
  1. Question illustration
  2. Question illustration
  3. Question illustration
  4. Question illustration
  5. Question illustration

Question 15

On Jump Street, there are 9 houses in a row. At least one person lives in each house. Any two neighbouring houses together are inhabited by at most six people. What is the largest number of people that could be living on Jump Street?
  1. 23
  2. 25
  3. 27
  4. 29
  5. 31

Question 16

Lucy and her mother were both born in January. Today, March 19 2015, Lucy adds the year of her birth, the year of her mother's birth, her age, and her mother's age. What result does she get?
  1. 4028
  2. 4029
  3. 4030
  4. 4031
  5. 4032

Question 17

The area of a rectangle is 12 cm². The lengths of its sides are natural numbers. Then, the perimeter of this rectangle could be:
  1. 20 cm
  2. 26 cm
  3. 28 cm
  4. 32 cm
  5. 48 cm

Question 18

Each of the 9 segments in the figure is to be coloured either blue, green or red. The sides of every triangle are to have different colours. Three of the segments have already been coloured, as shown. What colour can the segment marked with x have?

Question illustration
  1. Only blue
  2. Only green
  3. Only red
  4. Either blue, green or red
  5. Such a colouring is not possible

Question 19

In a bag there are 3 green apples, 5 yellow apples, 7 green pears and 2 yellow pears. Simon randomly takes fruits out of the bag one by one. How many fruits must he take out in order to be sure that he has at least one apple and one pear of the same colour?
  1. 9
  2. 10
  3. 11
  4. 12
  5. 13

Question 20

A new chess piece “kangaroo” has been introduced. In each move, it jumps either 3 squares vertically and 1 horizontally, or 3 squares horizontally and 1 vertically, as shown in the picture. What is the minimum number of moves the kangaroo needs in order to go from its current position to the square marked with A?

Question illustration
  1. 2
  2. 3
  3. 4
  4. 5
  5. 6