Skip to content / Đến nội dung
ThichHocToan.com

IKMC 2006 - Grades 5-6 - Self-study

Question 1

$3\times2006=2005+2007+\Box$. Find the missing number.
  1. 2005
  2. 2006
  3. 2007
  4. 2008

Question 2

Six numbers are written on the cards as shown. What is the largest number you can form with the given cards by placing them in a row?

Question illustration
  1. 9 876 543 210
  2. 4 130 975 682
  3. 7 568 413 092
  4. 7 685 413 092

Question 3

Four people can sit at a square table. For a school party, students join 10 square tables into one long table. How many people can sit at this long table?
  1. 20
  2. 22
  3. 30
  4. 32

Question 4

Choose the picture in which the angle between the hands of a watch is 150°.
  1. Question illustration
  2. Question illustration
  3. Question illustration
  4. Question illustration

Question 5

The left side of Main Street has all odd house numbers from 1 to 39. The right side has all even numbers from 2 to 34. How many houses are on Main Street?
  1. 35
  2. 36
  3. 37
  4. 38

Question 6

In how many ways can you obtain 2006 by following the arrows in the figure?

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

Question 7

One half of one hundredth is:
  1. 0.005
  2. 0.05
  3. 0.02
  4. 0.5

Question 8

The cube in the figure has one of the following nets. Which one?

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

Question 9

We need 9 kg of ink to paint the whole cube. How much ink is needed to paint the surface of the figure beside it?

Question illustration
  1. 4
  2. 5
  3. 6
  4. 9

Question 10

What is the difference between the sum of the first 100 strictly positive even numbers and the sum of the first 100 positive odd numbers?
  1. 20
  2. 50
  3. 100
  4. 200

Question 11

A regular-hexagon sheet of paper is folded so that the three marked corners meet at the centre. What figure is obtained?

Question illustration
  1. Six-corner star
  2. Hexagon
  3. Square
  4. Triangle

Question 12

The diameter AB of the circle is 10 cm. What is the perimeter of the figure marked by the dark line, if the rectangles in the figure are coincident?

Terminology note: the printed “coincident” is understood as “congruent” (equal-sized grid rectangles).

Question illustration
  1. 16 cm
  2. 20 cm
  3. 25 cm
  4. 30 cm

Question 14

Ali builds larger matchstick squares by adding small squares to the existing grid, as shown. How many matches must he add to the fifth square to build the sixth?

Question illustration
  1. 12
  2. 18
  3. 20
  4. 24

Question 15

The first three letters of KANGAROO are placed in equal squares of side 2 as shown. Find a false statement.

Terminology note: “perimeter” here means the total length of the drawn letter strokes.

Question illustration
  1. The perimeter of K exceeds that of A by 1.
  2. The perimeter of N exceeds that of A by 1.
  3. The perimeters of A and N are equal.
  4. The perimeters of K and N are equal.

Question 16

Complete the sentence correctly: If I look at your reflection, then…

Question illustration
  1. Your reflection looks at me.
  2. My reflection looks at you.
  3. My reflection looks at your reflection.
  4. Your reflection looks at my reflection.

Question 17

A 15 dm rod is divided into the greatest possible number of pieces with different positive integer lengths in dm. How many cuts are needed?
  1. 2
  2. 3
  3. 4
  4. 5

Question 18

A river crosses a city and has two islands and six bridges as shown. How many routes start at the shore point A and return at B while crossing every bridge exactly once?

Question illustration
  1. 0
  2. 2
  3. 4
  4. 6

Question 19

In which triple is the central number exactly halfway between the other two?
  1. $\frac12,\frac13,\frac14$
  2. 12, 21, 32
  3. 3, 7, 13
  4. $\frac13,\frac12,\frac23$

Question 20

What is the smallest number of dots that must be removed so that no three remaining dots are vertices of an equilateral triangle?

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