To make the big square symmetric about both diagonals, at least … additional small squares are needed to be colored black.. In a training program, an athlete must eat 154 eggs, during a[r]
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6th INTERNATIONAL MATHEMATICS AND SCIENCE OLYMPIAD FOR PRIMARY SCHOOL
IMSO 2009
SHORT ANSWER PROBLEMS
DIRECTORATE OF KINDERGARTEN AND PRIMARY DEVELOPMENT
DIRECTORATE GENERAL OF PRIMARY AND SECONDARY EDUCATION MANAGEMENT MINISTRY OF NATIONAL EDUCATION
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1 A big square is formed from twenty five small squares Some of the small squares are black To make the big square symmetric about both diagonals, at least … additional small squares are needed to be colored black
2 If , then =…
3 In a training program, an athlete must eat 154 eggs, during a period of time from November 8th till November 14th Every day in this period he must eat more eggs than the previous day The number of eggs he eats on November 13th is …
4 …
5 In the following grid, the area of the shaded region is … unit square
6 Danny wants to create a set of cards of sizes from a sheet of paper of size The number of cards that can be made by Danny is at most …
7 Mrs Anna has children: Alex, Brad, Christine, and Dennis Alex is not the youngest, but he is younger than Dennis If Brad’s age is the same as the mean of the ages of Alex and Dennis, then the oldest one is …
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A B
C D P
9 The following shape is made from horizontal and vertical lines The lengths of some of the lines are given The perimeter of the shape is … unit
10 Use numbers 2, 3, 4, 5, 7, and exactly once to form two three-digit numbers P and Q If is a positive number; the smallest possible value of is 11 The natural numbers bigger than are arranged in five columns as given by the
following figure The number 2009 appears in the … column and the … row
I II III IV V
2
9
10 11 12 13
17 16 15 14
12 The integer has two properties:
If the number is added, we get the number 9, which is a square number, i.e., = 33
Half of it is 4, which is also a square number, i.e., = 22 The next natural number which has the same properties is …
13 The next natural number which has the same properties is … ABCD is a trapezoid (trapezium) with AB parallel to CD The ratio of AB : CD is : The point P is on CD The ratio of the area of triangle APB to the area of trapezoid ABCD is …:…
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so that each number, except the first and last, is the sum or the difference of its two adjacent neighbors The value of X is
4 X
2
16 In a football competition, if a team wins it will get points If it draws it will get point, and if it loses it will get points After playing 20 times, Team B gets the total score of 53 Team B loses at least … times
17 Among points located in a plane, five of them lie on one line Any three points are selected from those points as corner points of a triangle There are at most … triangles that can be formed
18 Fill in all the numbers 0,1,2,3,4,5,6,7,8,9 on the ten squares below, so that the sum of numbers located on each arrowed line is 20 Two numbers are already filled in The number on the square with a question mark ("?") is
19 Nine dots are arranged as shown in the figure below, where ABCD is a square AT=TD, DS=SC, CR=BR, and AP=PQ=QB A triangle can be constructed by lining from dot to dot At most, there are … different right triangles that one can construct so that at least one of the dots P,Q,R,S, and T is its vertex
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21 In the diagram below, BC=5, DE=1 and DC=20, where D lies on AC and E lies on AB Both ED and BC are perpendicular to AC The length of AD is …
(Note: the figure is not in proportional scale)
22 The number N consists of three different digits and is greater than 200 The digits are greater than For any two digits, one digit is a multiple of the other or the difference is For example, 258 is one of such numbers There are at most … possible N
23 In the figure, two half-circles are inscribed in a square These two half-circles intersect at the center of the square If the side of the square has length 14 cm, then the area of the shaded region is … cm2
24 Replace the asterisks with digits so that the multiplication below is correct: The product is …
25 The areas of sides of a block are 44 cm2, 33 cm2, and 48 cm2 The volume of