Download [PDF] APMOPS (SMOPS) Invitation Round Sample Questions Mathematical Olympiad

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APMOPS: Sample Questions 1 © Hwa Chong Institution Invitation Round Q 1 There are 4 cards labeled with letters M , A, T and H respectively. A single -digit number is written at the back of each card. They are then placed side by side, as shown below, so that a four -digit number is obtained. Peter discovered that regardless of the number written behind the “ A” card, the differen ce between the four-digit number and hundred times of the sum of its digits is always 4212. Find the numbers written behind the cards labeled M, T and H respectively. M A T H Q2 Given that 1 11 111 1111 ... 111...1 100 1' S of s =+ + + ++  find the sum of the digits of S. Q 3 The diagram shows a 5 by 5 grid comprising 25 squares. Each square is filled with number 1, 2, 3, 4 or 5 in such a way that no row, column or the two main diagonal lines contain the same number more than once. Find the value of m . m 5 4 3 2 1 Q4 The diagram shows a square made up of nine rectangles. Rectangle E is also a square. Given that the areas of rectangles A , B and C are 7 cm 2, 21 cm 2 and 2 cm 2 respectively, find the perimeter of the rectangle labeled D .

APMOPS: Sample Questions 2 © Hwa Chong Institution Invitation Round E D C B A Q5 Given that 2009 248 2 2 11 1 1 1 1 1 1 1 1 ... 1 2 1 2 222 2 2 n        + ×+ ×+ ×+ ××+ = −               , find the value of n. Q6 The diagram shows an isosceles triangle ABC where AC = BC and  BAC = 80°. Given that AB = CD , find the value of  BDC . A B C D Solutions to this question by accurate drawing will not be accepted. End of Paper Answers : Q1 M = 5, T = 1 and H = 2 Q2 415 Q3

APMOPS: Sample Questions 3 © Hwa Chong Institution Invitation Round 1 3 5 4 1 2 2 3 4 5 1 2 3 4 5 1 2 3 4 5 5 4 3 2 1 Q4 2 2 11 3cm Q5 2010 Q6 150 ° End of Paper