Problems And Solutions SEAMO PAPER E 2016

The Southeast Asia Mathematical Olympiad (SEAMO) is an international Math Olympiad competition that originated in Singapore and was founded by Mr. Terry Chew in 2016 in 8 Southeast Asian Countries. Since then, it is growing its popularity around the world. In 2019 it was recognized by 18 countries. In 2020 total number of participating countries increased to 22, including students from Indonesia, Brazil, China, Newzealand, and Taiwan students enrolled in SEAMO 2022-23.

Problem and Solution SEAMO 2016 paper E. Soal ini bersumber dari seamo-official.org

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1. Given \(a, b\) and \(c\) are three consecutive even numbers and \(b^3 = 1728\). Find the value of \(ac\).

(A) 80
(B) 120
(C) 140
(D) 192
(E) None of the above

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Solution

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2. Find the simplest expression for \(\frac{3^{40}}{9^{20}}\).

(A) \(\frac{1}{3}\)
(B) \(\frac{1}{2}\)
(C) 1
(D) 2
(E) None of the above

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Solution

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3. Find the possible value(s) of \(m\) in

\(\frac{1}{m-2}+\frac{1}{m+1}-\frac{1}{2}=0\)

(A) 0, 5
(B) 1, 4
(C) 2, 3
(D) 3
(E) 6

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Solution

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4. Find the value of \(12345^2-12344^2\)

(A) 1
(B) 10 000
(C) 12 345
(D) 24 689
(E) None of the above

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Solution

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5. Given \(\overline{aabb}\) is a square number, find the value of \((a+b)\)

(A) 8
(B) 9
(C) 10
(D) 11
(E) None of the above

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Solution

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6. \(ABC\) is an equilateral triangle of side \(6\; cm\). It first rotates about \(B\), then \(C_1\), without sliding. As a result, Vertex \(A\) travels from \(A\) to \(A_1\) , then comes to rest at \(A_2\). Find the length, in \(cm\), of the path travelled by vertex \(A\), in terms of \(π\).

(A) 8π
(B) 10π
(C) 12π
(D) 14π
(E) None of the above

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Solution

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7. The figure shows a can of height 8 cm. The circumference of its base is 44 cm. Find the shortest distance from A to B, without cutting through the can.

(A) 18 cm
(B) 20 cm
(C) 22 cm
(D) 24 cm
(E) 26 cm

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Solution

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8. In triangle \(ABC , ∠ABC = 90° , AB = 7\;cm\) and \(BC = 24\;cm\) . \(P\) is a point inside the triangle such that its shortest distance to each side of the triangle is the same. What is this distance?

(A) 1
(B) 2
(C) 3
(D) 6
(E) 8

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Solution

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9. \(M\) and \(N\) are midpoints of \(AD\) and \(AB\) , respectively, in rectangle \(ABCD\). Lines \(BM\) and \(DN\) intersect at point \(P\) . Find \(∠MPD\) , given that \(∠MBC = ∠BCN + 31°\).

(A) 23°
(B) 31°
(C) 38°
(D) 42°
(E) None of the above

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Solution

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10. Suppose \(m^2+1=3m, n^2+1=3n\), then the value of \(\frac{1}{m^2}+\frac{1}{n^2}\) is …

(A) 5
(B) 6
(C) 7
(D) 8
(E) 9

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Solution

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11. Find the value of

\(\sum_{i=1}^{5}3a_i – \sum_{i=1}^{5}(2a_i – 3)\)

(A) 0
(B) 1
(C) 14
(D) 16
(E) 18

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Solution

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12. In the figure below, BA and BC are tangents to the circle with centre ) . Suppose EC = 3 cm, DA = 2 cm, find BC in cm.

(A) 2
(B) 3
(C) 4
(D) 5
(E) 6

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