SEAMO - KOMUNITAS JELAJAH NALAR https://jelajahnalar.com/community/kompetisi-matematika-2-seamo/ JELAJAH NALAR Discussion Board id Wed, 27 May 2026 01:27:31 +0000 wpForo 60 SEAMO X 2024 - Grade 11 & 12 https://jelajahnalar.com/community/kompetisi-matematika-2-seamo/seamo-x-2024-grade-11-12/ Wed, 20 May 2026 06:20:26 +0000

  1. Evaluate $$\frac{1}{\sqrt{8}+\sqrt{11}}+\frac{1}{\sqrt{11}+\sqrt{14}}+\frac{1}{\sqrt{14}+\sqrt{17}}+\cdot\cdot\cdot+\frac{1}{\sqrt{6038}+\sqrt{6041}}$$
  2. Yellow, Red and Blue are used to colour the rings shown below, such that no adjacent rings have the same colours; each colour is used exactly twice. How many ways are there to do so?
  3. How many real numbers satisfy the equation below? $$\frac{a^{5}+a^{4}-2a^{3}-a^{2}-a+2}{a^{3}-a}$$
  4. Let $x, y, z$ be three numbers all larger than 1 and let $w$ be a positive number such that $\log_{x}w=24$, $\log_{y}w=40$, and $\log_{xyz}w=12$. Find the value of $\log_{z}w.$
  5. Given that $a=\frac{\sqrt{5}-1}{2}$ , evaluate: $$\sin^{2}1^{\circ}+\sin^{2}2^{\circ}+\sin^{2}3^{\circ}+\cdot\cdot\cdot+\sin^{2}360^{\circ}$$
  6. How many numbers at the most can you select from $\{1, 2, 3, ..., 2024\}$ so the sum of any 3 of the numbers is divisible by 33?
  7. $E, F$ are points on $BC, CD$ respectively in rectangle $ABCD$. It is given $AE=4$, $EF=3$, and $AF=5.$ Find the area of $ABCD$ if $S_{\triangle ABE}=S_{\triangle ECF}+S_{\triangle ADF}.$
  8. $PA, PB$ are tangents to the circle. $PQR$ is a straight line cutting through the circle and intersecting $AB$ at $S$. $F$ is a point on $AR$ such that $QF \parallel PA$. $QF$ intersects $AB$ at $E$. Given that $QE=3,$ find $EF$.
  9. Find the value of: $$f(1)+f(2) + f (3) +\cdot\cdot\cdot+f(2024)$$
  10. Find the remainder when $1^{5}+2^{5}+3^{5}+\cdot\cdot\cdot+99^{5}+100^{5}$ is divided by 4.
  11. $DN$ and $AD$ are lines perpendicular to $AB$ and $BC$ respectively in $\triangle ABC$. $DM$ is perpendicular to $AC$. $NM$ and $BC$ produced meet at $E$. It is known $AD=DE=1$. Find: $$\cot \angle CAD \cdot \cot \angle BAD$$
  12. Suppose $a$ and $b$ are the roots of the quadratic equation $x^{2}+(\sin 10^{\circ})x+1=0$, and $c$ and $d$ are the roots of the quadratic equation $x^{2}+(\cos 10^{\circ})x-1=0$. Find the value of: $$\frac{1}{a^{2}}+\frac{1}{b^{2}}+\frac{1}{c^{2}}+\frac{1}{d^{2}}$$
  13. A point $(x, y)$ in the $xy$-plane is called a lattice point if both $x$ and $y$ are integers. For any integer $n$, let $f(n)$ be the number of lattice points on the line segment joining $(0,0)$ and $(n,n+5)$. For instance, we have $f(0)=6$ and $f(1)=2$. Find: $$f(1)+f(2) + f (3) +\cdot\cdot\cdot+f(2024)$$
  14. In the figure shown (in the file), $E$ is the midpoint of $BC$, $M$ is the midpoint of $AC$. Suppose that $D$ is a point on $AE$ such that $AD=BD=CD=169\text{ cm}$, and $EM=156\text{ cm}$. Find the length of $DE$.
  15. Let $\triangle ABC$ be an equilateral triangle inscribed in a circle, and let $M$ be a point on the arc $BC$ as shown. Find $AM$, given that $BM = 3$ and $MC = 5$.
]]> SEAMO Admin dot https://jelajahnalar.com/community/kompetisi-matematika-2-seamo/seamo-x-2024-grade-11-12/ SEAMO X 2024 - Grade 9 & 10 https://jelajahnalar.com/community/kompetisi-matematika-2-seamo/seamo-x-grade-9-10/ Wed, 20 May 2026 04:56:29 +0000

  1. Simplify $$\frac{11}{2\sqrt{5}-3}+\frac{5}{\sqrt{5}-2}-7\sqrt{5}$$
  2. Evaluate $$\sqrt{14+6\sqrt{5}}-\sqrt{14-6\sqrt{5}}$$
  3. Find the value of$$\cos^{2}\theta+\cos^{2}\left(\theta+\frac{2\pi}{3}\right)+\cos^{2}\left(\theta-\frac{2\pi}{3}\right)$$
  4. Factorize $x^{3}+4x^{2}+5x+2$
  5. The 3 sides of a right-angled triangle are all integers. One of the 2 shorter sides is 35. Find the minimum possible perimeter.
  6. $ABCD$ is a rectangle whose diagonals intersect at point $O$. $E$ is a point on $AB$ such that $CE$ bisects $\angle BCD$. It is known that $\angle ACE=15^{\circ}$. Find $\angle BOE$.
  7. Suppose $xy=144$ and $\log_{y}x+\log_{x}y=\frac{10}{3}$ with $x,y>0$. Find the value of $\frac{x+y}{2}$, leaving your answer in the simplest form.
  8. Given that $x+\frac{1}{x}=3$, evaluate $$x^{10}+x^{5}+\frac{1}{x^{5}}+\frac{1}{x^{10}}$$
  9. Find the remainder when $(257^{33}+46)^{26}$ is divided by 50.
  10. A positive integer is called friendly if it is divisible by the sum of its digits. For example, 111 is friendly but 123 is not. Find the number of all 2-digit friendly numbers.
  11. A candidate is required to answer 7 out of 15 questions which are divided into 3 groups $A$, $B$, $C$ each containing 4, 5, 6 questions respectively. He is required to select at least 2 questions from each group. Find the number of choices he can make.
  12. It is known that $\angle MAN=45^{\circ}$ in square $ABCD$, $M$ and $N$ are points on $BC$, $CD$ respectively. Given that $BM=3.5$ and $DN=2.5$, find the length of $MN$.
  13. There are 6 questions in Paper E for SEAMO X 2024. Exactly 500 participants answered each question correctly. For any 2 participants, there is at least one question they both got wrong. At least how many participants are there for this paper?
  14. $ABCD$ is a trapezium with $AD \parallel BC$. $AB=BC$ and $AD=AE$. Given that $\angle ABC=90^{\circ}$ and $E$ is a point on $AB$ such that $\angle BEC=75^{\circ}$, find $\angle DCE$.
  15. The radii of the 2 circles are 8 and 6 respectively. The distance between the centres of the 2 circles is 12. A line $QR$ is drawn through one of the intersections $P$ such that $QP=PR$. Find $(QP)^{2}$.

]]> SEAMO Admin dot https://jelajahnalar.com/community/kompetisi-matematika-2-seamo/seamo-x-grade-9-10/ SEAMO X 2024 - Grade 7 & 8 https://jelajahnalar.com/community/kompetisi-matematika-2-seamo/sasmo-x-2024-grade-7-8/ Wed, 20 May 2026 04:34:20 +0000

  1. Find the remainder when $2024^{2024}$ is divided by 7.
  2. In triangle 𝐴𝐡𝐢, 𝐴𝐡 = 3, 𝐡𝐢 = 4 and 𝐴𝐢 = 5. Given that sin 2𝐴 = $\frac{π‘₯}{𝑦}$ where π‘₯ and 𝑦 are coprime positive integers, find the value of π‘₯ + 𝑦.
  3. Find the remainder when $π‘₯^3 + 3π‘₯^2 + 2π‘₯ + 1$ is divided by (π‘₯ βˆ’ 2).
  4. Evaluate $$\sqrt{(2+1)(2^2+1)(2^4+1)(2^8+1)...(2^{256}+1)+1}$$
  5. Find the least value of $2 \log_{100} π‘Ž βˆ’ \log_π‘Ž(0.0001)$, for π‘Ž > 1.
  6. It is known that $\overline{π‘Žπ‘π‘π‘‘}$ is a multiple of 11 and 𝑏 + 𝑐 = π‘Ž, $\overline{𝑏𝑐}$ is a perfect square. Find the smallest such number, given that none of its digits is 0.
  7. It is given that $$y=\sqrt{\frac{x^2-2}{5x-4}}-\sqrt{\frac{x^2-2}{4-5x}}+2$$ Find the value of $x^2+y^2$.
  8. For each positive integer 𝑛, define $$A_n=\frac{20^n+24^n}{n!},\text{ where }n!=1\times 2\times 3\times \cdots \times n$$ Find the value of 𝑛 that maximises $𝐴_𝑛$.
  9. How many ways are there to put 7 different-coloured beads into 4 identical baskets so that each basket has at least ONE bead?
  10. Evaluate $$480(\frac{1}{2^2-1}+\frac{1}{3^2-1}+\cdots +\frac{1}{15^2-1})$$
  11. 𝛼 and 𝛽 are 2 distinct real roots of $π‘₯^2 + 2(π‘˜ + 3)π‘₯ + π‘˜^2 + 3 = 0$, where π‘˜ is an integer. Find the minimum value of $(𝛼 βˆ’ 1)^2 + (𝛽 βˆ’ 1)^2$.
  12. If π‘Ž, 𝑏 and 𝑐 are real numbers such that π‘Ž + 2𝑏 + 𝑐 = 4, find the maximum value of π‘Žπ‘ + 𝑏𝑐 + π‘π‘Ž.
  13. 𝐴𝐡𝐢𝐷 is a square with side of length 2 cm. 𝐡𝑃𝐢 is an equilateral triangle. If the area of βˆ†π΅π‘ƒπ· is π‘˜ $\text{cm}^2$, find the value of $\sqrt{3} βˆ’ π‘˜$.
  14. The figure below shows a solid cube of volume 1 $\text{cm}^3$. Let 𝑀 be the midpoint of the edge 𝐺𝐢. If the shortest path for an ant to crawl from the vertex 𝐴 to 𝑀 is $\frac{\sqrt{π‘Ž}}{𝑏}$ cm, where π‘Ž, 𝑏 are integers and π‘Ž has no squared factor, find π‘Ž + 𝑏.
  15. The point 𝐼 below is the in-center of βˆ†π΄π΅πΆ. The line 𝐴𝐼 produced meets the circumcircle at 𝐷. It is known that 𝐴𝐡 = 3, 𝐴𝐢 = 4, and $𝑆_{Δ𝐼𝐡𝐢} = 𝑆_{Δ𝐷𝐡𝐢}$. Find the value of 4𝐡𝐢.

]]> SEAMO Admin dot https://jelajahnalar.com/community/kompetisi-matematika-2-seamo/sasmo-x-2024-grade-7-8/ SEAMO X 2024 - Grade 5 & 6 https://jelajahnalar.com/community/kompetisi-matematika-2-seamo/seamo-x-2024-grade-5-6/ Wed, 20 May 2026 04:03:59 +0000

  1. 12 points on a rectangle are shown below. How many triangles can be formed by connecting any 3 vertices?
  2. Which of the following expressions has the largest value? $$2^{777}, 3^{444}, 5^{333}$$
  3. Find the last 2 digits of $3^{333}$.
  4. A new operation is defined as: $$π‘š βŠ— 𝑛 = π‘š^𝑛 + 𝑛^π‘š$$ Find the value of 𝑛 if $$π‘š^𝑛 + 𝑛^π‘š = 368$$ where 𝑛 > π‘š, and π‘š, 𝑛 are positive integers.
  5. Find the 2024th digit after the decimal point when $\frac{1}{13}$ is written in decimal form.
  6. The figure shows a triangle 𝐴𝐡𝐢. 𝐴𝐡 = 𝐡𝐷 = 𝐴𝐢, ∠𝐢𝐴𝐷 = 30Β°. Find the value of π‘₯.
  7. The figure shows 2 semi-circles. The length of chord 𝐴𝐡 is 24 π‘π‘š and 𝐴𝐡 is parallel to 𝐢𝐷. Find the area of the shaded region to the nearest whole number in $\text{cm}^2$. Take $\pi=\frac{22}{7}$.
  8. The following is a sequence of numbers: $$2, 2, 4, 6, 0, 6, 6, 2, 8, 0, …$$ where the first 2 numbers are 2, and the subsequent numbers are obtained by taking the ones digit of the sum of the two previous numbers. Find the 2024th number in the sequence.
  9. Numbers are filled in the following 3 Γ— 3 array such that the sum of the numbers in each column, row and diagonal is the same. Two numbers have been filled in. Find the number in the top right corner marked with π‘š.
  10. Each side of the small quadrilateral 𝐴𝐡𝐢𝐷 is extended to twice its original length. By connecting vertices, another quadrilateral π‘Šπ‘‹π‘Œπ‘ is obtained. Thus, 𝐴𝑋 = 2𝐴𝐡, π΅π‘Œ = 2𝐡𝐢, … and so on. If the area of π‘Šπ‘‹π‘Œπ‘ is 350 $\text{cm}^2$, find the area of 𝐴𝐡𝐢𝐷 in $\text{cm}^2$.
  11. A 2024-digit number is written as shown below. Find the remainder when it is divided by 9. $$1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 3 …$$
  12. The cost of a tennis racket increased by 10% this year. If the selling price remained the same, the profit would have dropped by 30% this year. However, the number of rackets sold increased by 50%. What is the percentage increase in the total profit from the sale of rackets this year?
  13. Let $\frac{4}{9}=\frac{1}{A}+\frac{1}{B}+\frac{1}{C}+\frac{1}{D}$, where $A,B,C,D$ are distinct factors of 36 in ascending order. Find $C$.
  14. Minh was walking from Town 𝐴 to Town 𝐡, at the same time Chatdanai was cycling from Town 𝐡 to Town 𝐴. After they met each other along the way, Minh took 4 times longer to reach Town 𝐡. Given that Minh’s walking speed was 80 m/min, find Chatdanai’s cycling speed.
  15. The queue of fans waiting to enter a concert hall is building up at a constant rate of π‘₯ people every minute. Each entrance gate can admit 40 people per minute. At the point the gates opened, the queue was 800 people long. Given that the queue cleared 20 minutes after 4 entrance gates were open, find the value of π‘₯.

]]> SEAMO Admin dot https://jelajahnalar.com/community/kompetisi-matematika-2-seamo/seamo-x-2024-grade-5-6/ SEAMO X 2024 - Grade 3 & 4 https://jelajahnalar.com/community/kompetisi-matematika-2-seamo/seamo-x-2024-grade-3-4/ Wed, 20 May 2026 03:37:48 +0000

  1. Find the value of π‘š below. $$(π‘š Γ· 3) + 8 Γ— 5 = 120$$
  2. Find the missing number. $$2, 2, 4, 6, 10, 16, 26, 42, (\text{ })$$
  3. How many quadrilaterals, or 4-sided polygons are there in the figure below?

  4. The teacher has a bag of sweets. If she gives each student 8 sweets, 3 sweets will remain. If she gives each student 9 sweets, she will need another 5 sweets. How many sweets does the teacher have?
  5. How many numbers greater than 4000 can be formed using the number cards below?
  6. The figure shows a square of side length 50 cm. Inscribed inside the square is a shaded semi-circle. The other shaded region is outside the quadrants shown. Find the total shaded area.
  7. In the figure below, find the value of π‘₯.
  8. $(2^{33} + π‘˜)$ is divisible by 31. Find the smallest possible value of π‘˜.
  9. Kenneth forgot his pencil box when he left home for school. His father cycled after him to give him the pencil box. 5 minutes after getting the pencil box from his father, Kenneth reached school and his father got back home. If his father cycles 4 times as fast as Kenneth walks, how many minutes did Kenneth take to walk from home to school?
  10. There is an array of whole numbers from 1 to 160. $$1, 2, 3, 4,… , 158, 159,160$$ In the first operation, the numbers at the odd positions are removed. $$2, 4, 6, 8,… , 158, 160$$ In the 2nd operation, again the numbers at the odd positions are removed. Continuing in this manner, what is the last number left behind?
  11. 𝐴𝐡𝐢𝐷 is a square, points 𝐸, 𝐹 are the midpoints of sides 𝐴𝐷 and 𝐴𝐡 respectively. Find the area of the square if the area of the shaded region is given as 48 $\text{cm}^2$.
  12. Evaluate $$2024 \times \left( \frac{1}{1 \times 2} + \frac{1}{2 \times 3} + \frac{1}{3 \times 4} + \dots + \frac{1}{2022 \times 2023} + \frac{1}{2023 \times 2024} \right)$$
  13. The figure shows a rectangle 𝐴𝐡𝐢𝐷. 𝐷𝐸 ∢ 𝐸𝐢 = 4 ∢ 5, 𝐴𝐹 ∢ 𝐹𝐷 = 7 ∢ 5. The area of βˆ†π΅πΈπΆ is 60 $\text{cm}^2$. Find the area of βˆ†π΄πΉπ΅.
  14. 793 and 399 have the same remainder 𝑛 when divided by a prime number π‘š. Find the biggest possible value of (π‘š + 𝑛).
  15. Find the value of $$\frac{1}{\frac{1}{2022\times 2023}+\frac{1}{2023\times 2024}+\frac{1}{2024}}$$

]]> SEAMO Admin dot https://jelajahnalar.com/community/kompetisi-matematika-2-seamo/seamo-x-2024-grade-3-4/ SEAMO X 2024 - Grade 1 & 2 https://jelajahnalar.com/community/kompetisi-matematika-2-seamo/seamo-x-2024-grade-1-2/ Wed, 20 May 2026 03:25:42 +0000

  1. Count the number of cubes.
  2. Find the colour of the circle marked with "?".
  3. FInd the value of $$1βˆ’ 2 + 3 βˆ’ 4 + 5 βˆ’ 6 + β‹― + 19$$
  4. Find the area of the triangle
  5. Draw the missing diagram in your answer script.
  6. Using $\to$ and $\downarrow$ movements only, find the number of shortest paths from $A$ to $B$, without passing through $x$.
  7. A wire of 98 cm is used to form a square of side length 16 cm. What is the remaining length of wire?
  8. Find the missing number below. $$3 βˆ— 5 = 14$$ $$5 βˆ— 6 = 31$$ $$8 βˆ— 7 = 71$$ $$10 βˆ— 8 = ?$$
  9. There are 11 girls and boys at a birthday party. Each boy gets 2 balloons, each girl gets 4 balloons. Altogether 34 balloons are given away. How many girls are at the party?
  10. Find the missing number below $$1, 4, 10, 22, 46, (\text{ }), …$$
  11. Mdm June has a basket of apples. If she gives each child 4 apples, 4 apples will remain. If she gives each child 5 apples, she will be short of 1 apple. How many apples does Mdm June have?
  12. It took Sam 2 minutes to vertically saw a log into 2 pieces. How many minutes did it take him to vertically saw the same log into 4 pieces?
  13. Study the number array below.

    In Mathematics, a prime number has only 2 factors – 1 and itself. The prime numbers in the array, up to 19, have been circled. What is the second prime number that is bigger than 60?
  14. A number multiplied by itself is called a Square Number. As shown below, 1, 4, 9, 16,… are square numbers. Find the sum of the first eight square numbers.
    1 Γ— 1 = 1
    2 Γ— 2 = 4
    3 Γ— 3 = 9
    4 Γ— 4 = 16
    …
    …
  15. John left home for the park at 0730 h, at a speed of 60 m/min. His brother returned from the park at the same time at 70 m/min. It is known that the distance between the park and their home is 2600 m. At what time did they meet along the way?
    Give your answer in 24-hour clock format (e.g. 0612 h means 6:12 AM)
  16. In Mathematics, 21 = 2, 22 = 2 Γ— 2 = 4, 23 = 2 Γ— 2 Γ— 2 = 8, ….
    Study the pattern below carefully

    What is the remainder when $2^{10}$ is divided by 3?
  17. The 6th of February many years ago was a Wednesday during a leap year. On which day of the week was the 10th of March that same year? Use the table provided to assist you.
  18. There are 8 steps on a flight of stairs at Don’s apartment. There are 2 flights of stairs from one level to another. It takes Don 90 seconds to climb one flight of stairs. How many minutes does Don take to reach his home on the 6th floor?
  19. Mother kept a birthday cake in the fridge in the morning. One of the children ate part of the cake in the afternoon. These were the answers when mother questioned them.
    Alice: I didn’t take the cake.
    Benson: Mother, I didn’t even know there was a cake.
    Chloe: Benson took the cake!
    Two of the children had lied. Who ate the cake?
  20. Find the area of the shaded region.

]]> SEAMO Admin dot https://jelajahnalar.com/community/kompetisi-matematika-2-seamo/seamo-x-2024-grade-1-2/ Informasi Lomba https://jelajahnalar.com/community/kompetisi-matematika-2-seamo/informasi-lomba-10/ Wed, 15 Apr 2026 09:03:19 +0000 SEAMO
(Southeast Asian Mathematical Olympiad)
Β 
Southeast Asian Mathematical Olympiad (SEAMO) adalah kompetisi matematika bergengsi internasional untuk siswa (TK-SMA) guna meningkatkan berpikir kritis. Kompetisi ini diadakan tahunan, mencakup babak penyisihan daring/luring dan final (SEAMO X) yang pada 2026 diadakan di Bali. Peserta mengerjakan soal berbasis berpikir tingkat tinggi (HOTS) dalam durasi 2 jam.
Β 
Detail Utama Lomba SEAMO:
  • Tingkat Peserta: Meliputi kategori Upper Kindergarten hingga Upper Primary (Grade 5-6), serta tingkat menengah (SMA).
  • Format Ujian:
    • Penyisihan: Biasanya dilaksanakan daring (online) dengan pengawasan ketat.
    • Final (SEAMO X): Dilaksanakan luring (penyertaan fisik/kertas), contohnya di Bali pada Januari 2026.
    • Soal: Umumnya terdiri dari 25 soal yang dikerjakan dalam waktu 2 jam.
  • Waktu Pelaksanaan: Pendaftaran dan babak penyisihan sering dibuka sekitar bulan September-Oktober (berdasarkan info 2025).
  • Penyelenggara: Didirikan oleh Terry Chew, pendidik matematika dari Singapura.
  • Biaya & Pendaftaran: Peserta dapat mendaftar melalui sekolah atau individu, dengan biaya (contoh sebelumnya) sekitar SGD 12.
  • Manfaat: Membangun mental juara, melatih problem-solving, dan memberikan sertifikat internasional.
Untuk informasi terkini, pendaftaran, dan detail soal, peserta dapat merujuk ke situs resmi SEAMO Official atau akun Instagram SEAMO Indonesia.
]]> SEAMO Admin dot https://jelajahnalar.com/community/kompetisi-matematika-2-seamo/informasi-lomba-10/