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ASMO - BorneoMath https://borneomath.com All about math problems Sun, 11 Dec 2022 09:37:48 +0000 en-US hourly 1 https://wordpress.org/?v=6.5.2 Asian Science And Math Olympiad (ASMO) 2019 For Grade 11 https://borneomath.com/asian-science-and-math-olympiad-asmo-2019-for-grade-11/ https://borneomath.com/asian-science-and-math-olympiad-asmo-2019-for-grade-11/#respond Sun, 04 Dec 2022 04:59:14 +0000 https://borneomath.com/?p=6054 Asian Science and Maths Olympiad (ASMO) is a competition platform designed to challenge and evaluate student’s knowledge in Mathematics and […]

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]]> Asian Science and Maths Olympiad (ASMO) is a competition platform designed to challenge and evaluate student’s knowledge in Mathematics and Science at their grade level. The questions in the Olympiad will stretch their knowledge and understanding of the concepts. Our syllabus fits nicely into the syllabus that concentrates on non-routine problem-solution to prepare the students for the competition. With the expansion of STEM education worldwide, ASMO certainly answers the need of it. Students will be well prepared with the skills to meet the science and technology challenges.

In Malaysia, ASMO is officially endorsed by Ministry of Education and all participants will obtain curriculum marks. In 2018 alone, Asian Science and Mathematics Olympiad has received 70,000 entries from across the ASEAN countries. We are targeting for the number to increase at 80,000 for 2019.

We are also proud to present that ASMO International is a new effort by ASMO Malaysia which started in 2017 in Pattaya, Thailand. When it was initially launched, the competition was setup via collaboration with ASMOPSS and ASMO Thai was the host for the competition. In 2018, Malaysia has become the host for the competition and it was participated by 10 Asian countries.

The idea of opening up a new competition platform which is ASMO International is to expand the level of competition and to provide more opportunities for primary and secondary school students to experience international engagement. (sc : http://asmo2u.com/about-us)

Berikut ini problems and solution ASMO 2019 grade 11

1. Let $a$ and $b$ be the roots of $x^2 + 2000x +1= 0$ and $c$ and $d$ be the roots of $x^2 – 2008x +1= 0$. Determine the value of $(a + c)(b + c)(a – d)(b – d)$.

Berdasarkan dalil vieta pada $𝑥^2 + 2000𝑥 + 1 = 0$
$𝑎 + 𝑏 = −2000$ dan $𝑎𝑏 = 1$
Berdasarkan dalil vieta pada $𝑥^2 − 2008𝑥 + 1 = 0$
$𝑐 + 𝑑 = 2008$ dan $𝑐𝑑 = 1$
berlaku juga $𝑐^2 − 2008𝑐 + 1 = 0$ dan $𝑑^2 − 2008𝑑 + 1 = 0$
Selanjutnya
$\begin{align}
(𝑎 + 𝑐)(𝑏 + 𝑐)(𝑎– 𝑑)(𝑏– 𝑑)&= (𝑎𝑏 + 𝑎𝑐 + 𝑏𝑐 + 𝑐^2)(𝑎𝑏 − 𝑎𝑑 − 𝑏𝑑 + 𝑑^2)\\
&= (1 + 𝑐(𝑎 + 𝑏) + 𝑐^2)(1 − 𝑑(𝑎 + 𝑏) + 𝑑^2)\\
&= (1 − 2000𝑐 + 𝑐^2)(1 + 2000𝑑 + 𝑑^2)\\
&= (1 − 2008𝑐 + 𝑐^2 + 8𝑐)(1 − 2008𝑑 + 𝑑^2 + 4008𝑑)\\
&= (8𝑐)(4008𝑑)\\
&= 32064𝑐𝑑\\
&= 32064\\
\end{align}$

2. Determine the value of the expression $3\sqrt{5\sqrt{3 \sqrt{5 \sqrt{…}}}}$.

$3\sqrt{5\sqrt{3 \sqrt{5 \sqrt{…}}}}=a$
$⇒3\sqrt{5\sqrt{a}}=a$
$⇒9(5\sqrt{a}=a^2$
$⇒45\sqrt{a}=a^2$
$⇒2025a=a^3$
$⇒2025=a^2$
$⇒a=\sqrt{2025}=45$

3. What are all the two-digit positive integers in which the difference between the integer and the product of its two digits is 12?

Misalkan bilangan dua digitnya adalah $ \overline{ab}$,

$\overline{𝑎b} − 𝑎𝑏 = 12$ atau $𝑎𝑏 − \overline{ab} = 12$

Kemungkinan 1
$\overline{𝑎b} − 𝑎𝑏 = 12$
$⇒10𝑎 + 𝑏 − 𝑎𝑏 = 12$
$⇒(10 − 𝑏)(𝑎 − 1) + 10 = 12$
$⇒(10 − 𝑏)(𝑎 − 1) = 2 = 1 × 2 = 2 × 1$
Untuk $(10 − 𝑏)(𝑎 − 1) = 1 × 2$, diperoleh $𝑏 = 9, 𝑎 = 3$, bilangan dua digit yang memenuhi adalah 39
Untuk $(10 − 𝑏)(𝑎 − 1) = 2 × 1$, diperoleh $𝑏 = 8, 𝑎 = 2$, bilangan dua digit yang memenuhi adalah $28$
Kemungkinan 2
$𝑎𝑏 − \overline{ab} = 12$
$⇒𝑎𝑏 − (10𝑎 + 𝑏) = 12$
$⇒𝑎𝑏 − 10𝑎 − 𝑏 = 12$
$⇒(𝑎 − 1)(𝑏 − 10) − 10 = 12$
$⇒(𝑎 − 1)(𝑏 − 10) = 22$
Karena $a$ dan $b$ bilangan satu digit maka kemungkinan dua tidak ada yang memenuhi
Jadi banyak bilangan yang memenuhi hanya $2$ yaitu $28$ dan $39$

4. Determine there are how many positive integer $x$ less than $2007$ we can find such that $[\frac{x}{2}]+[\frac{x}{3}]+[\frac{x}{6}]=x$
where $[n]$ is the greatest integer less than or equal to $n$. (i.e., $[3.5]=3$;$[6]=6; [-3.5]=-4 $etc.)

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5. A rectangle is made by placing together three smaller rectangles P, Q and R, without gaps or overlaps. Rectangle P measures 3 cm × 8 cm and Q measures 2 cm × 5 cm. Determine the number of possibilities are there for the measurements of R.

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6. Levine selects an integer, multiplies it by 8 then subtracts 4. She then multiplies her answer by 6 and finally subtracts 90. Her answer is a two-digit number. Determine the smallest integer she could select.

Misalkan bilangan yang dipilih adalah $x$ hasilnya adalah $y$ ($y$ merupakan bilangan dua digit)
Berdasarkan perintah soal diperoleh persamaan:

$(8𝑥 − 4)6 − 90 = 𝑦$
$⇒ 48𝑥 − 24 − 90 = 𝑦$
$⇒ 48𝑥 − 114 = 𝑦$
$⇒ 48𝑥 = 𝑦 + 114$
$⇒ 𝑥 =\frac{𝑦 + 114}{48}$

Karena $y$ bilangan dua digit dan $𝑦 + 114$ habis dibagi $48$, maka bilangan terkecil $y$ sehingga $x$ terkecil adalah $y=30$, diperoleh $𝑥 = 3$.

7. Three positive integers are such that they differ from each other by at most 6. It is also known that the product of these three integers is 2808. Determine the smallest integer among them.

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8. We consider a line segment AB with the length c and all right-angled triangles with hypotenuse AB. For all such right-angled triangles, determine the maximum diameter of a circle with the centre on AB which is tangent to the other two sides of the triangle.

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9. Solve the equation $|x-3|^{(\frac{x^2-8x+15}{x-2})}=1$

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10. We have a red cube with side length 2 cm. What is the minimum number of identical cubes that must be adjoined to the red cube in order to obtain a cube with volume $\left(\frac{12}{5}\right)^3$ cm³?

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Problem And Solution SEAMO 2017 Paper F
Asian Science And Math Olympiad (ASMO) 2018 For Grade 11

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]]> https://borneomath.com/asian-science-and-math-olympiad-asmo-2019-for-grade-11/feed/ 0 Asian Science And Math Olympiad (ASMO) 2019 For Grade 10 https://borneomath.com/asian-science-and-math-olympiad-asmo-2019-for-grade-10/ https://borneomath.com/asian-science-and-math-olympiad-asmo-2019-for-grade-10/#respond Sun, 04 Dec 2022 03:38:37 +0000 https://borneomath.com/?p=6039 Asian Science and Maths Olympiad (ASMO) is a competition platform designed to challenge and evaluate student’s knowledge in Mathematics and […]

The post Asian Science And Math Olympiad (ASMO) 2019 For Grade 10 first appeared on BorneoMath.

Berikut ini problems and solution ASMO 2019 grade 10

1. The sum of 18 consecutive positive integers is a perfect square. Determine the smallest possible value of this sum.

$𝑥 + (𝑥 + 1) + (𝑥 + 2) + (𝑥 + 3) + ⋯ + (𝑥 + 17) = 𝑛^2$
$18𝑥 + (1 + 2 + 3 + ⋯ + 17) = 𝑛^2$
$18𝑥 +\frac{18(17)}{2}= 𝑛^2$
$18𝑥 + 9(17) = 𝑛^2$
$9(2𝑥 + 17) = 𝑛^2$

$9$ merupakan bilangan kuadrat maka $(2𝑥 + 17)$ juga harus merupakan bilangan kuadrat. Nilai $x$ yang memenuhi adalah $4$. Jadi bilangan terkecil pada penjumlahan di atas adalah $4$

2. Simplify $\sqrt{2\left(\sqrt{1+\left(\frac{x^4-1}{2x^2})\right)^2}\right)}$ ,where $x$ is any positive real number.

$\sqrt{2\left(\sqrt{1+\left(\frac{x^4-1}{2x^2})\right)^2}\right)}$

$=\sqrt{2\left(\sqrt{1+\frac{x^8-2x^4+1}{4x^4}}\right)}$

$=\sqrt{2\left(\sqrt{\frac{4x^4}{4x^4}+\frac{x^8-2x^4+1}{4x^4}}\right)}$

$=\sqrt{2\left(\sqrt{\frac{x^8+2x^4+1}{4x^4}}\right)}$

$=\sqrt{2\left(\sqrt{\left(\frac{x^4+1}{2x^2}\right)^2}\right)}$

$=\sqrt{2\left(\frac{x^4+1}{2x^2}\right)}$

$=\frac{1}{x}\sqrt{x^4+1}$

3. Determine the value of the positive integer x if

$\frac{1}{\sqrt 4 +\sqrt 5}+\frac{1}{\sqrt 5 +\sqrt 6}+\frac{1}{\sqrt 6 +\sqrt 7}+…+\frac{1}{\sqrt x +\sqrt {x+1}}=10$

$\frac{1}{\sqrt 4 + \sqrt 5} =\frac{1}{\sqrt 4 + \sqrt 5}×\frac{\sqrt 5 – \sqrt 4}{\sqrt 5 – \sqrt 4}=\frac{\sqrt 5 – \sqrt 4}{5-4}={\sqrt 5 – \sqrt 4}$

Dengan cara yang sama penjumlahan

$\frac{1}{\sqrt 4 +\sqrt 5}+\frac{1}{\sqrt 5 +\sqrt 6}+\frac{1}{\sqrt 6 +\sqrt 7}+…+\frac{1}{\sqrt x +\sqrt {x+1}}=10$

Dapat disederhanakan menjadi

${\sqrt 5 – \sqrt 4}+{\sqrt 6 – \sqrt 5}+{\sqrt 7 – \sqrt 6}+…+{\sqrt {x+1} – \sqrt x}=10$
$⇒-\sqrt 4 + \sqrt{x+1}=10$
$⇒-2+\sqrt{x+1}=10$
$⇒\sqrt{x+1}=12$
$⇒x+1=144$
$⇒x=143$

4. Let $ABC$ be a triangle with $∠A=90°$ and $AB = AC$. Let $D$ and $E$ be points on the segment $BC$ such that $BD : DE : EC = 3 : 5 : 4$. Determine the angle $∠DAE$.

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5. What is the units digit in the answer to the sum $3^{2025} + 9^{677}$ ?

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6. Determine the greatest integer $x$ such that $\sqrt{2007^2 – 20070 +31} ≥ x$.

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7. Let $x, y$ and $z$ be three real numbers such that $xy + yz + xz = 6$ . Determine the least possible value of $x^2 + y^2 + z^2$.

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8. The internal bisector of angle A of triangle ABC meets BC at D. If AB=6 units, AC=9 units and BC=10 units, determine the length BD.

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9. Jason spent 100 dollars to get 100 toy animals. Jason bought at least one ant, one bat and one cat, and did not buy any other toys. Given the cost of an ant, a bat and a cat are 0.5 dollar, 3 dollars and 10 dollars respectively. Determine how many of each toy did Jason buy.

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10. Terry colours all the small squares that lie on the two longest diagonals of a square grid. He colours 2021 small squares. Determine the size of the square grid.

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Problem And Solution SEAMO 2017 Paper E
Asian Science And Math Olympiad (ASMO) 2018 For Grade 10

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]]> https://borneomath.com/asian-science-and-math-olympiad-asmo-2019-for-grade-10/feed/ 0 Asian Science And Math Olympiad (ASMO) 2019 For Grade 9 https://borneomath.com/asian-science-and-math-olympiad-asmo-2019-for-grade-9/ https://borneomath.com/asian-science-and-math-olympiad-asmo-2019-for-grade-9/#respond Fri, 02 Dec 2022 02:15:48 +0000 https://borneomath.com/?p=5990 Asian Science and Maths Olympiad (ASMO) is a competition platform designed to challenge and evaluate student’s knowledge in Mathematics and […]

The post Asian Science And Math Olympiad (ASMO) 2019 For Grade 9 first appeared on BorneoMath.

Berikut ini problems and solution ASMO 2019 grade 9

1. When two dice are rolled, find the probability of getting a sum that is divisible by 4.

Mata dadu berjumlah $4 : \{(2, 2), (1, 3), (3, 1)\}$ ada $3$
Mata dadu berjumlah $8 : \{(4, 4), (2, 6), (3, 5), (5, 3), (6, 2)\}$ ada $5$
Mata dadu berjumlah $12 : \{(6, 6)\}$ ada $1$
Jadi peluang jumlah kedua mata dadu habis dibagi 4 adalah
$\frac{3+5+1}{36}=\frac{9}{36}=\frac{1}{4}$

2. The tens digit of a two-digit number is two more than the units digit. When this two-digit number is divided by the sum of its digits, the answer is 6 remainder 3. Determine the sum of the digits of the two-digit number.

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3. The diagram shows a rectangle with length 9 cm and width 7 cm. One of the diagonals of the rectangle has been divided into seven equal parts. Determine the area of the shaded region.

ASMO 2019

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4. If $x + \sqrt{xy} + y = 9$ and $x^2 + xy + y^2=27$, then determine the value of $x – \sqrt{xy} + y$.

Misalkan

$𝑥 − \sqrt{𝑥𝑦} + 𝑦 = 𝐴$

Kurangkan persamaan $𝑥 + \sqrt{𝑥𝑦} + 𝑦 = 9$ dan $𝑥 − \sqrt{𝑥𝑦} + 𝑦 = 𝐴$, diperoleh

$2\sqrt{𝑥𝑦} = 9 − 𝐴 ⇒ 𝑥𝑦 = \frac{(9 − 𝐴)^2}{2}$

Jumlahkan persamaan $𝑥 + \sqrt{𝑥𝑦} + 𝑦 = 9$ dan $𝑥 − \sqrt{𝑥𝑦} + 𝑦 = 𝐴$, diperoleh

$2(𝑥 + 𝑦) = 9 + 𝐴$

Kuadratkan kedua persamaan

$4(𝑥^2 + 𝑦^2 + 2𝑥𝑦) = (9 + 𝐴)^2$
$⇒4(27 + 𝑥𝑦) = (9 + 𝐴)^2$
$⇒4 (27 + (\frac{(9-A)^2}{4}) = (9 + 𝐴)^2$
$⇒108 + (9 − 𝐴)^2 = (9 + 𝐴)^2$
$⇒108 = (9 + 𝐴)^2 − (9 − 𝐴)^2$
$⇒18(2𝐴) = 108$
$⇒𝐴 = 3$

5. There are 81 players taking part in a knock-out quiz tournament. Each match in the tournament involves 3 players and only the winner of the match remains in the tournament，the other two players are knocked out. Determine the number of matches that are required until there is an overall winner?

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6. Solve $12x^4-56x^3+89x^2-56x+12= 0$.

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7. The sizes in degrees of the interior angles of a hexagon are consecutive even numbers. Determine the size of the largest of these angles.

Misalkan keenam sudutnya adalah $∠𝑎_1, ∠𝑎_2, ∠𝑎_3, ∠𝑎_4, ∠𝑎_5$ dan $∠𝑎_6$ dimana $∠𝑎_1 < ∠𝑎_2 < ∠𝑎_3 < ∠𝑎_4 < ∠𝑎_5 < ∠𝑎_6$, karena keenam sudut membentuk pola bilangan genap berurutan maka diperoleh persamaan

$∠𝑎_1, +∠𝑎_2 + ∠𝑎_3 + ∠𝑎_4 + ∠𝑎_5 + ∠𝑎_6 = 720°$
$⇒∠𝑎_6 − 10, +∠𝑎_6 − 8 + ∠𝑎_6 − 6 + ∠𝑎_6 − 4 + ∠𝑎_6 − 2 + ∠𝑎_6 = 720°$
$⇒6(∠𝑎_6) − 30° = 720°$
$⇒∠𝑎_6 =\frac{750}{6}= 125°$

8. An integer is chosen from the set $\{1, 2, 3, …, 499, 500\}$. The probability that this integer is divisible by 7 or 11 is $\frac{n}{m}$ in its lowest terms. Determine the value of $n+m$.

Banyak himpunan bagian yang habis dibagi $7 : ⌊\frac{500}{7}⌋ = 71$
Banyak himpunan bagian yang habis dibagi $11 : ⌊\frac{500}{11}⌋ = 45$
Banyak himpunan bagian yang habis dibagi $77 : ⌊\frac{500}{77}⌋ = 6$
Jadi peluang terambilnya bilangan yang habis dibagi $7$ atau $11$ adalah $\frac{71+45−6}{500}=\frac{110}{500}=\frac{11}{50}=\frac{𝑛}{𝑚}$.
Nilai $𝑛 + 𝑚 = 11 + 50 = 61$

9. Determine all the possible three-digit numbers which are equal to 34 times the sum of their digits.

Misalkan bilangan 3 angka adalah $\overline{abc}$

$\overline{abc}= 34(𝑎 + 𝑏 + 𝑐)$
$⇒100𝑎 + 10𝑏 + 𝑐 = 34𝑎 + 34𝑏 + 34𝑐$
$⇒66𝑎 = 24𝑏 + 33𝑐$
$22𝑎 = 8𝑏 + 11𝑐$
$22𝑎 − 11𝑐 = 8𝑏$
$11(2𝑎 − 𝑐) = 8𝑏$

Bagian kiri adalah kelipatan $11$, maka hanya $1$ nilai $b$ yang mungkin yaitu $0$, dikarenakan nilai $𝑏$ selain $0$ hasil dari $8𝑏$ bukan kelipatan $11$.
karena nilai $b=0$ maka $(2𝑎 − 𝑐) = 0$, pasangan $(𝑎, 𝑏)$ yang memenuhi $2𝑎 − 𝑐 = 0$ adalah $\{(1, 2), (2, 4), (3, 6), (4, 8)\}$. Jadi banyak bilangan $3$ digit yang memenuhi ada $4$ bilangan yaitu $102, 204, 306,$ dan $408$.

10. How many integers between 1 and 1000, both 1 and 1000 inclusive, do not share a common factor with 1000?

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Problems and Solutions SEAMO PAPER E 2020
Asian Science And Math Olympiad (ASMO) 2018 For Grade 9

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]]> https://borneomath.com/asian-science-and-math-olympiad-asmo-2019-for-grade-9/feed/ 0 Asian Science And Math Olympiad (ASMO) 2019 For Grade 8 https://borneomath.com/asian-science-and-math-olympiad-asmo-2019-for-grade-8/ https://borneomath.com/asian-science-and-math-olympiad-asmo-2019-for-grade-8/#respond Thu, 01 Dec 2022 03:07:19 +0000 https://borneomath.com/?p=5972 Asian Science and Maths Olympiad (ASMO) is a competition platform designed to challenge and evaluate student’s knowledge in Mathematics and […]

The post Asian Science And Math Olympiad (ASMO) 2019 For Grade 8 first appeared on BorneoMath.

Berikut ini problems and solution ASMO 2019 grade 8

1. Determine the smallest natural number x which satisfies the inequality $x^{2006}>2006^{1003}$.

$𝑥^{2006} > 2006^{1003}$
$⇒ 𝑥^{2(1003)} > 2006^{1003}$
$⇒ 𝑥^2 > 2006$
Jadi nilai $x$ terkecil adalah $𝑥 = 45$

2. An amount of money is to be divided equally among a group of students. If there was 15 dollars more than this amount, then there would be enough for each student to receive 65 dollars. However, if each student was to receive 60 dollars, then 100 dollars would be left over. Determine the number of students in the group.

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3. Based on the diagram below, determine the height, h in units.

Gunakan perbandingan segitiga sebangun yaitu segitiga $𝐴𝐵𝐶 ≈ 𝐸𝐵𝐹$ dan $𝐴𝐵𝐷 ≈ 𝐴𝐸𝐹$
Pada segitiga $𝐴𝐵𝐶 ≈ 𝐸𝐵𝐹$

$\frac{𝑎 + 𝑏}{𝑏}=\frac{5}{ℎ}⇒ 𝑎 + 𝑏 =\frac{5𝑏}{ℎ}$

Pada segitiga $𝐴𝐵𝐷 ≈ 𝐴𝐸𝐹$

$\frac{𝑎 + 𝑏}{𝑎}=\frac{3}{ℎ}⇒ 𝑎 + 𝑏 =\frac{3𝑎}{ℎ}$

Samakam kedua persamaan

$𝑎 + 𝑏 = 𝑎 + 𝑏$
$⇒\frac{5𝑏}{ℎ}=\frac{3𝑎}{ℎ}$
$⇒5𝑏 = 3𝑎$

Diperoleh perbandingan $𝑎: 𝑏 = 5 ∶ 3$, misalkan $𝑎 = 5𝑥$ dan $𝑏 = 3𝑥$, subtitusi ke persamaan $𝑎 + 𝑏 =\frac{3𝑎}{ℎ}$, diperoleh
$ℎ =\frac{3𝑎}{𝑎 + 𝑏}=\frac{15𝑥}{5𝑥 + 3𝑥}=\frac{15}{8}$

Jadi panjang $h$ adalah $\frac{15}{8}$

4. Jess picks two consecutive integers, one of which ends in a 5. She multiplies the integers together and then squares the result. Determine the last two digits of her answer.

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5. Determine the last digit of $2^{2^{2007}} + 1$.

$(2^{2^2007}+ 1)\; mod\; 10$
Karena $2^{2007}\; mod\;4 ≡ 0$, maka bentuk di atas dapat disederhanakan menjadi $(2^4 + 1)\; mod\; 10 ≡ (16 + 1)\; mod\; 10 = 17\; mod\; 10 = 7$

6. The tens digit of a two-digit number is four more than the units digit. When this two-digit number is divided by the sum of its digits, the answer is 8 remainder 3. Determine the sum of the digits of the two-digit number.

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7. Consider the expression below,
$0+1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20$.
Determine the number of ways if three of the ‘+’ signs are changed to ‘–‘ signs so that the expression is equal to 100.

Misalkan hasil bagian penjumlahan adalah $A$ dan hasil bagian pengurangan adalah $B$

$𝐴 + 𝐵 = 210$
$𝐴 − 𝐵 = 100$
___________________-
$2𝐵 = 110$
$𝐵 = 55$

Karena $B$ merupakan penjumlahan $3$ angka minus maka banyak kemungkinan yang jumlahnya $-55$ adalah $(20. 19, 16), (20, 18, 17)$, hanya ada $2$, jadi banyak cara mengganti tiga tanda $“+”$ menjadi tanda $“-“$ sehingga jumlahnya $100$ ada $2$ cara

8. Carl tells Jill that he is thinking of three positive integers, not necessarily all different. He tells her that the product of his three integers is 36. Moreover, he also tells her the sum of his three integers. However, Jill still cannot figure out what the three integers are. Determine the sum of Carl’s three integers.

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9. Determine the sum of all the real numbers x that satisfy the equation

$(3^x – 27)^2 + (5^x – 625)^2=(3^x + 5^x – 652)^2$

Misalkan $3^𝑥 − 27 = 𝐴$ dan $5^𝑥 − 625 = 𝐵$

$𝐴^2 + 𝐵^2 = (𝐴 + 𝐵)^2$
$⇒𝐴^2 + 𝐵^2 = 𝐴^2 + 𝐵^2 + 2𝐴𝐵$
$⇒2𝐴𝐵 = 0$
$⇒𝐴 = 0 ∨ 𝐵 = 0$
$𝐴 = 0 ⇒ 3𝑥 − 27 = 0 ⇒ 𝑥 = 3$,
$𝐵 = 0 ⇒ 5𝑥 − 625 = 0 ⇒ 𝑥 = 4$

Jadi jumlah semua nilai $x$ yang memenuhi adalah 3 + 4 = 7[/latex]

10. If $x>0$ and $(x+\frac{1}{x})^2=49$, determine the value of $x^3+\frac{1}{x^3}$

$(𝑥 +\frac{1}{𝑥})^2= 49 ⇒ (𝑥 +\frac{1}{𝑥})= 7$

Bentuk lain

$(𝑥 +\frac{1}{𝑥})^2= 49 ⇒ 𝑥^2 +\frac{1}{𝑥^2} + 2 = 49 ⇒ 𝑥^2 +\frac{1}{𝑥^2}=47$

Jadi

$𝑥^3 +\frac{1}{𝑥^3} = (𝑥 +\frac{1}{𝑥})(𝑥^2 − 1 +\frac{1}{𝑥^2}) = 7(47 − 1) = 7(46) = 322$

Asian Science And Math Olympiad (ASMO) 2018 For Grade 8
GRADE 8-FINAL FMO 2021

The post Asian Science And Math Olympiad (ASMO) 2019 For Grade 8 first appeared on BorneoMath.

]]> https://borneomath.com/asian-science-and-math-olympiad-asmo-2019-for-grade-8/feed/ 0 Asian Science And Math Olympiad (ASMO) 2019 For Grade 7 https://borneomath.com/asian-science-and-math-olympiad-asmo-2019-for-grade-7/ https://borneomath.com/asian-science-and-math-olympiad-asmo-2019-for-grade-7/#respond Thu, 01 Dec 2022 02:25:27 +0000 https://borneomath.com/?p=5968 Asian Science and Maths Olympiad (ASMO) is a competition platform designed to challenge and evaluate student’s knowledge in Mathematics and […]

The post Asian Science And Math Olympiad (ASMO) 2019 For Grade 7 first appeared on BorneoMath.

Berikut ini problems and solution ASMO 2019 grade 7

1. Jessica walks from location A to location B in seven days, and back in six days. Each day, she walks one kilometer more than on the preceding day. Determine the distance between the location A and location B.

Misalkan hari pertama Jessica dapat berjalan sejauh $x$ km
Dari $A$ ke $B$ ditempuh selama $7$ hari
Jarak $A$ ke $B$ adalah $𝑥 + (𝑥 + 1) + (𝑥 + 2) + (𝑥 + 3) + (𝑥 + 4) + (𝑥 + 5) + (𝑥 + 6) = 7𝑥 + 21$
Dari $B$ ke $A$ ditempuh selama $6$ hari
Jarak $B$ ke $A$ adalah $(𝑥 + 7) + (𝑥 + 8) + (𝑥 + 9) + (𝑥 + 10) + (𝑥 + 11) + (𝑥 + 12) = 6𝑥 + 57$
Karena jarak $A$ ke $B$ dan jarak $B$ ke $A$ sama maka

$7𝑥 + 21 = 6𝑥 + 57$
$⇒7𝑥 − 6𝑥 = 57 − 21$
$⇒𝑥 = 36$

Jadi jarak $A$ ke $B$ adalah $7𝑥 + 21 = 7(36) + 21 = 252 + 21 = 273$ km

2. Winson thought of a whole number and then multiplied it by either 5 or 6. Erica added 5 or 6 to Winson’s answer. Finally Rachael subtracted either 5 or 6 from Erica’s answer. The final result was 73. Determine the number Winson thought.

Misalkan bilangan yang dipikirkan Wilson adalah $W$

Kemungkinan yang bisa menghasilkan $73$ adalah $6𝑊 + 1 = 73 ⇒ 6𝑊 = 72 ⇒ 𝑊 = 12$

3. Determine the largest integer $x$ such that $x^{6021}< 2007^{2007}$ .

$𝑥^{6021} < 2007^{2007}$
Kedua ruas dipangkatkan $\frac{1}{2007}$, diperoleh
$𝑥^3 < 2007$
Nilai $x$ terbesar yang memenuhi adalah $12$

4. Let $x$ and $y$ be two positive prime integers such that $\frac{1}{x}-\frac{1}{y}=\frac{192}{2005^2 – 2004^2}$. Determine the value of $y$ where $y > x$.

$\frac{1}{𝑥}−\frac{1}{𝑦}=\frac{192}{2005^2 − 2004^2}$
$\frac{𝑦 − 𝑥}{𝑥𝑦}=\frac{192}{(2005 − 2004)(2005 + 2004)}$
$\frac{𝑦 − 𝑥}{𝑥𝑦}=\frac{192}{4009}=\frac{192}{19 × 221}$
Jadi diperoleh nilai $y$ nya adalah $192$

5. In a certain triangle, the size of each of the angles is a whole number of degrees. Also, one angle is 60° larger than the average of the other two angles. Determine the largest possible size of an angle in this triangle.

not yet available

6. Find the sum

$\frac{2019}{1×2}+\frac{2019}{2×3}+…+\frac{2019}{2018×2019}$

$\frac{2019}{1×2}+\frac{2019}{2×3}+…+\frac{2019}{2018×2019}$
=$2019\left(\frac{1}{1×2}+\frac{1}{2×3}+…+\frac{1}{2018×2019}\right)$
=$2019\left(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+…+\frac{1}{2018}-\frac{1}{2019}\right)$
=$2019\left(\frac{1}{1}-\frac{1}{2019}\right)$
=$2019\left(\frac{2019-1}{2019}\right)$
=$2019\left(\frac{2018}{2019}\right)$
=$2019$

7. Ada thinks of a number. She adds 2 to it to get a second number. She then adds 3 to the second number to get a third number, adds 4 to the third to get a fourth, and finally adds 5 to the fourth to get a fifth number. Alan also thinks of a number but he subtracts 3 to get a second. He then subtracts 4 from the second to get a third, and so on until he too has five numbers. Finally, they discover that the sum of Ada’s five numbers is the same as the sum of Alan’s five numbers. Determine the difference between the two numbers of which they first thought.

not yet available

8. The figure shows part of a tiling, which extends indefinitely in every direction across the whole plane. Each tile is a regular hexagon. Some of the tiles are white, the others are black. Determine the fraction that the plane is white.

not yet available

9. In the following sum, O represent the digit 0. A, B, X and Y each represents distinct digit. Determine there are how many possible digits can A be.

Diketahui O = 0
karena XX adalah bilangan yang kembar maka nilai A+B hasilnya bilangan 2 digit yang kembar, Kemungkinannya hanya satu yaitu A + B = 11
Pasangan bilangan A dan B yang memenuhi adalah (2,9), (3,8), (4,7), (5,6), (6,5), (7,4), (8,3), (9,2). Banyak kemungkinan nilai A ada 8

10. The tens digit of a two-digit number is three more than the units digit. When this two- digit number is divided by the sum of its digits, the answer is 7 remainder 3. Determine the sum of the digits of the two-digit number.

Kemungkinan bilangan dua digit yang digit puluhannya lebih dari dari digit satuan adalah $\{30, 41, 52, 63. 74, 85, 96\}$, cek bilangan yang memenuhi jika dibagi dengan jumlah digitnya hasilnya adalah 7 dan bersisa 3.
$\frac{30}{3+0}= 10$ tidak memenuhi
$\frac{41}{4+1}= 8$ bersisa $1$ (Tidak memenuhi)
$\frac{52}{5+2}= 7$ bersisa $3$ (memenuhi)
Bilangan yang memenuhi adalah $52$, jumlah digitnya adalah $7$

11. Richard has four cubes all the same size: one blue, one red, one white and one yellow. He wants to glue the four cubes together to make the solid shape as shown in the figure below.
Determine the number of differently-coloured shapes can Richard make. [Two shapes are considered to be the same if one can be picked up and turned around so that it looks identical to the other.]

not yet available

12. Determine the sum of all corner angles of a 5-pointed star: $a+b+c+d+e.$

Jumlah sudut pada segitiga adalah $180°$, jadi

$𝑎 + 𝑏 + 𝑐 + 𝑑 + 𝑒 = 180°$

13. A 3-digit integer is called a ‘V-number’ if the digits go ‘high-low-high’ – that is, if the tens digit is smaller than both the hundreds digit and the units (or ‘ones’) digit. Determine the number of 3-digit ‘V-numbers’ that can be formed.

not yet available

14. Oscar wants to put the numbers 2, 3, 4, 5, 6 and 10 into the circles so that the products of the three numbers along each edge are the same, and as large as possible. Determine the product of the three numbers.

Hasil perkalian ketiga bilangannya adalah 60 dan 120. Jadi hasil perkalian terbesarnya adalah 120

15. A two-digit number ‘mn’ is multiplied by its reverse ‘nm’. The ones (units) and tens digits of the four-digit answer are both 0. Determine the value of the smallest such two-digit number ‘mn’.

not yet available

16. Simplify $\frac{2005^2(2004^2-2003)}{(2004^2-1)(2004^3+1)}×\frac{2003^2(2004^2+2005)}{2004^3-1}$

Misalkan $𝑎 = 2004$

$\frac{2005^2(2004^2 − 2003)}{(2004^2 − 1)(2004^3 + 1)}×\frac{2003^2(2004^2 + 2005)}{(2004^3 − 1)}$

$=\frac{(2004 + 1)^2(2004^2 − 2004 + 1)}{(2004^2 − 1)(2004^3 + 1)}×\frac{(2004 − 1)^2(2004^2 + 2004 + 1)}{(20043 − 1)}$

$=\frac{(𝑎 + 1)2(𝑎^2 − 𝑎 + 1)}{(𝑎^2 − 1)(𝑎^3 + 1)}×\frac{(𝑎 − 1)^2(𝑎^2 + 𝑎 + 1)}{(𝑎^3 − 1)}$

$=\frac{(𝑎 + 1)^2(𝑎^2 − 𝑎 + 1)}{(𝑎^2 − 1)(𝑎 + 1)(𝑎^2 − 𝑎 + 1)}×\frac{(𝑎 − 1)^2(𝑎^2 + 𝑎 + 1)}{(𝑎 − 1)(𝑎^2 + 𝑎 + 1)}$

$= 1$

17. Determine the value of $a+b+c$ if $a, b$ and $c$ stand for different digits.

Dengan melakukan percobaan diperoleh

Diperoleh $𝑎, 𝑏$ dan $𝑐$ nya adalah $3, 6$ dan $7$, Jadi nilai dari $𝑎 + 𝑏 + 𝑐 = 3 + 6 + 7 = 16$

18. Simplify the expression $\sqrt[n]{10\sqrt[n]{10\sqrt[n]{10\sqrt[n]{10\sqrt[n]{…}}}}}$ given that $n=2, 3, 4, 5, … .$

$\sqrt[n]{10\sqrt[n]{10\sqrt[n]{10\sqrt[n]{10\sqrt[n]{…}}}}}=a$

$⇒10\sqrt[n]{10\sqrt[n]{10\sqrt[n]{10\sqrt[n]{…}}}}=a^n$

$⇒10a=a^n$

$⇒10=a^{n-1}$

$⇒a=\sqrt[n-1]{10}$

19. Suppose that $x^2 + a = 2006, x^2 +b = 2007$ and $x^2 + c = 2008$ and $abc = 3$ . Determine the value of $\frac{a}{bc}+\frac{b}{ac}+\frac{c}{ab}-\frac{1}{a}-\frac{1}{b}-\frac{1}{c}.$

$𝑥^2 + 𝑎 = 2006 ⇒ 𝑎 = 2006 − 𝑥^2 = 𝑏 − 1$
$𝑥^2 + 𝑏 = 2007 ⇒ 𝑏 = 2007 − 𝑥^2$
$𝑥^2 + 𝑐 = 2008 ⇒ 𝑐 = 2008 − 𝑥^2 = 𝑏 + 1$

selanjutnya

$\begin{align}
\frac{𝑎}{𝑏𝑐}+\frac{𝑏}{𝑎𝑐}+\frac{𝑐}{𝑎𝑏}−\frac{1}{𝑎}−\frac{1}{𝑏}−\frac{1}{𝑐}&=
\frac{𝑎^2 + 𝑏^2 + 𝑐^2 − (𝑏𝑐 + 𝑎𝑐 + 𝑎𝑏)}{𝑎𝑏𝑐}\\
&=\frac{1}{3}[(𝑏^2 − 2𝑏 + 1 + 𝑏^2 + 𝑏^2 + 2𝑏 + 1 − (𝑏^2 + 𝑏 + 𝑏^2 − 1 + 𝑏^2 − 𝑏)]\\
&=\frac{1}{3}[2 + 1] = 1\\
\end{align}$

20. The difference between the highest common factor and the lowest common multiple of m and 18 is 120. Determine the value of m.

not yet available

21. The internal bisector of angle A of triangle ABC meets BC at D. The external bisector of angle A meets BC produced at E. If AB=6 units, AC=4 units and BC=6 units, determine the length DE.

sifat garis bagi pada segitiga

$nb=ma$

Buat segitiga baru yaitu $AFE$ yang kongruen dengan segitiga $ACE$.

Gunakan rumus garis bagi pada segitiga $BEF$

$4(6 + 𝑧) = 6𝑧$
$24 + 4𝑧 = 6𝑧$
$𝑧 = 12$

Gunakan rumus garis bagi pada segitiga $ABC$

$6𝑦 = 4𝑥$
$𝑥 : 𝑦 = 3: 2$

Panjang $𝑦 =\frac{2}{5}(6) =\frac{12}{5}= 2\frac{2}{5}$

Jadi panjang $DE = 12 + 2\frac{2}{5}= 14\frac{2}{5}$

22. In triangle ABC, D and E are points on AB and BC respectively. Given that AD:DB=2:3 and DE is parallel to AC, determine the ratio of the area of triangle BDE to the area of triangle ABC.

not yet available

23. In how many ways can the letters of the word MURMUR be arranged without letting two letters which are alike come together?

Banyak susunan seluruhnya adalah $\frac{6!}{2!.2!.2!} = 90$ susunan
Banyak susunan jika $UU$ berdekatan adalah $\frac{5!}{2!.2!}= 30$
Banyak susunan jika $RR$ berdekatan adalah $\frac{5!}{2!.2!}= 30$
Banyak susunan jika $MM$ berdekatan adalah $\frac{5!}{2!.2!}
= 30$
Banyak susunan jika $RR$ dan $UU$ berdekatan adalah $\frac{4!}{2!}= 12$
Banyak susunan jika $RR$ dan $MM$ berdekatan adalah $\frac{4!}{2!}= 12$
Banyak susunan jika $MM$ dan $UU$ berdekatan adalah $\frac{4!}{2!}= 12$
Banyak susunan jika $RR, MM$ dan $UU$ berdekatan adalah $3! = 6$
Jadi banyak susunan seluruhnya agar tidak ada huruf yang kember berdekatan adalah $90 − 30 − 30 − 30 + 12 + 12 + 12 − 6 = 30$ susunan

24. Determine how many numbers less than 2013 are both satisfying condition (1) and condition (2).
(1) the sum of five consecutive positive integers ; and
(2) the sum of two consecutive positive integers.

Dari syarat $(2)$ : penjumlahan dua bilangan bulat berurutan selalu bernilai ganjil
Dari syarat $(1)$ : misalkan bilangan tengahnya adalah n, maka penjumlahan lima bilangan berurutan dapat ditulis :

$(𝑛 − 2) + (𝑛 − 1) + 𝑛 + (𝑛 + 1) + (𝑛 + 2) = 5𝑛$

Dipastikan dari syarat $(2)$ bilangan yang memenuhi adalah bilangan kelipatan $5$, kecuali $5$ karena penjumlahan lima bilangan bulat positif minimal adalah $15$.
Dari gabungan kedua syarat bilangan yang memenuhi adalah bilangan ganjil kelipatan $5$ selain $5$.
Banyak bilangan yang memenuhi adalah $⌊\frac{2010}{5}⌋ − ⌊\frac{2010}{10}⌋ − 1 = 402 − 201 − 1 = 200$

25. We are given bases $|AB |= 23$ and $|CD|= 5$ of a trapezoid $ABCD$ with diagonals $| AC |= 25$ and $|BD|=17$. Determine the lengths of its sides BC and AD.

not yet available

The post Asian Science And Math Olympiad (ASMO) 2019 For Grade 7 first appeared on BorneoMath.

]]> https://borneomath.com/asian-science-and-math-olympiad-asmo-2019-for-grade-7/feed/ 0 Asian Science And Math Olympiad (ASMO) 2019 For Grade 6 https://borneomath.com/asian-science-and-math-olympiad-asmo-2019-for-grade-6/ https://borneomath.com/asian-science-and-math-olympiad-asmo-2019-for-grade-6/#respond Wed, 30 Nov 2022 03:09:32 +0000 https://borneomath.com/?p=5950 Asian Science and Maths Olympiad (ASMO) is a competition platform designed to challenge and evaluate student’s knowledge in Mathematics and […]

The post Asian Science And Math Olympiad (ASMO) 2019 For Grade 6 first appeared on BorneoMath.

Berikut ini problems and solution ASMO 2019 grade 6

1. Calculate：$238÷238\frac{238}{239}=?$

$\begin{align}
238 ÷ 238\frac{238}{239}&= 238 ÷\frac{238×239+238}{239}\\
&= 238 ×\frac{239}{238×239+238}\\
&=\frac{238×239}{238×239+238}\\
&=\frac{238×239}{238(239+1)}\\
&=\frac{239}{239+1}\\
&=\frac{239}{240}\\
\end{align}$

2. The sum of father’s and son’s age is 64 years old. Three times the son’s age is 8 years old older than father’s age. What are the ages of father and son respectively?

Umur Ayah : $𝐵$
Umur Anak : $𝐴$
$𝐴 + 𝐵 = 64$
$𝐵 = 3𝐴 + 8$
Subtitusi $𝐵 = 3𝐴 + 8$ ke persamaan $𝐴 + 𝐵 = 64$

$𝐴 + 3𝐴 + 8 = 64$
$⇒4𝐴 = 64 − 8$
$⇒4𝐴 = 56$
$⇒𝐴 = 56 ∶ 4 = 14$

Umur Ayah : $64 − 14 = 50$ 𝑡𝑎ℎ𝑢𝑛
Jadi umur Ayah adalah $50$ tahun dan umur anak adalah : $14$ tahun

3. The average value of A, B and C is 70. A has a value of 80 while B and C have the same value, what is the value of B?

$\frac{𝐴 + 𝐵 + 𝐶}{3}= 70$
$⇒𝐴 + 𝐵 + 𝐶 = 210$
$⇒80 + 𝐵 + 𝐵 = 210$
$⇒80 + 2𝐵 = 210$
$⇒2𝐵 = 130$
$⇒𝐵 = 65$

Jadi nilai $B$ adalah $65$

4. 150kg minus $\frac{1}{6}$ of its weight and $\frac{1}{6}$ kg. How much weight is remaining?

not yet available

5. Father has RM1500.00. He bought a table with 30% of his money. He bought a vacuum cleaner with 55% of the remaining money. Lastly, he gave half of the remaining money to mother. How much money did mother receive?

Membeli meja $: \frac{30}{100}× 1500 = 𝑅𝑀450, tersisa :1500 – 450 = 1050$
Membeli penyedot debu $: \frac{55}{100}× 1050 = 𝑅𝑀577,5$ , tersisa $:1050 – 577,5 = 472,5$
Uang yang diberikan ke Ibu $:\frac{1}{2}× 𝑅𝑀472,5 = 𝑅𝑀236,25$

6. The average value of 8 numbers is 180. After adding in 120 and 150, what is the new average value?

$\frac{𝑥_1 + 𝑥_2 + 𝑥_3 + ⋯ + 𝑥_8}{8}= 180$
$𝑥_1 + 𝑥_2 + 𝑥_3 + ⋯ + 𝑥_8 = 1440$

Tambah dua bilangan lagi yaitu $120$ dan $150$

$\frac{𝑥_1 + 𝑥_2 + 𝑥_3 + ⋯ + 𝑥_8 + 120 + 150}{10}=\frac{1440 + 120 + 150}{10}=\frac{1710}{10}=171$

Jadi rata-rata barunya adalah $171$

7. The current age for little brother is $\frac{1}{2}$ of big brother’s age. 9 years ago, little brother’s age is only $\frac{1}{5}$ of big brother’s age. How old is big brother now?

Misalkan umur kakak adalah $K$ dan umur Adik adalah $A$

$𝐴 =\frac{1}{2}$
$𝐾 ⇒ 𝐾 = 2𝐴$

$9$ tahun yang lalu umur adik hanya $\frac{1}{5}$ dari umur kakak

$𝐴 − 9 =\frac{1}{5}(𝐾 − 9)$
$5𝐴 − 45 = 𝐾 − 9$

Ganti nilai $K$ dengan $2A$

$5𝐴 − 45 = 2𝐴 − 9$
$5𝐴 − 2𝐴 = 45 − 9$
$3𝐴 = 36$
$𝐴 = 12$

Jadi umur kakak sekarang adalah $2(12)=24$ tahun.

8. To cut a piece of wood into 4 sections requires 6 minutes. How long does it take to cut the piece of wood into 8 sections?

Untuk memotong kayu menjadi 4 bagian maka kayu dipotong sebanyak 3 kali, 3 kali membutuhkan 6 menit, 1 kali potongan membutuhkan waktu 2 menit.
Jadi untuk memotong kayu menjadi 8 bagian dibutuhkan 7 kali potongan, waktu yang diperlukan adalah 7 × 2 = 14 menit.

9. If someone invests in a stock that reduces in value for 20% in the first year. How many percent must the stock increase in value so that the stock value comes back to its original value?

Misalkan investasi awal $$100$
Tahun pertama terjadi penurunan sebanyak $20%$ atau
$\frac{20}{100}× 100 = $20$. Modal Investasinya sekarang adalah $$80$.
Tahun berikut dia menginginkan uangnya kembali semula, berapa persen keuntungan yangharus diperoleh?
Supaya uangnya kembali ke awal maka harus naik $$20$.
Jadi persentase kenaikan
$\frac{20}{80}× 100\% = 25\%$

10. Two cubes with a bottom surface area of 20 cm² are combined to become a cuboid. What is the surface area of the cuboid?

Luas satu persegi (alas) = $20$ cm², pada saat di satukan membentuk balok banyak persegi yang terlihat sebanyak $10$ persegi. Jadi luas permukaan balok adalah $10 × 20 = 200$𝑐𝑚²

Asian Science And Math Olympiad (ASMO) 2018 For Grade 6
GRADE 6 – SAMPEL PAPER FINAL FMO 2021
Problem and Solution SEAMO 2017 paper C
Contoh Soal Lomba KST Kelas 6 Tingkat SD/MI

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]]> https://borneomath.com/asian-science-and-math-olympiad-asmo-2019-for-grade-6/feed/ 0 Asian Science And Math Olympiad (ASMO) 2019 For Grade 5 https://borneomath.com/asian-science-and-math-olympiad-asmo-2019-for-grade-5/ https://borneomath.com/asian-science-and-math-olympiad-asmo-2019-for-grade-5/#respond Wed, 30 Nov 2022 02:40:07 +0000 https://borneomath.com/?p=5943 Asian Science and Maths Olympiad (ASMO) is a competition platform designed to challenge and evaluate student’s knowledge in Mathematics and […]

The post Asian Science And Math Olympiad (ASMO) 2019 For Grade 5 first appeared on BorneoMath.

Berikut ini problems and solution ASMO 2019 grade 5

1.Calculate : $83.4 ÷ 2.3 + 31.6 ÷ 2.3 = ?$

not yet available

2. What is the perimeter of the below diagram (unit : cm)

not yet available

3. A fertilizer factory plans to make 10800 tons of fertilizer in 25 days. During the making process, the factory makes an extra 108 tons every day. At this rate, how many days earlier can the factory finish making the fertilizer?

not yet available

4. $\frac{1}{7}=0,142857142857…$ What is the $2019^{th}$ number after the decimal point?

not yet available

5. Based on the diagram below, the large square has and edge lenght of 12 cm. What is the area of the smallest square in the middle?

not yet available

6. There is a four-digit symmetry number. The sum of four digits is 10. The tens digit is larger than the ones digit by 3. What is this four-digit number?

not yet available

10. In the equation below， is filled with different numbers. What is the sum of these numbers?

X = 1995

not yet available

Problem and Solution SEAMO 2017 paper C
Asian Science and Math Olympiad (ASMO) 2018 For Grade 5
GRADE 5 – SAMPEL PAPER FINAL FMO 2021
Contoh Soal Lomba KST Kelas 5 Tingkat SD/MI

The post Asian Science And Math Olympiad (ASMO) 2019 For Grade 5 first appeared on BorneoMath.

]]> https://borneomath.com/asian-science-and-math-olympiad-asmo-2019-for-grade-5/feed/ 0 Asian Science And Math Olympiad (ASMO) 2019 For Grade 4 https://borneomath.com/asian-science-and-math-olympiad-asmo-2019-for-grade-4/ https://borneomath.com/asian-science-and-math-olympiad-asmo-2019-for-grade-4/#respond Wed, 30 Nov 2022 02:07:42 +0000 https://borneomath.com/?p=5936 Asian Science and Maths Olympiad (ASMO) is a competition platform designed to challenge and evaluate student’s knowledge in Mathematics and […]

The post Asian Science And Math Olympiad (ASMO) 2019 For Grade 4 first appeared on BorneoMath.

Berikut ini problems and solution ASMO 2019 grade 4

1. Calculate：$125×63×8= ?$

not yet available

2. Based on the diagram below, how many triangles are there?

not yet available

3. At the same time, two cars depart from A and B respectively. One of the car moves at a rate of 62km per hour while the other moves at a rate of 65 km per hour. After 5 hours, both of the cars meet together. What is the distance between A and B?

not yet available

4. A pond has a perimeter of 1500m. A tree is planted every 6m of the side of the pond. How many trees are planted?

not yet available

5. Calculate：$333×334+999×222= ?$

not yet available

6. A tourism company has 36 workers. 24 of the workers can speak English, 18 of the workers can speak French, 4 of the workers cannot speak both languages. How many workers can speak both languages?

not yet available

7. A television factory produced 3300 units of television in the first 10 days of June. 6300 units of television were produced in the remaining 20 days. What is the average number of televisions produced in a day for this month?

not yet available

8. There is a computer shop that sells computers. In the morning, the number of computers sold is 10 more than half of the computers in the shop. In the afternoon, the number of computers sold is 10 more than half of the computers remaining in the shop. At the end of the day, the number of computers remaining in the shop is 50 units. How many computers are there in the shop initially?

not yet available

9. 3 ducks require 5250g of food for 7 days. Based on the same calculation, how many grams of food is needed for 6 ducks for 15 days?

not yet available

10. When two people meet, they have to shake their hands once. Based on the same rule, how many times must 6 people shake hands when they meet?

not yet available

Asian Science and Math Olympiad (ASMO) 2018 For Grade 4
Problems And Solutions SEAMO PAPER B 2021
GRADE 4 – SAMPEL PAPER FINAL FMO 2021
Contoh Soal Lomba KST Kelas 4 Tingkat SD/MI

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]]> https://borneomath.com/asian-science-and-math-olympiad-asmo-2019-for-grade-4/feed/ 0 Asian Science And Math Olympiad (ASMO) 2019 For Grade 3 https://borneomath.com/asian-science-and-math-olympiad-asmo-2019-for-grade-3/ https://borneomath.com/asian-science-and-math-olympiad-asmo-2019-for-grade-3/#respond Wed, 30 Nov 2022 01:01:15 +0000 https://borneomath.com/?p=5927 Asian Science and Maths Olympiad (ASMO) is a competition platform designed to challenge and evaluate student’s knowledge in Mathematics and […]

The post Asian Science And Math Olympiad (ASMO) 2019 For Grade 3 first appeared on BorneoMath.

Berikut ini problems and solution ASMO 2019 grade 3

1. Calculate $299 999+29 999+2 999+299+29+9=？$

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2. What is the perimeter for the diagram below?

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3. How many quadrilaterals are there in the diagram below?

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4. Identify the pattern and fill in the blanks：

$1 × 9 + 2 = 11$
$12 × 9 + 3 = 111$
$123 × 9 + 4 = 1111$
.
.
.
$1234567 × 9 + 8 =(\;\;\;\;\;\;)$

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5. It is known that – = 36, =+++

find the value of

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6. $240，120，（ Y ），30，15，…$
Based on the pattern of the number line above, calculate the sum of the first and the third number.

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7. In between 10 and 40, how many multiples of 3 are there?

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8. 12 children line up to exercise. The distance between each child is 6m. How long is the line?

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9. Two boards that are nailed together has a length of 160cm. The overlapping section has a length of 45cm. One of the board has a length of 85cm, what is the length of the other board?

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10. Jia Xin used 3 days to finish reading a book. She read 27 pages on the first day and 54 pages on the remaining 2 days. What is the average number of pages read by Jia Xin each day?

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GRADE 3-HEAT ROUND FMO 2021
Grade 3-Sample Questions GJMOC
Contoh Soal Lomba KST Kelas 3 Tingkat SD/MI

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]]> https://borneomath.com/asian-science-and-math-olympiad-asmo-2019-for-grade-3/feed/ 0 Asian Science And Math Olympiad (ASMO) 2019 For Grade 2 https://borneomath.com/asian-science-and-math-olympiad-asmo-2019-for-grade-2/ https://borneomath.com/asian-science-and-math-olympiad-asmo-2019-for-grade-2/#respond Tue, 29 Nov 2022 12:37:33 +0000 https://borneomath.com/?p=5916 Asian Science and Maths Olympiad (ASMO) is a competition platform designed to challenge and evaluate student’s knowledge in Mathematics and […]

The post Asian Science And Math Olympiad (ASMO) 2019 For Grade 2 first appeared on BorneoMath.

Berikut ini problems and solution ASMO 2018 grade 2

1. Calculate：$21+79+88+99+12+1=？$

(A) 200
(B) 300
(C) 301
(D) 302

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2. $A, B, B, C, D, D, D, A, B, B, C, D, D, D, A, B, B, C, D, D, D, …$
Based on the pattern above, find out the 24th letter.

(A) A
(B) B
(C) C
(D) D

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3. How many triangles are there in the diagram below?

(A) 9
(B) 10
(C) 11
(D) 12

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4. Albert reads a book. He has read 26 pages which is half of the book. How many pages does the book have?

(A) 26
(B) 50
(C) 52
(D) 60

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5. A piece of wood is cut into 4 segments in 6 minutes. How many minutes are needed to cut the wood into 8 segments?

(A) 10
(B) 12
(C) 14
(D) 16

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6. Hung Hung has 28 pencils, Andy has 14 pencils. How many pencils does Hung Hung have to give Andy so that both of them have the same number of pencils?

(A) 7
(B) 10
(C) 14
(D) 28

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7. Based on the equation above, what is the value of 10 ‘a’？

(A) 7
(B) 14
(C) 63
(D) 70

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8. A child needs 5 minutes to finish eating an apple. How many minutes does it take for 4 children to finish 4 same apples?
(A) 5
(B) 6
(C) 8
(D) 20

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9. There are 27 trees. Every child plants 3 trees. How many children are there?
(A) 6
(B) 7
(C) 8
(D) 9

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10. Based on the pattern above, find the value of ( ? ).

(A) 20
(B) 18
(C) 16
(D) 14

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11. A number, if added by 2, then subtracted by 6, the answer will be 10. What is the number?

(A) 6
(B) 8
(C) 10
(D) 14

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12. Based on the diagram below, how many triangles are there?

(A) 6
(B) 10
(C) 13
(D) 15

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13. Edmund divides 20 flags into 5 inequal groups. What is the largest number of flags that a group can have?

(A) 4
(B) 5
(C) 10
(D) 16

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14. Calculate：$200-11-22-47-39-28-3=？$

(A) 123
(B) 50
(C) 23
(D) 11

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15. Below is a diagram of 3 arrangements of cuboids labelled with 1，2，3，4，5，6. Which of the following is correct?

(A) 5 at is the opposite of 1
(B) 5 at is the opposite of 4
(C) 6 at is the opposite of 2
(D) None of the above

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16. Harry is 5 years old this year. His cousin, Johnson is 3 times older than the age of Harry after two years. What is Johnson’s age this year?

(A) 15
(B) 21
(C) 23
(D) 25

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17. 6 sheep eat 96kg of grass in 8 days. On average, how much grass does 1 sheep eat every day?

(A) 2
(B) 4
(C) 6
(D) 12

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18. By using these four numbers 7，3，4，2, how many different 4-digit numbers can be made up?

(A) 24
(B) 20
(C) 16
(D) 14

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19. It is Tuesday on 1-3-2016. What day is it on 31-3-2016？

(A) Monday
(B) Tuesday
(C) Wednesday
(D) Thursday

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20. A type of plant will double its height every day. After 20 days, it has a height of 20 cm. When it has a height of 5cm, how many days has it taken?

(A) 19
(B) 18
(C) 10
(D) 5

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21. A pail is fully filled with water, the weight of the pail and water is 20kg. After half of the water is used, the weight of the pail and water is 11kg. What is the weight of the pail?

(A) 2
(B) 9
(C) 11
(D) 18

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22. There are 31 apples. How many apples have to be removed so that 9 children can get the same amount of apples? How many apples does every child get?

(A) 4;4
(B) 4;3
(C) 3;4
(D) 3;2

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23. In the range of 0~100，how many times does “5” appear？

(A) 10
(B) 18
(C) 20
(D) 25

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24. Use the smallest three-digit number to subtract the largest two-digit number and add the largest single digit number. What is the answer?

(A) 10
(B) 11
(C) 208
(D) 909

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25. While doing an addition question, Mulan accidentally viewed 1 as 7 on the ones position and 6 as 9 on the tens position. Her answer is 175. What should be the right answer?

(A) 78
(B) 114
(C) 139
(D) 231

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