Problems And Solutions Future Intelligence Student Olympiad (9-10 Grades)

“Future Intelligence Students Olympiad”

During this global pandemic periods we witness, students’ shift to the online learning system. A Mathematics, English and Science competition for students of grades 1 – 12, with six levels. In addition, Art competition for students of grades 1 – 12, with two levels. The key competence tested by FISO online is logical combination, not just pure knowledge of formulas.Aiming to encourage students to study and critical thinking. FISO Olympiad team decided to conduct an online Olympiad of FISO Mathematics, English, Science, Chemistry, Biology, Physics and Art Olympiad to boost the motivation of both teachers and students who have been bored, lost goal-oriented character and stimulus for study under this difficult global pandemic times, when most of the Olympiads and competitions are forced to be cancelled or postponed until unknown time. FISO Olympiad team also hopes this competition will help all types of schools to keep their students engaged and to observe their Mathematics, English, Science and Art education in an international arena. (sc : www.fisoolympiad.com)

Berikut ini Soal dan Solusi contoh soal lomba FISO level Grade 9 and 10

1) Find highest common factor of 25, 30 and 40.

A) 15
B) 600
C) 5
D) 72

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2) Sum of four consecutive numbers is 78. Find the biggest number?

A) 20
B) 19
C) 21
D) 17

misalkan keempat bilangan adalah \(𝑎, 𝑎 + 1, 𝑎 + 2, 𝑎 + 3\)

\(𝑎 + (𝑎 + 1) + (𝑎 + 2) + (𝑎 + 3) = 78\)
\(⇒4𝑎 + 6 = 78\)
\(⇒4𝑎 = 72\)
\(⇒𝑎 = 18\)

Jadi bilangan terbesarnya adalah \(𝑎 + 3 = 18 + 3 = 21\)

3) Solve

\(\left[\left(\frac{0,025}{0,05}\right):\left(\frac{1}{2}-1\right)\right]^{{-2}^2}=?\)

A) 2
B) – 1
C) 1
D) 4

\(\begin{align}
\left[\frac{(\frac{25}{1000}}{\frac{5}{100}}) : (−\frac{1}{2})\right]^{-4}&= \left[\frac{25}{1000}×\frac{100}{5}× (\frac{−2}{1})\right]^{−4}\\
&=\left[\frac{5}{10}× (\frac{-2}{1})\right]^{−4}\\
&= [−1]^{−4} = 1\\
\end{align}\)

4) Find the simplest form

\(\frac{1}{2}-\left(\frac{1}{5}-\frac{1}{10}\right)-\left(\frac{1}{2}-\frac{1}{10}+\frac{1}{5}\right)=?\)

A. \(\frac{1}{5}\)
B. 1
C. \(-\frac{1}{5}\)
D. 5

\(\frac{1}{2}-\left(\frac{1}{5}-\frac{1}{10}\right)-\left(\frac{1}{2}-\frac{1}{10}+\frac{1}{5}\right)=\frac{5}{10}-\left(\frac{2}{10}-\frac{1}{10}\right)-\left(\frac{5}{10}-\frac{1}{10}+\frac{2}{10}\right)= −\frac{1}{5}\)

5) Two pipes A and B can fill a storage tank in four and six hours respectively. A
drain C can empty the full tank in three hours. How long will it take to fill the tank if both pipes and the drain are open?

A) 9
B) 12
C) 18
D) 24

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6) Simplify

\(\frac{x^2-3x+2}{x-1}×\frac{x+2}{x^2-4}\)

A) x
B) – x
C) 1
D) – 1

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7) Find

\(\frac{\sqrt[3]{a^2}+a}{\sqrt[3]{a}+a}-\frac{\sqrt[3]{a}-1}{\sqrt[3]{a^2}+1}\)

A) \(a\)
B) -1
C) 1
D) \(\sqrt a\)

\(\frac{\sqrt[3]{a^2}+a}{\sqrt[3]{a}+a}-\frac{\sqrt[3]{a}-1}{\sqrt[3]{a^2}+1}\)

\(=\frac{𝑎^{\frac{2}{3}}+𝑎^{\frac{3}{3}}}{𝑎^{\frac{1}{3}}+𝑎^{\frac{3}{3}}} -\frac{𝑎^{\frac{1}{3}}-1}{𝑎^{\frac{2}{3}}+1}\)

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

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

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

8) Find the quotient

\(\frac{x^2+7x+12}{x^2-9}÷\frac{x^2+5x+4}{(x^2-3x)(x+1)}\)

A) 1
B) x
C) -1
D) -x

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9. find

\(2-\frac{1}{2-\frac{1}{2-\frac{1}{2-\frac{1}{2-…}}}}=?\)

A) 2
B) 4
C) 8
D) 1

Misalkan

\(2-\frac{1}{2-\frac{1}{2-\frac{1}{2-\frac{1}{2-…}}}}= 𝑥\)
\(2 −\frac{1}{𝑥}= 𝑥\)
\(⇒ 2𝑥 − 1 = 𝑥^2\)
\(⇒ 𝑥^2 − 2𝑥 + 1 = 0\)
\(⇒ (𝑥 − 1)^2 = 0\)
\(⇒ 𝑥 = 1\)

10) Find

\(\frac{\sqrt{6,3 · 1,7}·\left(\sqrt{\frac{6,3}{1,7}}-\sqrt{\frac{1,7}{6,3}}\right)}{\sqrt{(6,3+1,7)^2-4·6,3·1,7}}=?\)

A) 32
B) 1
C) 48
D) 72

Misalkan \(𝑎 = 6,3\) dan \(𝑏 = 1,7\)

\(\frac{\sqrt{6,3 · 1,7}·\left(\sqrt{\frac{6,3}{1,7}}-\sqrt{\frac{1,7}{6,3}}\right)}{\sqrt{(6,3+1,7)^2-4·6,3·1,7}}\)

\(=\frac{\sqrt{ab}·\left(\sqrt{\frac{a}{b}}-\sqrt{\frac{b}{a}}\right)}{\sqrt{(a+b)^2-4ab}}\)

\(=\frac{\sqrt{a^2} – \sqrt{b^2}}{\sqrt{a^2+2ab+b^2-4ab}}=\frac{a-b}{\sqrt{(a-b)^2}}=\frac{a-b}{a-b}=1\)

11) Find y=?

\(x-y+2z=2\)
\(x-y+z=2\)
\(x+y-z=0\)

A) -1
B) 1
C) 0
D) 2

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12) Solve

\(\left[\frac{(13,75+9\frac{1}{6})·1,2}{(10,3 – 8\frac{1}{2})·\frac{5}{9}} + \frac{6,8 – 3\frac{3}{5})·5\frac{5}{6}}{(3\frac{2}{3}-3\frac{1}{6})·56}\right]·6=?\)

A) 1
B) – 1
C) 169
D) 196

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13. Solve

\(\frac{0,4·10^{-2}-3·10^{-3}}{20·10^{-2}}=?\)

A) 0,002
B) 0,005
C) 0,001
D) \(\frac{1}{250}\)

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14) A machine produces 1250 pencils in five hours. How many pencils can the machine produce in 12.5 hours?

A) 3125
B) 2525
C) 3625
D)

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15. Solve

A) 1278
B) 3951
C) 5921
D) 87274

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16) Find \(n\)

\(\left(\frac{1}{3}\right)^{-2n} · 9^{n+1} ·27^{1-n}=81\)

A) – 2
B) – 1
C) 1
D) 2

\((3)^{2𝑛} ∙ (3)^{2(𝑛+1)} ∙ (3)^{3(1−𝑛)} = 3^4\)
\(⇒3^{2𝑛+2𝑛+2+3−3𝑛} = 3^4\)
\(⇒𝑛 + 5 = 4\)
\(⇒𝑛 = −1\)

17) If \(c = 2\) and \(d =\frac{1}{4}\), then find

\(\frac{\sqrt{c-d}}{c^2\sqrt{2c}}·\left(\sqrt{\frac{c-d}{c+d}} +\sqrt{\frac{c^2+cd}{c^2-cd}}\right)\)

A)0
B)1
C) \(\frac{1}{4}\)
D) \(\frac{1}{3}\)

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18) Find \(a·b\)

\(2^a=81\)
\(3^b=32\)

A) 20
B) 18
C) 16
D) 15

Cara logaritma
\(2^𝑎 = 81⟹𝑎 = \log_2 {81} = \log_2 {3^4} = 4 \log_2 3\)
\(3^𝑏 = 32⟹𝑏 = \log_3 {32} = \log_3 {2^5} = 5 \log_3 2\)
Selanjutnya
\(𝑎𝑏 = 4 \log_2 3 × 5 \log_3 2 = 20 \log_2 3 × \log_3 2 = 20 \log_2 2 = 20\)

19) Find the number which corresponds to the place indicated by the question mark.

A) 34
B) 58
C) 40
D) 84

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20) 80% of the students in a class pass a math exam. If six students failed the exam, find the number of students in the class.

A) 30
B) 24
C) 28
D) 22

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21) The sum of three numbers is 97. The third number is twice as large as the second. The second number is one more than twice the first number. Find the biggest number?

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22) Find the number which corresponds to the place indicated by the question mark.

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23) Evaluate

\(\sqrt{256} · sin\; 10° · sin\; 30° · sin\; 50° · sin\; 70° =?\)

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24) Find sum of areas

\([ABD] + [ADC] = ? 𝑐𝑚^2\)

\(\begin{align}
[ABD] + [ADC] &=\frac{1}{2}𝐴𝐷. 𝐵𝐻 +\frac{1}{2}𝐴𝐷. 𝐻𝐶\\
&=\frac{1}{2}𝐴𝐷(𝐵𝐻 + 𝐻𝐶)\\
&=\frac{1}{2}(5)(16)\\
&= 40\; 𝑐𝑚^2\\
\end{align}\)

25) Solve

\(\frac{2\frac{3}{4} ÷ 1,1 + 3\frac{1}{3}}{2,5 – 0,4·3\frac{1}{3}}÷\frac{5}{7}-\frac{(2\frac{1}{6}+4,5)·0,375}{2,75-1\frac{1}{2}}\)

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“Future Intelligence Students Olympiad”

\(\frac{x^2+7x+12}{x^2-9}÷\frac{x^2+5x+4}{(x^2-3x)(x+1)}\)

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