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 11 and 12

1. $$365m72$$ is a six-digit number where $$m$$ is a digit. If $$365m72$$ is divisible by $$9$$, find the sum of all possible values of $$m$$?

A) 1
B) 2
C) 3
D) 4

Belum tersedia

2. Find $$x$$ in the following equation.

$$\frac{2x}{3+\frac{4}{3+\frac{4}{3+\frac{4}{…}}}}+\frac{3x}{2+\frac{3}{2+\frac{3}{2+\frac{3}{…}}}} = 3$$

A) 1
B) 2
C) 3
D) 4

$$3+\frac{4}{3+\frac{4}{3+\frac{4}{…}}}=𝑎 ⇒ 3 +\frac{4}{𝑎}= 𝑎 ⇒ 𝑎 = 4$$

$$2+\frac{3}{2+\frac{3}{2+\frac{3}{…}}}=b ⇒ 2 +\frac{3}{b}= b ⇒ b = 3$$

Diperoleh

$$\frac{2𝑥}{4}+\frac{3𝑥}{3}= 3 ⇒\frac{3}{2}𝑥 = 3 ⟹ 𝑥 = 2$$

3. An electrical cut 53-meter-long piece of wire into three pieces, such that the longest pieces is four times as long as the shortest piece and the middle-sized piece is three meters shorter than twice the length of the shortest piece. Find the length of longest piece?

A) 8
B) 13
C) 22
D) 32

Belum tersedia

4. Two pipes can fill a pool in six hours. The larger pipe can fill the pool twice as fast as the smaller one. How long does it take the smaller pipe to fill the pool alone?

A) 3
B) 6
C) 9
D) 18

Belum tersedia

5. Solve

$$\left(\frac{1-\frac{1}{a^2}}{\frac{1}{a}+1}\right)\left(\frac{a^2}{1-a}\right)=?$$

A) $$a + 1$$
B) $$– a$$
C) $$a$$
D) $$– a – 1$$

$$\left(\frac{1-\frac{1}{a^2}}{\frac{1}{a}+1}\right)\left(\frac{a^2}{1-a}\right)$$

$$=\left(\frac{\frac{a^2-1}{a^2}}{\frac{1+a}{a}}\right)\left(\frac{a^2}{1-a}\right)$$

$$=\left(\frac{a^2-1}{a^2}\right)(\frac{a}{a+1})\left(\frac{a^2}{1-a}\right)$$

$$=\frac{(a+1)(a-1)}{a^2}(\frac{a}{a+1})\left(\frac{a^2}{1-a}\right)=-a$$

6. 6. A café offers chocolate, lemon, sour cherry and vanilla flavors of ice cream. A costumer can choose one, two or three scoops but the flavors must all be different. How many different possible ice creams can a customer order?

A) 4
B) 6
C) 10
D) 14

Belum tersedia

7. Simplify the expression

$$\frac{a^3 – b^3}{a^2b+ab^2+b^3}·\frac{2b^2+2ab}{a^2-b^2}=?$$

A) 1
B) 2
C) $$\frac{2}{ab}$$
D) $$\frac{2(a+b)}{ab}$$

$$\frac{a^3 – b^3}{a^2b+ab^2+b^3}·\frac{2b^2+2ab}{a^2-b^2}$$

$$=\frac{(a-b)(a^2+ab+b^2)}{b(a^2+ab+b^2}·\frac{2b(b+a}{(a-b)(a+b)}=2$$

8. Simplify

$$\frac{\log_x 8}{\log_y 3}·\frac{\log_y(\frac{1}{9})}{\log_x(\frac{1}{2})}=?$$

A) 6
B) 3
C) -4
D) $$\frac{\log_x 4}{\log_y 3}$$

$$\frac{\log_x 8}{\log_y 3}·\frac{\log_y 3^{-2}}{\log_x 2^{-1}}$$

$$=\frac{-2\log_x 8 × \log_y 3}{-1\log_y 3 × \log_x 2}$$

$$=2\log_2 8 × \log_3 3=2×3×1=6$$

9. In a polygon $$ABCDE, EK$$ and $$BK$$ are the bisectors of angles $$E$$ and $$B$$ respectively. Find the measure of angle $$EKB$$?

A) 125
B) 120
C) 110
D) 100

$$70° + 120° + 130° + 2(𝑎 + 𝑏) = 540°$$
$$320° + 2(𝑎 + 𝑏) = 540°$$
$$2(𝑎 + 𝑏) = 220°$$
$$𝑎 + 𝑏 = 110°$$
Dari segiempat $$EKAB$$
$$130° + 𝑎 + 𝑏 + ∠𝐸𝐾𝐵 = 360°$$
$$130° + 110° + ∠𝐸𝐾𝐵 = 360°$$
$$∠𝐸𝐾𝐵 = 360° − 240° = 120°$$

10. In the figure, $$ABCD$$ is a square. Find the measure of angle $$DCF$$?

A) 20
B) 30
C) 45
D) 55

11. O is the center of circle

A) 20
B) 40
C) 60
D) 75

jadi jumlah $$∠CEB + ∠CAB = 20°+20°=40°$$

12. In accordance with the relationship. Find the number which corresponds to the place indicated by the question mark?

A) 156
B) 438
C) 1032
D) 2811

Belum tersedia

13. Find the number, which corresponds to the place indicated by question mark.

A) 14
B) 17
C) 20
D) 23

Belum tersedia

14. Find the number, which corresponds to the place indicated by question mark.

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

Belum tersedia

15. Simplify trigonometric expression.

$$\frac{(\sin x + \cos x)^2 – 1}{(\sin x – \cos x)^2 – 1}$$

A) – 1
B) 0
C) 1
D) sinx + cosx

Belum tersedia

16. Simplify $$\frac{4·\cos 50°·\sin 50°·\cos 100°}{\sin 200°}$$

A) 1
B) $$\frac{\sqrt 3}{16} \cot 10°$$
C) $$\cot 10°$$
D) -1

Belum tersedia

17. Solve

$$f(x)=5^{2x-1}$$
$$fοf^{-1}(x)+f^{-1}οf(x)=?$$

A) $$x$$
B) $$5^x$$
C) $$2x$$
D) $$1$$

Belum tersedia

18. With the given information, find $$k$$?

$$x+4=y$$
$$y+5=z$$
$$z+x=2k$$
$$x+y+z=21$$

A) -6
B) $$\frac{43}{6}$$
C) $$7$$
D) $$\frac{51}{7}$$

$$𝑥 + 𝑦 + 𝑧 + 𝑥 + 9 = 𝑦 + 𝑧 + 2𝑘$$
$$2𝑥 + 9 = 2𝑘$$
$$𝑥 =\frac{2𝑘 − 9}{2}$$
Selanjutnya ubah $$y$$ dan $$z$$ dalam $$k$$
$$𝑧 = 𝑦 + 5 = 𝑥 + 4 + 5 = 𝑥 + 9 =\frac{2𝑘 − 9}{2}+ 9 =\frac{2𝑘 + 9}{2}$$
$$𝑦 = 𝑥 + 4 =\frac{2𝑘 − 9}{2}+ 4 =\frac{2𝑘 − 1}{2}$$
Subtitusi nilai $$x, y$$ dan $$z$$ ke $$𝑥 + 𝑦 + 𝑧 = 21$$

19. Find the quotient

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

A) 1
B) $$x$$
C) $$\frac{x}{x+1}$$
D) $$\frac{x}{x-1}$$

Belum tersedia

20. Solve

$$\frac{(x^2-y^2)(\sqrt[3]{x}+\sqrt[3]{y})}{\sqrt[3]{x^5}+\sqrt[3]{x^3y^3}-\sqrt[3]{x^3y^2}-\sqrt[3]{y^5}}-(\sqrt[3]{xy}+\sqrt[3]{y^2})=?$$

A) 1
B) $$x^2$$
C) $$\sqrt[3]{x^2}$$
D) $$x^2y$$

Belum tersedia

21. Simplify trigonometric expression.

$$\frac{1+\sin x}{\cos x}-\frac{\cos x}{1-\sin x}$$

Belum tersedia

22. Find the quotient

$$\frac{x^2 + 49x – 56}{x^2-4x-5}÷\frac{7x^2-56x}{4x^3-20x^2}$$

Belum tersedia

23. If $$x=\frac{\sqrt[4]{125}}{5}$$, then find

$$(x^4-7x^2+1)^{-2}·\left[(x^2+\frac{1}{x^2})^2-14·(x+\frac{1}{x})^2+77\right]$$

Belum tersedia

24. Find sum of all results of $$x$$

$$2x^2 + (2\sqrt 3 – 9)x – (2\sqrt 3 – 12x + 6\sqrt 3)=0$$

$$2x^2 + (2\sqrt 3 – 9)x – (2\sqrt 3 – 12x + 6\sqrt 3)=0$$
$$⇒2𝑥^2 + (2\sqrt 3 − 9 + 12)𝑥 − (2\sqrt 3 + 6\sqrt 3) = 0$$
$$⇒2𝑥^2 + (2\sqrt 3 +3)𝑥 − (8\sqrt 3) = 0$$

Misalkan nilai $$x$$ yang memenuhi $$a$$ dan $$b$$, berdasarkan rumus vieta Maka nilai dari $$𝑎 + 𝑏 =\frac{−(2√3+3)}{2}$$

25. Find $$x+y=?$$

$$(x+y)^x = (x-y)^y$$
$$\log_2 x – \log_2 y = 1$$

Belum tersedia