Problems And Solutions Future Intelligence Student Olympiad (5-6 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 5 and 6

1. There are some rabbits and chickens in a field. Together they have 65 heads and 192 feet. How many chickens are there?

A) 29
B) 31
C) 32
D) 34

Misalkan banyak rabbits adalah $R$ dan banyak Chickens adalah $C$
$𝑅 + 𝐶 = 65 … (1)$
$4𝑅 + 2𝐶 = 192 … (2)$
kurangkan persamaan $(2)$ dengan $2$ kali persamaan $(1)$
$4𝑅 + 2𝐶 = 192$
$2𝑅 + 2𝐶 = 130$
_____________________ –
$2𝑅 = 62 ⟹ 𝑅 = 31$
Karena jumlah rabbit dan chicken adalah $65$, maka banyak chicken adalah $65 − 31 = 34$

A truck owner will refuel his vehicle at a rate of 2 gallons of diesel fuel every 5 seconds. If diesel cost $1.25 per gallon, how long will it take for the truck owner to refuel his vehicle with $40 worth of diesel fuel?

A) 20 seconds
B) 1 minute
C) 1minute 20 seconds
D) 1 hour 20 minutes

harga pergalon $= $1.25$
Uang yang tersedia $= $40$
Kecepatan pengisian = $2$ galon full dalam waktu $5$ seconds
Kecepatan pengisian = $1$ galon full dalam waktu $2,5$ second.
Banyak gallon $\frac{40}{1,25}= 32$ 𝑔𝑎𝑙𝑜𝑛
Waktu untuk mengisi full $32$ galon adalah $32 ×\frac{5}{2}= 16 × 5 = 80$ 𝑠𝑒𝑐𝑜𝑛𝑑

3. A snail can move about 4m in 5 minutes. What’s the average speed of the snail on m/s?

A) 0.013 m/s
B) 0.13m/s
C) 1.3 m/s
D) 13 m/s

$\frac{4\;𝑚}{5\;𝑚𝑒𝑛𝑖𝑡}=\frac{4\; 𝑚}{5 × 60\;𝑑𝑒𝑡𝑖𝑘}=\frac{4\;𝑚}{300\;𝑠}= 0,013 𝑚/𝑠$

4. An athlete takes 10 rounds of a rectangular park, 50m long and 25m wide. Find the total distance covered by him.

A) 1250m
B) 125m
C) 150m
D) 1500m

the total distance covered by him $= 10$ (keliling persegi panjang)
$=10(2(𝑝 + 𝑙))$
$=10(2(50 + 25))$
$= 10(2(75))$
$= 10(150) = 1500 𝑚$

5. A car covers 301km in 3.5 hours. Find its average speed per hour.

A) 80
B) 86
C) 91,5
D) 9,15

$\frac{301}{3,5}=\frac{301}{\frac{7}{2}}= 301 ×\frac{2}{7}= 43 × 2 = \frac{86}{1}$

6. Find $\frac{0,5}{0,6+\frac{1}{0,5+\frac{1}{0,5}}}$

A) 0,05
B) 0,5
C) 5
D) 50

$\frac{0,5}{0,6+\frac{1}{0,5+\frac{1}{0,5}}}=\frac{0,5}{\frac{3}{5}+\frac{1}{\frac{1}{2}+\frac{1}{\frac{1}{2}}}}=\frac{0,5}{\frac{3}{5}+\frac{1}{\frac{1}{2}+2}} =\frac{0,5}{\frac{3}{5}+\frac{2}{5}}=\frac{0,5}{1}=0,5$

7. Solve $1,01 + 2,02 + 3,03 + … + 9,09 =?$

A) 45
B) 45,45
C) 54
D) 54,54

$\begin{align}
1,01 + 2,02 + 3,03 + … + 9,09 &= (1 + 2 + 3 + ⋯ + 9) + (0,01 + 0,02 + ⋯ + 0,09)\\
&= 45 + 0,45\\
&= 45,45\\
\end{align}$

8. Find the area of this figure?

A) 227
B) 150
C) 210
D) 212

Luas $A = 𝑎 × 𝑡 = 11 × 12 = 132$
Luas $B = 𝑝 × 𝑙 = 20 × 4 = 80$
Jadi luas bangun datar adalah $132 + 80 = 212$ cm²

9. Find the sum of:

$12 + 16 + 20 + … + 116 = ?$

A) 1619
B) 1728
C) 1816
D) 1921

Banyak bilangan $𝑛 =\frac{116−12}{4}+ 1 =\frac{104}{4}+ 1 = 26 + 1 = 27$

$12 + 16 + 20 + … + 116 =\frac{(12+116)𝑛}{2}=\frac{128(27)}{2}= 𝟏𝟕𝟐𝟖$

10. What is the surface area of this L – shaped prism?

A) 80
B) 95
C) 110
D) 120

$\begin{align}
Luas\; Permukan &= Luas\; depan × 2 + luas\; bawah × 2 + Luas\; samping × 2\\
&= (22 × 2 + 15 × 2 + 18 × 2)\\
&= (44 + 30 + 36)\\
&= 110\; cm^2\\
\end{align}$

11. A box contains seven different white rabbits and five different black rabbits. In how many ways can a conjurer pick out a pair of rabbits of different colors?

A) 12
B) 25
C) 35
D) 70

Belum tersedia

12. In how many ways can eight different charms be arranged on a circular bracelet?

A) 5040
B) 2520
C) 1520
D) 524

Belum tersedia

13. Find the smallest value of $x$?

$\frac{x-1}{4}-3<\frac{2x-1}{3}+x$

A) – 2
B) – 1
C) 0
D) 1

Belum tersedia

14. Solve

$x⊕y=(xy)^{yx}$
$=x⊗y=(\frac{y}{x})^x$
$1⊗(2⊕3)=?$

A) $3^6$
B) $3^9$
C) $2^6$
D) $6^6$

Belum tersedia

15. Solve $𝑎−(𝑏+1)−[2−(𝑎+1)]+𝑏−2𝑎=?$

A) – 2
B) – 1
C) 0
D) $a$

Belum tersedia

16. With the given information, find $y$?

$x+y-z=0$
$3x-y+z=4$
$2x+2y-z=9$

A) 7
B) 8
C) 9
D) 10

Belum tersedia

17. Find $a$?

A) 126
B) 136
C) 144
D) 152

Belum tersedia

18. Find the next one?

A) 30
B) 35
C) 40
D) 45

Belum tersedia

19. Open the lock with the given information.

A) 279
B) 672
C) 679
D) 769

Belum tersedia

20. Solve

A) 25
B) 27
C) 29
D) 32

Belum tersedia

21. Find the sum of: $17 + 21 + 25 + 29 + … + 81 + 85 = ?$

Belum tersedia

22. Solve $2210∙2212−2211∙2209=?$

Belum tersedia

23. What is the volume of this L – shaped prism?

Belum tersedia

24. Find the sum of area and perimeter of this figure.

Belum tersedia

25. Farmer has 30 chickens and rabbits altogether legs only 100. How many chickens are there?

Belum tersedia

“Future Intelligence Students Olympiad”

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