Quiz about Practice Questions for Math Olympiad (MTS Darul Ulum II)

Question 1

1. Nilai N dalam bentuk desimal apabila

$$N=\frac{1}{10}+\frac{2}{10^2}+\frac{3}{10^3}+...+\frac{11}{10^{11}}$$ adalah...

Accepted Answer

0,123456789011

Answer

1,234567890110

Answer

0,827635401721

Answer

0,9876543211

Question 2

Jika $$1+\frac{1}{4}+\frac{1}{9}+\frac{1}{16}+\frac{1}{25}+⋯=a$$ , maka $$\frac{1}{9}+\frac{1}{25}+\frac{1}{49}+⋯=...$$

Accepted Answer

$$\frac{3}{4}a-1$$

Answer

1

Answer

$$\frac{2}{3}a+1$$

Answer

$$\frac{1}{2}a$$

Question 3

Nilai dari $$\sqrt[]{(45+20\sqrt{5})}+\sqrt[]{(45-20\sqrt{5})}=⋯$$

Accepted Answer

10

Answer

1000

Answer

100

Answer

1

Question 4

Nilai jumlah Bilangan $$1^2-2^2+3^2-4^2+5^2-6^2+⋯2021^2-2022^2+2023^2=⋯$$

Accepted Answer

2047276

Answer

2015376

Answer

3367197

Answer

1234567

Question 5

Bila $$x+\frac{1}{x}=1$$ , maka nilai dari $$x^{10}+\frac{1}{x^{10}}=...$$

Accepted Answer

$$-1$$

Answer

1

Answer

0

Answer

$$x^{10}$$

Question 6

Diketahui nilai dari $$1+2+3+4+⋯+n=abab$$ , nilai dari $$a+b=⋯$$

Accepted Answer

5

Answer

-5

Answer

0

Answer

50

Question 7

Bila $$n=2023!,$$ maka nilai dari $$\frac{1}{\log_2⁡n}+\frac{1}{\log_3n}+\frac{1}{\log_4⁡n}+⋯+\frac{1}{\log_{2023}n}=⋯$$

Accepted Answer

1

Answer

$$-1$$

Answer

0

Answer

2023

Question 8

$$\log_2⁡3\cdot\log_3⁡4\cdot\log_4⁡5\cdot\dots\cdot\log_{1023}1024=⋯$$

Accepted Answer

10

Answer

9

Answer

$$-10$$

Answer

$$-9$$

Question 9

Nilai dari $$\frac{2}{13!}-\frac{4}{14!}+\frac{6}{15!}=⋯$$

Accepted Answer

$$\frac{366}{15!}$$

Answer

$$\frac{363}{15!}$$

Answer

$$\frac{364}{15!}$$

Answer

$$\frac{365}{15!}$$

Question 10

Banyaknya susunan kata berbeda dari huruf-huruf pada kata MATEMATIKA adalah...

Accepted Answer

151.200

Answer

217.810

Answer

145.300

Answer

216.186

Question 11

Hasil dari $$\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+...+\frac{1}{1260}$$ adalah...

Accepted Answer

$$\frac{2}{9}$$

Answer

$$\frac{7}{8}$$

Answer

$$\frac{8}{9}$$

Answer

$$\frac{2}{3}$$

Question 12

jika $$\left(M^2+A^2\right)\left(T^2+H^2\right)=7$$ , nilai dari $$M^2+A^2+T^2+H^2$$ adalah...

Accepted Answer

8

Answer

14

Answer

49

Answer

28

Question 13

Manakah yang berbeda dari yang lain?

Accepted Answer

Question 14

Nilai n yang memenuhi persamaan: $$n=\frac{\left(8^5+8^5+8^5+8^5+8^5+8^5+8^5+8^5 ight)}{\left(3^5+3^5+3^5 ight)} imes\frac{\left(6^5+6^5+6^5+6^5+6^5+6^5 ight)}{\left(2^5+2^5 ight)}$$ adalah...

Accepted Answer

1

Answer

8

Answer

$$-1$$

Answer

19

Question 15

Nilai dari $$(1+\frac{1}{2})(1+\frac{1}{3})(1+\frac{1}{4})\dots(1+\frac{1}{99})=⋯$$

Accepted Answer

50

Answer

1

Answer

99

Answer

100

Question 16

Bilangan $$8,\ 7,\ 6,\ x-1,\ 9,\ y+1,$$ dan $$8$$ mempunyai rata-rata 8. Nilai $$x+y$$ adalah...

Accepted Answer

18

Answer

25

Answer

24

Answer

30

Question 17

Banyak digit (angka) pada bilangan $$2^{2024}\cdot5^{2023}$$ adalah...

Accepted Answer

2024

Answer

2023

Answer

4048

Answer

4046

Question 18

Digit satuan dari $$3^{2013} imes7^{2014} imes13^{2015}$$ adalah...

Accepted Answer

9

Answer

1

Answer

7

Answer

3

Question 19

Terdapat tiga kelompok huruf hijaiyah, yaitu kelompok huruf idzhar halqi, idgam bigunnah dan idgam bilagunnah. Semua huruf-huruf tersebut akan disusun dalam susunan memanjang. Banyaknya susunan yang terjadi jika posisi hurufnya berkelompok sesuai dengan kelompok diatas adalah

Accepted Answer

207.360

Answer

218.270

Answer

308.455

Answer

315.375

Question 20

Three squares have the dimensions indicated in the diagram. What is the area of qudrilateral ABCD?

Accepted Answer

5,25

Answer

6,0

Answer

5,5

Answer

6,25

Question 21

Aku sebuah bilangan. Bila aku dikurangi 45 menghasilkan sebuah bilangan kuadrat dan bila ditambahkan dengan 44 menghasilkan bilangan kuadrat yang lain. Bilangan berapakah aku?

Accepted Answer

1981

Answer

2023

Answer

2013

Answer

2024

Create a free account and access millions of resources

Similar Resources on Wayground

Popular Resources on Wayground

Discover more resources for Mathematics