25 OSN SMP Mathematics Provincial Level Questions and Answers

Participants who pass the district/city selection should have example questions for the Provincial Level SMP Mathematics OSN. Example questions can help participants improve their understanding and management of problem-solving.

OSN This is an event organized by the Indonesian Talent Development Board (BPTI) to develop talents and achievements of students, especially in the field of science. There are three categories in the Junior High School level OSN: Mathematics, Natural Sciences (Science), and Social Sciences (Social Studies).

The OSN Mathematics Exam materials for junior high school students are created based on the applicable curriculum. Some of the syllabus topics include numbers, algebra, geometry and measurement, as well as statistics and probability.

1. Given that the function \( f \) satisfies \( f(x) + f(2x + y) + 5xy = f(3x - y) + 20x^2 + 12 \) for all real numbers \( x \) and \( y \). The value of \( f(10) \) is...

A. 1572

B. 1642

C. 1762

D. 1952

ANSWER: C

2. Many prime factors of 318 - 218 are...

A. 5

B. 6

C. 7

D. 8

ANSWER: B

3. Given that x is a real number with 2X = 3, then the value of 43X+1 =...

A. 1724

B. 2916

C. 3852

D. 4664

ANSWER: B

The minimum value (the smallest) of \( x^2 + 2xy + 3y^2 + 2x + 6y + 4 \) is ....

A. 1

B. 2

C. 3

D. 4

ANSWER: A

5. It is known that segitiga ABC.

AD is the angle bisector of angle BAC

BE is the height line from B to D

Point F is the midpoint of AB.

If AB = 28, BC = 33, CA = 37, then the length of EF is ....

A. 7

B. 9

C. 12

D. 14

ANSWER: D

6. The number 'SEEDER' is a number that satisfies the following condition:

1) That number is a prime number.

2) If read backwards from the back to the front, then the number obtained is also a prime number.

The product of its digits is a prime number. The largest 'PENABUR' number consisting of 3 digits is the number abc, then the value of a + b + c = ....

A. 5

B. 6

C. 7

D. 8

ANSWER: A

5! - 2 * 4! = 120 - 48 = 72

A. 10

B. 12

C. 15

D. 18

ANSWER: B

8. f (a,b) represents the sum of integers from a to b

Contoh:

f (1,5) = 1+2+3+4+5 = 15

f (12,16) = 12+13+14+15+16 = 70

Jika nilai f (1,33333, 533333) = K, then the sum of the digits of the number K is...

A. 24

B. 32

C. 36

D. 48

ANSWER: C

9. Diketahui p dan q merupakan prime number

If \( p^2 + pq + q^2 \) is a perfect square, then the sum of all values of \( p \) that satisfy this is...

A. 8

B. 10

C. 18

D. 24

ANSWER: A

10. A function satisfies f (2012x) + x.f (2012-x) = 2013 – x , for all real numbers x. The value of f (2012) is...

A. – 1

B. 0

C. 1

D. 2

ANSWER: A

11. There are 4 nurses taking care of a Covid-19 patient, namely Andi, Budi, Citra, and Deni. Nurse Andi takes care of the patient every 2 days, Nurse Budi every 3 days, Nurse Citra every 4 days, and Nurse Deni every 5 days. Because on Monday the Covid-19 patients were full, all four nurses first took care of the Covid-19 patient together on that day. When they will take care of the patient together for the third time, Andi is not on duty. On which day can they take care of the patient together again for the third time, and who will be on duty on that day?

A. Yours: Andi, Budi, Citra

B. Tuesday: Andi, Citra, Deni

C. Rabu: Budi, Citra, Andi

D. Thursday: Budi, Citra, Deni

ANSWER: D

12. Given two numbers m and n where:

m= 202120212021 × 2020202020202020

n = 202020202020 × 2021202120212021

What is the value of 2021m-n?

A. 1

B. 2

C. 3

D. 4

ANSWER: A

For the positive integer \( k \), the value of \( k \) that satisfies \( \frac{9k^2 - 9k + 2}{6k^2 - 28k + 16} \) being a positive integer is...

A. 4 to 10

B. 2 dan 5

C. 6 dan 4

D. 4 dan 15

ANSWER: D

14. A circle is known to have its center at point P(-10, -2). This circle touches the parabola \( y = ax^2 \) at a point A(x, y) in the second quadrant. It is also known that a straight line \( y = -3x - 2 \) touches the parabola at the same point A. Therefore, the value of \( a \) is ...

A. 1

B. 2

C. 3

D. 4

ANSWER: A

15. In a final competition, Andi and Budi are competing. Andi and Budi each have one box containing 15 black cards and 5 white cards. From their respective boxes, they each draw 3 cards one at a time randomly without replacement. Andi and Budi do not influence each other in drawing their cards. Calculate peluang that Andi and Budi are choosing cards alternately?

A. 212/5776

B. 225/5776

C. 236/5776

D. 242/5776

ANSWER: B

Let's denote the current ages of A and B as \(A\) and \(B\), respectively.

A. 31 years old

B. 32 years old

33 years old

D. 34 years old

ANSWER: D

17. In a secret competition, 12 students must form three different teams. The number of members in each team is determined by the root of the natural numbers from the following polynomial equation:

x³ - 12x² + 47x - 60 = 0.

There are many different ways to form that team...

3000

B. 3250

C. 3900

D. 3960

ANSWER: D

18. It is known that a and b are prime numbers that satisfy the equation:

(a^2 + b) * 3a - b = 256.

If x and y are solutions to the above equation, then the sum of all values of x and y that satisfy it is...

1. 7
2. 8
3. 9
4. 10

ANSWER: D

The sides of a triangle are known to be the square roots of the natural number solutions of the following polynomial equation:

x³ - 12x² + 47x - 60 = 0.

The area of that triangle is ... square units.

1. 4
2. 5
3. 6
4. 7

ANSWER; C

The smallest value of \( ab \) such that \( a + b \) is an integer, given the equation \( \frac{a}{b} + \frac{b}{a} = 2021 \) and \( ab > 1 \), can be found as follows: positive integers ?

A. 2025/2024

B. 2025/2023

C. 2025/2022

D. 2025/2021

ANSWER: B

21. Dina asks Rina about borrowing from Bank X. Rina had borrowed money from Bank X amounting to Rp. 1,000,000 per year, six times in total. She returned the money the following year. Rina must return the money under the following conditions:

1). In the first year, it amounts to Rp. 1,200,000.

In the second year, it amounts to IDR 1,300,000.

In the third year, it amounts to Rp. 1,350,000.

In the fourth year, it amounts to IDR 1,300,000.

However, Rina does not remember the amount of money she needs to pay in the fifth and sixth years. Rina only remembers that the amount of money returned in the fifth year is smaller than in the first year. Meanwhile, the amount of money returned in the sixth year is larger than in the third year. Furthermore, she remembers that the median, average, and mode of the interest rates are the same. Examine the possibility of the amount of money paid by Rina in the fifth and sixth years?

A. K5 < 1,200,000 and K6 < 1,450,000

B. K5 > 1,200,000 and K6 > 1,450,000

C. K5 = 1,200,000 and K6 = 1,450,000

D. K5 < 1,200,000 and K6 > 1,450,000

ANSWER: A

24. In a game, Suci and Rani ended up with the same score. To determine the winner, they had to play rock-paper-scissors. If Suci told Rani that she would not use "Rock" in the game, determine the probability that Rani will win and the highest probability that Rani will win if she uses Scissors, Rock, or Paper.

A. ½, scissors

B. 1/3, scissors

C. ½, stone

D. 1/3, batu

ANSWER: B

For the positive integer \( k \), the value of \( k \) that satisfies \( \frac{3k^2 - 3k}{2k^2 - 10k + 8} \) as a positive integer is...

A. 15

B. 16

C. 17

D. 18

ANSWER: B

A circle is known to have its center at point P(11, -2). This circle touches the parabola \( y = ax^2 + 1 \) at a point A(x, y) in the first quadrant. It is also known that a straight line \( y = 3x \) touches the parabola at the same point A. Find the value of \( a \).

A. 1

B. 2

C. 3

D. 4

ANSWER: B

25. Pada suatu kotak terdapat beberapa bola bernomor. Di antara nomor bola tersebut terdapat faktor prima dari 2021, serta akar bilangan asli dari polynomial equation berikut:

x³ - 9x² + 24x - 20 = 0.

If one ball is taken randomly, then the probability of drawing a ball with an even number is...

A. 25

B. 26

C. 27

C. 28

ANSWER: A

For more examples of OSN SMP Mathematics provincial level questions, you can see through the following link:

LINK EXAMPLE OSN SMP MATHEMATICS PROVINCIAL LEVEL DOWNLOAD

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