2025 Student Test | Test and Chat

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2025 Student (Grade 11 - 12)

Questions: 30 | Answered: 0

Q1. The number of the year 2025 is a perfect square, b ecause 2025  45 . How many years will pass until the next year whose number is a perfect square?

3 points

ABCDE

Question 1

Q2. Mike obtains a number x by dividing the number 11 by 3. Where is the number x located on the number line?

3 points

ABCDE

Question 2

Q3. Vasily has 20 balls. Each ball is either yellow, g reen, blue or black. Of the balls, exactly 17 are n ot green, exactly 15 are not black, and exactly 12 are not yellow. How m any of his balls are blue?

3 points

ABCDE

Question 3

Q4. Which interval contains the value of the product 77  777 ?

3 points

ABCDE

Question 4

Q5. Which of the following expressions has the same va lue as the square root of 16 ?

3 points

ABCDE

Question 5

Q6. The pictures shown are the first three pictures in a sequence. How many dots does the fifth picture in t he sequence consist of?

3 points

ABCDE

Question 6

Q7. A student throws five stones in turn, hitting a win dow at points A , B , C , D , and E . Whenever a stone hits the window, it creates cracks starting f rom that point. These cracks end either at the edge of the window or at an existing crack. In which order did he throw the stones?

3 points

ABCDE

Question 7

Q8. Silvia's favourite chocolate bars are sold in packe ts. There used to be five bars in each packet. Now there are only four in each packet, but the pac kets still cost the same. By how many percent has each bar become more expensive?

3 points

ABCDE

Question 8

Q9. ABCD is a rectangle (see diagram). The area of the quad rilateral ABPD is 4 cm² and

3 points

ABCDE

Question 9

Q10. In the xy plane, some points in the range 0  x  1, 0  y  1 are coloured black. A point ( x | y ) is coloured black if and only if the first decimal digit of both x and y after the decimal point is odd. What does the resu lt look like?

3 points

ABCDE

Question 10

Q11. Robert wants to choose four points in such a way th at the distances between any two of them are different. Which one of the points A , B , C , D or E must he remove?

4 points

ABCDE

Question 11

Q12. Among 10 different given positive integers, exactl y five are divisible by 5 and exactly seven are divisible by 7. Let M be the largest of these numbers. What is the smallest possible value of M ?

4 points

ABCDE

Question 12

Q13. In the diagram we see a quarter circle SP with centre O and radius r, as well as a triangle ORP . The two grey regions have the same area. How long is the segment OR ?  r 3 r 2 

4 points

ABCDE

Question 13

Q14. A student draws the graphs of two linear functions in a coordinate system as shown. What is certain about the expression ab  cd   ac  bd  ?

4 points

ABCDE

Question 14

Q15. When Grandma started knitting wool socks, she had a ball of wool with a diameter of 30 cm. After she ha s finished knitting 70 socks, the remaining ball of w ool has a diameter of 15 cm. How many more socks can Grandma knit?

4 points

ABCDE

Question 15

Q16. We consider a giant 4  4 chessboard. A kangaroo is standing on each of the 16 squares. On each move, each kangaroo jumps to an adjacent squar e (up, down, left or right, but not diagonally). All kangaroos stay on the chessboard. Several kangaroos can be on one square at the same time. What is the maximum number of unoccupied squares th at we can have after 100 moves?

4 points

ABCDE

Question 16

Q17. The five-digit number N 18 NN is divisible by 18. Which of the following stateme nts is true for the digit N ?

4 points

ABCDE

Question 17

Q18. The area of the black semicircle shown is 12 cm². What is the area of the large quarter circle?

4 points

ABCDE

Question 18

Q19. Three square Martians and three round Jupiterians a re sitting at a table as shown. One of the six has the key to the spaceship. Everyone from one planet always tells the truth, and everyone from the other planet always lies. When as ked "Does any of your neighbours have the key?" all six answer as shown. Who has the key?

4 points

ABCDE

Question 19

Q20. Points B and C lie on the diameter of a semicircle with diameter AD , and points E , F , G and H lie on the arc. How many triangles exist, whose vertices are three of these eight points?

4 points

ABCDE

Question 20

Q21. Four circular discs with radii r 1 , r 2 , r 3 and r 4 have their centres at the points (0|0), (1|0), (3|0) and (6|0). The di scs may touch each other but may not overlap. What is the largest possible value of r 1  r 2  r 3  r 4 ?

5 points

ABCDE

Question 21

Q22. On the map shown on the right, we see a city in wh ich there are four schools. Regions A , B , C and D each consist of the points for which the relevant school is closest. The coordinates of the school in region D are (9|1). What are the coordinates of the school in region A ?

5 points

ABCDE

Question 22

Q23. What is the smallest positive integer N such that the expression 2 3 N has an integer value?

5 points

ABCDE

Question 23

Q24. Fritz fills out a table with two columns and 51 ro ws. In the first row, he writes 5 on the left and 3 on the right. In each subsequent row he writes the sum of the two nu mbers from the row above on the left and the positi ve difference of these two numbers on the right. Which two numbers does he write in the bottom row?

5 points

ABCDE

Question 24

Q25. John writes a two-digit number on the board. If he erases the ones digit, the value of the number is reduced by p %. Which of the following numbers is closest to the largest possible value of p ?

5 points

ABCDE

Question 25

Q26. Julia and her little sister Paula start a bike rid e together. Julia cycles at a constant speed of 18 km/h and Paula at a constant speed of 12 km/h. They cycle along the sam e route. After 20 minutes, Julia is tired and turns around. When she meets Paula, she also turns around and the y both cycle home at their respective speeds. How many minutes does Paula arri ve later than Julia?

5 points

ABCDE

Question 26

Q27. In the diagram we see a regular hexagon ABCDEF . The point P lies on BC in such a way that the area of the triangle PEF is 64 and the area of the triangle PDE is 42. What is the area of the triangle APF ?

5 points

ABCDE

Question 27

Q28. In the picture we see a regular octagon with a sid e length of 1 cm. Eight circular arcs with a radius of 1 cm and with centres at the corners we re drawn as shown. What is the perimeter of the dark area?

5 points

ABCDE

Question 28

Q29. Patricia has written a number in each box of a 7  10 table. The sum of the numbers in each rectangle of size 3  4 or 4  3 is zero. Patricia reveals two of the numbers, as shown in the diagram. What is th e sum of all the numbers in the table?

5 points

ABCDE

Question 29

Q30. Mike has three bags. Each bag contains three balls. On one bag there is a sign saying "1 white, 2 black", on the second a sign say ing "2 white, 1 black" and on the third a sign sayi ng "3 white". However, the signs have been swapped so that none o f them is correct now. On each turn, Mike chooses a bag that still contains balls, draws one blindly and pl aces it visibly next to the bag. What is the minimu m number of balls that he has to draw to know for sure which sig n should have been on which bag?

5 points

ABCDE

Question 30

2025 Student Test | Test and Chat