2023 Junior Test | Test and Chat

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2023 Junior (Grade 9 - 10)

Questions: 30 | Answered: 0

Q1. A dark disc with two holes is place d on the dial of a watch as shown in the diagram. The dark dis c is now rotated so that the number 10 can be se en through one of the two holes . W hich of the numbers c ould one see through the other hole now ?

3 points

ABCDE

Q2. On her way to school Maria first ha d to run to the underground, she exited from that after two stops and subsequently walked the rest of the way by foot all the way to school. W hich of the following speed - time - diagrams best describes her journey to schoo l ?

3 points

ABCDE

Q3. The two integers 푚 a nd 푛 are positive and odd . Which of the following numbers is odd ?

3 points

ABCDE

Q4. A small square with side length 4 cm is drawn within a big square with side length 10 cm ; their sides are parallel to each other (see diagram) . W hat p ercentage of the figure is sh aded ?

3 points

ABCDE

Q5. Today is Thursday. What day of the week is it i n 2023 days ?

3 points

ABCDE

Q6. The big rectangle shown is divided into 30 equally big squares. The perimeter of the a rea shaded in grey is 240 cm. How big is the area of the big rectangle ?

3 points

ABCDE

Q7. If one adds the age s of all members of a family of five togeth er, one gets 80. The two youngest children are 6 and

3 points

ABCDE

Q8. A straight wo o den fence is made up of vertical beams stuck in the ground which are each connected to the next beam by 4 horizontal beams. The fence begins and ends with a vertical beam . Out of how many beams could such a fence be made ?

3 points

ABCDE

Q9. How many pairs of positive integers ( 푎 , 푏 ) fulfil the equation = ?

3 points

ABCDE

Q10. After playing 200 games of chess, Beth ’ s winning rate is exa ctly 49 %. What is the minimum number of games she has to still play to increase he r winning rate to 50 %?

3 points

ABCDE

Question 10

Q11. 1

4 points

ABCDE

Question 11

Q12. The diagram shows three adjacent squares with side lengths 3 cm, 5 cm a nd 8 cm. How big is the area of the shaded in trapezium ?

4 points

ABCDE

Question 12

Q13. A rope with length 95 m is cut into three pieces so that each piece is half as long agai n as the respective previous piece. How long is the longest of the three pieces ?

4 points

ABCDE

Question 13

Q14. The points M a nd N are the midpoints of two sides of the big rectangle (see diagram) . Which part of the area of the big rectangle is shaded ?

4 points

ABCDE

Question 14

Q15. The pentagon ABCDE is split into four triangles that all have the same perimeter (see diagram). Triangle ABC is equilateral and the triangles AEF , DFE a nd CD F are co ngruent isosceles triangles . How big is the ratio of the perimeter of the pentagon ABCDE to the perimeter of the triangle ABC ? 3 4 5 5

4 points

ABCDE

Question 15

Q16. A tower consists of blocks that are labelled from bottom to top with the numbers from 1 to 90. Bob uses these blocks to build a new tower. For each step h e takes the top three blocks from the old tower and places them on the new tower without changing their order (see diagram). How many blocks are there in the new tower between the blocks with the numbers 39 and 40 ?

4 points

ABCDE

Question 16

Q17. A staircase has 2023 steps . Every third step is coloured in black . The first seven steps of this staircase can be fully seen in the diagram. Anita walks up the staircase and steps on each step exactly once. She can start with either the right or the left foot and then steps down alternately with the right or left fo ot. What is the minimum number of black steps she sets her right foot on ?

4 points

ABCDE

Question 17

Q18. W e call a positive integer po werfree if none of its digits can be written as a power of an integer with a n exponent 2 bigger than 1. For example, t he number 53 is powerfree , but the number 54 is not powerfree since 4 = 2 . Which one of the following numbers is the difference between the biggest and the smallest two - digit powerfree number s ?

4 points

ABCDE

Question 18

Q19. A square with side length 30 cm is split i nto 9 squares . The big square contains three circles with radii 5 cm ( b ottom right ), 4 cm ( top left ) as well as 3 cm ( top right ) as seen in the diagram . How many cm² are shaded in grey ?

4 points

ABCDE

Question 19

Q20. hours if she surfs the internet continuously and 80 hours if she does not use it at all . Matilda boards a train with a half full battery . During her time on board she spend s the same amount of time each on phon ing, surfing the internet and not using the phone at all. Just when she arrives at her destination the battery is empty . How many hours did the train ride take ?

4 points

ABCDE

Question 20

Q21. The numbers from 1 to 9 should be distributed among the 9 squares in the diagram according to the following rules: There should be one number in each square. The sum of three adjacent numbers is always a multiple of 3 . The numbers 3 and 1 are already placed. How many ways are there to place the remaining numbers ?

5 points

ABCDE

Question 21

Q22. How many different ways are there to read the word BANANA in the following table if we can only c ross to a field that shares an edge with the current field and we can use fields several times ?

5 points

ABCDE

Question 22

Q23. S tarting with the four numbers

5 points

ABCDE

Question 23

Q24. A circle with midpoint (75|30) and radius 10 is cut f rom a rectangle with vertices (0|0), (100|0), (100|50) a nd (0|50). W hat is the gradient of the straight line that goes through the point (75|30) a nd divides the remaining part of the rectangle into two parts with equal area ?

5 points

ABCDE

Question 24

Q25. W hen Matilda’s s martphone is fully charged it has a battery life of

5 points

ABCDE

Question 25

Q26. Seven pairwise different single - digit numbers are distributed among the circles shown so that the product of the three numbers that are connected by a straight line is the same in all three case s . Which number is written in the circle with the question mark ?

5 points

ABCDE

Question 26

Q27. Consider the two touching semicircles with radius 1 and their diameters AB and CD respectively that are parallel to each other. The extension s of the two diameters are also tangents to the respective other semicircle (see diagram) . How big is the square of the length AD ?

5 points

ABCDE

Question 27

Q28. Leon ha s drawn a closed loop on the surface of a cuboid . W hich net cannot show his loop?

5 points

ABCDE

Question 28

Q29. Several points are marked on a straight line . Renate marks another point between each pair of adjacent points. She repeats this process three more times. Now there are 225 points marked on this straight line . How many points were marked to start with ?

5 points

ABCDE

Question 29

Q30. The diag ram shows the map of a big park. The park is split into several sections and the number in each section states its perimeter in km. How big is the perimeter of the entire park in km?

5 points

ABCDE

Question 30

2023 Junior Test | Test and Chat