2024 Junior Test | Test and Chat

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2024 Junior (Grade 9 - 10)

Questions: 30 | Answered: 0

Q1. W hich of the shown squares i s split into two parts that do n o t have the same shape ?

3 points

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Question 1

Q2. ×2 - squares . How many ways are there for her to do this ?

3 points

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Question 2

Q3. The number of points on opposite faces of a die is always 7. We define the vertex sum in a vertex , as the sum of the points o n the fa ces that meet in th e vertex. ( E . g . the faces of the die with 1, 2 and 3 points meet in P, therefore, the vertex sum in point P is defined as 1+2+3 = 6.) W hich of the following numbers is the biggest vertex sum in the vertices Q, R a nd S?

3 points

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Question 3

Q4. A type of hopscotch is played in the following way: each player jumps from one square to the next with the left foot, both feet, right foot, both feet, etc. alternat e ly on the floor as shown . Maya plays this game and jumps into exactly 48 squares starting with th e left foo t . How often is her left foot on the floor in th is game ?

3 points

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Question 4

Q5. Tim wants to draw the figure shown without lifting his pencil off the paper . He has to pass over s ome parts more than once . The segment lengths are stated in the figure . What is the minimum length of the total line he will draw if he can choose his starting point freely ?

3 points

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Question 5

Q6. The diagra m shows a square with four touching circles of equal size . What is the ratio of the area of the black part to the grey part ?

3 points

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Question 6

Q7. Let a a nd b be numbers from th e set {1,2,3,4,5,6}. For each pair ( a,b ) we draw a straight line with the equation y = ax + b a nd consider the triangle that this straight line forms with the co - o r dinate axes. How many pairs ( a,b ) create an isosceles triangle ?

3 points

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Question 7

Q8. John has a number of equally big light and dark c ubes. He starts with a dark cube which he places on the ta ble. Now , there are five faces of the cube visible . In his second step , he covers all visible faces of this cu be by adding five light cubes as shown. Now , he wants to add dark cubes again so that no light su rfaces are visible . What is the minimum number of dark cubes he will require ?

3 points

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Question 8

Q9. W e draw a square with vert ices A , B , C , D as shown , and a regular hexagon with side OC , w h ere O is the centre of the square . How big is angle  ?

3 points

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Question 9

Q10. Ardal fences a rectangular plot of land. The fence is 40 m l o ng. The lengths of all sides of the rectangle are prime numbers. What is the biggest possible area of the plot of land ?

3 points

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Question 10

Q11. A p alindrom e number is a number that is the same read from the front and the ba ck, e.g. 121 or 444. W hat is the sum of the digits of the largest three - digit palind r ome number that is also a multiple of 6 ?

4 points

ABCDE

Question 11

Q12. A rectangle is split into three pieces with equal area , as shown. One piece is an equilateral triangle with side s of length 4 cm . T h e other two pieces are trapezoids . How long is the short er of the parallel sides of the trapezoid ?

4 points

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Question 12

Q13. Jelena fills the 2×4 - table shown with the letters A, B, C a nd D . She wants to make sure that each letter appears exactly once in each row and in each of the three

4 points

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Question 13

Q14. Sanjay has three differently coloured circles. First he places them on top of each other as shown in ‚Figur 1‘ . Then he moves them so that they to uch each other pairwise as shown in ‘Figur 2’. In Figur 1 the visible black area is seven times as big as the area of the white circle. What is the ratio of the visible black areas in Figur 1 and Figur 2 ?

4 points

ABCDE

Question 14

Q15. The daughter of Mary’s daughter was born today. In two years’ time the product of Figur 1 Figur 2 Mary’s age , her daughter ’ s age and her grand - daughter ’ s age will be exactly 2024. Each of the three ages will then be an even number . How old is Mary today ?

4 points

ABCDE

Question 15

Q16. A point P is chosen inside an equilateral triangle ABC. Segments with the shown lengths of 2 m, 3 m, and 6 m are then drawn parallel to the sides of the triangles , as shown . What is the perimeter of the triangle ?

4 points

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Question 16

Q17. A number is written into each of the twelve circles shown . The numbers in the squares state the product of the four numbers in the vertices of the squares. What is the product of the numbers in the eight bold circles ?

4 points

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Question 17

Q18. Jean - Philippe ha s n cubes of equal size . He uses them to form one big cube and paints its surface. The number of small cubes with exactly one painted face is then the same as the number of small cubes with no painted face . What is the value of n ?

4 points

ABCDE

Question 18

Q19. Otis builds the net of a solid using a combination of squares and triangles as s hown. All sides of the squares and the triangles have side length 1. He proceeds to fold the net to form th e solid shown . What is the distance from A to B ? 5

4 points

ABCDE

Question 19

Q20. Vlado has part icipated in 31 cross - country races in the last five years. In the first year , he part icipated in the smallest number of races and he then successively increased the number of races each year. In the fifth year , he part icipated in three times as many races as in the firs t year. How many races did he part icipate in in the fourth year ?

4 points

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Question 20

Q21. How many integers k ha ve the property that k+6 i s a multiple of k - 6 ?

5 points

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Question 21

Q22. There are four bowls with sweets on a table . The number of sweets in the first bowl is equal to the number of bowls with one sweet. The number of sweets in the second bowl is e qual to the number of bowls with two sweets. The number of sweets in the third bowl is equal to the number of bowl s with three sweets. The number of sweets in the fourth bowl is equal to the number of bo wls with no sweets . How many sweets are in the bowls in total ?

5 points

ABCDE

Question 22

Q23. Cristina ha s 12 cards numbered from 1 to 12. She places eight of them in a circle so that the sum of any two adjacent numbers is a multiple of 3. Which numbers does Chr istina n o t use ?

5 points

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Question 23

Q24. Carl tells the truth on one day, lies on the next, tells the truth again the day after, etc. On one day he made exactly four of the following five statements. W hich statement can he not have made on that day ?

5 points

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Question 24

Q25. The sum of the digits of N is th ree times the sum of the digits of N +1. W hat is the smallest possible sum of the digits of N ?

5 points

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Question 25

Q26. Jill has some black and some white unit cubes. She uses 27 of them to build a 333  cube . She wants exactly one third of th e surface to be black. If A is the smallest possible number of black cubes that she can use and B the biggest possible number, what is the value of B – A ?

5 points

ABCDE

Question 26

Q27. Ann rolled an ordinary die 24 times . All numbers from 1 to 6 were rolled at least once. The number 1 was rolled more often than any other number. Ann then added all numbers that were rolled . Wh at is the biggest number she could have obtain ed in this way ?

5 points

ABCDE

Question 27

Q28. Olga wa s walking in the park. For h alf the time , she walked with a speed of 2 km/ h. For h alf the distance , she walk ed with a speed of 3 km/h. For t he remaining time , she walked with a speed of 4 km/h. Which fraction of the time did sh e walk with 4 km/h ?

5 points

ABCDE

Question 28

Q29. 20 points are distributed equally along a circle. How many of the segments connect ing two of those points are longer than the radius of the circle but shorter than the diameter of the circle ?

5 points

ABCDE

Question 29

Q30. Consider n different straight lines in a plane , labelled as 1 ,, n . The straight line 1 intersects 5 other straight lines, the straight line 2 intersects 9 other stra ight lines and the line 3 intersects 11 other straight lines . Which of the following number s is a possible value of n ?

5 points

ABCDE

Question 30

2024 Junior Test | Test and Chat