2022 Student Test | Test and Chat

Back to KangarooMath

2022 Student (Grade 11 - 12)

Questions: 30 | Answered: 0

Q1. Martin ‘ s s martphone displays the diagram on the right. It shows how long he has worked with four different apps in the previous week. The apps are sorted from top to bottom according to the amount of time they have been used. This week he has spent only half the amount of time using two of the apps and the same amount of time as last week using the other two apps. W hich of the following pictures cannot be the diagram for the current week ?

3 points

ABCDE

Question 1

Q2. How many positive three - digit numbers are divisible by 13 ?

3 points

ABCDE

Question 2

Q3. Bella is older than Charly a nd younger than Lily. Wh ich two can be the same age if Teddy is older than Bella?

3 points

ABCDE

Question 3

Q4. W hich one of the following numbers is not divisible by its own digit sum ?

3 points

ABCDE

Question 4

Q5. 5 8 pencils are distributed evenly among 25 empty boxes . How many pencils are in each box ?

3 points

ABCDE

Question 5

Q6. The product of the digits of a ten - digit number is 15. How big is the sum of the digits of this number ?

3 points

ABCDE

Question 6

Q7. Four circles with radius 1 intersect each other as seen in the diagram. What is the perimeter of the grey area ?

3 points

ABCDE

Question 7

Q8. All integers from 2 to 2022 which can be written using only the digits 0 and 2 are written in ascending order in a list. W hich number is the middle number on that list ?

3 points

ABCDE

Question 8

Q9. How many real solutions does the equation ( 푥 − 2 ) + ( 푥 + 2 ) = 0 have ?

3 points

ABCDE

Question 9

Q10. The points A, B, C a nd D are marked on a straight line in this order as shown in the diagram . W e know that A is 12 cm from C and that B is 18 cm from D . How far apart from each other are the midpoints of the line segments AB a nd CD ?

3 points

ABCDE

Question 10

Q11. Four straight lines that intersect in one single point form eight equal angles (see diagram). Which one of the black arcs has the same length as the circumference of the little (grey) circle?

4 points

ABCDE

Question 11

Q12. 푎 , 푏 a nd 푐 are real numbers not equal to zero . It is known that the numbers − 2 푎 푏 푐 a nd 3 푎 푏 푐 have the same sign. Which of the following statements is definitely correct ?

4 points

ABCDE

Question 12

Q13. W e check the water meter and see that all digits on the display are different. What is the minimum amount of water that has to be used before this happens again?

4 points

ABCDE

Question 13

Q14. The square pictured , is split into two squares and two rectangles. The vertices of the shaded quadrilateral with area 3 are the midpoints of the sides of the smaller squares. What is t he area of the non - shaded part of the big square ?

4 points

ABCDE

Question 14

Q15. W hat is the largest common divisor of 2 + 2 a nd 3 + 3 ? 2021

4 points

ABCDE

Question 15

Q16. The diagram shows a map with 16 towns which are connected via roads. The government is planning to build power plants in some towns. Each power plan t can generate enough electricity for the town in which it stands as well as for its immediate neighbouring towns (i.e. towns that can be reached via a direct connecting road). What is the minimum number of power plants that have to be built?

4 points

ABCDE

Question 16

Q17. I n a tournament with 8 participants the players are randomly paired up in four teams for the first round and the winner of each encounter then proceeds to the second round. There are two games in the second round and the two winners then play the final. Anita a nd Martina are the two best players and will win against all others; in case the y have to play against each other, Anita will win. How big is the chance that Martina wi ll get to the final ? 1 2 3 4

4 points

ABCDE

Question 17

Q18. A cuboid with surface area X is cut up along six planes parallel to the sides (see diagram). What is the total surface area of all 27 thus created solids ?

4 points

ABCDE

Question 18

Q19. The arithmetic mean of five numbers is 24. The mean of the three smallest numbers is 19 and that of the three biggest is 28. What is the median of the five numbers ?

4 points

ABCDE

Question 19

Q20. A circle with midpoint (0 | 0) ha s a radius of 5. How many points are there on the circumference where both co - ordinates are integers ?

4 points

ABCDE

Question 20

Q21. The vertices of a 20 - gon are labelled using the numbers 1 to 20 so that adjacent vertices always differ by 1 or 2. The sides of the 20 - gon whose vertices are labelled with numbers that only differ by 1 are drawn in red. How many r ed sides does the 20 - gon have ?

5 points

ABCDE

Question 21

Q22. Which two building blocks can be joined together so that the object shown is created ?

5 points

ABCDE

Question 22

Q23. A rectangle is split into 11 smaller rectangles as shown . All 11 small rectangles are similar to the init i al rectangle . The smallest rectangles are aligned like the original rectangle (see diagram). The lower side s of the smallest rectangles have length 1. How big is the perimeter of the big rectangle ?

5 points

ABCDE

Question 23

Q24. Two rectangles are inscribed into a triangle as shown in the diagram. The dimensions of the rectangles are 1  5 and 2  3 respectively . How big is the height of the triangle in A ? 7 8 6

5 points

ABCDE

Question 24

Q25. How many three - digit numbers are there that are equal to five times the product of their digits ?

5 points

ABCDE

Question 25

Q26. The numbers 1 to 10 were written into the ten circles in the pattern shown in the picture . The sum of the four numbers in the left and the right column is 24 each and the sum of the three numbers in the bottom row is 25. Which number is in the circle with the question mark ?

5 points

ABCDE

Question 26

Q27. A square is placed in a co - ordinate system as shown. Each point ( 푥 | 푦 ) of the square is 1 1 deleted and replaced by the point ( | ) . 푥 푦 Which diagram shows the resulting shape ?

5 points

ABCDE

Question 27

Q28. Let 푁 be a positive integer . How many integers are between √ 푁 2 + 푁 + 1 a nd √ 9 푁 2 + 푁 + 1 ?

5 points

ABCDE

Question 28

Q29. A sequence 〈 푎 푛 〉 has 0 < 푎 1 < 1 . For all 푛 ≥ 1 we know that 푎 2 푛 = 푎 2 ∙ 푎 푛 + 1 a nd 푎 2 푛 + 1 = 푎 2 ∙ 푎 푛 − 2 . W e know that 푎 7 = 2 . W hat is the value of 푎 2 ?

5 points

ABCDE

Question 29

Q30. Two circles intersect a rectangle AFMG as shown in the diagram. The line segments along the long side of the rectangle that are outside the circles have length AB = 8, CD = 26, EF = 22, GH = 12 a nd JK = 24. How long is the length x of the line segment LM ?

5 points

ABCDE

Question 30

2022 Student Test | Test and Chat