2019 Student Test | Test and Chat

Back to KangarooMath

2019 Student (Grade 11 - 12)

Questions: 30 | Answered: 0

Q1. ,2,3,4 and 5 appears exactly once in each row and in each column. Furthermore sthe sum of all numbers in the three black-bordered sections should always be the same. Which number has to be written into the top right cell?

3 points

ABCDE

Question 1

Q2. The numbers 1, 2, 3 and 4 are inserted into different cells of the 2 × 2 table shown. Then the sums of the numbers in each row and column are determined. Two of these sums are 4 and 5. How big are the two remaining sums?

3 points

ABCDE

Question 2

Q3. A rectangle is coloured in five different ways as shown. In which picture is the grey area biggest?

3 points

ABCDE

Question 3

Q4. Three triangles are connected to each other as shown. In which of the following pictures are the three triangles connected in the same way?

3 points

ABCDE

Question 4

Q5. A pyramid has 23 triangular faces. How many edges does this pyramid have?

3 points

ABCDE

Question 5

Q6. Three four-digit numbers are written onto three separate pieces of paper as shown. The sum of the three numbers is 11126. Three of the digits in the picture are hidden. Which are the three hidden digits?

3 points

ABCDE

Question 6

Q7. Reading from the left, what is the first digit of the smallest positive integer whose digit sum is 2019?

3 points

ABCDE

Question 7

Q8. How many of the numbers from 2 to 2 (including these two numbers) are divisible by 2 ?

3 points

ABCDE

Question 8

Q9. Each side of a die is marked with either 1, 2 or 3 dots so that the probability of rolling a 1 is equal to , the ଶ ଵ ଵ probability of rolling a 2 is equal to and the probability of rolling a 3 is equal to . ଷ ଺ Which of these pictures cannot be a picture of this particular die?

3 points

ABCDE

Question 9

Q10. Every day the three kangaroos Alex, Bob and Carl go for a walk. If Alex does not wear a hat, Bob wears a hat. If Bob does not wear a hat, Carl wears a hat. Today Carl does not wear a hat. Which kangaroos can one say for sure are wearing a hat today?

3 points

ABCDE

Question 10

Q11. Which is the highest power of three that divides the number 7! + 8!+ 9! ? (Hint: The expression n! is defined by n! = n  (n-1)  (n-2)  …  3  2  1.) ଶ ସ ହ ଺ ଺

4 points

ABCDE

Question 11

Q12. In this school year the number of boys in my class has increased by 20% compared to the previous year and the number of girls has decreased by 20%. There is now one person more than before in this class. Which of the following numbers could be the current number of students in my class?

4 points

ABCDE

Question 12

Q13. A cuboid-shaped container that is not filled completely contains

4 points

ABCDE

Question 13

Q14. Michael invents a new operation „ ⋄ “ for real numbers that is defined by 푥 ⋄ 푦 = 푦 − 푥 . Which of the following statements is definitely true if the numbers 푎 , 푏 , and 푐 fulfill the condition ( 푎 ⋄ 푏 ) ⋄ 푐 = 푎 ⋄( 푏 ⋄ 푐 ) ?

4 points

ABCDE

Question 14

Q15. The system shown consists of three pulleys that are connected to each other via two ropes. P, the end of one rope, is pulled down by 24 cm. By how many centimeters does point Q move upwards? ଶସ

4 points

ABCDE

Question 15

Q16. A positive integer 푛 is called good, if it’s biggest factor (apart from 푛 itself) is equal to 푛 − 6 . How many good positive integers are there?

4 points

ABCDE

Question 16

Q17. There are five balls in a box. Four of which contain chocolate, one contains one boiled sweet. Johann and Maria take it in turns to draw a ball from the box without replacing it. Whoever draws the boiled sweet wins. Johann starts. How big is the probability that Maria wins? ଶ ଷ ଵ ହ ଵ

4 points

ABCDE

Question 17

Q18. The diagram shows two adjoining squares with side lengths 푎 and 푏 (with 푎 < 푏 ). How big is the area of the grey triangle? ଵ ଶ ଵ ଶ ଵ ଶ ଶ ଵ ଶ ଶ

4 points

ABCDE

Question 18

Q19. What is the biggest integer smaller than 20 + ඨ 20 + ට 20 + ඥ 20 + √ 20 ?

4 points

ABCDE

Question 19

Q20. The points of intersection of the network of bars shown are labelled with the numbers 1 to 10. The sums 푆 of the four numbers on the vertices of each square are all the same. What is the minimum value of 푆 ?

4 points

ABCDE

Question 20

Q21. Let 푎 be the sum of all positive factors of 1024 and 푏 be the product of all positive factors of 1024. (Hint: 1 and 1024 are also factors of 1024.) Then ହ ହ ହ ହ ହ

5 points

ABCDE

Question 21

Q22. Which is the set of all parameters 푎 for which the equation 2− | 푥 | = 푎푥 has exactly two solutions?

5 points

ABCDE

Question 22

Q23. In order to determine the result of the calculation ( 푎 , 푏 and 푐 are positive integers), Sara inserts into a ௖ calculator 푎 + 푏 ÷ 푐 = and obtains the result 11 . Then she inserts 푏 + 푎 ÷ 푐 = and is surprised that the result is now 14 . She realises that the calculator follows the rules for the order of operations and does division before addition. ௔ା௕ What is the actual result of the calculation ? ௖

5 points

ABCDE

Question 23

Q24. Consider a cube. How many planes are there that go through at least three vertices of this cube?

5 points

ABCDE

Question 24

Q25. Four different straight lines go through the origin of the co-ordinate-system. They intersect the parabola ଶ 푦 = 푥 − 2 at eight points. What could be the product of the x-co-ordinates of these eight points?

5 points

ABCDE

Question 25

Q26. For how many integers 푛 is | 푛 − 2 푛 − 3| a prime number?

5 points

ABCDE

Question 26

Q27. A path 퐷퐸퐹퐵 with 퐷퐸  퐸퐹 and 퐸퐹  퐹퐵 lies within the square 퐴퐵퐶퐷 as shown. We know that 퐷퐸 = 5 , 퐸퐹 = 1 and 퐹퐵 = 2 . What is the side length of the square? ଻ √ ଶ ଵଵ

5 points

ABCDE

Question 27

Q28. The sequence 푎 ଵ , 푎 ଶ , 푎 ଷ , ... starts with 푎 ଵ = 49 . To work out 푎 ௡ାଵ 푓 or 푛 ≥ 1 you ଶ add 1 to the digit sum of 푎 ௡ and square the result. So e.g. 푎 ଶ = (4 +9 +1) =

5 points

ABCDE

Question 28

Q29. Three circles with radius 2 are drawn in such a way that each time one of the points of intersection of two circles is identical with the centre of the third circle. How big is the area of the grey zone? గ

5 points

ABCDE

Question 29

Q30. numbers are to be placed into the square grid shown, so that each of the numbers

5 points

ABCDE

Question 30

2019 Student Test | Test and Chat