2023 Student Test | Test and Chat

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2023 Student (Grade 11 - 12)

Questions: 30 | Answered: 0

Q1. W hat is the simpl ified representation of the following fraction ?

3 points

ABCDE

Question 1

Q2. Julia rolls 5 dice at the same time . S he obtains a sum total of 19 points . W hat is the biggest number of sixes she can have rolled ?

3 points

ABCDE

Question 2

Q3. A cylindrical tin is 15 cm h igh . The circumference of the base ci rcle is 30 cm. An ant walks from point A at the base to point B at the to p. Its path is partly vertically upwards and partly along horizontal circ ular arcs. Its path is drawn in bold on the diagram (with a solid line on the front and a dashed line at the back ). How long is the total distance covered by the ant ?

3 points

ABCDE

Question 3

Q4. !  4  3  2  1  24 . For a certain N the formula N !  6! 7! holds . How big is the sum of the digits of N ?

3 points

ABCDE

Question 4

Q5. Emma should colour in the three strips of the flag shown. She has four colours available. She can only use one colour for each strip and immediately adjacent strips are not to be of the same colour. How many different ways are there for her to colour in t he flag ?

3 points

ABCDE

Question 5

Q6. W e call a positive integer n two prim e , if it has exactly three different positive factors , namely 1, 2 and the number n i tself . How many two prim e numbers are there ?

3 points

ABCDE

Question 6

Q7. W hat is the unit s digit of the following product ?  5  1    5  1    5  1 

3 points

ABCDE

Question 7

Q8. W hat is the value of the followi ng sum ? 3 2 0 2 2 3 2 0 0 2 3 2

3 points

ABCDE

Question 8

Q9. 23 animals are sitting in the first row of a cinema . Each animal is either a beaver or a kangaroo . Each animal has at least one kangaroo next to it . W hat is the maximum amount of beavers in the row ?

3 points

ABCDE

Question 9

Q10. A square with area 84 is split into four squares . The upper left square is coloured in b lack. The lower right square is again split into four sq uares and so on. The process is repeated infinitely many times . How big is the area coloured in black ?

3 points

ABCDE

Question 10

Q11. The numbers from 1 to 9 are to be distributed to the nine squares in the diagram according to the following rules : T here is to be one number in each square . The sum of three adjacent numbers is always a multipl e of 3 . The numbers 7 and 9 are already written in . How many way s are there to insert the remaining numbers ?

4 points

ABCDE

Question 11

Q12. Two equilateral triangles of different size s are placed on top of each other so that a hexagon is formed o n the inside whose opposite sides are parallel . Four of the side lengths of the hexagon are stated in the diagram . How big is the perimeter of the hexagon ?

4 points

ABCDE

Question 12

Q13. Consider the f ive numbers a 1 , a 2 , a 3 , a 4 , a 5 with s um S . It is known that a k  k S f o r 15  k . What is the value of S ? 15 15

4 points

ABCDE

Question 13

Q14. In a three - sided p yramid all side lengths are integers . Four of the side lengths can be seen in the diagram . W hat is the sum of the two remaining side lengths ?

4 points

ABCDE

Question 14

Q15. How many pairs of integers  mn ,  fulfil the inequality 2 m  2023  2 n  m  1 ?

4 points

ABCDE

Question 15

Q16. The number 5 is to be written in the form n where n i s a natural number . W hat is the value of n ?

4 points

ABCDE

Question 16

Q17. Leon has drawn a closed path on the surface of a cuboid . W hich net can represent his path ?

4 points

ABCDE

Question 17

Q18. F or each positive integer n the number n ! is defined as the product of all number s from 1 to n . For example,

4 points

ABCDE

Question 18

Q19. The graphs of the functions y  x ³  3 x ²  ax  2 a  4 all pass through a common point independent of the choice of a . How big is the sum of the co - ordinates of this common point ?

4 points

ABCDE

Question 19

Q20. A pentagon is cut into smaller parts as shown in the diagram . The number s in the triangles state the area of the according tr iangle. How big is the area P of the grey quadril ateral ? 31

4 points

ABCDE

Question 20

Q21. The diagram shows a spiral of consecutive numbers starting with 1. In w hich order will the numbers 625, 626 a nd 627 a ppear in the spiral ?

5 points

ABCDE

Question 21

Q22. How many positive integers divide 23  but not 23  ?

5 points

ABCDE

Question 22

Q23. 13 athletes took part in a three - part climbing competition . There are no draws in any part. The final rank of each athlete is determin ed by arranging the product s of the ranks in each of the three parts: If an athlete for example comes 4th once, 3rd once and 6th once, he has 4  3 6=72 points . The higher the number of points, the worse the final rank. What is the worst possible final rank Hans can get to if he was 1 st in two of th e parts ?

5 points

ABCDE

Question 23

Q24. A game marker in the shape of a regular tetrahedron has one marked area. That side is placed on the triangle marked START. The marker is then moved within the diagram always to the next adjacent triangle by rolling it around an edge. On which triangle is the marker when it i s on the marked side again for the first time ?

5 points

ABCDE

Question 24

Q25. A part of a polynomial of degree fi ve is illegible due to an ink stain. It is known that all zeros of the polynomial are intege rs. What is the highest power of x  1 that divides this polynomial ?

5 points

ABCDE

Question 25

Q26. The big square shown i s split into four small squares . The circle touches the right side of the square in its midpoint. How big is the side length of the big square ? (Hin t : The diagram is not drawn to scale .)

5 points

ABCDE

Question 26

Q27. W hat is the biggest common factor of all numbers of the form

5 points

ABCDE

Question 27

Q28. The numbers from 1 to 11 are written in the empty hexagons . The sums of the three numbers in three hexagons with a common bold point are always equal . Three of the eleven numbers are already written in (see diagram) . W hich number is written in the hexagon with the question mark ?

5 points

ABCDE

Question 28

Q29. Two identical cylindric al glasses contain the same amount of water. The left glass is upright , while the right one rests against the other one at a slant . The water level in both glasses is at the same height . The water level in the leaning glass touches its bottom in exactly one point (see diagram). The base s of both glasses have an area of 3  cm². How much water is in each glass ?

5 points

ABCDE

Question 29

Q30. The product of six consecutive numbers is a 12 - digit number of the form abb cdd cdd abb , w here the digits a, b, c a nd d a re also consecutive numbers in any order . What is the value of the digit d ?

5 points

ABCDE

Question 30

2023 Student Test | Test and Chat