2024 Student Test | Test and Chat

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2024 Student (Grade 11 - 12)

Questions: 30 | Answered: 0

Q1. The angles in a triangle are in the ratio 1:3:5 . What is the biggest of those angles ?

3 points

ABCDE

Question 1

Q2. A tile pattern is made up of a number of identical ir regular pentagons . Which of the following tiles fits in to the hole in such a way that a closed curve is formed ?

3 points

ABCDE

Question 2

Q3. W hich of the following numbers is two less than a multiple of ten , two more than a square number and two times a prime number ?

3 points

ABCDE

Question 3

Q4. A kangaroo cuts a pizza into 6 pieces of equal size . After it has eaten one p iece , it re arranges the remaining pieces , so that the gaps between the pieces are all equally big . What is the angle in each gap ?

3 points

ABCDE

Question 4

Q5. Julia ha s the strange habit of draw ing the xy - plane with the positive direction s of the coordinate axes pointing to the left and downwards . W hat does the graph of the equation y = x + 1 l ook like in Julias co - ordinate system ?

3 points

ABCDE

Question 5

Q6. Kaito ha s manipulated a die . The probabilities of rolling a 2, 3, 4 or 5 are still 6 each but the probability of rolling a

3 points

ABCDE

Question 6

Q7. W hich of the following expressions h as the same value as 16  16 16 16 ?

3 points

ABCDE

Question 7

Q8. There are 6 coins on a table , each with heads facing up wards . On each move we turn over exactly 4 of th e co ins. W hat is the minimum number of moves we must make, such that all coins are left with heads facing downwards ?

3 points

ABCDE

Question 8

Q9. Noah starts with the number 1 and multiplies it with either 6 or 10. He then multiplies t he result again by either 6 or 10. He repeats this process several times. W hich of the following numbers can he not obtain in this way ?

3 points

ABCDE

Question 9

Q10. There are black and dashed path s in a park. Both paths divide the area of the park exactly in half . W hich of the following statements about the areas of the sections A, B and C is definitely correct ? 1 2 3

3 points

ABCDE

Q11. John ha s black and white unit cubes and wants to use 27 of them to build a 333  cube . He wants to make sure that the surface is ex actly half white and ha lf black. W hat is the minimum number of black cubes that he needs ?

4 points

ABCDE

Question 11

Q12. In a square with side length 6 a diagonal , a semi - circle and a quarter circle are drawn as shown . What is the area of the grey region ? 10

4 points

ABCDE

Question 12

Q13. The diagram shows four squares with the entire configuration resting on a horizontal straight line . The smaller squares have side length s a , b a nd c . The vert i ces A a nd C of two small squares co incide with diagonal ly opposite vertices of the big square. The vertex B of the third small square lies on a side of th e bi g square . Which of the following expressions is equal to the side length of the big square ?

4 points

ABCDE

Question 13

Q14. W e are given tw o positive numbers x a nd y with x < y . Which of the following expressions has the biggest value ? xy  3 xy  2 xy  2 xy  3 xy 

4 points

ABCDE

Question 14

Q15. The following shape is composed of identical squares. What is the maximum number of 2 × 1 - d omino e s that can be placed on the sh ape if each cover s exactly two squares ? The dominoes can be placed horizontally or vertically and are not allowed to cove r each other .

4 points

ABCDE

Question 15

Q16. How many three - digit numbers are there that contain at least one of the digits 1, 2 or 3?

4 points

ABCDE

Question 16

Q17. A teacher writes the 7 digits shown on the boar d . He asks a student to insert some multiplication signs (x) in such a way that the product of the resulting numbers (possibl y with multiple digits ) has the value 2024 . How many multiplication signs must be inserted ?

4 points

ABCDE

Question 17

Q18. A beaver wants to colour the squares and triangles in the pattern so that adjacent cells are never the same colour , even if they only touch each other in one corner . What is the minimum number of colours he needs ?

4 points

ABCDE

Question 18

Q19. W e know o f a po sitive integer n that exactly on e of the following statem ents is true . W hich is the true statement ?

4 points

ABCDE

Question 19

Q20. Two can d les of equal length are lit at the same time . One candle will burn down completely in 4 hours, the other in 5 ho urs . Both burn at a constant rate . How many hours do they have to burn until one ca nd le is exactly 3 times as long as th e other ?

4 points

ABCDE

Question 20

Q21. A three - sided pyramid has edges with side length s 5, 6, 7, 8, 9 a nd 10. The points M , N , P , Q , R a nd S are the midpoints of the edges , as shown in the diagram . What is the total length of the closed polyline MNPQRSM ?

5 points

ABCDE

Question 21

Q22. A quadrilateral ABCD ha s two right angles in the vertices B a nd C . It is known that AB = 4, BC = 8 a nd CD = 2. What is the smallest possible value of AX + DX , if X is a point on the segment BC ?

5 points

ABCDE

Question 22

Q23. W e have 6 cards and there is one number written on each side of each card . T he pairs of numbers on the cards are (5,12), (3,11), (0,16), (7,8), (4,14) a nd (9,10). The cards can be placed in the empty squares in any order with any side up . W hat is the smallest possible result of the calculation ?

5 points

ABCDE

Question 23

Q24. I have a four - digit number 푁 = 푝푞푟푠 . If I place a decimal point between the digits q a nd r , I obtain the number 푝푞 . 푟푠 . This is exactly the average of the two numbers 푝푞 a nd 푟푠 . What is the sum of the digits of N ?

5 points

ABCDE

Question 24

Q25. The diagram shows an object composed of 7 cubes with edge length 2. How long is the shortest path from M to N on the surface of the object ?

5 points

ABCDE

Question 25

Q26. Sylvia has several fair 12 - sided dice , each with the numbers 1 to 12 written on the ir faces . If she rolls all the dice simultaneously , the probability of rolling exactly one 12 is equally to the probability of not rollin g a 12 at all. How many dice does Sylv ia have ?

5 points

ABCDE

Question 26

Q27. It is known that the statements 23  , 27  a nd 67  are true . Which of the following relationships is therefore correct ? y x y x 1

5 points

ABCDE

Question 27

Q28. A function 푓 : 푅 → 푅 fulfils the condition f  20  x   f  22  x  for all real numbers x . It is kn own that f has exactly two real zeros . What is the sum of the two zeros ?

5 points

ABCDE

Question 28

Q29. A special four - digit number abcd fulfils the equa tion abcd  a  b  c  d . W hat is the value of a ?

5 points

ABCDE

Question 29

Q30. A game board is composed of 8 squares on which we want to stack coins. Initially, all squares are emp ty. On e ach turn we choose four adjacent squares and place one coin on ea ch of those squares. The numbers show how high the stack s are . Unfortunately, the table wobbled and five of the stacks fell over . How many coins were on the field indicated with a ques tion mark befor e the stack fell ?

5 points

ABCDE

Question 30

2024 Student Test | Test and Chat