2009 Student Test | Test and Chat

Back to KangarooMath

2009 Student (Grade 11 - 12)

Questions: 30 | Answered: 0

Q1. There are 200 fish in an aquarium. Of which 1% are blue, the rest are yellow. How many yellow fish have to be removed to make the number of blue fish equal 2% of the entire amount of fish?

3 points

ABCDE

Question 1

Q2. Wh ich of the following numbers is biggest?

3 points

ABCDE

Question 2

Q3. For how many postive whole numbers n is n² + n a prime number?

3 points

ABCDE

Question 3

Q4. Mari, Ville and Ossi are going to a coffee shop. Each of them has 3 glasses of juice, 2 cups of ice cream and 5 biscuits. What value could the total bill come up to in the end?

3 points

ABCDE

Question 4

Q5. The diagram on the right shows a solid made up of 6 triangles. Each vertex is assigned a number, two of which are indicated. The total of the three numbers on each triangle is the same. What is the total of all five numbers?

3 points

ABCDE

Question 5

Q6. The circles k 1 (with centre M 1 and radius 13) and k 2 (with centre M 2 and radius 15) intersect each other in the points P and Q. The length of the distance PQ is 24. What possible value could the di stance M 1 M 2 be?

3 points

ABCDE

Question 6

Q7. In a draw there are 2 white, 3 red and 4 blue socks. Lisa knows that one third of the socks have holes but she does not know the colour of the faulty socks. She randomly picks socks from the draw until she has a pair that is useable i.e. she has a pair without holes and of equal colour. What is the minimum amount of socks she has to draw to be certain to get a useable pair?

3 points

ABCDE

Question 7

Q8. The suare in the diagram has side length 1. The ra dius of the small circle would then be of the length 1 2 2 2

3 points

ABCDE

Question 8

Q9. Each side of a triangle ABC is being extended to the points P, Q, R, S, T and U, so that PA = AB = BS, TC = CA = AQ and UC = CB = BR. The area of ABC is 1. How big is the area of the hexagon PQRSTU?

3 points

ABCDE

Question 9

Q10. In the diagram on the right we want to colour the fields with the colours A, B, C and D so that adjacent fields are always in different colours. (Even fields that share only one corner, count as adjacent.) Some fields have already been coloured in. In which colour can the grey field be coloure d in?

3 points

ABCDE

Question 10

Q11. A (very small) ball is kicked off from point A on a square billiard table with side length 2m. After moving along the shown path and touching th e sides three times as indicated, the path ends in point B. How long is the path that the bal travels from A to B? (As indicated on the right: incident angle = emergent angle.)

4 points

ABCDE

Question 11

Q12. In a group of 2009 kangaroos each one is either light or dark. The smallest of the light kangaroos is bigger than exactly 8 dark kangaroos. One light one is bigger than exactly 9 dark ones, another light one is bigger than exactly 10 da rk ones, and so on. Exactly one light cangaroo is bigger than all dark cangaroos. How many light kangaroos are there?

4 points

ABCDE

Question 12

Q13. In the diagram to the right a 2 × 2 × 2 cube is made up of four transparent 1 × 1 × 1 cubes and four non - transparent black 1 × 1 × 1 cubes. They are placed in a way so that the entire big cube is non - transparent; i.e. looking at it from the front to the back, the right to the left, the top to the bottom, at no poi nt you can look through the cube. What is the minimum number of black 1 × 1 × 1 cubes needed to make a 3 × 3 × 3 cube non - transparent in the same way?

4 points

ABCDE

Question 13

Q14. On the island of the nobles and liars 25 people are stanging in a q ueue. The first person in the line claims that everybody behind him is a liar. Each of the other people claims that the person in front of him is a liar. How many liars are actually in the queue? (Nobles are always telling the truth and liars are always ly ing.)

4 points

ABCDE

Question 14

Q15. Determine the unit digit of the number 1² - 2² + … - 2008² + 2009².

4 points

ABCDE

Question 15

Q16. An equilateral triangle with side length 3 and a circle with radius 1 have the same centr e. What is the perimeter of the figure that is created when the two are being put together? p

4 points

ABCDE

Question 16

Q17. The adjacent diagram il lustrates the graphs of the two functions f and g. How can we describe the relationship between f and g?

4 points

ABCDE

Question 17

Q18. 100 students take an exam with 4 questions. 90 solve the first question, 85 the second, 80 the third and 70 the fourth. Determine the smallest possible number of students that have solved all four questions.

4 points

ABCDE

Question 18

Q19. In the diagram on the r ight we see the bird ’ s - eye view and front elevation of a solid that is defined by flat surfaces (i.e. view from obove and the front respectively). Which of the outlines I to IV can be the side elevation (i.e. view from the left) of the same object? Bird ’ s - Eye View (view from above) Front Elevation (view from the front)

4 points

ABCDE

Question 19

Q20. The sum of the number in each line, column and diagonal in the „ magic square “ on the right is always constant. Only two numbers are visible. Which number is missing in field a?

4 points

ABCDE

Question 20

Q21. Two runners each run with constant speed rounds around a racetrack. Both start at the same time at the same point. A is faster than B, takes 3 minutes to cover one lap and overtakes B for the first time after 8 min utes. How long does B take to cover one lap?

5 points

ABCDE

Question 21

Q22. Let Z be the amount of 8 - digit numbers that are made up of all different digits not equal to 0. How many of those number are divisi ble by 9? Z Z Z 8 Z 7 Z

5 points

ABCDE

Question 22

Q23. How many 10 - digit numbers exist that are solely made up of the numbers 1, 2 and 3 and where adjacent n umbers always differ by exactly 1?

5 points

ABCDE

Question 23

Q24. For how many whole numbers n ≥ 3 exists a convex polygon, whose angles are in the ratio 1 : 2 : … : n?

5 points

ABCDE

Question 24

Q25. 55 pupils are taking part in a com petition. A jury indicates each question with a „ + “ if it is solved correctly, with a „ - “ if it is solved incorrectly and a „ 0 “ if it was not attempted. It turns out that no two students had the same amount of „ + “ as well as the same amount of „ - “ . What i s the minimum number of questions that had to be asked in the competition?

5 points

ABCDE

Question 25

Q26. In a rectangle JKLM the angle bisector in J intersects the diagonal KM in N. The distance of N to LM is 1 and the distance of N to KL is 8. How long is LM? 2

5 points

ABCDE

Question 26

Q27. If k = = = . How many possible real values exist for k? b + c c + a a + b

5 points

ABCDE

Question 27

Q28. The number 1, 2, 3, … , 99 are divided up into n groups. The following rules apply: ¤ Each number is in exactly one group. ¤ There are at least two numbers in each group. ¤ If there are two number in the same group then their sum is not divisible by 3. Determine the s mallest n which fulfills those rules

5 points

ABCDE

Question 28

Q29. Samantha and her three sisters go to the theater. They have reserved a loge with four seats. Samantha and two of her sisters arrive early and they sit down without paying attention t o their seat numbers. Marie arrives later and insists to sit on the seat that is indicated on her ticket. What is the probability that Samantha has to change her seat, if now every sister who has to swap seats insists on sitting on the seat indicated on he r ticket.

5 points

ABCDE

Question 29

Q30. A sequence of whole numbers is defined by a 0 = 1, a 1 = 2 and a n+2 = a n + (a n+1 )² for n ≥ 0. When a 2009 is divided by 7 the remainder is

5 points

ABCDE

Question 30

2009 Student Test | Test and Chat