2011 Junior Test | Test and Chat

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2011 Junior (Grade 9 - 10)

Questions: 30 | Answered: 0

Q1. A zebra crossing has alternating white and black stri pes each 50cm wide. The first stripe is white and the last one is white. The zebra crossing in front of our school has 8 white stripes. How wide is the road?

3 points

ABCDE

Question 1

Q2. The area of the grey rectangle shown on the right is 13 cm . X and Y are the midpoints of the sides of the trapezium. How big is the area of the trapezium?

3 points

ABCDE

Question 2

Q3. Given are the following expressions S 1 = 2 × 3+3 × 4+4 × 5 , S 2 = 2 +3 +4 , S 3 = 1 × 2+2 × 3+3 × 4. Which one of the following statements is true?

3 points

ABCDE

Question 3

Q4. In the picture on the right a number should be written next to each point. The sum of the numbers on the corners of each side of the hexagon should be equal. Two numbers have already been written. Which number should be in the place marked ‘x’?

3 points

ABCDE

Question 4

Q5. If 2011 is divided by a certain positive whole num ber the remainder is 1011. Which number was it divided by?

3 points

ABCDE

Question 5

Q6. A rectangle with area 360 cm² is being laid out w ith square tiles. The rectangle is 24 cm long and

3 points

ABCDE

Question 6

Q7. All four-digit numbers whose digit sum is 4 are written down in order of size, starting with the biggest. In which position is the number 2011??

3 points

ABCDE

Question 7

Q8. The two bold lines on the right are rotations of each other. Which of the given points could be the centre of this rotation?

3 points

ABCDE

Question 8

Q9. Given are a regular hexagon with side-length 1, six squares and six equilateral triangles as shown on the right. What is the perimeter of this tessellation? √ ଷ

3 points

ABCDE

Question 9

Q10. In the picture on the left we see three dice on top of each other. The sum of the points on opposite sides of the dice is 7 as usual. The sum of the points of areas that face each other is always 5. How many points are on the area marked X?

3 points

ABCDE

Question 10

Q11. In a certain month there were 5 Mondays, 5 Tuesdays and 5 Wednesdays. In the month before there were only 4 Sunda ys. What will be in next month?

4 points

ABCDE

Question 11

Q12. Three racers take part in a Formula-1 Race: Michael , Fernando and Sebastian. From the start Michael is in the lead in front of Fernando who is in front of Sebastian. In the course of the race Michael and Fernando overtake each other 9 times, Fernando and Sebastian 10 times and Michael and Sebastian 11 times. In which order do those three end the race?

4 points

ABCDE

Question 12

Q13. How big is n, if 9 + 9 + 9 = 3 holds true?

4 points

ABCDE

Question 13

Q14. I have got two cubes with side lengths a dm and a +1 dm. The big cube is full of water and the little one is empty. I pour as much water as possible from the big one into the little one and now 217 ℓ remain in the big die. How many litres of water are now in the little one?

4 points

ABCDE

Question 14

Q15. A marble of radius 15 is rolled into a cone -shaped hole. It fits in perfectly. From the side the cone looks like an equila teral triangle. How deep is the hole?

4 points

ABCDE

Question 15

Q16. The cells of the 4 × 4-table on the right should be coloured either in black or white. The numbers determine how many cells in each row/column should be black. How many ways are there to do the colouring in?

4 points

ABCDE

Question 16

Q17. What is the biggest number of consecutive three-digit numbers with at least one odd digit each?

4 points

ABCDE

Question 17

Q18. Nick wants to write whole numbers into the cells of the 3×3-table on the right so that the sum of the digits in each in each 2×2-sub-table is always 10. Five numbers have already been written. Determine th e sum of the remaining four numbers.

4 points

ABCDE

Question 18

Q19. Jan cannot draw very accurately but nevertheless he tried to produce a road map of his village. The relative position of the houses and the street crossings are all correct but three of the roads are actually straight and only the Qurwikroad is not. Who lives in the Qurwikroad?

4 points

ABCDE

Question 19

Q20. In the triangle WXY points Z on XY and T on WZ are, as shown on the right. If one connects T with X, a figure with nine internal angles is created as shown in the figure on the right. From those 9 angles, what is the smallest number that could be a different size to each other

4 points

ABCDE

Question 20

Q21. Simon has a cube with side length 1 dm made of glass. He sticks several equally big black squares on it, as shown on the right so that all faces look the 2 same. How many cm were covered over?

5 points

ABCDE

Question 21

Q22. The five-digit number ܾܽܿ݀݁ is called interesting , if all of its digits are different and a = b+c+d+e holds true. How many interesting numbers are there?

5 points

ABCDE

Question 22

Q23. The numbers x and y are both greater than 1. Which of the following numbers is biggest? x x 2 x 2 x 3 x

5 points

ABCDE

Question 23

Q24. Given is a regular tetrahedron ABCD whose side ABC is on the plane ε . The edge BC is on the straight line s. Another tetrahedron BCDE has one common si de with ABCD. Where does the straight line DE intersect the plane ε ?

5 points

ABCDE

Question 24

Q25. Three big boxes P, Q and R are stored in a warehouse. The upper picture on the right shows their placements from above. The boxes are so heavy that they can only be rotated 90° around a vertical edge as indicated in the pictures below. Now the boxes should be rotated to stand against the wall in a certain order. Which arrangement is possible?

5 points

ABCDE

Question 25

Q26. How many ordered pairs of positive whole numbers (x, y) solve the equation + = ? x y 3

5 points

ABCDE

Question 26

Q27. For a positive whole number n ≥ 2 let n indicate the largest prime number less than or equal to n . How many positive whole numbers k fulfill the condition k + 1 + k + 2 = 2 k + 3 ?

5 points

ABCDE

Question 27

Q28. The two circles shown on the right intersect each other at X and Y. Thereby XY is the diameter of the small circle. The centre S of the large circle (with radius r) is on the small circle. How big is the area of the grey region? π 2 3 π 2 1 2 3 2

5 points

ABCDE

Question 28

Q29. In how many ways can one choose four edges of a cube so that no two of these edges have a common corner?

5 points

ABCDE

Question 29

Q30. Determine all n (1 ≤ n ≤ 8) for which one can mark several cells of a 5×5 table so that there are exactly n marked cells in every 3×3 subtable.

5 points

ABCDE

Question 30

2011 Junior Test | Test and Chat