2010 Junior Test | Test and Chat

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2010 Junior (Grade 9 - 10)

Questions: 30 | Answered: 0

Q1. What is the result when 20102010 is divided by 2010?

3 points

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Question 1

Q2. Ivan gains 85% of the points in a test. Tibor gains in the same test 90% of the points but only one point more than Ivan. What is the maximum number of points that can be gained in this test?

3 points

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Question 2

Q3. Which number goes in the cell with the question mark if the sum of the numbers in both rows is equal?

3 points

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Question 3

Q4. The object pictured is made up of four equally sized cubes. Each cube has a surface area of

3 points

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Question 4

Q5. On each birthday Rosa gets as many roses as she is old in years. She still has all the dried flowers and there are now 120 of them. How old is she?

3 points

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Question 5

Q6. Six points are marked on a square grid as pictured. Which geometric figure cannot be drawn if only the marked points are allowed to be used as cornerpoints of the figure?

3 points

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Question 6

Q7. In the picture opposite we see that 1+3+5+7 = 4 × 4. How big is 1+3+5+7+…+17+19?

3 points

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Question 7

Q8. Brigitte goes on holiday to Verona and plans to cross all five of the famous old bridges over the Etsch (Adige) at least once. She starts at the train station and when she returns there she has crossed each of the five bridge s but no others. During her walk she has crossed the river n times. What is a possible value for n?

3 points

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Question 8

Q9. In a box are 50 counters: white ones, blue ones and re d ones. There are eleven times as many white ones as blue ones. There are less red ones than white ones, but more red ones than blue ones. By how much is the number of red counters less than the number of white ones in the box?

3 points

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Question 9

Q10. Which of the numbers a, b, c, d and e is biggest if a – 1 = b + 2 = c – 3 = d + 4 = e – 4?

3 points

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Question 10

Q11. In the figure, ABCE is a square. CDE an d BCF are equilateral tr iangles. The length of AB is 1. How long is FD? 3

4 points

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Question 11

Q12. A paperstrip is folded three times in the middle. It is then opened again and looked at from the side so that one can see all 7 folds from the side at the same time. Which of the following views is not a possible result?

4 points

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Question 12

Q13. My teacher says that the product of his age and the age of his father is 2010. In which year could my teacher have been born?

4 points

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Question 13

Q14. How big is the angle indicated with a question mark?

4 points

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Question 14

Q15. How many whole numbers are there, whose digits sum to 2010 and have a product of 2?

4 points

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Question 15

Q16. In the diagram one should go from A to B along the arrows. Along the way calculate the sum of the numbers that are stepped on. How many different results can be obtained?

4 points

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Question 16

Q17. In one month three Tuesdays fall on even days. Which day of the week is the 21st of the month?

4 points

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Question 17

Q18. A circle of radius 4 cm is divided, as shown, by four semicircles with radius 2 cm into four congruent parts. What is the perimeter of one of these parts?

4 points

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Question 18

Q19. Five students carry out a run. Their results are recorded in the graph opposite, according to the time taken (Ze it) and the distance covered (Strecke). Who had the greatest average speed?

4 points

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Question 19

Q20. A triangle is folded along the dashed line as shown. The area of the triangle is 1.5 times the area of the resulting figure. We know that the total area of the grey parts is 1. Determine the area of the starting triangle.

4 points

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Question 20

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5 points

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Question 21

Q22. The big equilateral triangle consis ts of 36 small equilateral triangles which each have an area of 1 cm². Determine the area of ABC.

5 points

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Question 22

Q23. Lines drawn parallel to the base of the triangle pictured, separate the other two sides into 10 equally large parts. What percentage of the triangle is grey?

5 points

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Question 23

Q24. For how many integers n where 1 ≤ n ≤ 100 is n a square number?

5 points

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Question 24

Q25. Six-legged, seven-legged and eight-legged octopuses serve the king of the sea Neptun. The seven-legged ones always lie and the six-legged and the eigh t-legged ones always speak the truth. One day four octopuses meet. The blue one says: „We have 28 legs altogether.“ The green one says: „We have 27 legs altogether.“ The yellow one says: „We have 26 legs altogether.“ The red one says: „ We have 25 legs altogether.“ How many legs does the red octopus have?

5 points

ABCDE

Question 25

Q26. In the figure α = 7°. All lines OA 1 , A 1 A 2 , A 2 A 3 , … are equally long. What is the maximum number of lines that can be drawn in this way if no two lines are allowed to intersect each other?

5 points

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Question 26

Q27. In a sequence the first three terms are 1, 2 and 3. From the fourth term onwards each subsequent term is calculated from the three previous terms. The rule is that the third term is subtracted from the sum of the first two. This way we ob tain the sequence 1, 2, 3, 0, 5, − 2, 7, … What is the 2010th term of this sequence?

5 points

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Question 27

Q28. Along each side of a pentagon a positive integer is written. Numbers of adjacent sides never have a common factor bigger than 1 and non-adjacent sides always have a common factor bigger than 1. There are several possibilities for this situation but one of the following numbers can never be at one of the sides of the pentagon. Which one?

5 points

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Question 28

Q29. How many three-digit numbers have the properties that their middle digit is the average of the two other digits?

5 points

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Question 29

Q30. A barcode as pictured is made up of alternate black and white stripes. The code always starts and ends with a black stripe. Each stripe (black or white) has the width 1 or 2 and the total width of the barcode is 12. How many different barcodes of this kind are there if one reads from left to right?

5 points

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Question 30

2010 Junior Test | Test and Chat