2010 Student Test | Test and Chat

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2010 Student (Grade 11 - 12)

Questions: 30 | Answered: 0

Q1. In the picture opposite we see that 1+3+5+7 = 4×4. How big is 1+3+5+7+...+17+19?

3 points

ABCDE

Question 1

Q2. f () x + 3 f ⎜ ⎟ = 5 x . Determine the value of f(6). ⎝ x ⎠

3 points

ABCDE

Question 2

Q3. The hollow spaces of two empty containers are cubic and have a base area of 1 dm² and 4 dm² respectively. The big container is to be be filled with water, us ing the small one as a scoop. How many full scoops are necessary to fill the big cube?

3 points

ABCDE

Question 3

Q4. How many four-digit numbers, made up of odd digits only, are divisible by 5?

3 points

ABCDE

Question 4

Q5. The managing director of a company claims „Every on e of our employees is at least 25 years old.“ It turns out, he is wrong. Which of the following statements is correct?

3 points

ABCDE

Question 5

Q6. In the box are seven blockss. You want to rearrange the blocks so that another block can placed. What is the minimum number of blocks that have to be moved?

3 points

ABCDE

Question 6

Q7. The triangle pictured is right-angled. M is the midoint of the hypotenuse AB and ∠ BCA = 90°. How big is ∠ BMC?

3 points

ABCDE

Question 7

Q8. Which of the following numbers could be the number of edges of a prism?

3 points

ABCDE

Question 8

Q9. How many two-digit numbers with x in the tens-c olumn and y in the unit-column have the properties (x − 3)² + (y − 2)² = 0?

3 points

ABCDE

Question 9

Q10. In the figure the square has side length 2. The semi-circles pass through the midpoint of the square and have their centres on the corners of the square. The grey circles have their centres on the sides of the square and touch the semi-circles. How big is the total area of the grey parts? 3 1

3 points

ABCDE

Question 10

Q11. The numbers 7 , 7 und 7 are, in this order consecutive terms of a geometric sequence. Determine the next term. 9 5 10

4 points

ABCDE

Question 11

Q12. The chord AB touches the smaller of the two concentric circles. The length AB =

4 points

ABCDE

Question 12

Q13. The integers x and y fulfill the condition 2x = 5y. Only one of the following numbers can be considered for x+y. Which?

4 points

ABCDE

Question 13

Q14. The big equilateral triangle consists of 36 small equilateral triangles which each have an area of 1 cm². Determine the area of ABC.

4 points

ABCDE

Question 14

Q15. In a bag are blue, green and red balls (at least one ball of each colour). If we randomly take five balls out of the bag, we know: At least two balls are red and at least three are of the same colour. Ho w many blue balls are in the bag?

4 points

ABCDE

Question 15

Q16. Which of the following graphs represents the solution set of (x-|x|)² + (y-|y|)² = 4?

4 points

ABCDE

Question 16

Q17. If we connect three cornerpoints of a regular 14-sided polygon then a triangle is created. How many of those triangles are right-angled?

4 points

ABCDE

Question 17

Q18. Each star in the expression 1 ∗ 2 ∗ 3 ∗ 4 ∗ 5 ∗ 6 ∗ 7 ∗ 8 ∗ 9 ∗ 10 is either replaced by a „+“ or a „ × “. Let N be the biggest number possible that can be obtained this way. What is the smallest prime factor of N?

4 points

ABCDE

Question 18

Q19. The side-lengths of a triangle in cm are given by the natural numbers 13, x and y. Determine the perimeter of the triangle if xy = 105.

4 points

ABCDE

Question 19

Q20. A strip of paper is folded three times as shown. Determine β if α = 70°.

4 points

ABCDE

Question 20

Q21. Lines drawn parallel to the base of the triangle pictured separate the two other sides into 10 sized parts. What percentage of the triangle is grey?

5 points

ABCDE

Question 21

Q22. 100 people take part in a race where no-one can tie. Everybody is questioned after the race as to which place they have ach ieved and all answer with a number between 1 and 100. The sum of all answers is 4000. What is the minimum number of people who have lied about their result?

5 points

ABCDE

Question 22

Q23. I roll an ordinary die once. What is the probability that I rolled ‚2’ at least once under the condition that the third number is equal to the sum of the first two?

5 points

ABCDE

Question 23

Q24. A barcode as pictured is made up of alternate black and white stripes. The code always starts and ends with a black stripee. Each strip (black or white) has the width 1 or 2 and the total width of the barcode is 12. How many different barcodes if this kind are there if one reads from left to right?

5 points

ABCDE

Question 24

Q25. The picture on the right shows a tile pattern. The side length of the bigger tiles is a and of the smaller ones b. The dotted lines (horizontal and tilted) include an angle of 30°. How big is the ratio a:b?

5 points

ABCDE

Question 25

Q26. The numbers from 1 to 10 are writte n 10 times each on a board. Now the children play the following game: One child deletes two numbers off the board and writes instead the sum of the two numbers minus 1. Then a second child does the same, and so forth until there is only one number left on the board. The last number is

5 points

ABCDE

Question 26

Q27. The expression is equal to 2048 3

5 points

ABCDE

Question 27

Q28. 0 ⋅ 44 1 2 K 3 4 is written as a decimal. What is the 100th digit after the decimal point?

5 points

ABCDE

Question 28

Q29. A function maps all positive real numbers to real numbers. For all x the following holds true: x ∈ R : ⎛ 2010 ⎞

5 points

ABCDE

Question 29

Q30. On the two catheti of a right-angled triangle (with lengths a and b respectively) points P and Q respectively are chosen. Let K and H be the endpoints of the perpendicular lines from P and Q respectively, to the hypotenuse of the triangle. How big is the smallest possible value of KP + PQ + QH? 2 2

5 points

ABCDE

Question 30

2010 Student Test | Test and Chat