2013 Student Test | Test and Chat

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2013 Student (Grade 11 - 12)

Questions: 30 | Answered: 0

Q1. Which of the following numbers is biggest? 0+13 13 3

3 points

ABCDE

Question 1

Q2. The regular eight - sided shape on the right has sides of length 10. A circle touches all inscribed diagonals of this eight - sided shape. What is the radius of this circle?

3 points

ABCDE

Question 2

Q3. The surface of a prism is made of 2013 faces. How many edges does the prism hav e?

3 points

ABCDE

Question 3

Q4. The third root of 3 3 takes which value? (Note : aa bb = () .) 3 3 2 3

3 points

ABCDE

Question 4

Q5. The date 2013 is made up of four consecutive digits 0, 1, 2, 3. How many years before the year 2013 was the date last made up of four consecutive digits?

3 points

ABCDE

Question 5

Q6. Let f be a linear function for which ff (2013) −= (2001) 100 gilt . holds true. What is the value of ff (2031) − (2013) ?

3 points

ABCDE

Question 6

Q7. We know that the relationship 2 < x < 3 is valid for a number x . How many of the following statements are true in this case?

3 points

ABCDE

Question 7

Q8. Each of six lone heros has captured wanted people. In total they have captured 20 wanted people: the first hero one wanted person, the second hero two wanted people, the third hero three wanted people. The fourth hero has captured more wanted people than any other hero. Determine the smallest number of wanted people that the fourth hero could have captured, so that this statement could be true.

3 points

ABCDE

Question 8

Q9. Inside the cube lattice pictured on the side one can see a solid, non - seethrough pyramid ABCDS with square base ABCD , whose top S is exactly in the middle of one edge of the cube. If you look at the pyramid from above, from below, from the front, from the back, from the right and from the left – which of the following views cannot be possible?

3 points

ABCDE

Question 9

Q10. If a certain substance melts the volume increase s by 12 1 . By how much does the volume decrease if the substance solidifies again?

3 points

ABCDE

Question 10

Q11. Ralf has a number of equally big plastic plates each in the form of a regular five sided shape. He glues them together along the sides to form a complete ring (see picture). Out of how many of these plates is the ring made up?

4 points

ABCDE

Question 11

Q12. How many positive integers n are there with the property that 3 n as well as 3 n are three - digit number s ?

4 points

ABCDE

Question 12

Q13. . A circular carpet is placed on a floor which is covered by equally big, square tiles. All tiles that have at least one point in common with the carpet are coloured in grey. Which of the following cannot be a result of this?

4 points

ABCDE

Question 13

Q14. We are looki ng at the following statement about a function defined for all integers x fZ : → Z : "For each even x fx () is even ." What would be the negation of this statement?

4 points

ABCD

Question 14

Q15. Amongst the graphs shown below there is the graph of the function fx ( ) = ( a −− xb )( x ) 2 with ab < . Which is it ?

4 points

ABCDE

Question 15

Q16. We are considering rectangles which have one side of length of 5.0 cm. Amongst these there are some that can be cut to make a square and a 2 rectangle, one of which having an area of 4.0 cm . How many such rectangles are there?

4 points

ABCDE

Question 16

Q17. Peter has drawn the graph of a function fR : → R which consists of two rays and a line segment as indicated on th e right. How many solutions has the equation fffx ( ( ( ))) = 0 ?

4 points

ABCDE

Question 17

Q18. How many pairs of positive integers (,) xy solve the equation x 2 × y 3 = 6 12

4 points

ABCDE

Question 18

Q19. In a box there are 900 cards that are numbered from 100 to 999. On any two different cards there are always different numbers. Franz picks a few cards and works out the sum of the digits on each card. What is the minimum number of cards he has to pick to have at least three with the same sum?

4 points

ABCDE

Question 19

Q20. In a triangle ABC the points M and N are placed on side AB so that AN = AC and BM = BC. De termine ∠ ACB if ∠ MCN = 43°.

4 points

ABCDE

Question 20

Q21. How many pairs of integers (,) xy with x ≤ y are there such that their product is exactly five times their sum?

5 points

ABCDE

Question 21

Q22. The function fR : → R is defined by the following properties: f is periodic with period 5, and for - 3 ≤ x < 2 f (x) = x² holds true. How big is f (2013)?

5 points

ABCDE

Question 22

Q23. The cube pictured on the side is intersected by a plane that passes through the three points adjacent to A, that is D , E and B . In a similar way the cube is also intersected by those planes that go through the three points adjacent to each of the other sev en vertices. These planes dissect the cube into several pieces. What does the piece that contains the centre of the cube look like?

5 points

ABCDE

Question 23

Q24. How many solutions (,) xy with a real x and y has the equation xy 22 += | x | + | y |?

5 points

ABCDE

Question 24

Q25. Let fN : → N be the function that is defined by fn () = fo r even n , a nd by fn () = for odd n . If k is a positive 2 2 integer then let fn k () describe the expression ff ( (... fn ( )...))) , in which f appears k - times. The number of solutions to the 2013 equation fn () = 1 is

5 points

ABCDE

Question 25

Q26. On the co - ordinate plane a number of straight lines have been drawn. Line a intersects exactly three other lines and line b intersects exactly four other lines. Line c intersects exactly n other lines with n ≠ 3, 4. How many lines were drawn on the plane ?

5 points

ABCDE

Question 26

Q27. If you add the first n positive integers, you obtain a three - digit number with all digits being the same. How big is the sum of the digits of n ?

5 points

ABCDE

Question 27

Q28. On an island live only Truthtellers (who always speak the truth) and Liars (who never speak the truth). I met two inhabitants and asked the taller one whether they are both Truthtellers. He replied but from his answer I couldn't decide which group they belonged to. So I asked the smaller one whether the taller one is a Truthteller. He answered and then I knew which type they both were. Which statement is correct?

5 points

ABCDE

Question 28

Q29. Julian wrote an algorithm to form a sequence of numbers. a 1 = 1 a nd a mn + = a m ++ a n mn holds true for all positive integers m and n . Determine the value of a 100 .

5 points

ABCDE

Question 29

Q30. Five cars enter a roundabout at the same time (see picture). Each car leaves the roundabout having completed less than a whole round and exaclty one car leaves at each exit. How many different combinations are there of how the cars can leave the roundabout?

5 points

ABCDE

Question 30

2013 Student Test | Test and Chat