2012 Student Test | Test and Chat

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2012 Student (Grade 11 - 12)

Questions: 30 | Answered: 0

Q1. A clo c c k has three hands in dif f f erent lengt h h s (for seco n n ds, minutes and hours). We don’t k n n ow the leng th of each h a nd but we k k now that t h h e clock sho w w s the corre c ct time. At 12:5 5 5 :30 the han d d s are in th e e positions s h h own on the right. What does the cl o o ckface look lik e e at 8:10:00 ? ?

3 points

ABCDE

Question 1

Q2. The w w ater level i n n a port rises and falls on a certain d d ay as show n n in the diag ram. How many h o o urs on that day was th e water level over 30 cm?

3 points

ABCDE

Question 2

Q3. How m m any differ e e nt rectangl e e s with area 6 60 and wh o o le number e e d side lengt h h s are there ? ?

3 points

ABCDE

Question 3

Q4. The p ositive whol e numbers a a re being col oured in or d d er, in red, b lue and gre e e n, i.e. 1 red , 2 blue, 3 green, 4 4 red, 5 blue, 6 green, an d d so on. Wh i i ch colour c o o uld the su m of a red nu m m ber and a b b lue number be?

3 points

ABCDE

Question 4

Q5. The n umber ඥ 2 √ √ 2 is equal t o o ల య

3 points

ABCDE

Question 5

Q6. In a li s s t of five nu m m bers the fi r r st number i s s 2 and the l ast one is 1 2 2 . The produ c ct of the firs t t three number s is 30, of th e middle th r r ee 90 and o f f the last th r ee 360. W h h at is the mi d d dle numbe r r in that list?

3 points

ABCDE

Question 6

Q7. A rec t t angular pie c c e of paper A A BCD with t h h e measure m m ents

3 points

ABCDE

Question 7

Q8. The s u u m of the di g g its of a nin e e digit numb er is 8. How big is the pro d d uct of the d igits of this n n umber?

3 points

ABCDE

Question 8

Q9. The b iggest possi b b le natural n n umber n, fo r which ݊ ൏5 hol d s true is

3 points

ABCDE

Question 9

Q10. The age of Quin t t us is a two d d igit power o o f five and t h h e age of Se k k undus is a t w w o digit po w w er of two. If one a d d ds the digit s of their ag e e s the total o o btained is a a n odd num b b er. How big is the prod u u ct of the digits o f f their ages?

3 points

ABCDE

Question 10

Q11. Ho w w big is the a n n gle  in th e e regular five e ‐ sided star s s hown?

4 points

ABCDE

Question 11

Q12. A re a a l number x fulfills the c o o ndition x³ < < 64 < x². W h h ich of the f o o llowing statem e e nts is defini t t ely true?

4 points

ABCD

Question 12

Q13. A tr a a vel agency o o rganises fo u u r different t t rips for a c e e rtain group. Each trip h a a s a particip a a tion rate of 80%. W h h at is the mi nimum perc entage of th h e group whi ch has take n n part in all f o o ur roundtri ps?

4 points

ABCDE

Question 13

Q14. For a a ski race co n n secutive st a a rting numb e e rs are han d d ed out. One number wa s accidental l l y given out twice. T he sum of al l the numbe rs handed o u ut is 857. W h h ich numbe r r was given o o ut twice?

4 points

ABCDE

Question 14

Q15. In o n n e class a te s s t did not yi e e ld a very su c c cessful res u u lt because t he average m m ark was ex actly 4. The boys ha v v e done slig h h tly better w w ith an avera a ge mark of 3 3 .6, while th e e girls have r r eceived an a a verage mark of 4.2. Which o o f the follo w w ing stateme nts is correc t?

4 points

ABCDE

Question 15

Q16. In t h h e diagram w w e see a ros e e bed. White roses are g r r owing in th e e squares that are eq u u ally big, red ones are in the big squ a a re and yell o w ones in t t he right ‐ an g g led triangle . The bed h a a s width and height 16 m m . How bi g g is the area o o f the bed?

4 points

ABCDE

Question 16

Q17. A ri g g ht ‐ angled t r r iangle with s s ide lengths a = 8, b = 1 5 and c = 17 i s given. H ow big is th e e radius r of t t he inscribe d d semicircle shown?

4 points

ABCDE

Question 17

Q18. A sq uare ABCD h h as side ‐ len g g th 2. E is th e e midpoint o f AB and F the mid p p oint of AD. G is a point on the line C C F with 3CG = 2GF. How big is th e e area of th e e triangle BE G G ? ଻ ସ ଼ ଷ ଺

4 points

ABCDE

Question 18

Q19. The clock show n n has a recta n n gular clock face, the ha nds howeve r move as usual in a consta n n t circular p a a ttern. How b b ig is the di s tance x of t h h e digits 1 a a nd 2 (in cm ), if the dist a a nce betwee e n the numb e e rs 8 and 10 is given as s 12 cm?

4 points

ABCDE

Question 19

Q20. Ren a a te wants to glue togeth er a numbe r r of ordinary dice (whos e e number of points on o p p posite side s s always a a dds up to 7 ) ) to form a “ d d icebar” as s s hown. Doin g this she o n n ly wants to g glue sides t o o gether with an equa l number of points. She w w ants to ma a ke sure tha t t the sum of a a ll points on the non ‐ glu e e d sides equ u als 2012. H o o w many di ce does she have to glu e e together?

4 points

ABCDE

Question 20

Q21. Whi c c h of the fol l l owing func t t ions fulfills f f or all x ് 0 t t he conditio n n ݂ ቀ ቁ ൌ݂ ሺ ሺ ݔሻ ? ௫ ଶ ଵ ଵ ଵ ଵ ଵ ଵ

5 points

ABCDE

Question 21

Q22. The solution set of the ineq u u ality |x| + | x x ‐ 3| > 3 is

5 points

ABCDE

Question 22

Q23. Let a a > b. If the e e llipse show n n rotates ab o o ut the x ‐ axi s an ellipsoi d d E x with vol u u me Vol(E x ) i s s obtained. I f it rotates a bout the y ‐ a a xis an ellips o o id E y with v o o lume Vol(E y y ) is obtaine d d . Which of t t he followin g g statement s s is true?

5 points

ABCDE

Question 23

Q24. In a game with f r r actions I a m m allowed to carry out t w w o operation s, namely ei t t her increas e e the numera t t or by 8 or i n n crease the d d enominato r r by 7 witho u u t simplifyin g during the e game. Star t t ing with the ଻ fraction after n su c c h operatio n s I again ob t t ain a fractio n with equa l value. Wha a t is the sma l lest value ଼ of n?

5 points

ABCDE

Question 24

Q25. An e e quilateral tr iangle is bei n n g rolled ar o o und a unit s q q uare as sho w w n. How lo n n g is the pat h h that the point show n n covers, if t he point an d d the triangle are both ba c c k at the sta rt for the fir s s t time? ଶ଼ ଵସ ଶଵ

5 points

ABCDE

Question 25

Q26. Ho w w many per m m utations (x 1 , , x 2 , x 3 , x 4 ) o f f the set {1, 2 2 , 3, 4} have property th a a t the numb e e r x 1 x 2 + x 2 2 x 3 + x 3 x 4 + x x 4 x 1 is divisi b b le by 3?

5 points

ABCDE

Question 26

Q27. Afte r an especia lly intense l e e sson the gr a a ph of the f u u nction y = x ² ² was still on the board a s well as

5 points

ABCDE

Question 27

Q28. Thr e e e corners o f f a die (not a ll on one fa c c e) have the coordinates P(3,4,1), Q( 5 5 ,2,9) and R ( ( 1,6,5). What a r r e the coordi nates of the midpoint o f f the die?

5 points

ABCDE

Question 28

Q29. In t h h e sequence 1, 1, 0, 1, ‐ 1 , , … the first t t wo terms a 1 1 and a 2 are e e ach 1. The t t hird term is the differen ce of the pr e e vious two a nd a 3 = a 1 – a a 2 holds tru e e . The fourt h one is the s s um of the p r r evious two with a 4 = = a 2 + a 3 . Th e e n a 5 = a 3 ‐ a 4 , a 6 = a 4 + a 5 , and so on, a a lternating d ifference an n d sum. How big is the sum of t t he first 100 terms of thi s s sequence?

5 points

ABCDE

Question 29

Q30. Ger h h ard choose s s two numb e e rs a and b f r r om the set { { 1, 2, 3, …, 2 6 }. The prod uct a  b of t h h ese two number s is equal to the sum of t t he remaini n n g 24 numb e e rs from this set. How bi g g is |a ‐ b|?

5 points

ABCDE

Question 30

2012 Student Test | Test and Chat