2012 Junior Test | Test and Chat

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2012 Junior (Grade 9 - 10)

Questions: 30 | Answered: 0

Q1. Whic h h of the sha p p es to the righ t t has the lar g g est area?

3 points

ABCDE

Question 1

Q2. 11.11 1 ‐ 1.1111=

3 points

ABCDE

Question 2

Q3. A wri s s twatch was laid on a ta b b le in such a way that th e e minute ha n n d pointed northea s s t. How ma n n y minutes m m ust pass be f f ore the min ute hand is p p ointing northw e e st for the fi r r st time?

3 points

ABCDE

Question 3

Q4. M an d d N are the m m idpoints of the equal si d d es of an is o o sceles trian g g le. How big is the area o o f the quadr i lateral (mar r ked ?)?

3 points

ABCDE

Question 4

Q5. cm res p p ectively, a t t riangle with area 8 cm a a nd the gre y y parallelogr a a m. What is the area of the para l l lelogram?

3 points

ABCDE

Question 5

Q6. A cub o o id is forme d d from 3 pie c c es (see pict t ure). Each p iece is mad e e from 4 cub e e s of the sa m m e colour. W W hat shape d d oes the wh ite piece ha v v e?

3 points

ABCDE

Question 6

Q7. The d i i git sum of a seven digit number is 6 . . What is th e e product of t t he digits?

3 points

ABCDE

Question 7

Q8. ABC i s s a right ‐ ang l l ed triangle w w ith shorter sides 6cm a nd 8cm. K, L L , M are the m m idpoints o f f the sides o f f triangle AB C C . What is t h h e perimete r r of triangle KLM?

3 points

ABCDE

Question 8

Q9. The q u uadrilateral A A BCD with s ide length 4 c c m has the s s ame area a s s triangle EC D D . What is t t he perpen d d icular dista n n ce from poi n nt E to the li ne g?

3 points

ABCDE

Question 9

Q10. Alic e e and Bob se nd each oth e e r secret m e e ssages. To p p ut their me s s sages into c o ode they us e e the followin g g system: Fi r r st each lett e e r is given a n number in o rder: A = 1, B B =2, C = 3, . . . . Z = 26. Th e e n the letter n u u mber is do u u bled and 9 i s s added. Bo b b received a message w h h ich began 1 9 9 – 37 – 48 – – 19 – ... Which o f the followi ng message s s had Alice s e e nt to Bob?

3 points

ABCDE

Question 10

Q11. In fo ur of the fol lowing calcu lations you c c an swap th e e number 8 w w ith anothe r r positive nu mber without changing th e e answer to the sum. Fo r r which calc u u lation does it not work ? ?

4 points

ABCDE

Question 11

Q12. Wh e e n Adam sta n n ds on a tab l e and Mike o on the floor , , Adam is 80 c c m taller th a a n Mike. Wh en Mike stands o o n the table a a nd Adam o n n the floor, M M ike is one m m etre taller t t han Adam. H How high is t t he table?

4 points

ABCDE

Question 12

Q13. Wh e e n the numb e e rs 144 and 220 are divi d d ed by the s a a me positiv e e whole nu m m ber x, both h h ave remaind er 11. Find x x .

4 points

ABCDE

Question 13

Q14. Tom and Mary p lay a game w w ith a coin. W W hen the co in shows he a a ds, Mary w i ins and Tom must give her two sweets . . When the c c oin shows t a a ils Tom win s and Mary m m ust give hi m m three sw e e ets. After 30 throws of t h h e coin they each have t h h e same nu m m ber of swe e e ts as they h h ad at the st a a rt of the game. H ow often ha s Tom won?

4 points

ABCDE

Question 14

Q15. One of the two s ides of a re c tangle has l e e ngth 6cm. I n the rectan g le circles are dra w w n next to e a a ch other in s uch a way t t hat their ce n n tres form a n equilatera l triangle. What is the shortest di s s tance betw e e en the two grey circles ( ( in cm)? గ

4 points

ABCDE

Question 15

Q16. On e e ach of the f o o ur walls in B B illy’s room h h angs a corr ectly workin g clock, but each on e e runs eithe r r behind or a a head of the correct tim e e . The first c lock is incorrec t t by 2 minut es, the seco n n d by 3 min u u tes, the thi r r d by 4 minu tes and the fourth b y y 5 minutes. Billy wants t o know wh a a t time it is a a nd sees the following times; 6 minutes to 3 3 , 3 minutes to three, 2 m m inutes pas t t three and 3 3 minutes p a a st

4 points

ABCDE

Question 16

Q17. The d d iagram sho ws a right ‐ a n n gled triangl l e with side l engths 5, 1 2 2 and 13. What is t t he length o f the radius o f the inscri b b ed semi ‐ cir cle?

4 points

ABCDE

Question 17

Q18. Ho w w many num b b ers from 10 00 to 9999 a a re there w h ich have 3 a s the hundr e e d digit, and for which t h h e sum of th e e remaining three digits is also 3?

4 points

ABCDE

Question 18

Q19. A nu mber from 1 1 to 9 is to w w ritten into e ach of the 1 2 fields of t h e table so t h h at the sum of each c c olumn is th e e same. Als o o the sum of each row m ust be the s a a me. A few n n umbers have alr e e ady been w w ritten in. W h h ich numbe r r should be w w ritten in th e e grey squar e e?

4 points

ABCDE

Question 19

Q20. The r r unners Kan n, Gu and R u u are favouri tes to win t h h e maratho n . Before the race three e e xperts gave th e e ir predictio n n s for the ou tcome of th e e race. Expert 1 : “Either Ka n n n or Gu will win.” Expert 2 : “If Gu is se cond Ru will win.” Expert 3 : “If Gu is th i i rd Kan will n n ot win.” Expert 4 : “Either Gu or Ru will c o o me second. ” ” After th e e race all fo u u r prediction s were prov e e n correct. I n n which ord e e r, did the t h h ree runner s finish the race ?

4 points

ABCDE

Question 20

Q21. Two sides of a q u u adrilateral h h ave length s s 1 and 4. O n n e of the dia g g onals has l e e ngth 2 and s s plits the quadrila teral into t w w o isosceles t t riangles. W h h at is the pe rimeter of t h h e quadrilat e e ral?

5 points

ABCDE

Question 21

Q22. A go ldsmith has 12 double ‐ li n n ks of chain . . Out of these h e e wants to m ake a single closed chai n n with 24 links. W h h at is the mi nimum num ber of links t t hat he must op en (and clos e again)?

5 points

ABCDE

Question 22

Q23. Pete r wrote the number 201 2 in the for m m 2012 = m (m – k) wh e e re m and k a a re natural n n umbers. Find the value of k.

5 points

ABCDE

Question 23

Q24. Wha t is the last n n on zero dig it of K = 2 ൈ ൈ 3 ൈ 5 ?

5 points

ABCDE

Question 24

Q25. A re c c tangle ABC D D with dime n n sions 16cm by 4cm wa s s folded alon g the line MN so that c c orner C me e e ts corner A . What is th e e area of the Pentago n ABNMD'?

5 points

ABCDE

Question 25

Q26. It ta k k es 8 secon d d s for train G to pass by a a milestone. Shortly afte r r wards the t r r ain meets t r r ain H. It takes 9 s s econds for t t he trains to pass each o t t her. Train H H then takes 12 seconds t t o pass by t h h e milesto n n e. What ca n n be deduce d d about the l ength of th e e trains?

5 points

ABCDE

Question 26

Q27. The s s hape pictu r r ed, is made out of two s s quares with side length s s 4cm and 2

5 points

ABCDE

Question 27

Q28. Of 5 lamps each one can be s s et to “ON” o o r “OFF”. Ea c c h time whe n the switch h of one lam p p is change d d , not only d o o es the stat u u s of that pa r r ticular lam p p change bu t also that of f one other l a a mp chosen a a t random. I f f the same s w w itch is cha n n ged several times not a l l ways the sa m me other la m m p changes . Initially all l l amps are s e e t to “OFF”. T T hen 10 swi t t ching opera t t ions are ca r r ried out. Af t t er that one can say that

5 points

ABCDE

Question 28

Q29. The n n atural num bers from 1 to 120 wer e e written as show n n into a tabl e e with 15 co lumns. In w h h ich column ( ( counting fr o o m left) is th e sum of th e e number s s the largest ?

5 points

ABCDE

Question 29

Q30. Posi t t ive number s s were writt e e n in a 3  3 grid in such a way that t t he product o o f the numb ers in each ro w w and each c c olumn is ex a a ctly 1. The p p roduct of t h h e four num b b ers in each 2  2 grid t h h at can be foun d d inside the 3 3  3 grid is 2 2 . Which nu m m ber is writ t t en in the ce ntre of the 3 3  3 grid?

5 points

ABCDE

Question 30

2012 Junior Test | Test and Chat