Understanding mathematics is the ability to comprehend

To create an Olympiad aimed at excellence in education and knowledge, leading Turkish world and international youth to success in mathematics.

1. GER the value of) “it

ey
HONTE 52 SOLUTION: xo EE
(2x +4y = 48) 7“ X +24 324): 5x Hoy =|20

LR = ae,
MEL vbs
[39 = 18 e ta
y=b a, le e Ue
yo 2]

2. 10. Find the value of 2+6+18+54+... +1458 + 4374. 3
RE %
ION:
_ Last x Multipier - First
Mene 7

Mulbiplier- -|

4374 x 3 -2 _ 13120
3-1 2 |

3. ES NY
11. Ifa 9-digit number 1158583 P4is divisible by 33, find the value of P.

SOLUTION:
Div by SS div by 1123
div by. à [er grs y FR PHY
E LH
p= (147) ÁUVE18= 0 sen
y 2=0
Ay byl * (145454344) = 18 [Pi]
(il igrl +p) = Dre
M 9-18 = Il

p =u te 17

4. ven x > O and x + = = 4, find the value of x* + +.

SOLUTION: ;

EL oo

Kr girl = Ib 2

e x +l
werd, > 16-2> 14 ried,
Geren ME

ADEME 7 Y exe 140-2

5. a)
13. A 4-digit number has a remainder 4 when divided by 5, has a remainder 6 when divided
by 7 and has a remainder 8 when divided by 9. What is the minimum value of the 4-digit
number?

D aw b e ar SOLUTION:
vi ‘tm,
= \ pe | les thin He divi Gv
7 6
q g Leu (s,7,4) = 315
315 x4 = 1260

207

o. Y

6. —— =
14. It is known that x isrational,x > Oandx = IN = DE: Find He value of Ox.

SOLUTION:

Kl = 0
(x+4)(x-8) =D

14450 x-6:0
% =" x28

7. 15. It is known that n! = nx(n-1)x(n-2)x. . .«1. Find the number of “0” at the end of 193!.
SOLUTION:

a5
(0) Si u. = (931 JE).

| 31. 9
eve US ©

æ +7 += fe] ale

8. pose A DEF is a right-angled tria 2 F to the mid-point ap

of DE is 12m, find the maximum value of the area of A DEF .
SOLUTION:

bre max =? FE=0F
Isasce les vight zn

DE= 24
E AR

1

2 ax = 24° 214
GON ae ee
Aras? NCO» ah

9. = az
18. Nine of the exterior angles of an irregular decagon measure 17°, 23°, 51°, 32°, 68°, 13°,36°,

Tlc,and 33°. What is the measure of the tenth exterior angle?
SOLUTION:

Sum £ Ext, argles = 860"

PR)

NS
360 - (11:3 HS] +324 62+ B43 6 #7 | + 3)
w ro ae

360 - 34-16" wu

10. ng Lou ace viewing Coach or’ screen ln tala
19. There are 12 points on a circle. How many different nonagon(s) can we draw with those
points as its vertices?

SOLUTION:
À point at verticts 2

ber LEA x D0
ST |

= xx
= 200

11. 20. A triangle has sides with lengths 32, 60 and 68. Find the area of the triangle.

4X8 JE, Jan
68
Bisa py thagarean tn pt ”
ke eh 32 (00) |
a,

Hs rule

A= 32 6 ate re A, ENS (s-a) (sb) (s-C)
b= =

ou = 3246049 Vo Caan
2 = A) Bx0X 8 Ab x1 0x2 «246
"lo: SEULS
FE

=8x 1DXbaz Qn x = à

az

12. 0 en as

21. If Douglas goes from point A to point B, in which he can origi move down or move right,
how many way(s) is/are there?
SOLUTION:

13. [oJ © necoráng | |_Youare viewing Coach Jom's screen MS
22. Two fair 6-face dice are thrown. Find the probability that the sum of numbers obtained
is a multiple of 3.

Re son 12
ESCOCIA NE
1 GG TRATOS 36
(DE (64)

ex C= 36

14. H 3 time in haus Hur hard, 30 degrecs i

Mating in moutes SOLUTION: +2

07 lon oi) Is Mn thus LL
90, H= 6 :
0= nr. re
(da = 1006) om -Gole) vos =0
a yt GM - 180 -0.5M =o

2x Ca =)
fone M = 36D
Were M +360 - 32%
m

15. [© Recoräng | |_ You are viewing Conch Jom scree” MA | a vie |
24. There are six yellow and eight blue balls. Find the probability that three yellow and four
eS a

blue balls are chosen from those balls.

Ase rs

GC3 x 8C4 E 324-343 x HL! 2377
4C7 ABS Aa
TEAR GA

= SHTNS -|105
1311 3-8 qa

16. ER... 4 digits, without repetition, from 1, 3, 5, 6, 7 to construct 4-digit numbers. Of
these 4-digit numbers, how many of them are divisible by 3?
SOLUTION:

o Nr BC4= 5
336 7 ES + 12,56 VA

ls 13,51 x
(35,61) +. 2: 15,67%

Tr GTV
Ari 42) Vag

ui