Sunway a Level Math Logic Challenge 2010

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Sunway A-Level Math & Logic Challenge

2010

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Round 1: Objective Questions (MCQ: 20 Questions, 45 minutes)

1. 2002 is a sum of eeven consecutive inte!e"s. #$ic$ of t$e foo%in! is t$e smaest inte!e" amon! t$em&

'. 1 *. 1 C. 1+ . 1-0 . 1-1

2. (/  2)  ( 3 1)  (" 3 )  (s  4)  0. 6ind t$e vaue of /    "  s.

. 7$e /e"imete" and dia!ona en!t$ of a

"ectan!e a"e "es/ective8 100 units and 9 units. 6ind t$e a"ea of t$e "ectan!e. 'ns%e" in te"m of 9;

4. <iven t$at u0  4. =f f(u0)  un1, n >0. *ase on t$e "i!$t tabe,

?nd t$e vaue of u2002.

5. @un Aao is t8/in! a numbe". Ao%eve", $e mist8/ed t%o 1s, and t$e numbe" a//ea"s to be 2002.

Ao% man8 /ossibe numbe"s a"e t$e"e if @un Aao doesnBt mist8/e an8 numbe"&

. Coc oses 1 minute eve"8 $ou", %$ie coc * !ains 2 minutes eve"8 $ou". 7$e ?"st coc %as %ind

acco"din! to t$e second coc at midni!$t. #$en t$e time a""ives at noon, $o% man8 minutes is

coc * a/a"t f"om coc '&

. 555_{ 5}55_{ 5}55_{ 5}55_{ 5}55_{ 5}"_{. "  &}

-. On t$e ea"ie" 8ea", @ia C$oon %as t$i"teen 8ea"s od 2 da8s a!o. On ne9t 8ea", $e is si9teen 8ea"s od.

6ind $is date of bi"t$.

'. 0 ec *. 1 ec C. 1 @an . 2- 6eb . 2+ 6eb

+. 7$e en!t$ of "ectan!e ' and * is "es/ective8 - and +, %$ie t$e %idt$ of "ectan!e ' and * is

"es/ective8 5 and 4.

6ind t$e a"ea of s$aded "e!ion.

9 1 2  4 5

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10. =f a t$e sma cube b"ics on t$e "i!$t dia!"am b"ea u/, %$at is t$e tota su"face a"ea inc"eased&

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11. D is ocated at t$e co"ne" of t%o %as and a ceiin!. ' E8 is E8in! nea" to D. =t is 1m a%a8 f"om a %a

and -m f"om anot$e", %$ie D is +m a%a8 f"om t$e E8. 6ind t$e $ei!$t bet%een t$e E8 and t$e ceiin!.

12. #$ic$ of t$e foo%in! of net of /8"amid is fase& FOMOG R'# =7;

1. 7$e"e a"e ines of 1m, 2m, m, 2001m, 2002m, and 200m. Ao% man8 diHe"ent t"ian!es can t$ese

ines fo"m&

14.

F$an! @an /a"tici/ated in an a"c$e"8 contest. 6ind t$e vaue of 9.

15. ao F$8an sco"ed - ma"s in a 203uestions uiI. 6o" an8 co""ect ans%e"s, $e !ains  ma"s. 6o" an8

inco""ect ans%e"s, $e oses 2 ma"s. Go ma"s a"e deducted if no ans%e"ed. Ae $ad not ans%e"ed $o%

man8 uestions&

1. ' %$ee %it$ diamete" of 0m $ad 240 "evoutions to t"ave on a distance. Ao% man8 "evoutions $ad a

%$ee %it$ diamete" of 20m t"ave on a same distance&

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1-. aKb  (a10b)K(b10a);  2. 6ind t$e vaue of aKb.

1+. #$ic$ of t$e foo%in! is not a facto" of 50L (50 facto"ia)& a. 51 b. 52 c. 5 d. 54 e. 55

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Round 2: ive 'ns%e"in! Fection

ANSWER QUESTION NO. 1 WITHIN 1 MINUTE (INCLUDE READING THE QUESTION)

a, b ,c ,d , 0, 1, 1, 2, , 5, -N 7$e vaue of a te"m is t$e sum of its eft t%o te"ms. 6ind t$e vaue of a.

1 log

₂

100 !

+

1 log

₃

100 !

+

1 log

₄

100 !

+

…

+

1 log

₁₀₀

100 !

=

?

' fami8 consists of fat$e", mot$e" and some c$id"en. 7$e fat$e" is 4- 8ea"s od. 7$e mean a!e of t$e fami8 is 20, %$ie t$e mean a!e of t$e fami8 e9cudin! t$ei" fat$e" is 1. Ao% man8 c$id"en does t$e fami8 consist of&

ANSWER QUESTION NO. 4 WITHIN 1½ MINUTE (INCLUDE READING THE QUESTION)

=n a diHe"ent 23di!it numbe", t$e sum of t$e cu""ent di!it is  times t$e 23di!it numbe". *8 inte"c$an!in! t$e di!its, t$e sum of t$ei" ne% di!it is n times t$e inte"c$an!ed di!it. 9/"ess n in te"ms of .

' cube %it$  units is s$o%n on t$e eft dia!"am. #$at is t$e su"face a"ea of t$e cube&

C$en! an! sta"ts "eadin! a boo at /a!e 1. Ae sto/s "eadin! at t$e /a!e %it$ t$e "d_{numbe" of P1. #$ic$ /a!e does $e sto/ at&}

Doint O is t$e inte"section /oint b8 "i!$t an!e of t%o ines, %$ie D is 500m a%a8 f"om O. Q moves on t$e o//osite of D %$ie D is movin!. 'fte" 2 minutes, t$e8 a"e

euidistant f"om O. - minutes ate", t$e8 a"e euidistant f"om O a!ain. 6ind t$e "atio of veocit8 of D and Q.

 

9 M    M    7  & 7 7 7

=f an amount of coins is divided to  /eo/e, t$e"e a"e 4 coins "emainin!. =f is divided to 5 /eo/e, t$e"e a"e 5 coins "emainin!. On t$e east amount of coins, if it is divided

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to  /eo/e, $o% man8 coins "emain&

ANSWER QUESTION NO. 1 WITHIN 1½ MINUTE (INCLUDE READING THE QUESTION)

'i, *a"e8 and Cu""8 is "unnin! on a 1m t"ac. 7$e8 "un at a constant s/eed, %$ic$ *a"e8 and Cu""8 a"e "es/ective8 at -00m ma" and 00m ma" %$en 'i "eac$es t$e end. #$at is t$e veocit8 of Cu""8 %$en * ?nis$es t$e t"ac&

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' t"a/eIium $as a on!e" base of + units. =ts dia!ona ine is  units f"om t$e mid/oint. 6ind t$e s$o"te" base of t$e t"a/eIium.

41 students /a"tici/ated in an e9am %it$ ma"s bet%een 0100 "es/ective8. =f 1 student is "emoved, t$e mean of ma"s of t$e "emainin! students is eua to t$e mean ma"s of 41 students. #$at is t$e ma" of t$e student "emoved&

√

M

√

M

√

M

√

M

√

M

√

M

√

M



M

x

6ind t$e vaue of 9.

ANSWER QUESTION NO. 14 !LAST QUESTION" WITHIN 2½ MINUTE (INCLUDE READING THE QUESTION)

6ind t$e "atio of t$e a"ea of a sua"e insc"ibed in a semici"ce to t$e a"ea of a sua"e insc"ibed in a ci"ce.

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Answers:

Round 1: Round 1: 1. * 2. 0 . 1250 S

X

_²

2

4. 5 5. . 24 .

5

56 -. +.  10. * 11.  12. C 1. 14. 15. 1. 0 1.

3

32

1-. 1+. C 20. Round 2: Round 2: 1. 3 2. 1 .  4. 113 5. 2 . 110 . 2: -. 21 +. 0 10. 250 11. +1 12. -0

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1.

63

64

14. 2:5