2007 Metro Bank MTAP Math IV

2007 Metro bank MTAP MTAP – DepEd Math Challenge Fourth Year   Name:  !"hool:   !ol#e ea"h $tem and %r$te the an&%er on the blank be'ore the number( )ea#e *our rad$"al& $n *our an&%er&( +$#e e,uat$on& a& a- . b* . " / 0( &e     3(1 1( 4h$"h 4h$"h o' the the 'ollo%$ 'ollo%$ng ng $&5ar $&5aree 'un"t$ 'un"t$on& on&66 2 2 2 A(  y   x   x ( -  . * / 38

C( *

³

3- 9

D( * / 3- – 2

 x   2

2( '  f     < x;  3( ( ?( 8( 7(

= '$nd '<3;(  x 2  1 4hat 4hat $& the doma$n doma$n o' the the 'un"t 'un"t$on $on $n number number 26 ' ' <-; / 3- –  and  g < x;  x 2  > = F$nd F$nd <'og; 'og;
-

92

91

0

1

2

*

1

92

93

92

1

@( 4hat 4hat $& the range range o' * / 3- – 7 "m -B 9 £  - £  ? >( ' * / @ – 33- $& $& gra graphe phed d on on -B -B 93 £  - £  7= %hat are the "oord$nate& o' the r$ght end po$nt o' the graph6 10( ' the - and * $nter"ept& $nter"ept& o' a l$ne are 2 and 93= %hat $& $t& e,uat$on6 11( 4hat $& the e,uat$on o' the l$ne through <2= 3; parallel parallel to * / 3- – ?6 12( 4hat $& the e,uat$on o' the l$ne through <93= 2; perpend$"ular to * / - – 36 13( !ol#e 'or 'or - and and *:

?



 x

3  y



7  and

  x



?  y



36

1( 4r$te r$te * /2-2 – ?- – 3 $n the 'orm * / a<-9h;2 . k( 1?( 4hat $& the the range o' the 'un"t$on 'un"t$on $n number number 16 18( ' - / 92= * / 1?= 'or %hat other other #alue o' - $& * / 2-2 – ?- – 3 e,ual to 1?6 17( ' P <-; / 2-3 – -2 . 3- – 7= %hat $& the rema$nder $' P<-; $& d$#$ded b* -.26 1@( ' P<-; P<-; / 2- . 8-3 9 ?-2 – 7- . 8= D<-; / 2-2 93 and P <-; $& %r$tten $n the 'orm P<-; / <-;D<-;.<-;= %hat $&  <-;6 1>( F$nd the the root& root& o' 33-3 – @-2 .3- .2 / 0( 20( 4hat $& the ,uot$ent ,uot$ent $' -? .23 $& d$#$ded b* -.36 21( ' P<-; P<-; / 3-3 . A-2 . - – 10= P<1; / 9 and P<93; / 9( '$nd A( 22( et%een %hat po&$t$#e $ntegral #alue& #alue& o' - doe& P <-; / -. 2-2 – @ ha#e a real ero6 23( 4hat $& the range o' o' <-; / ?- – 3 6 2( At %hat po$nt po$nt %$ll %$ll the graph graph o' * / 2-92 $nter&e"t the *9 a-$&6 2?( ' the &um o' the $nter$or angle& o' a pol*gon $& t%$"e the &um o' the e-ter$or e-ter$or angle&= ho% man* &$de& ha#e the pol*gon6 28( n the '$gure '$gure at the r$ght= r$ght= '$nd Ð D(

100G

27( 27( ' @- / 18<219-;= '$nd -(

2-

2@( ' ' <-; / 3  = %hat $& the doma$n o' '6 2>( 4hat $& the range o' the 'un"t$on $n number 2@ 6 30( Ho% man* term& are there $n a ar$thmet$" &e,uen"e $' the '$r&t term $& 100= the la&t term $& – 1 and the "ommon d$''eren"e $& 92( 31( 4hen -.?-39A- .  and A-2.- – 1are ea"h d$#$ded b* -.1= the rema$nder& are 7 and 98 re&pe"t$#el*= '$nd A and ( 3 x  2

32( E#aluate and &$mpl$'*:

log2 @ log2 3 

33( !ol#e 'or - : log2<-2 – 1; – log2<-91; . log2 <-.?; / ?( 3( ' <

1 2

= * ; $& on the un$t "$r"le= '$nd *(

3?( 4hat are the "oord$nate& o' the term$nal po$nt o' an ar" o' length

@>   3

6

38( Change – ?0I to rad$an mea&ure(  3 x   37( 4hat $& the per$od o'  y  &$n   6   2   3@( ' P< q  ; l$e& on the l$ne Jo$n$ng the or$g$n to the po$nt <93= ; '$nd &e" q ( 3>( Kn  2  £ q  £ 0 'or %hat #alue<&; o'

q  %$ll "&"q 



2 3 3

6

0( ' the length o' the m$nute hand o' a "lo"k $& 1 "m= '$nd the length o' ar" $t %$ll tra"e $n 3? m$nute&( L&e  / 2257 1( E#aluate: &$n 2( ' "o&q   

2   3 3

2

"o&

?   8



"o&

2   3

&$n

?   8

(

and &$n q   0= '$nd tan q (

3( !ol#e 'or - on 0 £  - £  2  O  &$n 2- –  &$n - .1 / 0( ( The length o' a re"tangular garden $& 8m longer than $t& %$dth( ' ea"h d$men&$on %ere $n"rea&ed b* 3m the area %ould be $n"rea&ed b* ?7 m2( F$nd the or$g$nal length o' the garden( ?( The d$''eren"e o' t%o number& $& 1 and t%$"e the &maller number $& ? le&& than the larger number( F$nd the larger number( 8( A balloon $& 1@00 't h$gh( t& angle o' ele#at$on 'rom ob&er#er A $& 30 I and 'rom ob&er#er = $t $& ?I( 4hat $& the ma-$mum d$&tan"e bet%een A and 6 7( From a l$ghthou&e to%er 80m h$gh( The angle o' depre&&$on o' a boat $n the &tra$ght l$ne %$th the ob&er#er $& 30 I( Ho% 'ar $& the boat 'rom the l$ghthou&e6 @( T%o po$nt& M and N are on oppo&$te &$de& o' r$#er( C $& a po$nt on the &ame &$de o' the r$#er a& M &u"h that Ð  MCN / 80 I ' MC / ?2m and CN / 72 m '$nd ho% 'ar M $& From N( >( The ,u$ &"ore& o' +reg are @= >= ?= 7= @= 8= >= -( 4hat mu&t be the #alue o' - &o that the mean $& 7(?6 ?0( ' - /  $n the ,u$ &"ore& o' +reg= %hat $& the med$an6

GOOD LUCK  By: JOE I. TITULAR