Metrobank-MTAP-DepEd Math Challenge 2013 Grade Z Narne:
School: Instruetioa: Write your alswer on the space provided before each item- Give all fractione ir1 lo*tet terms and all expressions in exparided form.
simpriry:
lr,u,':
1,s1
IY,o:f*
tr:
(r- ;) -r- (, - i) _l (r- 1\ 4)
{a,b,c,d,,e}, B
mt" ,Orffi
:
{a.e,i,o,u!, andC= {e,f,s,h,il. Find
(,4 n
B) u (B n C).
in s€ientific notation.
4. Nonoy left Butuan City to drive to Cagayan de Oro City at 6:15 pM and arrived g:1b pM. If he averaged 80 kph and stopped 30 minutea for dimrer, approcimately how far is Cagayan de Oro from Butua.n?
simpritu: (r-,)'- (r-,-i)' r--:3-'. tq,fifF.
'Ll
,y,'r,t,t.t.t
1cl'
ser u be {1,2,3,...,20i. If 18,20}, tud (S u E u T)/.
*t,.O",niversal
T W-^ *14
:
{1.1. 16, 17,
r.
wuu, i" tnu product of two
8,
Two
^tl
angl,es are
s = {2,4,6,8,
consecutive odd nurnbers
10,
12}, E
=
{3,6,9, 12, 15,r8}, and
if the largqer number is Bo -
4?
supplementary. One angle ie 2lo less than thrice the othbr. What is the complement
o{ the smalier angle?
as/ !r',rt
OE
-+-
9. Simoiify: ffi.
;-;
ln Ler recept mo'thly paydsy, ehe receivEil Php 2r 0oo- Hqw much was her total 12. Sirnplifu:
It
(r+
-2)
- (x+2)(a-
3)
+ (, + 3)(o
-
+)
- (o + a)(a - b).
13. How many two-digit prime numbers are there whose ureits digit is greater than its tens digit?
c AJ-*J-- 74. Nila is now years
lt_
-71+2?
1)(o
saleg laat.Eonth?
age ten
old. Three years ago, her brother fucky was twice as old from now in terms of c. yea.rs
as she.
write Ricky's
15. In the Math Department ofa school, l0 teachers have Yahoo! accounts, 13 have Gmail accounts, and 6 have bottr accounts. Hon' many teachers in the department have Yahoo! or Gmail acmurrts? 18. Together, Peari and Ha.rrey a.re going to visit their aunt on sunday. If Pearl visits their aunt every 6 days, while Harvey every 8 da1's, on what day will they visit their aunt together agsin? L7. What should be added
to
(.r
-
3)(z + 2) in order to get (r
-
4)2?
_tep 14" Sirnplify: /li.a " rOo -. 2.55 x toal * 6.9 x looo _ 19. Iu a triangie, one r"gle ie tvrice the second, end the third angle is 20o lesq than the second. what 103.
Nwtr1*-" qtn.t xr+t t2{ .::::,::lT:: ,- ZQ. :.;}: It'cbsts (c+3) peaos per :i:i square foot to painl a wall. If the wall stands (,lr+B) ft highand (7r-2) ft.long, how much. does it. c€6t to paiat the wall?
2.9 :i
l'aN |
, V
21^
In a class of 4o students, 27 like Math and 25 like FilipiEo. At mo8t hos, mary students do not like at least one of these subjects?
,,.
How many four-digit numbers are multiples of 9? can walk &om his house to his. school at the rate of 5.4 kph, and bact at the rate of kph. What is his average speed for the entire walk in meters per second?
--23. Manuel
3"6
Pcge 1 o! 2
J
. lx)and
24. A polynomial has quotient (r2
remainder (c2
-
1) when dividod by
('f - 1)
What
is
the polynomi&l?
-
first Pieoe' Aldo cut a lon6 piece of baEboo ioto fout piec€s. Thc Eecond piece was one''third of the the third' of ore'third piece was the third piece was oaethird of the seooad, and finally tbe fourth If the smallest piece was 2 dm, how lon6 waa the barnboo before it wa6 cut?
1b'llr-,*.
_61 ,,. - Lz- .i,,. /rhn
In Teacher Ella'e cla^*s, a Btudedlt receiYee a final grade of A if the student garners an average of at At least least g27a in the fiwe Iong t€sts. After four l,ong test6, Jonathan Bot a.n &verage of 9I% of A? grade get a final how much should he get i! the lasi long ieEt to What is the largest prime factor of 2013? passed Algebra, 26
clase of 4? EtudeDts took erGsrinations in Altebra alrd in Geometry. IJ 29 passed Geometry, aad 4 failed iu both subje,ots, how rna'ny passed both Eubjects?
A
A runner started a coulBe at a steady rate of 8 kph. Five minutes later, a second flrnner s-t&rted the 6ame course at 10 kph. tlow long did it take for the second runuer to oYertal@ the fir6t? 3o. A rectaugle has sides (2r + 3) cm ard (4s + 5) cm' How many squares of sides c cm can be cut from it?
Jto)"n*,". nqll^ ,a
g g(t"
'
-
e4
at.
I-Er ABC
-82. The
ML-**.
ad-wt
DE be e regular pentagon. What h the measwe
average of five numbera ie 20.
j a.l
/rl -
1-41.
:
28, rc
b
=
3%, or c
---;.-1-* |
7 m, how loug is
If. Zo:14
40. If
*
bx3
+ 4.a2
-
d,a
*
Ze
=
-
7(2
-
c) 2 2(2a
-
7)?
4. Wtat is the remainder when 2n is divided by
iE
7?
what percent of the origiaal volume is the new volume? (2s
-
3X, + 1)(o - 2)(3o + 1), what is ah +
cd
+
e?
d?#? and3
Which is smaller, ,4
43. If
5%?
=
tbat sati8fi€s ihe inequality a(c + 3)
=
(2015)(2014)(2013)(2012)(2011)
tf 12 - 3z r 1 = 0, find the talue
Nv+y'*rr..
28, what G the avsra.e of
Man in is 107o taller than Homer, and Homer is 10% taller than AugUBt. How much (in percent) is Marvin taller than August?
-,"_sa. If the sides of a cube are tripled, ss'
ii
the steel ba.r?
3?. Wlren 3n is dividei by ?, the remainder
79
='*
the eum of two of the numbers
A long straight steel bar is to be cut in the ratio 2: 3 ; 5' If the middle piece is
36. What ls the Ieast va.lue of
:7;3Ju
lC AD?
the other three numbers?
&5. W'lrich is the largest, a
.5.
If
of.
o( ,' *
*.
(z+3)(r-2)(c+1) =@+2)Q@) + (c + 3)(r -
44. AII fares of a 4-inch cube have
or B = 2013s?
painl been painted.
Ilthe
2), what is Q@)?
cube i6 cut into f-inch snialler cubes, how ma[y
of them ltar"e no paint on all theA faces?
45. tf
t:
-1, find ttre value of
2
ol3n2o13
+
2012,2012 12g11r2o11
+ 2010o110
+.. .+
2a2
+ x.
46. The sum of two mrmbers is 20 and their product is 15. Find the sum of their cubes'
4g e-O€
4?. Hcw m.any positive factors
doee 62 x- (633
632
10600 is e:rpreased a.s the Eum Iaxgest arnong t'he odd integers?
48. If the uumber
49, How many positjve integers n "atisfy | <
{,
+
5o, What is the least number o{
+ ffi + 1) *
t
have?
of 100 consecutive odd positive integers, what is the
n -4, l3-E'
squaxe pieces
into rvhich a cardboard, 13 feet long and 8 feet wide,
can be cut?
Page 2 of 2
Metrobank-MTAP-Dep0d Math Challenge 2013 Second Year Score: School: Instmction: \[,rite your a]rswer on the spare provided before each item. Give all frartions in lowest terrns, and a1l expressi
Narne:
a4 +V lOnfa--
ZI
-
1. Sirnplif-v: (a 2, The tli{lcrencc
b)2
(t'-l-
h)2
+
2a2b2.
bctwer:n thc squarcs of two conseortive positive integers is 2013. What is the
Iarger integer?
3. When writtel
4tl x
irr tlecirnal reprcserttation, how rnany digits does
520 have?
('.') t! , ( - "\ - 2- )::J-5. sor ve,.., :::",i'":,^ ,\,,";-r'. ^ "- JJl+-_6. Sinrplifr. / l25f f \\t /3 b' -lt
4. sirrrplif5 (,,2
1,r,
=
r':'
\nJu')
7.
o
Solve for :r ilr the equation x4
2l-t 12 ' I r--l
'
tA.
-
-r
5x2
\\'Irar slroutd be a.ddcd ro
0.
I
9, Tlre roots of the qua.dratic equation
to.
+4:
j#"
n2
7x + c rliller by 1. Find c..
-
,o g.t
;:,? its tot,l surfiu e area?
X -1
tl" l t? '-4 n,zL
"7 r'*r
12. simplify
1'
rr+1'FT
-
13.
Solve
[r-rr .r'
in the equation
14. Find tire value of thc 15.
?rc.
expression (r'?+-10c
+25)t/2
Ji: \/Ir:"T1. is defined by ar:3 and tr,,-'1:
Solve for -c in the equatior
The sequence.{n,}
{nfr :2. -(22-
102
*25)1/2*'nn*-*r.
3+
4 (52" r) - I0 (5r.Sirnlr)ify - - =U'-,
(-1)"o"
*7
for n
> 1. Wirat
is o5?
,
17.
l-q-t ,di*18.
In the a.rithmeric sequerrce l0 + 10\,6, 11 +9/3,
19. If r + Y : l2 and ng :
6ull^Id4ro.
.)
Fhctor a2 +bz
50, what is 12 +
lz+B\,E,...,
Y2?
+2ab+ ae*bc.
21. What is the sum of the firsi ten terrn of the geometric
191o.
i
f
tlfl
sequence 4, 8, 16, . . .?
zz. If the product of two consecutive odd integers is 783, what is the surn of titeir
f tptv n. 11
whar rerm has no yB?
simpliry
squares?
(1-;)(1- *)(1- i)(1, *) (1 #)
24. For what value(s) ofk
docs theeqrralion (,k
-
1)r2
F
(k-
1)r
*4:0
have equal rools?
25. One number is 54 more than the other. If twice the larger number is divided by the smaller smaller, the quotient is 6 and the rernainder is 16. What is tite sum of the nurnbers?
26, What shoulrl be subtracted from
5 - At'z 13ru l L--y;: i r 3 to get5uz '
Page 1 of 2
27. If 3'+1
3
4, what is 32"*1
?
dalg ,r. A storage battery discha.rges at a rate
which is proportional to the stolage. If the charge is reduced by 25% of its origina.l ralue at the end of 3 days, how long wil{take to reduce the charge to 10% of its original charge?
I,l \o
:
9()
e4{r",r;t
1
If r and s are the root5 of the equation 2r;2 - 3r +
4
:
0, what is 4r2 + 7r s + 4s2?
30. The value of d va,ries directly with r and the square of y and inversely with the cube of z' If each of r, y and z are to bc increa^sed by 50%, what would be the efrcct on the value of C'! 31. If the sum of the reciprocals of the roots of the equation 3n2 +7r + /c is
l{/f gt"t
-{,
what is ft?
in tire ratio of 7 : 3 : 2. If the shortest piece is 16 cm, what is the area of the largest rectangle that can be created using the iongest piece?
32. A long wire is cut into three smaller
pieces
- 20132012 : 2012 ' 20131 1i 34. Find the largest integer n such that 1+2+3+..'*n < 500. 35. A boat takes ! as much time to travel downstream as to return. If the rate of the river's hI rl. f,h I current is A kph, what is the rate of the boat in still water? 2n1
7*
33. Find the
va,lue of
r
in the equation
20132013
o 'ra.aEv]'113. rr a.oz, : b2l.bs7e4l,what is 0.8073? V w"t - ft, 37. Find the value(s) ofr so that o,2x*7
il
ae. rr t6to11010 *...*
5J
ro,
7 +4"
ol
+1
Ll ,l ,
-t\ABC.let D is ICAD?
4O. Let
{a"}
-41. what
+fu1,gq1a_ 42.
/YL' tI
r"
be a poiht on sirle B(7 srrch
fourth
The operation
I
root'
of
44a
form
geometric sequence.
l!
that AB
:
AC
- BH+ lW
aa
- )7 and oo :
a2
- 8. What is (2013 I2012)I(2012
'-rriaalt
67, what is a1?
I b:
I2011)?
45. Ttiangle.ABC is ieosceles with AB : AC. Ler D be the foot of the altitude from Aon BC, and iet E be the point on side AC such that D-E bisects IADC. lf IDEC : 67', wirat is IBAC?
M.
Let at,azta3,. . . be a non-constant arithmetic sequenca. lf a1, aa and os form a geometric sequeBce, what is the common ratio of this geometric sequence?
4s. What is the grearest inreger
lX''
46. rf
a* y:3
-a7. \f 12 -3c *
and 12 + y2 1
:
:6,
less than or eq,:al
to
(Z
+
yE)22
what is x3 + y3 + *2y + ay2
0, find the value of z3
-
+ $.
48. simplifv: --l---= + --)"":+ --=-l-...-: +" "'+ -=-1 -. -'-'-'-'-'--e-t + A- 7/zr r/i'./i + r/n t/6+ r/s t) lir; lr*r 3
- th
a,
?
is defined by a
l,
i2 ,
10r- Twill
t01o: 10', what is r?
be an arithmetic sequence.
is the
and
.
4e'
sorve'.'"'l- =Vt."*rl-n
*u
2x
*
2y
?
