individual finals - 2013 mtap deped math challenge reviewer

8/9/2019 Individual Finals - 2013 MTAP DepEd Math Challenge Reviewer

1/6

Naune:

Metrobank-MTAP-DeplEd

Math

Challer:ge

2Ot3

Individual

Finals o

Third

Year c

Category

A

School:

Score:

Part

I' trVrite

your

arrswer

on thc

spa.e be.fore

each

itenr. Lqlve

radicals

turd

n in

yolr

ans\eers.

Each correcr

a|lswer

eaJrs

2

points_

1'

,4

arr(i

B

are

positive

integexs,

where

,4

is

between 3

and

tg

(inclusive).

^nd

B

is

bctwc,

5

r*rd

20

(inclusive).

Find the

positive

differeiic

betwee. the

lareiest and

srnalitxr

pussibre

v;rrucs

,r

z1/,iJ.

2-

A rectangle

h&s

area

(2r2

c-.21)

co2.

n'ind its

pe.ri:netcr

if

itiasabaseof

(s*lt)


2/6

Metrobank-M1lAP-DepE


3/6

5.

2cm

(1

point)

Letting

r

bc

the

radius,

arrd the

points

of tangcncy

as

indicated,

wc

har"e

_B-D

:

BE

:

r.

Therefore.

AD

:

5

-

r

utd, CE

:

t2

-

r.

(l

point)

Since

Ir

is the

point

of tangency

on

-4C,

*rc

have,4F:

lD

=

b- r

ati

CF,

=

CE

-

t2

_r.

Since the hl.poteruse

is

13,

thu

(5

-

r)

+

(t2

-

r)

-

i3.

(l

point)

This

equation yields

r

--

2.

Part

III

t.

t4/9

(I

point)

Thc tcrms

are

ar

-

a, a4

:

a

+

kL and o12

=

a

1

114.

(1 point)

Siuce thcy

form a gcornetric

squcDce,

ff

=

ff,*

(ai

3d)2

=

a111q 11,11.

(2

points)

SirupJifvr

a2

+6ad+93: a2

+

llad

g*

:

s"a

(l

point)

The

n


4/6

3.6

(3 points)

It

csr

be showa that

lBlD

:

ICAD

:0-

One

way

of shordng this

is

by letting

ZCIP

:

d.

Since A,4PC

-

ACPD,

it follows

that ZPCD

:

0. Norr,

sioce APCD

-

ABID

(theae

are both

rieht

tris,ngles with

ZADR

=

ICDP),tr

folows

that

ZBAD:

IPCD-0.

(1

point)

ln

the

righr triangle

ABC,

AB: t

+3\/,

and

tbelefor-e,

AC:

\/r(r

+l\f\.

AlterDati.\,1y,

one

Eay

just

note

that

f

.,/2,

f

-itloot

"*pr"oirg

this in

terc

of ,.

Since AD is

an

aogle

bisrtor

of

A.ABC,

we

t'a.,.

4

-

?*'

*

=

rfr.

3\,/2

BD

AB

(1

p


5/6

Narne:

Metrobank-MTA-F-DepEd

4ath

ChalleDge 2013

Indiwidual Finals

o

Gnade

7

.

Category

A

Schoon:

Scorel

-

art

I.

Write

.v_(nrr

answer orr thc space

before each item- Eact

corect amwer

earns 2

points.

1. wlrat

is

tlx,

larg{rst

diBit

A that will

DBke

67n,312 divisible by

12?

2.

lf

26 increased

by 4 ti]]n{l a number givs the sa.me

nd*rlt. a.s I nrrea,wri by

I

rirrrs rhe nDmber,

v/hat is

tbe nrrmber?

3.

Ilcne is

8

ye.lrs

Jrounger

than

Ricky.

n

ast

year,

Ricky

wa.s

twice

as old

as

I*:re

Hrw olri will Rrrre

be next

;'ean?

4,

Thc

prodlct

of two

prxitive

integers

is

10,

584 and their ',CM is 252.

What is their

GCF

1

5.

A

store

sold

8

rrrore

Php

150 slrits tlur.n

Php

175

slirts

if

it

receired Php 2500,

how nrarry

PI4:

175 shirts

did

it

sell?

6.

Two

milk

c-aDs, A

and B,

coutain

a iotal of

60

pinls

of

milk.

If

12

pints

are removed $orrr B, ihere

rernairs

il

B

half of wbat

,4

contains-

Hou much miik does

,{

cortaiD?

7. Wlut

is the remainder whe.o

3x13 is di"ided bI,

8?

8.

'l'he

surn of

two

rumbe.6

er(c-eds

t

he.ir d|,fetence by

tr2.

if

their

product

i$ 102,

what

are

t]1e

nDmbers?

9.

If n

is

the

srnallest positive

integei

that

ieave,

a reErainCer of 4 when

divi(led by each of 5,

6.

and

7.

what

is the

product

of

the

digits of

r?

10. If2*3:9.3*2.11,3*5:X4,and5x3

18, what

is

6

*

5?

11. What is the largest

iDteger le,s tha.n 2013 that is divisiblc

by 1231

12.

Find the

largest digit

B such thet 145,648 is divisible by 21.

13. A can

@DtaiDs Php 19.50 roorth ot XGcertal() and

2}centavo

@iDs_ Ii there

are l2J coiDs

in

oll.

how

nrany

lGce[tavo

coirs

dos

the

c-an

containl

14. A ..ircul^r

ffower

gardeo

is 6ur.round6i

by a

path

of

uniform

width.

If

the diametcr of thc

garden

is l0 m. and the widnh

of the

path

is 2 ]n, what is rhe

arer of the

patb

in tc,nDs of

7r?

15. What is the area

of the triangle with veftics ai

(

X,1),(a,t),anrl

(6,3):

Part

II. Write a complete

aDd

neat

solution

to

eatrtt

problera.

Eadh colr rt

solution eaxns

3

poirts-

1.

A

wooden cube is

ofside

18cur.

What is the volurne (in terms of 7r) of thc

largr:st sp)rcrc that c&D bccrrt

from

it?

2. Ii is estimatpd

that tlrc average diameter

of

peetreri

logs {nr-oing

k)

a

sawmill

is

20 in

What

is

the

qoss-se.tiou

axea of the largest square timber

post

thet can

be

cut ftoD it?

3,

The

lenglih

of the

&tllle

t

joinilrg

the nroi

ts

(-6,4)

and

(r',-2)

is

10

units.

Fird

all

possibie

values

of

r.

4.

'l'he

lirre that

pa.is..s

throtgh

(-I,-4)

and

(2,5)

alm

pnrsesr

throrgh (/i,2).

Find

t.

5.

A right rcctalgr)lar

prism

hrr"s &

vohlrire

of 180(rr3.

Frlge ts is twir:e erlge ,4,

while

*lge

C

js

1

rrrr

rnore

1,Lan tlrree times edge ,4.

Find

the r,lirnensions of the

prism.

Part III.

Write a s)rnplete

a

l rezt nolrlti(xr to $r,ch

proble.rn.

Fhr]) @rre,ct

soluti()D earns

5

points-

1.

What is

thc

area of

the

peutagon

lrith

\,{'.rtices at

A(-5,5),

B(2,9),

C(6,9), D(10,1), and

E(0.0)l

2. A swinrrrrhrg

pool

is

50

m long

ald

30

no wide.

lt

is 3 ryi

(ieep

at one eird and

t

m deep at the other end

.Whal

volume

of

water will

fill it

l,o

wii,hiD 2 drn frorn the bnir:1?

3.

Find all ordered

pairs

(o,b) of

pG;tive

int

ers tllat

satisfu

thecquation4a*7h:72.


6/6

Metrobank-MTAp-DepEd

Math

ChnXtenge

2O13

IndividrBl

F.iEaIE.

Grade

Z

r

Oategory

A

o

Auswer

Key

Part

I

1.

5

4. 42

7.

3

x@.

23

a:,.

75

2.

5

5.

4

8.

6andl7 1I. 196g

14.

Z4tr

n2

3.

l0 years

old

6.

32

pints

9. 8

tZ.

g

15.

S squaxe unitA

Part

II

1.

mdiu

of the

sphere:

f

:9cm

(r

pt);

lolume of

the sphere

=

f,rrt:

fur1f1

:

g72zrcm2

1z

pts;

2.

Let 2 be

one

side

oi

the squaie

cross

6tion.

By lpphagoreao

Tlreoreno,

we

have I

+

cz

=

202.

(l

pt)

A-ea

of rhe

square

cross

section

-

12

=

200crn2

(2

pti)

3. (z

+

6)'z

+

(-2

-

4),

:

102

(1 pt)i

(

j,

+

6),

:

64

(t pt);

l':2or6=_14(1

pt)

4.

skrpe of

the line

jon,ins

(-t,

4) and

(2,5):

ffi-,

qronl

srr,r)c,,f

rhe

rirrejoirins

(2,5) llnd

(a,2):

=-

*

(r

pt)

l'l1ra(ing

ihe

two

slopo,

-1

3

---?

l.

-

I

(t

pi)

5, Let

o be

the

length

of edge

,4. Then

edge

B has Iengtlr

2c,

while

edge

C has

length

:lo

+

t.

(f

pt)

Volume of

rectangular prism

=

a(24)(3o

+

i)

=

180+

o=

3 tbe

ody

rcnl

lalue (1

pt)

Dimersiors

of the

prism:

3 by

6 by t0

cnc

(n

pt)

Part

III

1.

Let w(-5,9),

X(10,9),

Y(n0,0),

and

Z(-5,0).

Theu

IVXyZ

is a

rcctanst,

(1

pt)

I(]

e (ABCDE):

xa(WXyZ)

-

erca(Aw

Bl

*o:a(CXD)

_

area(DyE)

_

area

(AZLJ

f

pt\

:

(e)05)

_;(7)(4)

_;(4X8)

_

*(r0X1)

_;(5)(5)

(2

pt'

:

87.5 square

uDits.

(I

pt)

2, Let

1, be

the volwne

of

thc *ratcr,

yr

the

rolurne

of tlre

w*ter i,,

tbe lowe,

txiangular

part

of the poo1,

and

y2

the vdume

of the

water in

the rIJ)per

rx*aDgular

part

of rhe pool.

Tlen

i

:

Vi

+Vr.

yr

-

(width

of the

pool)

x

(area

of the triangular

ooss_section)

:30

x (;(50)(2))

(lpt)

=

1500

(1pt)

y2

:

(width

of

the

pool)

x

(length

of the

poot)

x

(height

of

the wnter)

:30

x

50

x

0.8

(lpi)

:1200

(lpt)

Thus.

Y

.1500+

1200-

2700m3.

(1

pt)

3.

Foro

)

1, we must

harc

I

individual finals - 2013 mtap deped math challenge reviewer

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