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NAME: CLASS:

AdditionalMathematicsPaper 1Oct2012I hour 15 min

MARA JT]NIOR SCIENCE COLLEGE

SEMESTER 2 EXAMINATION 2OT2

FORMFOUR

ADDITIONAL MATHEMATICS

Paper I

One hour fifteen mirutes

DO NOT OPEN THIS QUESTION PAPER UNTIL YOU ARE INSTRUCTED TO DO SO

1. This question paper consists of l6 questions.2. Write your answer clearly in the spaces

' proided in the question paryr-3. Sho* your working. It may help you to get

your marlcs.

4. The diagrams provided are nol drawnaccording to scale unless stated.

5. The mark allocated for each question andsub-Wrts of a question are shown inbrackets.

6. You may use a non-programmablescientific calculator.

7. A list offormulae is provided in page 2.

8. This question paper must be handed in atthe end of the examinatiotl

www. myschoolch ildren.com

Question Marks MarksI 3

2 33 4

4 45 36 37 38 4

9 310 a

1t 412 2

13 4

l4 315 a

t6 3

TOTAL 50

This question paper consists of I I printed pages

www.myschoolchildren.commore examination papers at :

CONFIDENTIAL'Ihe fotlawingformtlae may be helpful itr answering the questions'

commonly used.

ALGEBRA

4251t

The symbols given are the ones

s_

8.

9.

t2-

13.

2.

3.

4.

5.

6.

7.

{x{ : {*'

d+d = d-"

({)": {"

logomn: logom + logn.

lrci*o ! =6U-^'ro*,n

loq.,, n{ : n log, m

uer= ffiTo = a+(n-lY

10. 5, = llz.a + (n -\dl

I l. T, = arn-l

,^= *f,"--rt) = 4-!), '+r

: *.r,r.,

-Ixl. r:?STATISTIK (STATISTICS)

' (riv - r\5- n=L+lt, lc\ Jn I

:wt = 9-xrc}

Ao

; - LvJ,,- zw,

: @_-;Y',r

x., = ,.faz.l 6.

7.3.

4.

GEOMETRI (GEOMETRY)

r. l"l= $;7

.ri + y j

TRIGOIIOMETRI

(TRIGONOMETRY)

1. Paniang lengkok, s = 1'8

Arc length, s = r0

2. Luas sekt or,1 = ! i2 e

Area of sector = ! ,zo2

xz +y2.,


CONFIDENTIAL 4251t

GEOMETRI (GEOMETRY)

r. l.l = $;7

^ - .ri +Yi, ,F;7

TRIGONOMETRI

0?rcoiloMETRY}

1. Panjang lengkol s = B

Arc length, s = rO

Luas sektor, L = ! ;2e2

Area of sector = ! ,'O2


CONrIDENTIAL

[ 50 marks ]Answer oll questions.

I Diagram I shows a circle at centre O.

42gt

Diagmm

Given the radius is 7 cm. Find the area of major sec tor OAB' Give your answer

in terms of ,r.13 narks I

tt-rad,1


CONFIDENTIAL

2 Diagram 2 shows sectors QORand PO.S with centre O.

o

ail1

The radius of the wtor QOR and the length SR is 7.5 cm and 2.5 cm respectivety. Find the

perimeter ofthe shaded region PQRS.

13 nmlrs\-

_,s


CONFIDENTIAL 4251L

3 a) Given that the median for the set ofdatax, x+4, ll' 14, 13, 12, tl and 14is 12.5.

Find the range ofvalues ofx.b) Calculate the new median if3 is added to each data

f3 narksl

4 Table 4 shows the distribution of ages for 50 teachers in SMK Bunga Raya'

Aee (yecrs) Frequency?5-29 630-34 7

35-39 ilN_M t345 -49 8

50-54 5

Table 4

the modal class,

the mean.

13 narksl

Find

a)

b)


CONFIDENTTAL

5 simpliS 272m rg3m+l ' 312m-l

6 Given that log x = rn, express in terms of zr of fog , fi

7 Solve the equ ation 2n.3 t-2bl =56.

' 425n

13 nartrsl

13 narlcsl

[4 norlcsl


COMIDENTIAL8 The fint three terms of an arithmetic progression s ue 2, 2x + I ,

y', and the tast term of the

progression is I19.Find

a) thevalue ofx, where x > 0,

b) the number of terms of the gogession.

t 2. Fina9 The fint two term of a geometric progression * i -d o

a) the common ratio,

b) the sum of the first I 0 tems.

14 narksl

13 narks]


COMilDEI{TIAL

l0 Tbe commn ratio of a geomtrb pr,ogrcssbn is 0.4 aod the sum to infinity of tbcsc progressba

fu 9. fid the fnst term of the progressbn3

tZnnbl

11 In Diagram I l, r ard y are related by the equatiotr log ! = 2(a + log r), where a is a onstd.The graph of str-aight line is ohained by ploaing bg y against log * as shown bcbw.

(5,0)

Find the value of a ad of b.Diagram 11

14rrlrirlsl

12 Given a= 12i-9jard1 -aj, find I l-rl.12na*al

42511

9


COMIDENTIALl3 It is given that fr = ( ),Te : C), and B(l'2).

Find

a) coordinarc ofpoint ,{,

b) Ed in terms ofri +Jri

14 Diagram 14 shows a parallelogram ODEF drawn on a Cartesian Plane' '

14 narksl

[3 narksl

{z$n

Diagram 14

Given that Od : (-:) andD? -- (-l). rina unit vector of DF'

10

-I


L

CONflDENTIAL 4251I15 A plate of Nasi Goreng costs RM 3.00 in the year 2010 and RM3.60 in the year 2012. Find the

price index for a plate ofNasi Goreng in the year 2012 based on the year 2010.

l2 narksl

16 Table 16 shows the price indices for four typei of fruits sold at a stall in the year 2010 based on theyear 2009 with respective weightages.

Fruit Price Index WeightageDurian Il0 8

Papaya l0s kMango 120 4Rambutan t25 3

Table l6

Given that the composite index for the four types of fruits in the year 2010 using 2009 as the base

year is I13, find the value oft

13 nadrsl

END OF QUESTION PAPER

11


AdditionalMathbmeticsPrper 20c[2012I hour 45 min

MARA JUMOR SCIENCE COLLEGE

SEMESTER 2 EXAMINATION 2012' FoRMFoUR

ADI'ITIONAL MATHEMATICS

PaPer 2

One hour Jorty five minates

IX) NOT OPEN TIIIS QUESTION PAPER UNTIL YOU ARE INSTRUCTED TO IIO SO

l- This qrcstion papgr consist*oftwo sections : Seciion A azd Section B.

2- Answer all qzeslr'ons iz Sectioa A and thte quesliozs lz Section B-

j. Show your working- It mcy lwlp Jnu to get your marks-

4. The diagrons provided are not drawn according to scale unless stated.

5. The mok allocated lor each question and sub-parrs oJa question are shown in bractzts.

6. You nay use 4 non-pBogram mable scienlfic calculator-

7. A list offormulae k prwided in page 2.

This question paper consists of 13 printed pages


CONI'IDENTIAL

List of Formalae

Tlc followingformuloe may be helpful in answering tle questions.commonly used-

425n

The symbols given are the ones

2.

J.

4.

5.

{xd = [*"

t+d: f-'

(ff = [^

log.mn-logm+logon

log. Y =1o*^ -ro*,n

loq.- rf = nlog" m

ff,,*'I

ALGEBRA

8.

9.

10.

I l.

12.

13.

bg,b = YEe!-togc a

Tn : a+(n-l)d

6.

7.

s" = llz.a+(n-tyl

T, : aro-l

- - a(r" - l) -o, - ---:-

-,,-l

sl--,4 ,;r;<.l-r

STATISTIK (STATISTIES)

5.r. ;= E'

,tv

2. ;-zf'>f

^ = '-(!f)'I- 9-xrco

Qo

-, - Lw'I,,-m6.

7.3.

4. WE(r-*)


CONNDEI\TIAL

GEOMEITI(GEOMEIIY)

1' bl=,lW

2. ^ _ xl+yiJr'*v'

4?Sn

IXIGONOMEITI(IPJGONOMEIRT)

l. Panjangleogtolq s =i0Arc lcngth, s = rO

t"2. Llas seltor,l = ! i'o2

Arca of scct' = ! ,2 o2

abca

-:-

r' shl sh.B 3bC

''

4 S- 6t+& -?Jrurra

5 ArEe oftiaosle : LabsfuCz


CONHDENTIAL

:T"."-l4A marksl

Answer all questions from this section

I Tabte I shows the distribution of marks obtained by 50 students in a test.

Length (cm) Frequency

0- 19 4

20 -39 6

40-59 t8

@-79 l2

80-99 l0

Table I

Find

(a) the median,

@ the standard deviation.

13 narksl

l3 narksl

4


CONT.IDENTIAL 425n

2 Diagram 2 shows an arrangement ofcircle ofdifferent size.

The radius ofthe first circle is r cm and the radius ofeach subsequent circle increase by 2 cm'

oooDiagram 2

Given the wire with a specific length, were cut to formed these circles'

(a,) Calcutate the total length, in cm, of the wire of the first l0 circle, in terms ofrand n.' 13 narlsl

'l(b) Given that the total lengh of wire of the first l0 circle is220n cm'

Find the value ofr.

Pnartu)

(c,) Find the total length of wire, in cm, for 206 and 2l't circle in terms of r'

l3 narts-l


CONFIDENTIAL 425D

$ narksl

[3 morltsl

[3 narksl

3 (a) Solvetheequati.r SF=rh.

13 marbl

If log,5 = nr, an d logry=n exprcss in terms ofzr and nof logrS.,lY

Diagram 4 shows the semi circle OICD, centre O with radius 7 cm.

1o

Diagram 4

[Use z : 3.142]

Calculate

(a) the length rifstraight linelC

@ the area ofthe shaded region.


. CONIIIDEI{TIAL 425N

' s ttisgiventhat D7=[i)ar'r-=(T) RisapointonPpsuchthat

1Pt=:PO. Find

j

(a) F0, t2 marksl

(b) A, 13 nortrsl

(c) lOil 12 narksltt


CONflDENIIAL

6. Diagram 6 shows triangle AED. AEC is . straigh line'

Diryram 6

Given that I BAC = 60", AB = Jgm, S@ 8cm, AE= 8.5sn ard ED = 15'6 cm'

Calcul*e

i) The lenglhof EC

ii) The ottuse angle of I AED, if the area of triangle AED is 54 cm1

4Un

t3 ru*sl

[2 narks]

\e


42SrLCOMTDENTIAL

Section B

130 .rr,arfsl

Auswer any three qucations fmm this section'

7 use graph paper to answet this qrestion '

Table 7 shows the values of two variables, x and y, obtained from an experimenl

Variables x andy are related by the equation y = td + ;,x , where t and ft are constants.

x 1.00 0.71 0.58 0.50 0.45 t''v 5.00 2.86 2.15 1.75 1.55 1.38

Table 7

(a) plot { ,ginst l using a scale of 2 cm to I unitonth64 axis and 2 cm to 2 unit on

the 4 axis.

Hence, draw a line ofbest fit.

15 nartsl

(b) Use the graph in 7(a) to find the value of

i) h,

ii) k,

iil $*tten a=3.5.

15 norlal


COMII'ENTIAL

8 Indiagram 8, three straight line AB, BC and CD arejoint to each other.

ag2

pnarlrol

Unulcl

14 narksf

Diagram 8

Giventhat fr =2t,Ed =or_, BE=:'EC,artd CD=2CF.

(a) FindZE -

@,) It is given th atE6=!x+hy, where fi is constant.)

Express, in terms of4 x andy.

DC6,

ii, EF

(c) lf pints A, E and F are collinear, find the value of i.

10

D

F

c


CONIEDENEIAL

g. Diagram 15 shows a quadrilateral ABCD where the sides AB and DC are pcallel'

4BAC is anobmse mgle.

GivdthatAB = l4cm, BC=2llcr.'{ ACB =30" aodDC: AIi = 3 :7'

Calculate

q) *BAc,

b) The lengtb, in cm, of diagonal BD,

c) Thc area in cm2 of Era&itateral ABCD

4rsn

[3 marks]

t3 na*sl

t4 martsl

11


COIYFIDE.NTIAL 42512

10 Table l0 shows the prices, price indices and perceniage ofusage of four itemsA, B, Cand'D which is are the main ingredients in bread making.

Ingredient Price (RM) per kg Price index in theyear 2012 based

on the year 2010

PerEentage

ofusage2010 2012

A x 6.5 t30 48

B 3.5 ' 5.6 r60 I6

c 4 4-4 v t2

D 2.2 z r50 24

Table l0

/a) Find the value of x, y and z.

13 narl*

ft) Calculate the composite indo< for the cost of making the bread in the year 2012 based

on the year 2010.

12 narksl

(c,) The cost of making one packet of bread in the year 2010 was RM3.00.

Calculate the corresponding cost in the year 2012.

[2norlal

(d/ The composie index for the cost of making these bread is expected to increase by 50olo

from the year 2012 to the year 2014.

Calculate the composite index for the cost of making these bread in lhe yeat 2014

based on tlre year 2010.

13 nar*sl

END OF QT'ESTION PAPER

t2


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