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1.

2

Answer.4II the questions-(50 marks)

(a) Find the LCM of 18, 36 and 48.

O) Find the smallest integer n, such that 48n is a perfect square.

Answer:(a)_ t21

(b)--- trl

) Express 5 as a recurring decimal.

Evaluate 2.83 + 5l correct to 3 significant figures.

(a)

(b)

Answer:(a)_ tll

Bukit Merah Secondary SchoolEnd-of-Year Examination 201 I

Secondary 1 Express

MATHEMATICS

Paper I I I Oct 2011

Candidates answer on the Queslion paper. lh

E

l'or Examiner's Use

READ THESE INSTRUCTIONS FIRST

Write your class, register number and name on all the work you hand in.Write in dark blue or black pen_You may use a pencil for any diagrams or graphs.Do not use staples, paper clips, highlighte.r, glr" o. correction fluid.

Answer all questions.The number ofmarks is given in brackets [ ] at the end ofeach qucstion or part question

Ifworking is needed for any question it must be shown in the space below that question.Omission of essential working will result in loss of marks.The total of the marks for this paper is 50.

You are expected to use a scient.ific calculator to evaluate explicit numerical expressions.Ifthe degree ofaccuracy is not specified in the question, urd ifth" answer is noi exact, give theanswer to three significant figures. Give answer in degrees to one decimal place.For zz, use either your calculator value or 3.142-

This document consists of i/ printed pages including this cover page.

BMSS Se I Erpr6s End{f-Y6r Paperl 20t,

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Danyal Education

3.

l

The water levet ofa Marina Barrage increases by an average of28o/" 1o I 76 cm during

th€ wet seasm- l*ovever, during the dry season dr water level decreases to an

av€r'ageof 96 qo-Fird

(a) Thc origiod water levoil before is increase of287e,

(b) The peroerqe decrease, correct to 3 sigrrificirt figures' of the original water

level during lhe dry season-

Azswer:{a\ cm t2l

(b) t2l

Factorise complddy

(a) t5azb'-i3abt

O) 8px -l1ry-6py +2oax

4

The ratio of the age of Lisa to the age of her mother is r : 4 - The ratio of the age Lisa'smother to the age of Lisa's grandfarher is 5;9 .

If Lisa's graodf-ather is 72 years old, 6nd:

(D thc age of Lisa's mother,

(ii) the ageof Lis4

(iiil ratio of rhe age of Usa to the age of Lisa's moth€r' lo the age of Lisa'sgrandfailher-

Anooer:(i) vansold

(ii)

4.

Ansto*:(a) 'tl]-

12)

I2l

I2t

Irl{

BitlSS S€ I FlPIs fr&of-Yd P:9dl 201 I

(b)

t3+BMSS 56 I Elprs Ead{f-Yar P4El 20t I

(iii)

vezn old

II

Danyal Education

56

that DB = DC , IABF = 40o and IBEC = I t4", calculate the value of(a) p,(b) q,

(c) r,

6. Solve

(a)

o)

(c)

3x = -21

3;'-to=!,423t -l2l +f

Answer :(a) x =

(b)':

(c)r =

In the diagram, .qaco is a trapezium. BEc is a semicircle with centre o and a radius

of 3 cm. lf ag : l2 cm and DC = 5cm, calculate the following:

(a) the area of trapezium ,lBCo

(b) the area of the shaded rcgion ,t a t, c o and correct to I decimal place (1-ake

r = 3.r42).

5cm

12 cm

tll

t2)

tzl

Answer :(a)

(b)

8. Inthediagram, ABC isastraightlineand cE isaparallel to rr .GivenBMSS Sec I Eipr6s tnd-of-Year Papcrl 201 I

Eo

l2l

t2)

Ansoer :(a) p =

O)q =

(c)r =

ttl

tlj

tzl

9. a) Using your ruler,

BIVISS Se I Expr6s End-ofya, paptrl 201 I

cm

compasses, protractor and set squares, construct a []]

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87

quadrilateral ABCD sttch that AB: 7 cm, BC: 5.5 cm and zABC = I l s.. Inthis quadrilateral, CD is parallel to lB and lD is parallel to -BC.

(b) Construct the perpendicular bisector of lB,(c) Construct the angle bisector of angle ZBAD .

Answer:

7cm

illtll

4:6=

10:r6:

02 +4

l2 +5

zz +6

32 +7

b2 +8

I\

y2 +50

(u) Find the values of a and b.

(b) Hence, by observing the pattem, find the values of x and y

IB

-rA

Answer:(a)o= _b=_ 12)

(b)x = _, 12)

10- Consider the pattem:

BMSS Se I Express End-of-Y@r Paperl 201 I

11. The diagram shows the uniform cross-section of a sofa. EFG is a

BMSS 56 I Expras Endof-Yar Paperl 201 l.

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semicircle, AB=75 cm, BC=20 cm, CD=45 cm, AG=63 cm and the rength ofthe sofa is 2.3 m. Find

G) thearea ofthe cross-section ofthe sofa,

(b) the volume of rhe sofa in mr.

63 cm45 cm

Answer:(a) "*2

(b)"-l

Answer :(12(i) t2)

(12(iD) tl]

l0

Heieht (x cm) ll0<ril20 120 <-r ( 130 130<x(140 140<rSl50Nrmrberof

boys4 x 5 2

G

(a) Find the value of -r.

(b) The information is to be represented in a histogram- Complete the histogrambelow.

C

20 cm

cm

Answer :(b)

Ansroer :(a)

140

lrj

t2)

t'2)

I3l

0o@oEJz

12. (i)

(i')

2

1

110 120 130

Height (cm)

13. The height of l8 boys lrom Bukit Merah School is shown in the table belowBMSS Sec I Express End-of-year papnl 201 I

I

tE

BMSS Sec I Exprs End{f-Y6r Pap6l 20t I

- END OF PAPER -

Solve the inequality x+ 2 < 3x -16.Hence, find the smallest odd number that satisfies the inequality x+2 <3x _16

I

Danyal Education

?Aa" ) - 6hSSAnswer,4ZZ the questions.

(50 marks)

l. (a) Giventhat x-4, y=5 and z=-8,findthevalueof s*-117 +2Y . lz)

4.

2

Two towns, A and B, are 198 km aPart,

(") Jimmy travelled by car from town I to town B at an average speed of 66

km./h. How long did the journey take?

O) He travelled back by car from town B to town d in 5 hours 30 minutes.

Find his average speed, in kilometres per hour, on the retumed joumey.

(c) Jimmy left town I at 07 30. He stayed in town O for I of an hour.4

At what time did he arrive back in town I ?

(d) Calculate the average speed for the entire trip in km/n-.

Mrs Loh keeps a monthiy account of four items of expenditure. The figures for a.

particular month are shown in the tatrle below.

Item Amount ($)

Food 300

Utilities a

Entertainment 180

Transport

Thc information is also illustrated using a pie chart-

o)

(c)

Simprito # +Evaluate

[(il ( il]-(-ti), gi,ing vouransweras a fraction in its

t2)

t21

tll

tll

t2)

{2)simplest form.

.''.5.

., In the diagram, P,Q,R and S are

polygon. ZPQR=156"

1 560

S

P

(a)

(b)

Calculate

(i)

(ii)

IPRQ,

ZPSR

What is the exterior angle of the regular polygon?

How many sides does the polygon have?

trltl l

tllltl

(i)

(ii)

-t. Salina has two pieces of ribbon, A and B . The lengths of .4 and B are 165 cm

and 270 cm, respectively. She wants to cut up both pieces of ribbon into smaller

strips all ofequal length so that there is no ribbon left over-

(a) What is the longest length of each strip of ribbon Salina can obtain?

(b) Hence, find the total number ofstrips she obtained.

(a)

(b)

(c)

How much did Mrs Loh spend on the four items in that month?

Calculate the angle ofthe sector representing entertainment.

Find the percentage ofthe amount money spent on transport.

t2)

l2l

tzl

TransportFood

Entertainment

Utilities

rJr

t2l

tr l

BMSS S@ I Expres End'of-Yar P2 201 I

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95 cm

Calculate(i) the radius of the trunk in metres,

(ii) the volume of the trunk in ml

6. A2litrebottleoforganicpeanutoilissoldfor$15.e:]-tltrebonleofoliveoilis2

sold for $28,

G) Suppose both types ofoil are equally good for cooking, which one is better t2)value for mone/

(b) A bottle ofpeanut oil wasused up in 16 days. Find its consumption rate in tllI / day.

(c) Ifthe consumption rate ofthe bottle ofolive oil is the same as that ofpeanut oil, il]how long can it last?

The diagram below shows part of a tree trunk in the shape of half a bylinder. It is 4 mlong and its semi-circular end has an arc length of 95 cm. (Take r =i.l+21

8.

4

7 Mn Lim was givensome money to buy fruits for making a fruits hamper- She canbuy roranges at a price of 3 for $1,00 and she would be left with $0.80.Altematively, she can buy (x+9)apples at $0.20 each and she would be left with$0.60.

(a) Write down an expression in terms of r for

(i) the amount of money Mrs Lim spent buying oranges in terms of x,

(iD the amount of money Mrs Lim spent buying apples in terms of x.

(b) Hence form an algebraic equation in terms of x and solve for the value of x.

(") How much money does Mrs Lim have for buying fruits?

(d) During a fund raising campaign, each fruits hamper was sold at $ l6.70.Find theminimum number of hampers needed to be sold if at least $5000 is to be raisedduring the campaign.

(iii) calculate the total surface area of the semi-circular trunk in m2 ,

(iv) the cost ofpainting the trunk, correct to the nearest cent, given that itcosts 70 cents to paint one square metre.

tllt1l

t2)

t2)

t2)

L2l

l2l

t3l

lll

9. A company offers 2 different pay schemes for annual pay increase to theiremployies:

_ Scheme A: Annual pay rise of golo of present salary

Scheme B: Annual pay rise of $40 plus 67o of present salary

(a) David is an employee who eams $2400 a month. which scheme should hechoose in order to receive more pay in the following year? Justify youranswer.

(b) Steven, another employee finds that both schemes give the same amount ofpayraise. What is Steven's present salary?

t3l

t2)

BMSS SG I Expres End-of-Y6r P2 201 I

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BMSS 56 I Expres End{f-Yar P2 20t I

. END OF PAPER -

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I (a)

(b)

,lrnn^u Bfh gsAnswer ALL the questions.

(50 marks)

Find the LCM of 18, 36 and 48.

Find the smallest integer n, such that 48n is a perfect square-

2'18,36,48

3lg,lg,24

2|.3,6,8

313,3,4

1,1,4 l*llLCM :2x3x2x3x4=144 ["1]

48=22 x22 x3

48n:22 x22 x3x3

n:3 lbtl

Answer:( L2l

lll

,, 5(a) Express i as arecurring decimal.

(b) Evaluate 2.83 + 5l correct to 3 significant figures.

(a) s

1l

:0.45

(b) 2.83 + 5l = 0.05549

= 0.0555(3srg)

lBll

lBll

Answer:(,a) trll4rtll(bi

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3. The water level of a Marina Barrage increases by an average of 28%o to 176 cm duringthe wet season. However, during the dry season the water level decreases to anaverage of96 cm. Find

(a) The original water level before its increase of Zgyo,

(b) The percentage decrease, correctlevel during the dry season.

to 3 significant figure, of the original water

(a) 128% -->176cm

t% -+176 -ll128 8

100% + l-lxloo8

=137.5cm

Lmt)

lall

(b)Percentage J _(r:z.s-qo),,r,

t37.5:30.18oh

=30.2%(3sfs)

t2l

I2l

Imt]

t"t)

4. Factorise completely:

(a) l5a2b2 -33ab3

(b) 8pr-l5ay-6py+20ax

(a) l'azbz -33ab3

=3ab2 (sa -ttu)

(b)

lDll

8 p* -15ay - 6 py + 20ax: 8px+20ax-l5ay-6py: ax(Zp +sa)-ly(5a+2p)= ax(2p+5a)4y(2p+sa)

= (zp+sa)(ax4y)

[*t)

trl

BMSS lExp End-olYearPl 201 I

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5. TheratiooftheageofLisatotheageofhermotheris l:4-TheratiooftheageLisa'smother to the age of Lisa's grandfather is 5:9.

If Lisa's grandfatherisT2 years old, find:

(i) the age of Lisa's mother,

(ii) the age of Lisa-

(iii) ratio of the age of Lisa to the age of Lisa's mother to the age of Lisa'sgrandfather

(i) 9 -> 72yrs

I -+? =8 lml)9

Lisa's mother age : 5x8

= 40yrs L"tl

(ii) 4 --> 40yrs

I -+4:to4

Lisaage : lxlO: l0yrs

l*t)

lat)

t2l

{2)

ll l

(iii) Ratio of Lisa age to the age of Lisa's mother to the age of Lisa's grandfather:10:44:12: 5:20:36 [bl]

BMSS I Exp End-of-Year P I 201 I

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6. Solve

(a)

(b)

(c)

(b)

(c)

3x:-21

3 ,-lo:l ,423t -l

--

I

2t+3

3x=-212tJ

(a)

lbtl tll

121

3 ,-lo:l ,423 r-l ,:lo421r=lo4

r =40

l*tlLat)

3t -l2t +33t -l = I (zt +Z\

3t -l =l4t +21

3t -14t:21+1-llt =22

.\L _ _L

[*t)

Lcrll

l2l

7 In the diagram, ABCD is a trapezium. BEC is a semicircle with centre O and aradius cif 3 cm. lf AB : 12 cm and DC: 5 cm, calculate the following:

(a) the area of trapezium ABCD

(b) the area of the shaded region ABECD and correct to I decimal place (Taken:3.142).

Ia) Area of trap :;

" (t +12)x6

: 5l cm2

5cm

Lzl

tTl

C

Eo

l*t)

["r]

BMSS I Exp End-of-Year Pl f0l I

12 cm

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9 5

b) Area of shaded region :St-1 x3-142x322

= 36.861

=36-9cm2 (r"rg)

[m1]

latl

[*t)

latj

In the diagram, ABC is a straight line and cE is a parallel to BF - Giventhat DB = DC , IABF :4A" and ZBEC =114", calculate the value of(a) p,(b) Q,

(c) r,D

B C

a)/p = lQo (Corr. Rs) lbl)

b)Zq = 180-l 14-40=26o lbt)

c) ICBD : 180- 40-3(26)

= 62o

=180-62-62= 56"

8.

lll

L1l

lrtzl

BMSS I Exp End-ot-year pl 201 I

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e. (a)

(b)

(c)

6

Using youl ruler, compasses, protractor and set squares, construct aquadrilateral ABCD such that AB:7 crrt, BC:5.5 cm and aABC = r rs". Inthis quadrilateral, CD is parallel to AB and AD is parallel to BC -

Construct the perpendicular bisector of AB ,

Construct the angle bisector of angle ZBAD .

t3l

tlltll

Answer:(a)

B 7cm

m1

(lm

A

BMSS I Exp End-of-Year P I 201 I

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10. Consider the pattern:

4- G+q6- 72+5

10: 22+6

16: 32 +7e: bz +8

I\

x: yz+50

(a) Find the values of a andb .

(b) Hence, by observing the pattem, find the values of x and y .

(a) b:4 [bl], a = 42 +B:24 tbll

(b) y = 50-4: 46 trll

x=462 +50:2166 tbll

t2)

{2t

BMSS I Exp End-oFYear Pl 201 I

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11. The diagram shows the uniform cross-section of a sofa. EFG is a

sanicircle, AB:75 cm, BC:20 cm, CD=45 cm, AG:63 cm and the length ofthe sofa is 2.3 m. Find

(a) the area of the cross-section of the sofa,

(b) the volume of the sofa in ml.

Cross section area

f2lt3l

(a)'' j.

(b)

F

= (+s x zo) + (at" :01 *(i "

3.142, I 5' ) l*11

G

63 cm

A

=3743.5 cm'

Cross section area in m2

:3143.5* I :0.31435 m210000

Volume of Sofa :0.37435x2.3

0.123 m'

f"tl45 cm

c20 cm

lmtl

L"t)

75 cm

l*t)

12. (i) Solve the inequality x + 2 < 3x -16 .

(ii) Hence, find the smallest odd number that satisfies the inequality x + 2 < 3x - l6 .

(r) x* 2 <3x- l62+16<3x-x18 <2x [*l)9<xx>9 1"1)

(,,) I I

tll

BMSS lExp End-of-Year Pl 201 I

lbll

tl l

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13. The height of l8 boys from Bukit Merah School is shown in the table below-

(a)

(b)

Find the value of x.

The informationis to be represented in a histogram. Complete the histogrambelow.

t1la)x-18-(4+5 +2):7b)

[61]

1

8

L2)

o

.8oo)-oEfZ

Correct width: B1

Correct height -_- U t5

4

2

1

110 120 130

Heiqht (cm)

140 150

Height (x crn) ll0<x<120 120<x<130 130<x<140 140<x<150Number of

boys4 x 5 2

I

. END OF PAPER -

BMSS lExp End-of-year pl 201I

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h"r w(f,r - Bhs3 ({)qr 9Maths 1E Paper 2 - 2011- Answer:

aGiven that x : 4, l= 5 and z : -8, find the value of Sr-1[7 *2* .

-tltZVZ)x-<lz' + '

[mt\

latl

x

x

5(4)-i[57.uG]t!)20-4-204 I2l

b

2(x ++) -: (s -:-r)Imt)

lat)

x+4 5-3x96

l8

x+4 5-3xSrmnlrtv 96

l82x+8-15+9x

l8llx-7

t2)

c 12)

2 a

[mr]

lall

(,) [bl]

lbl)

)

/64

(,,) IPSR=ryaffr:24o

_r1JIl.(

+l

[r;l ( ;

l- [-,

zPRe: -! t9-1r9 :12o

:[*

:,,

_916

12)

b (i) Exterior Z. of polygon = 180 - 156 = 24" Ib1) It l(ii) No. of sides of polygon: 360

- l5 sides24

t l

J a

5

3

lmll

165 27033 54

lr r8

ts1

1

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t2)

bTotal number of strips obtained - 165+270

l5:29 strips lbll ttl

4 aTime=198 =3 h.,

66tDll lll

bAvg Speed:#=36 km/h [Dl] tll

c Time spent travelling from A to B:3 hrs

Time spent stayin gat B:0.75 hrs

Time spent travelling from B to A:5.5hrsTotal time spent on round trip back to I

: 3+0.75+5.5 [ml ]: 9.25 hrs : t hrs l5 mins

Jimmy arrived back at A: 07 30 hrs + 9 l5 hrs

: 16 45 hrs lal l tzl

d Total DistanceAverage speed for entire joufi)e):Totaltime

396o1<

= 42.81 l<rn/h

l*t)

lal l 12)

.5 a Amount Mrs Loh spend on the four items in that month:

=135" +$300

: lo$300

135

=360o + $3oox36o135

= $800

[*1)

lal l

L2)

2BMSS IE EOY P2 20I I

HCF=5x3

= 15 [a1]

The longest Iength of each strip is 15 cm.

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b Angle of the sector representing entertainment:

= 5300 + 135"

:$l -+ 135

300

=$l8o+ l35 rl80300

:8lo

[*t)

lallt2)

c Percentage of amount money spent on transport

_ 360-135-54-81xl00360

lmrl

["1]=25%o

tTl

6 a)Unit price of organic peanut oil in: lI

: $7.50 / I

Unit price of olive oil in = ?93.5

=$8/l-

[ml]

Organic peanut oil is value for money. lal] t2)

b)Consumption rate tbr organic peanut oil :2-

t6

:f,r rao, lbtl tllc)

Consumption rate for olive oil = 1 I / day

A bottle of 3.51 of olive oil will last for: *;:28 days lbll tll

7 a)i)(i)Amount of money spent on buying oranges: (x)

=${J

lbll trl

a)ii) Amount of money spent on buying

apples= (x+ l)(o.z)

= $(0.2x + r.8) tbtl I I l

JBMSS IE EOY P2 2OI I

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b) Amount of money spent on buying oranges +0.80: Amount of moneyspent on buying apples+0.60x 8 2x 18 6

310101010x 2x 18 6 8

--T3r0l0l0l028

l*tl

Iot)15 5

x =12

t2l'

c)Amount Mrs Lim has : = trl(j)- o.a

:l?+0.8J

= $4.80

[*t]

lat) r21d) Minimum number of hampers needed to be sold:

Let the number of hampers to be sold be y

16.7 y > 5000

5000'

16.7

y > 299.41

[*1]

Minimum no. of hamper to be sold : 300 [al]

Or

5000l*1)

16.7

=299.41

Minimum No. of hampers need to be sold: 300 [bl]

t2 l

8 i) Radius of the trunk in metres:I

-xLxrxr:0.95 l*l)2

0.95

3.142

r =0.30236m

r = 0.302m [a1]

12)

4BIVISS lE tsOY P2 201I

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ii) IVolumeof trunk: - lx z x0.302362 x4

2

= 0.57449

= 0.574m3

[^1)

[atl

t2)

iii) Total Surface Area:

=(4xzxo.3on6)+2

:6-5061m2

()"r.ror"o-tozto'))+ (o.ls"+) t*2)

l"\

iv) Cost of painting the trunk : 6.5061x 70

:455.42

= 455cents [b1)

t I l

(a) I Under scheme A, he will have apay rise of$2400x8/100=$192 lMll

Under scheme B, he will have a pay rise of$2400 x 6/100 + $40: $184 lMll

David should choose scheme A [Al ]

t3l

(b) Let y be steven's present salary.

SYoofY:6o/oofY+402 u : ]v+4025' 50'

lv : +o50-

Y:2000

lMll

lAll

Steven's present salary is $2000

t2 l

Its

5BT/SS I E EOY P2 20 I I

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