103

05Class Register Number Narne

READ THESF] I NS'I'III] (ITIONS I.-IRST

write your class, register number and name on all the work you hand in.write in dark blue or black ink in the spaces provided on llre euestion papelYou may use a soft pencil for any diagrams or graphs-Do not use staples, paper clips, highlighters, glue or correction fluid-

Answer all questions.

If working is needed for any question it must be shown in the space below that question-Omission of essential working rvill result in loss of marks.Calculators should be used where appropriate.If the degree of accuracy is not specified in the question, and if the answer is not exact, give theanswer to three significant figures. Give answers in degrees to one decimal ptace.

The number of marks is given in brackets [ ] at the end of each question or part question-The total marks for this paper is 50,

This document consists of t0 printed pages including the cover page.rn over

-..+,-t*.3'i*

wcHr.r SECONDARY (TOA PAYOH)

END-OF-YEAR EXAIVIINATION 2013SECONDARY 1 (EXPRESS)

MATHEMA'I'ICS 407ilA7

Paper I 4 October 2013

Candidates answer on the Question Paper

FOR. EXAMINER'S

USEPAPER I

TOTAL s0

a

.10:J

t hour

Danya

l Edu

catio

n

2

PAPER I 150 marl<.sJ

Answer ALL the questions- All tvorking must be clearly shoryn in the space provided.

l- (a) Find the smallest value ofp for which 23 x5x1.2 x13xp is a perfect square.

Answer

(b) Write 198 as a produ* of its prime factors.

Ansyer

(c) Given that 9900 : 22 x 33 x 52 x 1 r, find, Ieaving your answer in the primefactorised form,

(i) the grearesr inreger thar wiil divide both l9g and 9900,

(ii) the smaltest whole number thar is divisibte by borh i9g and 9900.

Answer (i) -

(il. ....

106

tll

trl

irlII]

2.When a number is ,clivided by 3 and has l0 subtracted from it, the result is 1 of the

4

number. Find this number-

t21Answer

chijscctp.sec I E.eoy,math I .2013 o

104'i

a

Danya

l Edu

catio

n

105

t07J

J A dress shop owner is off-ering some specially-designed red and white clresses for sale

in celebration of Singapore's 48'h birthday. She is giving a 4To/,discount on each,lress

but wants to make a20oh profit on its cost price. lf she bought the dresses for $82 each,

find the marked price of each dress-

Answer 12)

4- (a) It cost i company $12000 to manufacture a car. The cost of manulacruring the car

is made up from three parts, materials, \.vages and other texpens"s in the ratio ol3: 4: 5. Find the wage cost for the manufacture of each car.

(b) It takes 5 technicians to build 2 cars. The company needs to fill an order for 62 cars.

Find

(i) the number of technicians neederl ro fill this order,

(ii) the amount of wages paid to each technician.

Answer (a)

(b)(t)

(b)(ii)

chijsectp-sec I E.eoy.math I 20 l],,

tlltrltrl

-

Danya

l Edu

catio

n

106

4

5 r0B

tr) withour the use of a calcularor, esrimare rhe value * J*:l:r:7y2, giving

(;9.8s4)

your answer to I significant figure.

Answer

(b) State all possible number(s) of significant'figures in the following numbers:

(i) 1000

(ii) 0.00501

Answer (i)...

12]

lrltr l(ir.......

6. A purse contains 36 notes, in $2 and $50 dollar denominations, with a total value of$1272. Find the number of each kind of notes.

[3]

chijsectp-sec I E-coy-math l -201 3,ro

-

I

Danya

l Edu

catio

n

107

109l. (a) Arrange the following numbers in ascencling order:

s. r6, - s! , -5 2,+ , - s.t6i

Answer

(b) For the fo)lowing numbers:

Answerfor (iii)

t, ,r , J4 ,| ,'^f-* , 5.22, s.2

(i) list down the prime number(s)

(ii) list down the irrarional number(s)

(iii) represenl the numbers on the number line below, one has already been

marked out for you:

t2l

L2)

4-3-2 l9l 234 5

Answer (i)

(ii)llllll

ch ijscctp.scc I Eeoy. nradrF2o I ]ui

-

)

Danya

l Edu

catio

n

108

-6

8 Simplifu the foliowing expressions_(a) 2x+ y-[y-a{5v -3x)J

(b) ^ x+v Ix*zy + -x'34

Answer .--..- t2)

110

121

chijsectp.sec I E-eoy.rnath I -20 lfr,n

a

I

Answer

Danya

l Edu

catio

n

109

tl9- Simplify

(b) (2p)',.,F

Answer (a) tllt7)(b) ...

7

l0' Subtracr. 2xo -3x3 +5x2 +x+3from the sum of zx3 +x-l ,4xo +3xz -l and g-.x3-

Leave your answer in ascending powers of x -

c}rijsccrp.scc I Leoy.marh l-201]e9

t3lAnswer

a

Danya

l Edu

catio

n

110

o

I I. (a) Two interior angles of a decagon are I 40" , l32o .

The remaining angles are (3x - l3)" each, Find the value of x_

(b) Tbe interior angle of a regular polygon is 156" greater than the exterior angle.

Calculate the number of sides of the polygon

Answer (a)

(b)

112

L2)

t2)

12.

F

In the figure, ABC ll DE /l FG and BD // EF. ZABC: 30o, and EF : EG(i) Find the reflex IBDE.(ii) Find / FEGState all geometrical reasons-

Ans'vver (i)

(i,12)

121

chijscctp-sec I E.eoy.math I -2013 ,,

a

Danya

l Edu

catio

n

111

9t3 ri. e

P

W

PQRS is a square and RTSW is a kite. ISTR = 56"and ISRW = 32'. Find

(a) I.TRQ

(q zrsg(c) LQSW

It.

Answer (a)

o)

k)

T

a R

lrl121

tr]

chijsectp-sec I E.eoy.math l -20131 1 1

a::

Danya

l Edu

catio

n

112

14.

!0

2cm

The diagram shows four squares of sides 2 cm. The given arcs are all quadrants ofcircles. Leaving your answer in terms of zr, find

(a) the area ofthe shaded region,

(b) perimeter of the shaded region.

Answer (a)

(b)

End ofPaper I

chijscctp-sec I E,eoy.math l -201 3t2

114

t2]

17)

a

Danya

l Edu

catio

n

113

15Class

This document consists of l0 printed pages including the cover page.

over

a

Regis{er Number Name

.:1:=\z'-=3"i*'

ffi,.4*i==7.

CHIJ SECONDARY (TOA PAYOH)END OF YEAR EXAMINATION 2013

SECONDARY r (EXPRESS)

MATI{BMATIC-S 4416t02

Paper 2 4 October 20 t 3

'Candidates arswer on the Question Paper. I hour 30 minutes

FOR. EXAMINE,R'S

USEPAPER 2

READ THESE INSTRUCTIONS FIRST I

write your class, register number and name on all the work you hand in.write in dark blue or black ink in the spaces provided on th; euestion paper.You may use a sofi pencil for any diagrams or graphs-Do not use staples, paper clips, highlighters, grue or correction fluid.

Alrswer all questions,

If working is needed for any question it must be shown in the space below that question.omission of essential working wirt resurt in loss of marks.Calculators should be used where appropriate.If the degree of accuracy is not specified in the question, and if the answer is not exact, give theanswer to three significant figures. Give answers in degrees to one decimal ptace.

The number of marks is given in brackets [ ] at rhe end of each question or part question-The total marks for this paper is 50-

TOTAL 50

I t:l

Danya

l Edu

catio

n

114

2

116PAPER 2 [50 marlisl

Ansrver- ALL the questions. All rvorking must be clearly shorvn in the -space provided

Solve the following equations-(a) 2(P-2)=l-(3-P)

Answer -

(b)

Answer .

1,t- 4q)'-s

2r+l 3-r r+3

trl

t2)

ch ijsectp.sec I E.eoy.rnath2-201 3

(c)3 24

12]Annver

a

ll,1

l.

Danya

l Edu

catio

n

'l 15

L7J

) Sharon is 5 times as old as her daughter- 4 years ago, the square of the sum of

their ages is equal to 256. Find their presenr ages-

Answer t3l

) on children's Day, students in a school rvill get a treal from three stalls in the

school's canreen. Slall A will prepare 630 hotdogs, Stall g wiil prepare 945 plates

of noodles and Stalt C will prepare 1575 cups of'milkshake

(i) What is the greatest number of students in the school if each student

receives the same amount of hotdogs, noodles and milkshake?

(ii) How many of each item will each stuclent receive?

chijscctpscc I Lcoy.nrath2-2O 1 ] 1 ;

t3I

lll

-..

(i,Answer (i)

Danya

l Edu

catio

n

116

4118

4. The S-E.A Aquariunt has an perinreterof 3 cm on a map. If,the actual perimeter

of the aquarium is 3.15 km,

(a) find the scale of the map in the form I : r

A model of the aquarium is n:ade 10 the scale of I : 400

(bxi) A pillar on the nrodel is 4 c_m long. whar is rhe actual length of the

pillar in metres.

(ii) Calculate the floor area olthe aquariurn moclel in square centimetres, ifthe floor area of the aquarium is i62 m2.

Answer (a)

(b)(i)

(b)(ii)

chijsectp.scc I E.co)-math2-20 I 3 n

llltrl

12)

a

Danya

l Edu

catio

n

Countries Temperature

Antartica -45

Beirut 26

Cape Town 12

,lLondon l6Nuuk -5

117

19)

5. fhe table shows the ternperature at a parlicular time in five locations-

(a) List the locations according to remperarure, from the warmesr ,o ih" coldest.

(b) Find the greatest temperarure difference amongst the five Iocations-

(c) It was found that rhe temperature in Nuuk increased steadily by 0.3"c pcr

hour. Given that the temperature at 1000 hours is -- 5.C , find the temperature

at I I45 hours.

(b)

k)

chijsectp-sec I E-eoy.math2-201] 1 7

tlltr l12]

-

I

Danya

l Edu

catio

n

118

.6

6.120a) In 201I, the price of a scientific calculator was $24 and a roral of 120, 000

' calculators were sold. Find the total amount c[money collected from t]re sale ofthe calculators.

b) In 2012, the price of the graphic calculator increased by 15% while rhe number

of calculators sold dropped by 20%%. Find the total amount o[ money collected

lrom the sale of the calculators-

c) In 2013, in a bid to boost sales, the company decided to give a discount of lOYo

on the previous year's price- Find the least number of calculators that must be

sotd to exceed the total sales of 201 l.

Answer (a)

{b)

(c)

chil-sectp.sec I E.eo/. math2-20 l3 o

0It3l

l2l

a

Danya

l Edu

catio

n

L2L1

Joan was travelling across the country to visir her grandmother. Her brrs ro the

train station, travelling ar an average speed of 60 km/h, covered a distance of 30

km before it broke down. She had to wait 15 minutes lor the next bus which

travelled the remainirry24 km at an average speed of 72km/l't. She hnally arrive<l

at the train station at l4 12_

(a) Find

(i) the average speed for her entirejourney,

(ii) the time the firsr bus broke down-

(b) The train left the station at I -5 38 and travellecl a disrance of iO+O km at a

an average speed of 124 km/h. Find

(i) in hours and minutes, ro the nearest minule, the time taken for the

train joumey,

(ii) the time she arrived at her destination.

Answer (a) (i)

(il(b) (i)

(ii)

tllI2lti l

ch ijsectp-scc I Ecoy-marh2-2OtSl I

119 l

Danya

l Edu

catio

n

120

8

t22oo G

A

F

E D

In the figure, ABCDEF is a regular hexagon, BCJHG is a an regular pentagon,

L KLM is an equilateral triangle, DKL is a straight line and CD // LM,

(t) /BCJ(1i) /.DCJ

$i1)tcDK(iv) lCJK

(b) State, showing your reasoning- whethe r CJ isparallel ,.; ,r.

Answer (a) (il

(i)(ii,(iv)

H

J

D

I

K

tlla)

trI12\

trl

chijsectp.sec I LeoY-rnath2.20 lfr,,

a

Danya

l Edu

catio

n

121

239

o

D C15m

Z

20

P S

O 9m R

Figure I Figure 2

Figure I shows a cylindrical rnetal basin with diamerer of 4 m and Iength 20 m-

The basin is filted with water. (Take , =?)7'(a) Jim wants to painl $e 6xternat surface of the basin. If 5 lirres of paint is

needed lo paint a surface of 2 m2, calcuiate how rnuch paint Jim needs-

(b) Jim decides to transfer all the water into rhe container shown in Figure 2-

Determine the deprh of water in the container after the.transfer.

i

4m

'6-

Answer (a)

a)[3]

t3I

chijsectp-scc I E-eoy.math2-20 I ]r,

a

Danya

l Edu

catio

n

122

1.0

12410. 15 carpenters can finish making 45 tables in27 days.

(a) Find how tirany carpenterswoulc.l be needed if 63 tablesare to be made in-

81 days.

(b) After working lor 9 days, 4 of the carpenters resigned and the job was

completed by the remaining carpenters. Find the total number of days it

will take to make the 63 rables.

Answer (a)

(b)

chijsecl!!-.sec I E-coy.math2.20 I 3r,

tzl

t3lEnd of Paper 2

-

Danya

l Edu

catio

n

123

t 25

Sec One EOY 2013 paper I Ansryers

Sec One BOy 20i3 peper Z Ansx,er.s

Qla) p: Ii0 Qlb)l98:2xj2xlI QIc) (i) 2x32 xtl QIc)(ii) 2x32 x5x7tQ2) r20 Q3) $189.23 Qaa) $a000 Q4b) (i) I55 reclrnicians Q4b) (ii) $ 1600Qsa) 0.s Q5b (i) 1,2,3,4 Q5b) (iD 3 Q6) I I $2 nores, 25 $50 nores

Q7a) - 5.2, -5.t6i , -sI

- , 5.t6,b

45 Q7b) (i) Ji , p

2 Q7b) (ii) z

l02

s522

it <1JLJN

4 1I ) ? 43 .-2 19

Q7b) (iii)

{ei

QBa) i0(2y-x) qsb) 1-lL?8/Q9a) 4m Q9b) l2s

Ql0) 3 -2xt +4x3 +Zxo Qll a) x_.-53 QI i b) 30 sides Qt2 (i) 330"- Qr2 (ii) r20"

Ql3a) 28" Qr3b) r7" Ql3c) 77" Q I aa) 6r - 8cm2 .or2(3r - 4)'cnt2

Q14b) 6r + 4cm2(3r +Z)cm

QIa) p: 2 Qlb) q =I

2 Qlc) ,' = 1t7

Sharon is 20Q2) yEars herold, IS 4daughter years old.

Q3) (i) 3t5 srudents Q3 ir) 1( 3 ate ofSholdogs, pl 5 ofnoodles, milkshakecupsQaa) I : 125000 Qab) (i) l6 m Q4b) (ii) t0.tL5 m2

Bei Town, AntarticaQ5a) tut, London, Cape Nuuk, Q5b) ft5?5+g zt".Q5c) -a.475"C

Q6a) $2s80000 Q6b) 52633040 Q6c) I 15943 calcularors

Q7a) (i)ae ll-lcnlhl3 Q7a) (ii) 133,7 h Q7b) (iD 0001 h

Q8a) (i) l0s" Q8a) (ii) 132" Q8a) (iii) 60" Q8a) (iv) I08b

interiorISCJQ8b) not to BLparallel because andZDCJ ZCDK notare and hencesupplementarynot

Q9a) 3454t1,

Q9b) I .75 m QiOa;7 carp,enters Ql0b) 177 calpenrers

-

t'2:j

Q7b) (i) 8h 23 min

Danya

l Edu

catio

n