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CHIJ SECONDARY (TOA PAYOH)END-OF.YEAR EXAMINATION 201 3

SECONDARY 2 (EXPRESS)

MATHBMATICS

Paper 1

Candidates answer on the Question Papcr-

4016/01

3 October 2013

I houi

Register NumberCiass

FOREXAMINER'S

USEPAPER 1

READ THESIi INSTRUCTIONS FIRST' i

write your class, register number and narne on ail the u,ork you hand in.write in dark blue or black pen in rhe spaces provi<ied on rhe euestion paperYou may use a soft pencil for any diagrams or graphs-Do not use stapli:s, pape-r clips, highlighrers, glue or correcrion fluid.

Answer all questions--The

number of n:arks is given in brackets [ ] at the end of each question or part question.Show all your working_in the space below the question-Omission of essential workinq rvill result in loss of ntarks,

The total nrarks for this paper is 50-

You are expected to use an electronic calculator to evaluate numerical expressions.If the degree !f.ac9u1acy is not specified in the question, and if the ,rr*., is not exact, give theansw9r to'three'signifiiant figures- Give answers in degrees to one decimal place-

ITOTAL 50

This document consists of -1I_ prinled pages including tlre cover page.

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PAPER 1 [50 marksJ

,{nsrver ALl, the qucstions- AII rvorldng must be clearly shorvn in the space provided^

1- Factorisecompleteiy

(u) l0l -- 3x- i8,

(a).

(b) (o-b)2 - 5a+-5b,

(b)

. Ir ]

t21

(.) ,2 -4 -91

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a

chi isucro.scc2E eov.maih 1.20 I ltlt

1

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139J

2. Given thalp + 29 = -2 and p -2q: 18, find rhe vajue of pz + 4qz

- .t3j

3- (a) Solve gbz :3 - IOb

(a)-.. - l2l

ch iisccltt.sic2 E-col-fi atl: 1,20 I 3

(b) Given that x: 5 is a solution ro the equation hf _ 17x + j5 : 0,

(i) calculate rhe value of &.

(,i) Hence, find the orher solution of the eguation.

-

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4- (r) Express as a single fraction in it simplest fon-n-

) x+4T4-2x e-r)2 x-2

(b) Make m thesubjectolthe formula k -3rr2

(a)--------

5nt2

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2

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4

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141

-) Given thaty is inversely proportional to the square rool of x, and y= f *h.n , =2!-3-4'(a) find the relalion betr.veen x and y,

(a). --- .t2l

(b) calculate the value of

(D ywhenx=9

(ii) xwheny=2

(bxi) '-"'-,,11]

a

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)

(bxii)............-....-.-...-......,il]

chijsectp.s'ec?E.coy.mattr I -20 I 3

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6- Observe the panerns:

1x8+ I =917x8+2 =98

l23x 8 +3 =987

Pattern A

(a) Write riown the 7d line of the patteni A.

(b) Deduce the 8'h Iine of the pattem B-

Sequer:ce C is given as: 9,

Sequence D is given as: l,Sequence E has the following ruie.

9.-0 -998-9 =89

987-98 =889

Pattern B

889

rrl

ttl

trl

Ir]

89,

11,

rrth term of Sequence E : ,,ztl' lerm of Sequence C + rth lentt of Seqtrelrce D

(c) Write the nb term of Sequence E as a power of l0

(d) Hence find the sum olthe first 9 terms of Sequence E.

clrijsectp,sec2E,cov.rnaf,(20 I

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7. ABCD is a rectangle. The diagonals AC and BD intersect ar p

C

DWrite down(r) a pair of congruent triangles.(b) the total number of pairs oFcongruent triangres in rectangle ABCD.

(a)..

(b).

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B. In a triangle ABC, AD : ll cm and BC : x cm.l) is the foot of the perpendicular lrom B to the side AC, B

rcm

D ycn) C

Find(a)(bxi)(bxii)

/.BACthe vaiue ofxthe value ofy.

A cnl

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4cm

-

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(bXD.:

(bxii)

tzl

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t44

9 The marks of a Mathematics test taken by a class of srudents are given in the table

below-

(a) Estimate the mean nrark obtained for this test-

(a)

Does the mean score,gffer the best average mark of the class?

Give a reason for your answer.

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Marks 0<rn<10 l0<m<24 2A<m<30 30<z(40 40<rn<50Frequency 2 4 1 2l I

.201 3

B

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I0. The height of a class of 30 Primary Two girls was recorded and the data is presented inthe stem-and-leaf diagram shown below-

Stern

It01il112I ii114

il5

(a)

Leaf345802517799

I I 3659

0r1345623589

(b)(c)(d)

If the tallest girl stands at a height of I 15,9 cm, wrire down rhe height of theshortest girl.Find the median heiglrtState the modal heighr-The school ',vould like to encourage all girls above the height of I I4 cm roparticipate in the annual "Reach ior the stars" competition.What percentage of girls would be eiigible to register?

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. .(b)

(c)

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A con-rpany received an order for I 000 party hats to be made in the shape of a cone.'

The hats made had a base radius of I ? cm and a slant side of length 24 cm.

However, w-hen it was lried on, they were found to be too big. It rvas found that hats

with a base radius of I0 cm flned better.

(a)(b)

If rhe base radius of the hat is i 0 cm, find the length of its slant side-

Hence, find in krmsr, the tot-al area of material, in mz thal has to be cut offlrom ali the hats.

- l2_cor

(a)

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(b)

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12. The grid below shows rhe graph of y = 4x + l.(a) By adding a suitable staight line to rhe grid, solve rhe following simuhaneous

equations.

Y-4x:lx+y:_4

(b) Find the area enclosed by the 2 lines and rhey_axis.

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(b)

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, End ofPaner Il:'

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149

CIass Register Number Name

MATHEMATICS

Paper 2

Candidates answer on the euestion paper

4016/02

3 October 201 3

I hour 30 mintrles

f'-..s}+

wcHrJ SECONDARY (TOA PAYOH)

END-OF-YEAR EXAMINATION 201 3SECONDARY 2 (EXPRTSS)

FOREXAMINER'S

usePAPER 2

READ THESE INSTRUCI'IONS FIRS,I'

write your class, register nurnber and name on ail trre u,ork you hand in.v/rite in dark biue or blac-k pen in rhe spaces provided on the euestion.paper.You may use a soft pencil for any diagrams or graphs.Do not use staples, paper clips, highlighrers, glue or correction fitrid-

Answer ill questions-The number of marks is given in brackets [ ] at th-e end of each question or part questionlhoy all your working in rlre space below jfre question.Omission of essential working.rvill result in loss of nrarks.

The total marks for rhis papcr is 50.

I^u-u ul" expected to use an etectronic calculator lo evaluate numerical expressions-

If &e degree of accqracY,js lot specified in the question, and if the answer is not exact, give rhe

answer !o'three significaht figures- Give unr*.r, in degrees to one decimal place-

TOTAL 50

rn oYer

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l2t

This docume,t consisrs of p printed pages including the cover page.

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2

PAPER 2 {50 marksJ

Ansryer ALL the questions. All rvo;-l<ing must be clearly shorvn in the space provided.

l. Simplifu4yz -lly-3 .lt4y

9.+3x x2 +3x

L2l

2- Solve9 _3 _ y-5

y +2 y Un2)7

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151)

3. A shopkeeper bought x pencil cases for $108.

(a) write down an expression in terms of-:; for the cost price, in doljars, of onepencil case-

(b) The shopkeepersold l0pencil cases at a profit of$1.50 each and rheremaining at $7.50 per pencil-case. Write an expression in terms ofx, for thetotal amount of rioney received frorn the sale of,the pencil cases-

(c) Given that he made a profit of $12 from the sale, form an equation in x andshow lhat it reduees to I - 24x + 144: A-Hence find the nurnber of pencil cases bought by the shopkeeper.

(u)

(b)

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752.4

A q is di:ectlv lroportionalto pn-Pairs oicorresponding values are given in the table

below-

(r) Find the equation lhat connects g andp.

(a)

(b) Find tlie value of a and the value of 6-

(b)

(c) Find the percentage change in q if p is halved-

(.) .. ......

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153

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5

In the figure PSB and PTR are stra;ght lines and ZPST: IPRQ -

PS '. 4 cm, QR = IOcm, RT :3 cm, SI= 5cm, PT : x cm and QS : y cm-

4cm

.I- cm cm

3cm I0 cm

Name a pair of similar triangles and prove that they are similarFind the value ofx and the value ofy.

P

P

s

O

,R

(^)(b)

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(b)

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6

6. The figure shorv sorne lootpaths in a park. Path AB : 175 m, path DC : 186 m,

IBCD= 58o and IADB = I DBC : 90o-

i86 m

175 m

Find

D

B

(aXi)(ii)

the length of path DB,I ABD.

Mr Lee strolled from B to A at an average speed of l -5 m/s. Eind the time, in

rninutes and seconds, to the nearest second, he took to reach the point where he

is closest to D.

(aXi)

(aXii).- . 12)

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(b)

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155'7

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C A

B

The diagram above shows some concentric triangtes divided inlo segments A, B and CThe first triangular ring contains I, 2 and 3 in selments A, B and c respectivery-The second triangular ring contains tJle numbe.. q, S, and'6.The third tnangular ring contains rhe numbers 7, g and 9The pattern continues with subsequent rings containing,numbers arranged in aclockwise manner.

(aXi) Write down the rhree numbers in rhe 5rh ring. :

(aX,).

(ii) Find the number in segnrent B of rhe I lrh ring.

(a)(ii)..._

(iii) Find the sum of the firsl g numbers in segment C.

(a)(iii)

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(a)(iv) In which segment will the number 292be f,ound?

7(b) The sum of the nurnbers in the nth triangular ring,.S,, where n = 1,2,3 and 4 is given

in the table below

n I 2 J 4

s" 6 15 24 ))

(i) Express S,in terms of n-

(bxi) --.. .trl

(ii) In which ring is the sum of thc numbers equal to 528?

trll:t'2

chi.jscctp-scc2 E.coy, math220 I3

a-1 -

(bxii)

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757

8.

9

A jelly mould is made up of a frusrum of a pyramid fused to a hollow cuboid as shownin the diagam below.

(a) Find the volume of rhe frush:m_(b) 350 ml of warm liquid jeliy was poured into-the mould and allor,ved to set-

Find the heiglt ofrhe jelly formeci.(c) The solidified je-lly was.invert-ed on a circular plate of diamerer y cm,where y

is an integer. What is thL minirnum value ofyi

<-- 8 cm

I

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l? cm

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(b)

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r58r0

9 Answer the rvhole of this question on a sheet of graph paper-

The table below gives sorne values of r and the corresponding values ofy fory:-* -5x-l- l-

x -3,5 -J -2.5 1-L -1.5 -l -0-5 0 05

v 4 -)-z I , 4 4 J I -2

(a) Using a scale of 2 cm to 0-5 unit on the x-axis and 2 cm to 2 units on the y-axis,drawthe graph of.y: -2* -5x+ I for -i 5<x<0-5.

(b) The point (-0.6, k) lies on the graph. l-ind the value of t-ill

(c) Using your graph, find

(i) the largest value of - 2? - 5x t' 1,

trl

(ii) the values of x for whichy : --1.4

(cl) By drawing a tangent, find the gradient of the curve at the point rvherer - -2.)-

II]

(e) (i) On the same axis, draw the graph of y : -- 2^-

tll

(ii) Write down the x coordinates of the points of intersection of thetwo graphs

lil

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r -,r&1 Sec 2 EOY 2013 Ansrr-ers

5

IJ-

2Jx It

(a) s3.t"(td.p)(b) 6.67 (3s-f)(c) 5-33 (;s-,f)l(a) (2r-3)(sx+6)

I (b) (a-b)(a-b-s) sb(i)

Iv---'69

(a) 30.s marlcs(3s.f)(b) N o, due to extrem e va lu es -

I(c) (x + 1)(x -t)(x'1 -7) sb(ii)

IY-_

(a) I10.3 cnt(b) tt2.2cmi6 10

123 4567 x 8+7:9876543

98765432 - 9876543 = saessegq

7 164 6(a)

3(a)b

I--or*

4I

I;L 6(b)

3b(i) h:2 6(c) T":10" t0

(c) 1l l.J cm(d) 20%

3b(ii),:t: (other sotn)

6(d) 1lr1l1I110 ll

(a)20 cm

(b) 8.8r m22x2 -t-x-142(2 - x)2 7 (z) LABD = LDCA tz

(a)x: *1,1t,: .l{b) 2.5 unit2

m:4: 2k

5+6x 7(b) oo rS

Sec 2 EOY 20Ij Ansrvers

(2rt3)(sx+6)5

IY - --'-' ZJx 8

(a) s3.1"(td.p)(b) 6-67 (3s."f)(c) s.33{3s.f)

(a-b)(a-b-5) ,5b

Iv=e

9

(a) 30.5 marks (3 s.f)(b) No, due to extrente va iues.

(r-r- l)(x - lXr'- 7) IT5

I

i6A3 cm

2.2crit

(a)11(6) 11

164 7 x B+7:98765431234s6

b = ! or-l!42 98765432 - 9876543 = B8B9

h=2(c) I1|.J cnt

@) 2a%

x=3 (other soln)I

2 d I 1 0 11

@)2A cm

(b) 8-8r m2

2x2 +x-142(2- x)'7 1 a 12

{a)x=-7,!=-3(b) 2.5 unitz

m* 2k

5+6x

a

b

1

t0

T,=la'IO

AABD = LDCA

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Ita

p', Sec 2 EOY 2013 Ansrvers

1(a)

,(v -l)f s(a)

LPRQ similar to LPSTLRPQ similartoASPTLPQR sifiitar ro A.PTS 7

("X.) Segment A(bX, 3(3n -t)(6Xi, 5gthring

z

dY=-3or --5

s(b) y = 6,x:5 8

(a) 252cm311

(b)Heieht -10' ' cm'-32B (c) 12 cm

3(a) '[Y) 6(a) l58m

3(b)s, o[Y - r.s)+ z.s(x - r or

6(b) 25.7"

3(c) x :12 6(.) I rrrin 35 s 9

(b)3 4

(c)(r) a.l

4(a)rJq:Jp 7(aXi) 1f ,14,1 5 I

(c)(ii)x : -2.9 or 0.4

(d) 5.0s

4(b) ct = -3,b= 24 7(a)(ii)11)L 9

(e)x=-l-775or y=A-3

a(") --875% i08

I

7(a)(iii)

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