Name : DUNEARN SECONDARY SCHOOL End-of

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Register
Nurnber
DUNEAULsLco^,Dsnyscrool
DUNEARN SECONDARY SCHOOL
End-of-Year Examination ZAl3
Mathcmatics (paper 1)
Secondary 2 Express
Wednesday
9 Oct
2013
0800 _ 0900
hrs
I
hour
Ed
u
,NSTRUCTIONS TO CANDIDATES
write your name, crass and register number in the spaces
at the top of this page.
Answer all questions.
.i
Write your answers in the spaces provided on the question
paper.
All working must be shownomission of essential working will result in the loss of marksDo not use highlighters,
correction fluid or correclion lape_
INFORMATION FOR CANDIDATES
al
The number of marks. is given in brackets
[ at the ent] of each question or part question.
You should not spend too much time on ,ny] on" questionlf the degree of accurac.y is not specified inihe question,
and if the answer is not exact,
the answer should be given lo thiee significant frgures.
Answers in degrees, if not exact, are td be giveniorrect
ro one decimar prace.
For n , use your calculator value, unless-the question
requiies the answer in terms
of ir
.
Da
PARENT'S
SIGNATURE
ny
Electronic calculators may be used in this paper.
FOR
USE
EXAMINER'S
P
This ques-tion paper consisrs of
4A
Setter: Ms. Melissa Lim
B
printed pages, incruding this cover page.
I
t7;
a
178
2l?
Ansrver all qqestigllj; ( 40 marks )
The table belora, shorvs the marks of a scienee tesl scored by a group of studenls.
Marks
Number
of
23
24
?5
26
27
28
0
t4
4
5
x
)
Find
al
Ed
uc
ati
o
students
n
1)
(a)
the smallest possible value
(b)
the largest possible value of x
of-r if the modal mark
if
is 27,
the median is 25-
Answer:(a)x=.---[]
'
(b)x=
7)
On the Venn Diagram shou,n in the answer space below, shade the region that represents
$w B)n
(a)
A'
.
e
IJ
tll
ny
A
Express, in set notation, the set represented by the shaded region in the Venn Diagram below.
t
Da
(b)
[l]
trl
Ansrver : (b)
2
t78
a
179
2t3
j)
A lefter is to be chosen randornry from the rvord 'DLTNEARNITE,Find
(a)
the
probability ofchoosing a vorvel-
ati
on
4)
..
,N',
Arswer : (a)
I 1l
Answer: (b)
ir I
The figure formed below consisrs of two overrapping congruent quadrilaterars-
Given that
ZAFC
:
62"
Ed
uc
(b),
the probabiliry of choosing the letter
, Z.flDC = I03o
LJ
and
LBCF:
90o,
F
G
I
A
E
f')
03"
al
I
B
ny
state the quadrilateral &at is congru entlo ABCF,
find the value
(i)
of
x.
(ii)
"
v-
Da
(a)
C
Answer:\a)ABCF=
-
Answer: (b)(i)
!)
tr
l
ill
Answer: (b)(;i)
3
li!l
"a
180
214
Expand and simplily
Go+
l)2 (2a -5).
Ed
u
ca
tio
n
5)
___ t3l
Answcr
-
Z)'?
:
36-
al
Solve the equation (3x
Da
ny
6)
Answer
:x=
or
t3t
4
I t1{}
a
181
215
Simpli$r as a single fracrion \;'x3 yz!*
27yr'
7
-
8x
ry
--
(-4r)'
Ed
uc
ati
o
n
t)
Ansrvet
Solve the follorving simultaneous equations
:- J.5
+Jy
3x
--l2y = l!
ny
al
4x
Da
8)
tjl
Answer:
_r
=
3l
')
5
r3r
-
182
276
9(a)
-6b2 completely-
Hence, given that 74o2
-
662
= 108 and 2a +
b: 3, find the value of
2a
*
b-
uc
ati
on
(b)
Factorise Zqd
:(a)
t2]J
Anqwer:(b)
12)
10)
Ed
Ansra,er
A map is drawn to a scale ol I cm to 2 km- The distance
Bukit Timah Nature Reserve is
between
Road and
18 km,
(a)
Write down the representative fraction of rhe map in the form
(b)
Find rhe distance between Bukit Panjang Road
an<J
f
.
Bukit tirrrl'Nu,u.e Reserve on
rhe map-
ny
al
On the map, Bukitl-imah Nature Reserve has an area of 0-4 cm2. Find, in krn2, tl.re actual
area of the reserye.
Da
(c)
Bukit Panjang
Ansrver:(a)
[l]
Ansrver :(b)
Il]
Answer
:(c)----_cm km'lZ}
6
I
a
ri2
183
l
Thg test scores of 25 Secondary Two students in a class are shorvn
in the table and stemand-leaf diagram belorv. Tbe passng mdrk for rhis rest is 50-
66
16
56
69
6s
52
Stem
4
J
0
0
6
4
1
0
2
2
a
2
50
14
86
66
42
86
46
68
74
a)
l)
16
4A
AO
AO
70
64
?4
64
6
B
6
)
tt
6
J
4
Key:
ol a.
56
72
l E
du
ca
tio
n
r 1)
4
6
4
I
9
4
6
6
0 represents 40 marks
-
'
(o)
Find rhe value
(b)
Find the percenlage of studenrs wlro passed rhe
(c)
Given that 6oYo of the students did not qualiS to take Addirional
Mathenratics !n the
followingyear, find the Ieast scoreneeded to'qualifytotake Additional
test.
-
:
Marhernarics-
The mean score of the 25 students is 64-52. A new
student just joined rhe class- wherr rlie resr
score of the new student is included, Lhe mean scoreof
the ciass becomes 6j-5 marks. Did
this student pass tlre test? Explain your answer by showing
your
working crearry.
ny
a
(d)
Da
al
Answer:(a) _-
Ansrver:(b)
Answer :(c)
Answer :(d)
_
.ltl
:_
_%[tJ
_ marks
Il]
l
I
a
iJ:',
184
2t8
In the figure, a pyramid of volume 640 cm3 is cut oui from a soiid cuboid-
n
12)
8cm
15 cm
uc
ati
o
23-75cm
(a)
Firrd the volurne of the rernaining solicl.
(b)
Find the height of the abor.e
(c)
The remaining solid is then rnelted anrl moulded into another square,based pyramid. Giveri
that the height of this pyramid is 29.5 cm, Ilnd the lengh of each side of irs base-
pyrarnid-
Da
ny
al
Ed
I
p
(a) . _
Answer. (b)
Ansrver:
Ansrver:
(c)
.
cnrr
121
_ cm
l7l
cm
[2]
-
END OF PAPER I
8
t8{
a
220
a
A.nsrver Scl: e,me fgr. p?.pgl-!
I ( a ) Srrrallesr possible value ofx = I5
)
(b
Largest possiblc value
olx -
6
ui
)
Mcthod
(3x-2)r =36
BI
9
I
n
io
(3x-2)=+6 or (3x-2)e-(
2(a)
3x=3 or 3x=-4
I
B
x
Method
DI
(b)I'nC'
l(a)
(b
)
c
u
(3x-2)r -36
BI
gx2
P(c.hoosing'N')-
+=l
t0 5
P ( choosinga vorvel )
Bt
-,
5)
r0
d
E
l
a
y
n
L
AI
i
-)Zx+4-36=0
gxt-izI-Jz=o
N.{ I
(3x-8)(3x+4)=0
BI
2
MI
t
a
-2?ll s, .r . -11
2
MI
MI
(3*-8)=0 or(3x+4)=Q
1(a)
DCR|{
(bxi)
Z.FAB
- Z.llDC
- l03o
Zx = 369"
=
(ii) Zy=
-
l03o -620 -900 -900
l5n
IOJo
BI
"
+ l50
=1180
5
,.
t.
)
(:a + t)r (zo
BI
-s)
=
19at + 6a +l)(Za
o
lSnr
-
igor
-l3at*zga-5
=
45ot +
-
5)
l1a| -3pa .* ?.a -
5
a
D
M
I
lvl
I
corrccr expansion
, -'
, =z? or,
JJ
(3x) yz)z
8.r
9x'
= ..'>l
-.,.,,,!
ol
7
x-+4
vt z1
=
-ll
AI
3v
(-4 z)'
7 - 64zl
x4x-
8.r
'
. 3y
(3o + t)r
M2 ,Expansion of (3x!yz)' &(-42))
AI
{
A]
9
r0
.l
@
(,
17)
8)
4x
+3y
3x
-
-).J
't
-----------"-.--- ( | )
12y * 2a ---..-^-.---.. ( 2 )
) Distance
(b
on map
( | )*C I l6x+t21,=14 ---."-----:.---(3)
i
(3)+(2)
Mt ( able ro show how
eiimination/substitution is
dono),
(c)
l9x = 38
AI
c
u
0,4an2 re p0.4 x 4
Sub.r=2 in())
ti+
3, -
=
3.5
t 1'
= -o't
/- -1.5
9(a)
24a7
6(4a)
=
6(2a + b)(2o
-il)
MI
-
b)
*
rg
3(2a-b) -
18
(2a+b)(zo-6)
(za'b) =
1
l
t0(a) lbnr:2km.
'
I c'm 1200000cm
np
a=
.l
=200000
9crn
6
MI
A]
Nll
AI
a
BI
84%
BI
25
(c)
(d
n
io
B1
4
60
ex
100
25
=
l5 scudents did
AI
(b) 6\za+b)(2a-g* fig
I
II(a)
*
1.6 km2
(b) !xrcA% *
-6b1
-
d
E
l
a
y
n
a
D
Al
[
t
a
lcmt2ktn
lcml '.4knt
t=2
=
Least score needed
)
=
qualily
ot
'10
Total score ol25 sruden(s
=
"
Totai score ol26 studerrrs -
25x64.57
t6l3
26x67
=
Nerv srudenl's scor.e
nor
5
165;
1651-1513
=38
MI
No, the studenr did not pass rhe resr.
BI
u
I
t1
@
@
't
224
l2 (a
)
Velgmg of remaining sotid
=(15xgx23,75)_640
=
(b)
:J x('15x8)xi
MI
l0 cml
AI
l
640
,
640x 3
=
(c)
22
l5x8
MI
l6 cm
AI
I*brruo,"o*29.5 = 22jo
basearea
-
2710x3
?o
s
_ aac.t\)/ol/
Lengtlr
ol I side
ofbase
=
ctn,
v1
d
E
l
a
y
n
a
D
14.99152103
JnTJtiffi
=
= l5.0crr ( ro 3 s,l
t.
I
,z
J
)
AI
t
a
c
u
n
io
L
1
t
{
l3
t4
@
-{
))A
Regis ter
Nu m bor
Naurc
A ngty
ts.!R 4rhttt tailllot
rJ(r a,rr-^ I-rq^?.r 7, (r @ L ouFa/ M itaa|urtt,N trco,\'Dt tctt,t . ou*tttt stcoi|itt tcu"or. rrt,\tlrn.ta.Arttatrctiltr,
,t r@r
ru^-t, i,;iitriaiiiiii)l,t
t,^e.r _\.t or1,/rt f .\.tiou.
ruF... \ !.c^ria rr$pt,ot nvritt tii"i, irliii i,i
hv''t..^ t..oLD..t t.rt,u,. o(r4aa.
t.aotn.,t\c"at ri"i.i"-ti:itio.i,.iiifii,i i,'tijii!:!ii2jiilii!;:,r,niixit:r'r{l;i;iii';itrit
t.. (.v tlcnrl,,(t.ar@L n!4a@|iiD_ittt raueL
Dt+
Secondary 2 Express
\\'edncsdn),
2 Ocl
1,0t,'l
0600 - 0930
hrs
I lour
J0 nrinurcs
INSTRUCTIONS TO CANO]DATES
Write your name, class and register nun)ber in the spaces al
lhe lop of lhis page.
(b)
ons,.l40- F.p LEs)
Expand and
simplity r2 -ln-a)(n+a)...
Maie
FOR EXAMINER'S
SIGNAIURE
USE
a
D
r
l
a
y
n
PARENT'S
of n
)
5)
page,.
6947
I
n
io
-
I
694a x I 6950
as a singte lraction
t
a
the subject
oI the lorrnula
Flcnce, find thevalue
Civen
z
in its simplest form.
=,F
of:rwhens=4, w= l4
and
th6(.r=-f ira solutiorr of lheequation
)
calculate the valuc
z= l.
trl
;3j
tjj
i
tll
2x'+ px= l5,wherep isa
ofp,
L2j
hence, llnd lhe otlrer solution of the equation
t3l
In the dlagram below, I and B are two kites that are 100 m above the
ground R,S. Kite B is directly abovc S.
Civen rhat rt{
= I l0
rn and BB
=
125 m,
B
,4
110 m
109
60
Se[er: Ms Melissa Lrnr
This qucstion paper consists of 6 printcd pagcs, including this cover
r
c
u
d
E
(b)
(t
INFORMATION FOR CANOIDATES
I
3(a)
(a)
The number of marks rs given rn.brackets (
latthe end of each question pr parl quastion.
Yorr should not spend (oo much time on anyone question.
lf lhe deg/ee ol acatacy is notspecified inine question, and ir {ho
answer is not exact,
lhe answer should be_-glven lo three signilicanl figures,
Answers in degrees, iF not exacl, are to be giveniorrect to one declmal place.
For i , use your calcularor value, unless the quesrion requlres
the answer in terms
of
-14
Express {-.
4n +3n
2n+n-:--:
con stan t,
Or COrfeCliOn lape,
Electronic calculators may be rrsed in this paper.
Hence, find rhe value
2)
4)
Answer all queslions.
Wrils ysur answers on lhe writing paper provided.
A lworking rnus[ be shown.
::.,::1":?'i,.,j::ll1ll?ills wirr resulr in rhe ross or marks. Do nor use hishlishrers,
z
aJJ g u es(i
0u\-a
DUNEARN SECONDARY SCHOOL
End-of-Yca r Exa min a tion 2013
i\,[a thenratics (paper 2)
W
l, l'
t
l(a)
trr'1/AF,rfct,,\naarJL/4ot,
correcllOn,rrl0
g
$
fr
D
(S)
find
(b)
ll;rd the
{
Z.BRS;
distancE between
tZJ
A
pl
and B,
)
@
(o
227
228
6)
Let
(= (r:xisan
8=
(r : r
is a
inreger, l S rsl0),
multiple of 2),
A- {x:x
is
aprime numberi and
8)
l.
G)
List the elements in
(b)
Drarv a cleorly labelled Venn diagram ro jJlLrstrate the sers
(c)
Lisr the elcments in rhe ser
(d)
Find
set
The table shows rhe numbcr oftimes thar a group
one. year period.
fr1
I
r(lnB')
l, 0, and {.
t2l
u 1,,
tll
,,
Irl
(a)
(b)
Number of visirs
0
Free uency
J
40 students took I Hisrory resl. The marki are shoryn in rhe bgck-ro.back
s(em-and.
leaf diagra;n below,
Bo,vs
Oirls
0
t
a
I
2
3
a
d)n
99 5 I
7 7 55 5
2t 0
5
I
6
3
0
?
I
r4
8
(b)
Write down rhc median of the boys, marks,
l
a
a
D
comparc the performance orthri boys ani girrs. whar concrusron can you
draw?
I
.
l7
y
n
means4S marks
Write down rhe rnodc olrhe students, marks.
(d)
9I
8 99
.
A studenr-is.selectei at random. Find rhe probability tliar
.less than 50 marks.
and
l?.
Il]
eqtralion t2l
l'.
(31
",,ri
lntlrediagram,fp,Rsisasq\rareofside
l7crn. A,B,Cand.Datepointson(hesides
- Sn = CS = DP and ABCD is a square,
PQ, QR, t?S and SP respectively such that AQ
(a)
tll
(b)
12}
(c)
Given that AP ^
x
cm.
triangleAPD.
lf
the area
of
square
rvrirc dolvn 0n cxpression, in terms of .r, for the area ol'
ABCD is 205 cm2, write clown an cqua(ion in terms of x
to rl - [7x + 42 = 0,
and show that it reduces
Solvc this equati;n and hence rvrite dorvn tlre length
rhan to
s
P.
lll
4
(,)
2
crn
3
O
4
itredrrqest0,+/=
of-t
-:
a
IA
trl
rhe student,s mark is
.t
Sentosa duting
P
,
5s
(a)
(c)
i]:
8
889
I 5 39
4 ? 88
9
Key 4
I
4
)
8
Fcont your answer in parrs (a) and (b), find (lre values
e)
8
7
Given also that the mean number of visits is 2,3, lornr another linear
tc 3x + 4/ = 56.
c
u
d
E
(c)
n
io
I
r0
Forma linearequation inxandyattdshowthnl
anC show rhat it reduces
7)
ol40 adults visitcd
tll
l3l
of APif A is nearer ro p
[3]
't
'I
230
l0)
ayc a designer in chargc of crearing (he
ne\\, yourh Olympic torch [or
Jou
2014. The nrcral (orclr thar you creared is nrade up
ola cone rvith height 50 cm
and radirrs 9 cm, A hcmisplrere oldiarncler
6 cm has been carved ou( from rlrc
.
ccntrc of lhe conc.
crrr
il)
The (able below gives sonre values
.9
A
Ansu'er the lvholc of thls qu"rtion on a single shcet of graph paper,
where
y=3+4x-rl,
D
-\-
-t
0
_)
3
n
io
t
a
c
50 cm
(a)
Find the value
(b)
Using a scale of 2 cm to represen(
of
.y=3+4r-xr,
V
(a)
(b)
t2l
Thc lorch is lo be rrade.of alunrinurn wirh a density
olZ.7 glg.1r
Oivcn
that
Densiry =
rnake rhis rorch.
(c)
u
d
E
l
a
y
n
a
D
Find lhc slant length, I/,{, ofrhe conc.
lf
#,calculare
Yotumc
.
the mass of alumirrum rcquired to
and the conesponding values
I
I
I
ofr
nr,
for thevalues
I unit
ofx
2
3
4
'l
6
3
on both axcs, draw the graph
in the range
(c)
Draw and label rhe equo(ion
(d)
From your graph, find the value(s)
(e)
On (hesame axes, drarvand label the graph of
the coordinates of tlre points of intersection.
-l
wiil i! cost to
ofr
I
rill
of
S.r S 5,
(ll
ill
t3l
paint it?
[4]
END OF PAPER
D
t3l
y = I + Z. Hence, write down
,l
5
I'
wheny e d,
t
1,.1.
5
ofthe line ofsymmetry olthe graph,
t2)
ir costs $0.50/cm, ro painr tl)c torch, h.w rnuch
Correct your answer to thc ncarcst dollar,
of/,
2
(o
232
I
A ns.u,e r
-S.gh er:n c.Jo
l(a)
t
!lp
ner
(b)
I
r!-(n-o)(r+a)
-
. ,lt -(,r? -n,)
= a!
(b)
2(4)(l 4)
I=-
MI
4(a)
5uD
=
Letn=16947, q-3
-*
t
a
c
LJJ,
^,
=9
DI
Answer rnust show conrrcction to (
n
t
n)(An
4(2u * n)
]1r) lZiiii
+
l7nr+)n-gr,-4,,
(Tnt+ n)(An+3n)
4m+Jn
(2m + n)(4m
+Jn)
tr;a
3(a)
V*
,
Zj
2xz1
r
2;-
2srt-
|
u
d
'2x
=2sw-1
2.rY'?z?
-_'
M]
E
l
a
y
n
a
D
;5ry
N4 I
.
I
I
I
AI
2.r'-x-15=0
MI
(2x+s)(x-3)=0
fvl
(2x+5)=0 or (x-3)*0
2x=*5 or x=3
.u
I
= *z-L
2
The other solution is x = 3.
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=.,'.:--
=
r,114,,,
='l
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(b) Equation: Zrt-x=15
4nt +3n
3(4t,7 a 3,r)
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P
I
a)
31
Znt+
(Zrn
l, f.
) )'a e t)
55
__ltr=_
)' )
---
_
"Bl
n
io
tnlo equalion
zGsl'-lo=rs
Hence, 16947t *16944 x )6950
?)
I
55.5 i ssl
)
5
.Y
-
.Ml
,A)
5
(a)
sin
Z8B.t
=
MI
'1.00.
t25
. (.-l
LUI\S = Stn-,_t00.
'125 '
.
both sides )
(b
)
r..53. I 300
r 53.lo ( to l dp:)
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Let lhe perpendiculardislance frorn A to RS be AX.
.: '
:
Usirrg Pyhagoras theorem,
I
nx
=
Jl lo) -loo)
"
a5.8?5'15
lvt
I
i
7
8
@
(r)
233
234
Ji;}:IT6I
=
^S
|
(c
?5
AB =
75
(a)
A
-
mark =
74
n
io
59
N4l
Therelore perfornrance ofboys in Histoiy is bettet'
AI
than girls.
:-45.825'75
t
a
29.1'142s
(d
x 29.2n (ro 3 sf )
6
,
of boys mark =
Median olgiris
MI
t
=
) Median
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) P ( scoring less than 50 nrarks )
c
u
d
E
8(a) 3+10+E+x+y+2=40
{2,:, s, z}
BI
6J
40
DI
't
2A
tsr
x+Yr17(showh)
(b)
(b)
B
.+o
I
l(x)
+
aQ) + 5(2)
-a
l
l\'1
|
4c
l0+16+3.\+4),r10=92
t0
J>
0(3) + l(10) + 2(S) +
y
n
9
Dl
-
Label
l
a
(c)
3x+4y=56(shovn)
x+yEt1 -.-.------( i
3x+4y-
56-.-----"--( 2
)
)
(l)"3:
Dl -Correctelernents
(c.) tsva' =
{1,2,4,6,8,9, t0}
(d)
\ 7(a)
n(A^B')
=
3
Mode=75
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a
2
.
a
D
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8l
rl3+'?5
a
B]
=?4
3-t+3Y=51-"-""'(3)
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(2)-(3)
dl
-y^r
SubY=5.in(l)
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x=12
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0
t0
$
r
O)
236
e(a) -lx(I7-x)xr
oR
z2
(b
)
It
(l7xl7) -4f-x(t7-;r)xxJ
.?
289
-
2.r(l
7
-
r)
ry{
Bt
=205
Ml
=
2.r-)
(c
.
N,r I
-34.r+84=0
lA(
a)
orx=.J
Al
Ml
9t + 50r
=
2581
(b
)
(ro3s/.)
=
Vol of
- ;l)z(9), (50) * i,r(
J
.
:
=
l' l'
Mass
3"
cone
-
Vol olhemisplcrc
y
n
j)r
4050
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3
-lqn
I332.c
olalurniniurn
=
l
a
.At.
a
D
Z.Z*Clg4.60lals
ilZ98.a2:87g.
=llJ008(ro.rs1;
1416.4.?5342 cmz
n
io
=
r1.z
=
r(9)'?
=
226.1946711 cmz
- ml
-z(3)r
=
*
MI
I
Za,rr
56,54866776 om2
I
= 1436.436342 + 2?6.194671) + 59,5ag65776
=
$0,50
t7t9.l7968lcmr
x
Ml
l'719.17968t
$ 859.s898a0a
- $860
M;
Volume of torch
cost =
=
Al
l/A = JQ.$Q)54
ry50.Bcrr
c
u
d
E
Total
.....'-...-...-......
V,tz =
=
t
a
Toral surlace area
Ml
=ldcrrr
= trxgxJlffl
Curved surface of hemisphcrc
(x-14)=0 or,(x-3)=0
At)
Curyed surface area of cone
Srrrlace arca of base
205
.t'- l7.r+d2=g (shown )
(c) (x-la)(.r-l)=0
.r=14
)
( to nearcst dollar
)
A
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ll
l7
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vi
n
o
i
t
a
c
u
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x
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2
4
2
4
6
poinrs of iniersecr;o6
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i......
t
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g
l
a
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y=3+4r-*
^.'
k
b
)
y
n
(c)
,
a
D
Conccr scale for x and y.axls
Plotring of polnrs
Smooth curve
DI
DI
0r
ongraph
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.(d)..x=0.3and3.?
( acccpt I0, l')
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I
il
ri
....i
'., ..1......t.. . ... t.' ....{
1
N
(
1
.0.3, l.?
)
A
I
and (3.i,5.3) Al
( accept 10. I )
6
(a)2.6
=
d
E
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11
14
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r
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't
197
on
239
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n
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