sec 4e5na prelim emaths paper 1 marking scheme (ngee ann)
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8/10/2019 Sec 4E5NA Prelim EMaths Paper 1 Marking Scheme (Ngee Ann)
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8/10/2019 Sec 4E5NA Prelim EMaths Paper 1 Marking Scheme (Ngee Ann)
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3 ' men ta=e # days to compete painting 8 houses. At the end o the 2ndday, # wor=er quit
the >o%. Assuming the wor=ers wor= at the same rate, how many days wi the remaining
wor=ers ta=e in order to compete the >o%?
Answer !!.................................... "2$
4 iven that n
xx
xx=
3
3'
, ind n.
Answer (b) !!.................................... "2$
5 A map is drawn to a scae o # @ 8 .
(a) *ind the distance in centimeters, on the map %etween 2 towns that are '.2 =m apart.
Answer (a) !!................................ cm "#$
(%) iven that a town has an area o 8.28 =m2, ind in square centimeters, the area
representing the area o the town on the map.
Answer (b) !!.............................. cm2 "2$
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' men # days 8 houses' men 2 days # houses# man days # house
3 men3A days # house
9#
3 men 3
A'
days ' houses
oin a specia cu%. *ind the percentage o students who >oin the specia
cu%.
Answer (b) !!!..............................& "#$
(d) 0raw a %oxDandDwhis=er pot to represent the mass distri%ution o the girs.
Answer "2$
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57 'g B1
52 'g B1
B1
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8/10/2019 Sec 4E5NA Prelim EMaths Paper 1 Marking Scheme (Ngee Ann)
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:he irst our terms o a sequence : are :#, :2, :3and :'.
:#< # J 3 < ' < 2K2
:2< # J 3 J 8 < C < 3K3
:3< # J 3 J 8 J 7 < #6 < 'K'
:'< # J 3 J 8 J 7 J C < 28 < 8K8
(a) Brite down the ith term, :8o the sequence in a simiar orm.
Answer (a) :8 < ...................................... "#$
(%) ow many odd num%ers are there rom # to '8?
Answer (b) !.!!................................. "#$
(c) *ind the sum o # J 3 J 8 J 7 J C J ! J '8.
Answer (c) !.!!................................. "#$
(d) Express :nin terms o n.
Answer (d) :n< !................................. "#$
(e) ; :n< #6, ind the vaue o n.
Answer (e) n< !.................................. "#$
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:8
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An attic is a space ound directy %eow the roo o a house.:he diagram %eow shows
the mode o an attic. :he dimensions o the oor are #8m %y 8m and the wa is 2m
high. :he wa is perpendicuar to the oor.
(a) *ind the voume o the attic.
Answer (a) !.!!........................... m3 "2$
(%) *ind the tota interna surace area o the attic.
Answer (b) !.!!........................... m2 "3$
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15m
5m
!m
Volume = 37882#82
#m= [M1][A1]
Le!th o" roo" = m282#8 22 =+ [M1]
Total sur"ace area =262#8
2
#28#882828 m=+++
[M1][A1]
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8/10/2019 Sec 4E5NA Prelim EMaths Paper 1 Marking Scheme (Ngee Ann)
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:he oowing two thermo as=s are geometricay simiar and have capacities o '32 m "
and 2 ".
(a) *ind, in its simpest integer orm, the ratio o the height o the smaer thermo as=
to the height o the arger thermo as=.
Answe
r
(a) !!!......... @ ..................... "#$
(%) :he %ase area o the smaer thermo as= is '8 cm2, ind the %ase area o the arger
thermo as=.
(b) !!.............................. cm2 "2$
(c) iven the height o the arger thermo as= is 32 cm, ind the height o the smaer
thermo as=.
(c) !!!............................ cm "#$
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#28
27
2
'323
==
=
#
$
#
$
%
%
&
&
8
3=
#
$
%
%
ratio = 3 5 !!!!!!B1
28
C
8
3 2
=
=
#
$
A
A
28
C'8=
#A !!!!!B1
C
28'8=
#A
= 125 cm2 !!!!A1
328
3
8
3
32==
$
$ %%
t#us$ #eig#t o) smaller )las' = 19.2 !!!!!!B1
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:he oowing diagram shows the distanceD time graph o an o%>ect.
(a) *ind the speed o the o%>ect in =mh when the time is # minutes.
Answer (a) .......................... =mh "#$
(%) *ind the acceeration o the o%>ect when it was traveing rom oint A to F.
Answer (b) !.................... =mh2 "#$
(c) *ind the average speed o the o%>ect in =mh or the whoe >ourney.
Answer (c) .......................... =mh "#$
(d) /n the axes in the answer space, s=etch the speedDtime graph o the o%>ect or the
same >ourney.
"2$
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#pee$ = %km 2'28.
6= B1
Acceleratio = 0 %m&h2 B1
A'era!e spee$ = %km 3
2#
78.
= B1
#pee$ (%m&h)
Time (mi)
24
12
0 15 5 45
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22 (a) :he oowing s=etch represent the graph o naxy = . Brite down a possi%e vaue
o n.
Answer (a) n ' ........................... "#$
(%) (i) -=etch the graph o ( )22C += xy .
Answer(%)(i)
"2$
(%) (ii)Brite down the equation o the ine o symmetry o the curve.
"2$
Answer (b)(ii) (!!! , !! ) "#$
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x
y
n= 1 !!!!!!B1
x = 1 !!!!!!B1(c *#a+e !!B1
,ssential +oints
es+ (2$ 9 any!interce+t !!!!!B1
y
x
(2$ 9
5
3 1
x= 2 !!!!!!B1
Answer (b) (ii) ........................... "#$
Answer (b) !!........................... "#$
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8/10/2019 Sec 4E5NA Prelim EMaths Paper 1 Marking Scheme (Ngee Ann)
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23
;n the diagram, =() p, =(* q, ()*+ 2= and )*)$3
#= .
(a) Express each o the oowing in terms opand q$
(i) ,($
Answe
r
(a) (i) !!................................. "#$
(ii) (+
Answe
r
(a) (ii) !................................. "#$
(%) Bhat can you deduce a%out , $and+? -tate a reason or your answer.
Answer (b) !!......................................................................................................
!!......................................................................................................
!!...................................................................................................... "#$
(c) *ind()+*
()*
oarea
oarea
Answe
r
(c) !!!................................. "#$
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p
q
O
P
S
Q
R
( ) ,--,-)*-)$()($3#
32
3#
3# +=+=+=+=
F#
-,(),*+(*(+ 22 +=+=+=F#
, $and+are coinear
-ince ( ) (+,-($3
#2
3
#=+=
F#
3
#
oarea
oarea=
()+*
()*
F#
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8/10/2019 Sec 4E5NA Prelim EMaths Paper 1 Marking Scheme (Ngee Ann)
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24 /n the ine %eow, mar= and a%e pointBsuch that it is 7 cm rom pointA.
(a) 0raw the ineBC$ such that oABC 8= .
(%) iven that pointDis equidistant rom inesAB andBC, and that it is aso
equidistant rom pointsAandB, measure the distanceBD. "3$
Answer (a) and (%) "#$ , "2$
(a) orrect ange F#
(%) onstruction o ange %isector F#
onstruction o perpendicuar %isector F#
9easurement o F0 F#
Answe
r
(b) BD< ............................. cm "#$
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A
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End o aper
#(a) #2.7& (%)
400
47 #8
2(a) 832
3
(%) 3
3
3
2#)
or ## days
'
3
#7=n
#628
'
3# +
8
(a) .' cm (%) .2#cm
2 #7 (a) 87 (%) 82
(c)
6(a)
sm 3#33 (%) #.2 miiseconds # (a) 6 x 6 (%) 23 (c) 82C
(d) :n< ( nJ #)2 (e) 3C
7
(a) g
kT = (%) 2C.3&
#C (a) 78 (%) 6
)72)(32( yy 2 (a) 3 @ 8 (%) #28 (c) #C.2
CC
3
#2
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