Sec 4E5NA Prelim EMaths Paper 1 Marking Scheme (Ngee Ann)

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$

+EEA++-E/+0A1-//42## -E' E58+A 9A:E9A:;-# '#6#1E4;9

2##

4

' 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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11

57 'g B1

52 'g B1

B1


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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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: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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14

#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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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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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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Sec 4E5NA Prelim EMaths Paper 1 Marking Scheme (Ngee Ann)