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9
BEATTY SECONDARY SCHOOL
MID-YEAR EXAMINATION 2017
SUBJECT:
Mathematics
LEVEL:
PAPER:
2
DURATION: 1 hour 30 minutes
SETTER:
Mr Alvin Lim
DATE:
.s
g
12 May 2017
NAME:
REG NO:
ut
Additional Materials: Writing paper
or
CLASS:
Sec 1 Express
READ THESE INSTRUCTIONS FIRST
ile
T
Write your name, class and index number in the spaces on the top of this page.
Write in dark blue or black pen.
You may use a pencil for any diagrams or graphs.
Do not use staples, paper clips, highlighters, glue or correction fluid.
Answer all questions.
S
m
If working is needed for any question, it must be shown with the answer.
Omission of essential working will result in loss of marks.
You are expected to use a scientific calculator to evaluate explicit numerical expressions.
If the degree of accuracy is not specified in the question, and if the answer is not exact, give
the answer to
three significant figures. Give answers in degrees to one decimal place.
For S , use either your calculator value or 3.142, unless the question requires the answer in
terms of S .
The number of marks is given in brackets [ ] at the end of each question or part question.
The total number of marks for this paper is 50.
For Examiner’s Use
50
This paper consists of 4 printed pages (including this cover page)
Answer all the questions
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[Turn over
10
2
1
The numbers A, B and C, written as the products of their prime factors, are given below.
A 22 u 34 u 52
B
24 u 36 u 52
C
37 u 52 u 7
Giving your answers in index notation, find
[1]
(b)
the lowest common multiple of A and C,
[1]
(c)
the square root of B.
.s
g
the highest common factor of A and B,
[1]
or
The local time of Rio de Janeiro in Brazil and that of Singapore is GMT 3 and
GMT 8 respectively. The World Cup soccer final game is played at 16 00 on 13 July
in Rio de Janeiro.
Find the local time and date in Singapore when the soccer game is played.
(b)
It takes 30 hours to travel from Singapore to Rio de Janeiro. Mr Beatty
departs from Singapore on 12 July at 17 00 to Rio de Janeiro. Find out if he is
in time to watch the soccer game.
[2]
ut
(a)
[1]
5
[3]
The smallest of three consecutive odd numbers is x.
S
4
11
1
of the audience were students, of the remainder
15
4
were parents and the rest were teachers, What fraction were teachers?
At the school Sports Day,
m
3
ile
T
2
(a)
(a)
Express the sum of the three consecutive odd numbers in terms of x.
[1]
(b)
Find the largest number if the sum is 321.
[2]
(a) Without using a calculator, express
(b)
5
as a recurring decimal.
18
Find the fraction that is exactly halfway between
In its simplest form.
4
4
and . Give your answer
5
6
[2]
[2]
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11
3
6
The salary of a car salesman with Company A includes a fixed monthly amount of
$1 250 and an additional $650 for every car that he sells.
Another car sales salesman with Company B does not have a fixed component in his
salary and is paid $875 for every car that he sells.
In a particular month, both salesmen sold n cars.
[1]
(b)
Express, in terms of n, the monthly salary of the salesman with company B.
[1]
(c)
If both of them sold 6 cars in a particular month, deduce which company’s
salary package is more attractive.
[3]
.s
g
Express, in terms of n, the monthly salary of the salesman with company A.
In the figure, angle ABG
such that BG //CD .
39q , angle FED 152q , AC //EF and B is a point on AC
or
7
(a)
B
A
ut
C
G
T
D
E
ile
F
Giving your reasons, find
[2]
(b)
acute angle CDE,
[3]
(a)
A school has both primary and secondary sections. The bell of the primary
section goes off every 30 minutes while the bell of the secondary section goes
off every 35 minutes. The first bell at both primary and secondary sections
goes off at 07 30.
m
reflex angle ACD,
S
8
(a)
When will the bells of both schools next go off at the same time?
(b)
[3]
Amy wants to pack 56 apples, 72 bananas and 104 cherries into as many fruit
Bags as possible without leaving any fruit unpacked. Every fruit bag must
contain the same number of apples, bananas and cherries.
Find
(i)
the greatest number of fruit bags that can be packed,
(ii) the number of cherries in each fruit bag.
[3]
[1]
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12
4
Express
(b)
Simplify 4a 3b 8 ª¬3 a b 2 º¼ .
[3]
(c)
(i)
Factorise ax ya .
[1]
(ii)
Hence, without the use of a calculator, find the value of
321u 37 27 u 321
[1]
.s
g
Solve
(a)
x3
(b)
2
2x 5
(c)
3x x 1
5.
5
3
[3]
or
661 4 9 x3 ,
3
,
5 x
[3]
[3]
[3]
T
10
x4 x
x as a single fraction.
6
9
(a)
ut
9
S
m
ile
End of Paper
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13
.s
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S
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14
BEATTY SECONDARY SCHOOL
MID-YEAR EXAMINATION 2017
SUBJECT:
Mathematics
LEVEL:
PAPER:
1
DURATION: 1 hour 15 minutes
SETTER:
Mr Alvin Lim
DATE:
.s
g
11 May 2017
NAME:
RE NO
REG
NO:
READ THESE INSTRUCTIONS FIRST
or
CLASS:
Sec 1 Express
T
ut
top
page.
Write your name, class and index number in the spaces oon
n the
the tto
th
op of
of tthis
hiiiss pa
h
page
ge..
ge
Write in dark blue or black pen.
You may use a pencil for any diagrams or graphs.
Do not use staples, paper clips, highlighters, glue or correct
correction
c ion fluid.
Answer all questions on the question paper.
m
ile
If working is needed for any question, it m
must
shown
with
ust be
us
b sho
hown
wn w
ith
it
h th
tthee answer.
Omission of essential working will result
marks.
resul
ultt in lloss
osss of m
arks
ar
k.
You are expected to use a scientific calculator
callcu
cula
lato
torr to eevaluate
valu
va
luat
ate explicit numerical expressions.
fied
ed in
n th
thee qu
ques
esti
tion
on, and if the answer is not exact, give
If the degree of accuracy is not specifi
specified
question,
a swer to three significant
an
sign
g ificant figure
es.
s G
ive answers in degrees to one decimal place.
iv
the answer
figures.
Give
our calculator
calc
lculator
or vvalue
alue
al
ue oorr 3.142,
3 142, unless the question requires the answer in
3.
For S , use either yyour
terms of S .
S
The number off m
marks
arks
ar
ks iiss gi
give
given
en in bbrackets
rackets [ ] at the end of each question or part question.
ber ooff m
arrks ffor
o this paper is 50.
or
The total numb
number
marks
For Examiner’s Use
50
This paper consists of 7 printed pages (including this cover page).
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15
2
For
Examiner's
Use
Answer all the questions.
1
For
Examiner's
Use
Evaluate the following.
(a)
$11.30 26¢ $2.75
(b) 10 3 8 5
$8.81 [B1]
Answer (a) $ ………………… [1]
2
Evaluate
.s
g
1
[B1]
b ……………………… [1]
(b)
0.8562
. Give your answer correct to
8.593 13.89
or
(a) 3 decimal places,
ut
(b) 3 significant figures.
0.038
0.
0
.03
38 [B
[B1]
B1]
Answer
Answe
weer (a)
w
((a
a) ……………………
……
………
…………
………
… [1]
T
The numbers a, b, c and d are represented
represe
s nt
nted on a number
numb
nu
mber
er lline.
ine.
ile
3
0
.03
0381 [B1
B1]
B1
0.0381
[B1]
(b) ……………………
……
………
……………… [1]
S
m
< <
2
3.14
14, 3 .
It is given tha
that
at th
the
he nu
numberss ar
aree S , 1 , 33.14,
3
Find a, b, c aand
nd dd..
4
2
3
1
3 , c
A
Answer
nswer a ……… , b ………
< <
3.14
……… , and d
S [B2] (2 correct, 1 mark)
……… [2]
By writing each number correct to 1 significant place, estimate the value of
59.4 u 0.493
. Show your working clearly.
2.16
59.4 u 0.493
2.16
60 u 0.5
2
15
[M1]
[A1]
Answer ……………………… [2]
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16
3
For
Examiner's
Use
5
It is given that x
(a)
5y 2 xy 3 ,
(b)
x y
.
y x
4 and y
2
(a)
5 u 3 4 u 3
3
3 . Evaluate
5 u 9 4 u 27
153
Answer (a) …………………… [1]
[B1]
b ……………………… [1]
(b)
Factorise the following.
(a)
4m 4n
or
6
4 3
3 4
1
2
12
[B1]
.s
g
4 3
3 4
(b)
For
Examiner's
Use
ut
(b) 15ax 20ay 10a
4 mn
[ 1]
Answe
wer (a)
we
(a) ……………………
(a
……
………
…………
………
… [1]
Answer
9
2x 5
3.
T
Solve
ile
7
5a…3……
x…
4……………
y 2 [ B1][1]
b ……
[
………………………
(b)
9
3
2x 5
9 3 2x 5
[M1]
m
9 6 x 15
1
6 x 24
2
4
[A1
[A1]
A11]
A
S
x
8
Answer x
………………… [2]
(a) The nu
nnumber
mber of students in Beatty Secondary School is 1300 correct to the
nearest hundred.
d
Write down the least possible number of students in the
school.
school
(b) Without using a calculator, estimate the value of
working clearly.
(a)
1250
(b)
98
100
|
20.019
20
10 1
20 2
98
. Show your
20.019
[B1]
[M1]
Answer (a) ……………………… [1]
[A1]
(b) ……………………… [2]
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[Turn over
17
4
For
Examiner's
Use
9
In the figure, three straight lines intersect at a point. Giving your reasons clearly,
find the values of
For
Examiner's
Use
(a) x,
(b) y.
x 52q (vert opp ‘s)
[ A1]
(b)
[M 1]
x y 2 y 10q 180q (adj ‘s on a str line)
52q 3 y 10q 180q
3 y 180q 42q
138q
[A1]
y 46q
Answer (a) x ……
…………………
…………
………… [1
[[1]]
or
.s
g
(a)
(b)
b) y
Consider the following numbers.
List down all the
3
<
1 S
2, 42 , 27, 29, 0.7, 3.21, 1 ,
6 2
T
0,
ut
10
…………………
…
……
……
…………
… [2]
ile
(a) irrational number(s),
(b) composite
comp
m osite number(s).
(c) integer(s)
m
0, 42 , 27, 29 [B2] [2]
(c) ………………………
S
11
S
2,
[B1]
2
Answer (a) …………………… [1]
27, 42
[B1]
(b)
b ……………………… [1]
3
Express the
th
he following word statements algebraically in their simplest form.
(a) Subtract
b.
S btract a from the cube
c be of b
(b) Divide the product of 2c and 3 by the square root of d.
(c) Multiply 3f to the sum of 4f and 5f.
(a)
(b)
(c )
b3 a
6c
d
3f u 4 f 5f
[B1]
Answer (a) …………………… [1]
[B1]
(b) ……………………… [1]
[M1]
(c) ……………………… [2]
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3 f u9 f
27 f 2
18
5
For
Examiner's
Use
12
(a) Simplify
2x 1 x
.
3
12
For
Examiner's
Use
(b) Expand and simplify 3 2 x 3 4 x 1 .
(b)
4 2x 1
x
12
12
8x 4 x
12
12
7x 4
12
3 2x 3 4 x 1
[M1]
[A1]
.s
g
2x 1 x
3
12
(a)
6 x 9 4 x 4 [M1]
[A1]
or
10 x 13
(b)
((b
b) ………………………
……………
……
…
…… ……
……… [2]
(a) Express 60 and 72 as thee product of their prim
prime
i e ffactors.
T
13
ut
Answerr (a)
((a
a) ……………………
……
…
……………
… …… [2]
(b) Find the lowest common multiple of 60 and 72.
72
2.
which
Find the smallest positive
ve iinteger
nteg
nt
eger
er n fo
forr wh
whic
ichh
m
(d)
ile
(c) Write down the smallest po
ppositive
sitiive
v iinteger,
nteg
ger, m,
m, su
such
ch tthat
hat 60m is a perfect
square.
60 22 u 3 u 5
60
[B1]
[B
B1]
1]
72 23 u 32
72
[B1]
[[B
B1]
(b)
23 u 32 u 5 3360
60
[B1]
(c )
3 u 5 15
[B1]
(d )
n 32
[B1]
S
(a)
9
72
is a perfect cube.
n
Answer (a) 60
………………… [1]
72 ………………… [1]
(b) ……………………… [1]
(c) m
………………… [1]
(d) n
………………… [1]
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[Turn over
19
6
For
Examiner's
Use
14
The diagram shows a rectangle ABCD with a square PBQR of side x cm
removed. It is given that AP 3 cm and QC 4 cm.
A
3
P
B
R
Q
For
Examiner's
Use
D
.s
g
4
C
S
(a) Find, in terms of x, an expression for the area of the rectanglee RQCS.
RQCS
CS.
or
rectangle
(b) Find, in terms of x, an expression for the area of the rec
cta
tang
ngle
le APSD.
APSD
AP
SD.
rectangle
RQCS.
The area of the rectangle APSD is twice the area of the re
ect
c an
ng
glle R
QCS
CS.
ut
(c) Form an equation in x and solve it.
(d) Hence find the area of the rectangle APSD.
Area of rectangle RQCS
4u x
T
(a)
(b)
S
(d )
[A
[A1]
A1]
Area off re
rrectangle
ccttan
a gl
gle APSD 3 u 4 x
Area
S
Areea of
of the APSD
m
(c )
ile
4 x cm
cm 2
12 3 x ccm
m2
[A1] o.e.
2 u Area of RQCS
12
12 3 x 2 u 4 x
12
12 3 x 8 x
5 x 12
x 2.4
[M1]
[A1]
Area of rectangle APSD 12 3 2.4
19.2 cm
[A1]
Answer (a) ………………… cm2 [1]
(b) ………………… cm2 [1]
(c) x
………………… [2]
(d) …………………… cm2 [1]
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20
7
For
Examiner's
Use
15
(a) Construct a triangle ABC such that AC
AB has already been drawn.
8 cm and angle ABC
50q .
[2]
For
Examiner's
Use
(b) Measure and write down the angle BCA.
(c) Construct the angle bisector of angle BAC.
[1]
(d) Construct the perpendicular bisector of AB.
[1]
The bisectors in (c) and (d) intersect at the point X.
((e)) Label the ppoint X.
.s
g
(f)
[1]
[ ]
Construct a circle with centre X and which passes through A and
nd B.
B.
or
(g) Write down the radius of the circle.
[1]
S
m
ile
T
ut
Answer (a), (c), (d), (e), (f)
B
A
(b) ………………… q [1]
(g) ……………… cm [1]
End of Paper
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[Turn over
21
6
Paper 2 Solutions
4(a) x x 2 x 4
1(a) HCF 22 u 34 u 52
(b) LCM 22 u 37 u 52 u 7
(c) Square root of B 22 u 33 u 5
[B1]
[B1]
[B1]
(b) 3 x 6 321
3 x 315
Rio
io de Janeiro 16 00, 13 July
1600
600 1100
110 2700
0.277
5(a) 18 50
36
T
Reached
eached Rio de Janeiro at Singapore
a
time:
2 July at 17 00 + 1day 6h = 13 July 2300
12
OR
R
Reached
eached Rio de Janeiro at Rio de Janeiro time:
13
3 July 2300 – 1100 = 13 July 1200
m
ile
[A2]
A2]
? he is in time to watch the soccer game. [A
S
Fraction
n that were parents
1
1 4
u
4 1155
1
=
15
4 1
Fraction that were teachers
15 15
3
=
15
1
=
5
4
15
[A1]
[M1]
[M
140
14
40
126
1
12
26
1140
40
40
1126
26
6
14
ut
(b) Flight
ight time = 30h = 1day 6h
=
x4
105 4
109
or
[A1]
? Singapore 0300, 14July
par
arents
Fractionn that were teachers & parents
[M1]
.s
g
2(a) Time difference = 8+3 = 11 hours
2700
700 2400 0300 1
[B1]
x 105
Largest number
3
3x 6
5
1188
<
0.2
0.2 7
[A1]
[A
§4 4·
(b)) ¨ ¸ y 2
(b
©5 6¹
11
15
[M
[M1]
[A
[A1]
111
[M1]
[M1
M ]
15
6(a) $ 1 250 650n
[M1]
[B1]
[B
(b) $875n
(c) $ 1 250 650 u 6
$875 u 6 $5 250
[B1]
[B
$5150
Company B, $5 250>$ 5150
[M1]
[M1]
[A1]
[A1]
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22
7(a) ‘BCD 39q corr. ‘s
[M1]
7
9(a)
Reflex ‘ACD 360q 39q ‘s at a point
321q
(b)
[A1]
B
C
Z
A
D
G
E
F
raw line ZD // to FE
E and CA.
Draw
[M1]
‘EDZ
180q 152q int ‘s
[M1]
‘CDE
28q
39q 28q 67q
[A1]
[A1]
[M1]
[M
4a 3b 8 3a 3b 2
a6
[M1]
[M
[A1]
[A
(c)(i) ax ya
a x y
or
39q alt. ‘s
[M1]
4a 3b 8 ª¬3 a b 2 º¼
4a 3b 8 >3a 3b 2@
[B1]
[B
(ii) 321u 337 227
7 u 321
321 32
321
21 37 27
ut
‘CDZ
[M1]
.s
g
(b)
x4 x
x
6
9
3 u x 4 2 u x 18 x
18
18
18
3x 12 2 x 18 x
=
18
12 13 x
18
21u10
=321
=321
2100
=3210
[A
[A1]
300 2 u 3 u 5
355 5 u 7
CM 2 u 3 u 5 u 7
LCM
210
[M1]
23
8
(ii) No. of cherries 104 y 8 13
661
6 1 36 4 x3
66
3
625
6
3
[M1]
[M1]
125
5
(b)
[M1]
[M1]
[A1
[A
1]
[A1]
2
3
2x 5 5 x
2 5 x 3 2x 5
[M2]
10 2 x 6 x 15
8 x 25
8
1
x 3
8
722 23 u 32
HCF
x3
x
(b)(i) 566 23 u 7
104=2
04=23 u13
661
66 4 9 x3
5x
S
077 30 03 30
11 00
x3
125
1
5
x3 12
3h30 min
m
10 min
210
ile
8(a)
T
10(a)
(c)
[A1]
[A1]
[A1]
[M1]
[M1]
[A1]
3x x 1
5
5
3
3 u 3 x 5 x 1 75
[M1]
15
15
15
9 x 5x 5
75
15
15
15
9 x 5 x 5 75
[M1]
4 x 80
xNeed
20 a home tutor? Visit smiletutor.sg
[A1]
[Turn over
23
.s
g
or
ut
T
ile
m
S
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24
1
Calculator Model:
Name:
Class
Class Register Number
.s
g
Parent’s Signature
Writing paper
or
Additional Materials:
3 May 2017
2 hours
ut
Mathematics
MID – YEAR EXAMINATION 2017
SECONDARY 1
READ THESE INSTRUCTIONS FIRST
T
Do not open this booklet until you are told to do so.
ile
Write your name, class and index number on all the work you hand in.
Write in dark blue or black pen on both sides of the paper.
You may use a pencil for any diagrams, graphs or rough working.
Do not use highlighters or correction fluid.
Answer all questions in Sections A and B.
S
m
If working is needed for any question it must be shown with the answer.
Omission of essential working will result in loss of marks.
The use of an approved scientific calculator is expected, where appropriate.
If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to
three significant figures. Give answers in degrees to one decimal place.
For S , use either your calculator value or 3.142, unless the question requires the answer in terms of S .
At the end of the examination, fasten all your work securely together.
The number of marks is given in brackets [ ] at the end of each question or part question.
The total number of marks for this paper is 80.
Section A : Answer the questions in the space provided.
Section B : Answer the questions on the writing paper provided.
For Examiner’s Use
Section A
/ 40
Section B
Total
/ 40
/ 80
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2017 Mid-Year Examination/S1/Mathematics
113
2
Section A: Answer all the questions.
1
Round 0.999 to 2 significant figures.
Answer: ……...….…...........………..…. [1]
(b)
Write your answer to part (a), correct to 3 significant figures.
.s
g
(a)
ut
or
2
0.42153
Calculate 3
. Truncate your answer to 6 decimal places.
645 3.5
(b) ….……………..…….….…… [1]
ile
Find 3 1728 by using prime factorisation.
S
m
3
T
Answer: (a) …..…………..……….....…… [1]
Answer: ……...….…...........……….……. [3]
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3
4
(a)
Express 90 as a product of its prime factors, giving your answer in index
notation.
(b)
ut
or
.s
g
Find the smallest possible value of n such that 90n is a perfect cube.
Answer: 90 =…..………………….....…… [1]
T
ile
Consider the following numbers :
5
S
0, 4, 3 27,
, 5, .
4
3
(a) Write down the
(i)
irrational numbers,
(ii)
positive integers,
m
5
n = ….…………..…….….…… [1]
S
(iii) prime numbers.
(b)
Represent all the numbers on the number line below.
Answer: (a)(i)..…………………………....……….. [1]
(a)(ii).................………………………….. [1]
(a)(iii)................………………………….. [1]
(b)
6
5
4
3
2
1
0
1
2
3
4
5
6
[2]
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4
(a)
Express 125 g as a percentage of 5 kg.
(b)
Find the value of 4.5 % of $8.
or
.s
g
6
ut
Answer: (a) …..……………….....…… % [2]
(b) $ ….…………..…….….…… [2]
3
Evaluate, without the use of a calculator, ª8 4 º > 2(12 3) y 3@ , showing all
¬
¼
T
7
S
m
ile
your working clearly.
Answer: ……..…............................…….… [3]
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116
5
Simplify the following
(a)
x(2 x 3) 7(3x 1) ,
(b)
5a u (2b) u 3 125a3 .
ut
or
.s
g
8
Answer: (a) ..….……….………....……… [2]
(b) ..….…………..…………….... [2]
(a)
15a 2b 6ac ,
(2v w)( p 1) 2w( p 1) .
S
m
(b)
T
Factorise the following expressions
ile
9
Answer: (a) ….……….……….....……… [1]
(b) ..….………………....……… [2]
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6
Given that a 3 , b 2 and c
(a)
2a 3c ,
(b)
ab 2 3a
.
c
1
, evaluate
2
or
.s
g
10
ut
Answer: (a) ….……………..…………… [2]
(b) ..….…………..…......……… [2]
A train 320 m long passes through a tunnel 5.2 km long.
T
11
ile
The average speed of the train is 28 km/h.
(a) Convert 28 km/h into m/s.
(b) Calculate the time taken for the train to pass completely through the tunnel.
S
m
Give your answer in minutes.
Answer: (a) …..…………….......…… m/s [1]
(b) ………………..…….….. min [3]
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7
12
A factory produces a type of baking powder made with baking soda, cream of tartar
and cornstarch. The amount of baking soda, cream of tartar and cornstarch are in the
ratio of 7 : 3 : 4 respectively.
(a)
In a small bag of baking powder, there are 60g of cornstarch.
What is the weight of the baking powder in the small bag?
(b) Bags of baking powder are filled at a rate of 180g per second.
.s
g
How many bags of baking powder weighing 1.5 kg each can be filled in
S
m
ile
T
ut
or
3.5 hours?
Answer: (a) …..……………….......…… g [2]
(b) ……………….…….….. bags [3]
End of Section A
2017 Mid-Year Examination/S1/Mathematics
119
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8
Section B: Answer all the questions.
(a)
Write down an algebraic expression for each of the following statements.
(i)
2 y 3[ x 4( x y)] ,
(ii)
3n m 2n m
.
4
5
[2]
If a : b = 5 : 4 and b : c = 4.2 : 0.65 , find a : c.
store. What is the original price of the shoes?
[2]
ile
[2]
Marcus wants to change 600 Singapore Dollars (S$) to Thai Baht (THB).
m
15
[3]
Joey paid $28.80 for a pair of shoes after a discount of 25% from a departmental
T
14
(i)
ut
(c)
Simplify the following.
or
(b)
[2]
Subtract 5x 3 from 3x 2 5 .
.s
g
13
The exchange rate is S$1 = 24.72 THB.
(a)
Find the amount of Thai Baht (THB) Marcus will receive if he changes 600
[1]
S
Singapore Dollars (S$).
(b)
The money changer is only able to change amounts in multiples of 1000 THB.
The money changer decides to round up the amount in (a) to the nearest 1000
THB.
Find the amount in S$ that Marcus needs to top up for the extra amount, giving
[3]
your answer to the nearest cent.
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120
9
16
One pen costs x cents. An eraser costs 30 cents less than a pen and a ruler costs
two-third of a pen.
Find a simplified expression for
[1]
(i)
the cost of an eraser in cent,
(ii)
the total cost of an examination goodie pack consisting of 3 pens, 1 eraser and
1
x,
5
(a)
1
(b)
2(5 y 3) 2 y 14 .
ut
1
x
2
or
Solve the equations:
[2]
[2]
[2]
18
ile
T
17
.s
g
2 rulers in cent.
Susan cycles from home to a coffeeshop to purchase dinner before continuing the
journey to her grandmother’s place.
m
Susan cycled at a speed of 4 m/s to the coffeeshop for 3 minutes, took another 10
minutes to buy dinner and continued the rest of the journey to her grandmother’s
house at a speed of 6 m/s. Given that the total distance travelled is 4500 m,
find the distance between Susan’s house and the coffeeshop.
[1]
(b)
Find the average speed for the whole journey in m/s.
[3]
S
(a)
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121
10
19
(a)
Mr Lee was paid a monthly basic salary of $3 850 since January 2015.
At the end of 2015, he was given a bonus of 13.5% of the value of sales that he
has made during the year. If the total value of his sales in 2015 was
$300 000, calculate Mr Lee’s total income in 2015.
(b)
[2]
Mr Lee has to pay income tax in January 2016 for the annual income earned in
.s
g
2015. The relief amount that will not be subjected to income tax is shown in
the table below.
Amount
Personal relief
$1000
or
Type of relief
Child relief
$5000 each child
$17 340
Voluntary donation
Three times the amount donated
ut
CPF
T
Mr Lee has only one child and he has been making voluntary donation of $50
every month to an approved organization. The gross tax payable for the first
ile
$40 000 is $550 and the tax rate for the rest is 7%. Calculate his income tax
payable for 2015 using the information given above.
In January 2016, Mr Lee’s basic monthly basic salary was cut by $200.
m
(c)
[3]
(i)
Calculate the percentage decrease in the basic monthly salary from 2015
S
to 2016, giving your answer to three significant figures.
(ii)
[2]
In 2016, he was paid a bonus of 15.5% of the value of his sales that he
has made during the year. Given that his bonus in 2016 is $33 790,
calculate the total value of his sales in 2016.
[2]
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11
20
Kale ordered one set meal at $55.60 and an ice cream for $12.90 at a restaurant.
Below shows Kale’s bill before payment.
$55.60
Ice cream
$12.90
SUBTOTAL
$68.50
10% Service Charge
$6.85
7% Goods and Services
Tax (GST)
.s
g
1 set meal
$5.27
or
Currently, the restaurant is offering two discount packages that Kale can choose
Discount Package I:
ut
from.
Enjoys 10% off the subtotal of the bill, which is thereafter subjected to 10% Service
T
Charge first and then 7% GST.
ile
Discount Package II:
There is no service charge and the subtotal is subjected to 7% GST.
Explain, showing all necessary working, which discount package is a better option
[5]
S
m
for Kale.
~ End of Paper ~
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12
S
m
ile
T
ut
or
.s
g
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Calculator Model:
Name:
Class
Class Register Number
.s
g
Parent’s Signature
MID – YEAR EXAMINATION 2017
SECONDARY 1
Wednesday,
Wedn
We
dnesda
ay, 3 Ma
May
y 2017
Writing paper
2 hours
ut
Additional Materials:
or
Mathematics
READ THESE INSTRUCTIONS FIRST
Do not open this booklet until you are told to do so.
ile
T
Write your name, class and index number on all the work you hand in.
Write in dark blue or black pen on both sides of the paper.
You may use a pencil for any diagrams, graph
phs
s or rough
rou
ugh
g working.
working
ng.
graphs
Do not use highlighters or correction fluid.
Answer all questions in Sections A and B.
S
m
If working is needed for any question it must
musst be
b shown
sho
h wn with
witith
h the
th
he answer.
Omission of essential working
g will result in
n lloss
oss of marks.
os
The use of an approved sci
scientific
cien
e ti
tifi
f c calcul
calculator
ulat
ator
or is
s ex
expe
expected,
p cted, where appropriate.
If the degree of accuracy
accurac
acyy is not
not
o specified
spe
eci
cifi
fied
ed in
in the
the question, and if the answer is not exact, give the answer to
three significant figures.
figure
es.
s Give
Giv
i e answers
an
nsw
swer
e s in degrees
deg
egrees to one decimal place.
For S , use either your calcul
calculator
ulat
ator
or vvalue
a ue o
al
orr 3.142, unless the question requires the answer in terms of S .
At the end of the ex
exam
examination,
amin
inat
a ion,
n, ffasten
aste
as
t n all your work securely together.
The number of mark
marks
rkss is given
givven in brackets [ ] at the end of each question or part question.
The total number of ma
mark
rkss fo
fforr this paper is 80.
marks
Section A : Answer the questions in the space provided.
Section B : Answer the questions on the writing paper provided.
For Examiner’s Use
Section A
Section B
Total
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125
2
Section A: Answer all the questions.
1
Round 0.999 to 2 significant figures.
Answer: 1.0 [1]
0.42153
. Truncate your answer to 6 decimal places.
3
645 3.5
(b) Write your answer to part (a), correct to 3 significant figures.
2
0.42153
3
645 3.5
3
0.014568
= 0.0146 (to 3 s.f.)
or
(b)
0.42153
3
645 3.5
0.014568 (truncated to 6 d.p.)
An
nsswe
w r : (a)
(a
a) 0.014568
0.01
0145
4568 [1]
Answer
ut
(a)
.s
g
(a) Calculate
(b)) 0.
(b
0.01
0.0146
0146 [1]
1728
864
432
216
108
54
27
9
3
1
3
26 u 33
1728
3
26 u 33
Answer: 12 [3]
S
4
1728
22 u 3
12
m
ile
2
2
2
2
2
2
3
3
3
T
Find 3 1728 by using prime factorisation.
(a) Express
Expres
esss 90 as
as a product of its prime factors, giving your answer index notation.
(b) Find thee smallest
sma
m llest possible value of n such that 90n is a perfect cube.
2
3
3
5
90n
n
90
45
15
5
1
90 2 u 32 u 5
23 u 33 u 53
2 2 u 3 u 52
Answer: 90 2 u 32 u 5 [1]
n 300
n=
2017 Mid-Year Examination/S1/Mathematics
300 [1]
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3
5
Consider the following numbers :
0,
4,
3
27,
(a) Write down the
5
S
, 5,
4
3
(i) irrational numbers,
.s
g
(ii) positive integers,
(iii) prime numbers.
(b) Represent all the numbers on the number line below.
(b)
6
5
4
T
ut
or
An
Answ
swer
er:: (a)(i)
(a)(i
(i))
Answer:
3 2
27
0
0
S
4
1
2
4
3
5
3
4
4,, 5 [1]
4
(a)(ii)
(a)(
)(ii
ii))
(a)(iii)
(a)(
(a
)(ii
iiii) 4
4,, 5 [1]
5
5
6
[2]
(a) Express 125 g as a percentage off 5 kg
kg.
(b) Find the value of 4.5% of $8..
125
u
u10
100%
10
00% 2.5%
%
5000
0
m
6
1
ile
3
5 S
[1]
,
3 4
(a)
4..5
4.5
$8 $0.36
$0.36
6
u $8
100
10
00
S
(b)
Answer : (a) 2.5 % [2]
(b) $0.36 [2]
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4
7
3
Evaluate, without the use of a calculator, ª8 4 º > 2(12 3) y 3@ , showing all your
¬
¼
workings clearly.
ª8 4 3 º > 2(12 3) y 3@ [8 (64)] [2(15) y 3]
¬
¼
[8 64] [30 y 3]
56 (10)
56 10
Answer : -46 [3]
Simplify
x(2 x 3) 7(3x 1) ,
(a) x(2
(b)
5a u (2b) u 3 125
125a
a3 .
or
8
.s
g
46
(a) x(2 x 3) 7(3x 1) 2 x 2 3x 21x 7
(b) 5a u (2b) u 3 125a3
ut
2 x 2 18 x 7
5a u ( 2b) u ( 5a)
T
50a 2b
ile
2
Answer
A
nswer : (a) 2 x 18x 7 [2]
(b) 50a 2b [2]
m
9 Factorise the following expression
expressions
ns
2
(a) 15
15a
a b 6ac ,
(b)
(2v w))(( p 1
1)) 2w( p 1
1)) .
S
(a) 15a 2b 6ac
3a((5
5ab 2c)
(b) (2v w)(
)( p 1)
1) 2w( p 1)
1 ( p 1)(2
1 2v w 2w)
( p 1)(2
1 2v w)
Answer : (a) 3a(5ab 2c) [1]
(b) (p+1)(2v+w) [2]
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128
5
10 Given that a 3 , b 2 and c
(a)
2a 3c ,
(b)
ab 2 3a
.
c
1
, evaluate
2
or
ut
3(2) 2 3(3)
1
2
12 9
1
2
3u 2
6
ile
T
ab 2 3a
(b)
c
.s
g
1
2(3) 3( )
2
3
6
2
1
4 or 4.5
2
(a) 2a 3c
1
4 or 4.5
Answer : (a) 2
[2]
m
(b)
11
6
[2]
S
A train 320 m long
lon passes
passe
sess th
thro
through
roug
ugh
h a tunnel 5.2 km long.
The average speed of tthe
he ttrain
rain
ra
in is 28 km/h.
Convert
(a) Con
nve
vert
rt 28
8 kkm/h
m h in
m/
into
to m/s.
Calculate
(b) Calc
lcul
ulat
atee th
thee ti
time
me taken for the train to pass completely through the tunnel.
answer
Givee yyour
our an
ou
answ
swer in minutes.
a)
28km
1h
28 u1000m
1u 3600 s
28000m
3600 s
7
7 m/s
9
b) Total length of the tunnel and train = 5.2km + 0.32 km
= 5.52 km
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129
6
5.52
28
69
=
h
350
Time taken =
Time taken in minutes = 11.8 min (3 s.f) or 11
29
min
35
(b)11.8 or 11
29
min [3]
35
A factory produces a type of baking powder made with with baking soda,
sod
oda, cream
ream of
cre
tartar and cornstarch. The amount of baking soda, cream of tartar and
and cornstarch
corn
rnst
staarch are in
the ratio of 7 : 3 : 4 respectively.
(a) In a small bag of baking powder, there are 60g of corn
nst
star
arch
ch.
cornstarch.
bag?
What is the weight of the baking powder in the smalll b
ba
ag
g??
(b) Bags of baking powder are filled at a rate of 180g
0gg pper
eerr ssecond.
eco
ec
on
nd
d..
1.5
.5 kkgg each
How many bags of baking powder weighing
g1
eac
ach can
ccaan be ffilled
ille
il
led
le
d in
3.5 hours?
ut
or
12
7
m/s [1]
9
.s
g
Answer: (a) 7
60
u14
4
= 210g
0g
ile
T
(a) Weight of baking powder in the small bag =
(b) 3.5 hours = 12600sec
0.18 u12600
1.5
= 1512
S
m
Number of bags
gs of 1.5
1.55 kgg each
each that
tha
hatt can be filled in 3.5 hours =
Answer: (a) 210 g [2]
(b) 1512 bags [3]
End of Section A
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130
7
Section B: Answer all the questions.
13
(a)
Write down an algebraic expression for each of the following statements.
(i)
Subtract 5x 3 from 3x 2 5 .
[2]
3x 2 5 (5 x 3) 3x 2 5 5 x 3
(b)
Simplify the following:
(i)
Simplify 2 y 3[ x 4( x y)] .
[2]
2 y 3[ x 4(
4 x y )] 2 y 3[ x 4 x 4 y ]
3n m 2
2n
nm
.
4
5
[3]
5(3
( n m) 4(2n m)
20
20
15n 5m 8n 4m
20
23n 9m
20
m
ile
T
3n m 2n m
4
5
ut
(ii)
or
2 y 3[5 x 4 y ]
2 y 15 x 12 y
15
15 x 14 y
.s
g
3x 2 5 x 2
(c)
If a : b = 5 : 4 an
and
nd b : c = 4
4.2
0.65
.2
2 : 0
.65 , find a : c.
[2]
S
b : c = 4.2
2: 0
0.65
.65
= 42
420
20 : 665
5
a : b = 5 : 4 b : c = 420 : 65
a : b = 525 : 420 b : c = 420 : 65
a : c = 525 : 65
= 105 : 13
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131
8
14
Joey paid $28.80 for a pair of shoes from a departmental store. If the store made a
[2]
loss of 25%, what is the original price of the shoes?
Original price of shoes =
100
u $28.80
75
15
.s
g
= $38.40
Marcus wants to change 600 Singapore Dollars (S$) to Thai Baht (THB).
The exchange rate is S$1 = 24.72 THB.
Find the amount of Thai Baht Marcus will receive if he uses S
S$600.
$600
$6
00..
or
(a)
S$600 = 600 u 24.72
The money changer is only able to change amounts iin
n multiples of 10
1000
000 THB.
T
(b)
ut
= 14832 THB
[[1]
1]
[3]
THB.
ile
The money changer decides to round up the amount iin
n (a
(a) to the nearest 1000
Find the amount in S$ that Marcus needss to top
top up for the extra amount,
m
giving your answer to the nearest
cent.
nearesst ce
cent
nt..
Amount that Marcus
Marc
Ma
rcus
u needs
ds tto
o top
top up in Thai Baht = 15000 – 14832
S
= 168 THB
168 THB
B = S$ 6.7971
6.7797
971
1
Amount off S$ that
tha
hatt Marcus
M rcus needs to top up = S$6.80 (rounded to nearest cents)
Ma
16
One pen costs x cents. An eraser costs 30 cents less than a pen and a ruler costs
two-third of a pen.
Find a simplified expression for
(a)
the cost of an eraser in cents,
[1]
Cost of an eraser = ( x 30 ) cents
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132
9
(b)
the total cost of an examination goodie pack consisting of 3 pens, 1 eraser and
[2]
2 rulers in cents.
2
Total cost of examination goodie pack = 3x ( x 30) 2( x)
3
3 x x 30 4
x
3
Solve the equations:
1
x
2
1
x
5
1
1
x
2
1
x
5
2(5 y 3)
3 2 y 14
14 .
m
(b)
ile
1
1
x x 1
2
5
5
2
x x 1
10
10
3
x 1
10
3 x 10
1
x 3
3
[2]
or
1
ut
(a)
T
17
.s
g
16
( x 30)) cents
3
[2]
2(5 y 3)
3 2 y 1144
S
10 y 6 2 y 1144
8y 8
y 1
18
Susan cycles from home to a coffeeshop to purchase dinner before continuing the
journey to her grandmother’s place.
Susan cycled at a speed of 4 m/s to the coffeeshop for 3 minutes, took another 10
minutes to buy dinner and continued the rest of the journey to her grandmother’s
house at a speed of 6 m/s. Given that the total distance travelled is 4500 m,
(a)
find the distance between Susan’s house and the coffeeshop.
2017 Mid-Year Examination/S1/Mathematics
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133
10
Distance between coffeeshop and Susan house = 4 u180
= 720 m
(b)
Find the average speed for the whole journey in m/s.
[3]
Time taken to travel from Susan to Grandma’s house =
4500 720
6
Average speed for the whole journey =
.s
g
= 630 s
4500
180 630 600
19
(a)
9
m/s
47
or
= 3.19 (3 s.f) or 3
Mr Lee was paid a monthly basic salary of $3 850 since
sincce Ja
JJanuary
an
nu
uar
ary 20
2015.
015.
[2]
ut
At the end of 2015, he was given a bonus of 13.5%
% ooff tth
the
he va
he
vvalue
alu
lue o
off ssales
ales
al
es tthat
hatt
ha
he has made during the year. If the total value of his saless iin
n 2015 was
was
T
$300 000, calculate Mr Lee’s total income in 2015.
ile
§ 13.5
·
12)
u3
300000
(3850
0 u1
2) ¨
00
0000
000 ¸
Mr Lee’s total income in 2015 = (3850
10
00
© 100
¹
= $8
$867
$86700
6700
00
Mr Lee has to pay income tax in Ja
Janu
January
nuaary 20
2016
1 for the annual income earned in
[3]
m
(b)
2015. The reli
l ef amount
am
mou
ount tha
hatt wi
willl not
not bbee subjected to income tax is shown in
relief
that
S
the table below.
w
Type off re
reli
relief
lief
ef
Amount
Personal relief
rellie
ieff
$1000
Child relief
$5000 each child
CPF
$17 340
Voluntary donation
Three times the amount donated
Mr Lee has only one child he has been making voluntary donation of $50
every month to an approved organization. The gross tax payable for the first
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11
$40 000 is $550 and the tax rate for the rest is 7%. Calculate his income tax
payable for 2015 using the information given above.
Amount of relief = $1000 $5000 $17340 3(50 u12)
= $25140
Amount taxable = $86700 $25140
Amount of tax payable = 550 .s
g
= $61 560
7
(61560 40000)
100
= 550+1509.20
In January 2016, Mr Lee’s basic monthly basic salar
salary
ary
yw
wa
was
as ccu
cut
ut b
by
y $$200.
200.
20
Calculate the percentage decrease in the basic m
monthly
on
o
nthl
thly
th
ly ssalary
alarry fr
fro
from
om 22015
015
01
5
[2]
to 2016, giving your answer to three significant figures.
200
u100%
3850
T
(i)
ut
(c)
or
= $2059.20
Percentage decrease =
ile
= 5.19
5.1948%
948
4 %
m
= 5.19
9% (3
(3s.f.))
5.19%
In 2016,
6 he
he was
w s paid
wa
id a bonus
bon
onus
us of 15.5% of the value of his sales that he
(ii)
[2]
has made dur
during
urin
ingg th
thee ye
year
year.
a . Given that his bonus in 2016 is $33 790,
S
calc
lcul
ulat
atee th
thee to
tota
tall va
vvalue
lue of his sales in 2016.
calculate
total
Total value of sales =
$33790
u100
15.5
= $218000
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135
12
20
Kale ordered one set meals at $55.60 and an ice cream for $12.90 at a restaurant.
[5]
1 set meal
$55.60
Ice cream
$12.90
SUBTOTAL
$68.50
10% Service Charge
$6.85
7% Goods and Services
Tax (GST)
$5.27
.s
g
Below shows Kale’s bill before payment.
or
Currently, the restaurant is offering two discount packages that Kale can
can ch
choo
choose
oose
se
Discount Package I:
ut
from.
Enjoys 10% off the subtotal of the bill, which is thereafter subjected
sub
ubbjjeect
cted
ed to 10%
10% Service
Serv
vic
icee
ile
Discount Package II:
T
Charge first and then 7% GST.
10% Service Charge is waived, which is thereafter
the
here
reaf
after subjected
subj
su
bjec
ecte
ted
d to
t 7% GST.
Explain, showing all necessary working,
g which
ch discount
dis
isco
coun
untt package is a better option
for Kale.
m
Discount
Disc
count Package I:
S
Bill subjected to Service
Seerv
rvic
icee Charge
Chhar
arge
ge aand
nd G
ST = 90% u $68.50
GST
= $61.65.
Total amount paid
pai
aid
d in Discount
Dissco
coun
unt Package I = (110% u $61.65) u1.07
= $72.56
Discount Package II:
Bill subjected to GST = $68.50
Total amount paid in Discount Package II = $68.50 u1.07
= $73.30
Since amount paid in Package II is more than amount paid in Package I, therefore
Package I is a better option for Kale.
~ End of Paper ~
2017 Mid-Year Examination/S1/Mathematics
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136
.s
g
or
ut
T
ile
m
S
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137
Pasir Ris Secondary School
Name
Class
Register Number
SECONDARY 1 EXPRESS
.s
g
MID-YEAR EXAMINATION 2017
MATHEMATICS
03 May 2017
2 hours
Additional Materials:
Electronic calculator
READ THESE INSTRUCTIONS FIRST
or
0800 – 1000
ut
Wednesday
Write your name, class and register number on all the work you hand in.
Write in dark blue or black pen.
T
You may use a pencil for any diagrams or graphs.
Do not use staples, paper clips, highlighters, glue or correction fluid.
ile
Answer all questions.
If working is needed for any question it must be shown with the answer.
Omission of essential working will result in loss of marks.
m
You are expected to use a scientific calculator to evaluate explicit numerical expressions.
If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three
significant figures. Give answers in degrees to one decimal place.
S
For S , use either your calculator value or 3.142, unless the question requires the answer in terms of S .
The number of marks is given in brackets [ ] at the end of each question or part question.
This paper consists of 2 sections, Section 1 and Section 2. The marks for each section is 40 marks.
The total number of marks for this paper is 80.
This document consists of 14 printed pages.
[Turn over
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Setter: Mr Daniel Chng
225
2
PRSS_2017_MYE_1E_MATH
Section 1 [40 marks]
For
Examiner’s
Use
Answer all the questions.
(a)
Rearrange the following numbers, in descending order, on the number line provided.
9,
7
,
22
S,
State the number(s) which are irrational.
(a)
Answer
ut
or
(b)
x
3.142 , 3.18 .
.s
g
1
[1]
(b)
Write down the first 5 figures of
3
ile
2 (a)
T
(b) ……………………………….. [1]
26.6 u 19.9 2
.
49.6 529
Use your calculator to evaluate the value of
26.6 u 19.912
, giving your answer
49.63 529.01
m
correct to
3
(i) 2 decimal places,
S
(ii) 1 significant figure.
Answer(a) ……...………………………….. [2]
(b)(i) ….…………………………….. [1]
(ii) ………….……………...…….. [1]
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3
For
Examiner’s
Use
x x
(a)
Express 100 u 0. 4 7 as a recurring decimal.
(b)
Find the value of 100 u 0. 4 7 0. 4 7 .
(c)
Hence, express 0. 4 7 as a fraction in its lowest terms.
x x
x x
x x
ut
or
.s
g
3
PRSS_2017_MYE_1E_MATH
Answer (a) ………...…..……………….. [1]
4
(c) ………...………….………... [1]
ile
T
(b) ………...………….………... [1]
Factorise completely
(a) 8 x 2 y 20 xy 3 ,
2(m 5n) m(m 5n) .
S
m
(b)
Answer (a) ………...…..……………….. [1]
(b) ………...………….………... [1]
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4
In a particular shopping centre, the ground level is indicated by 0 and the basement levels are
indicated by 1, 2 and so on. The shopping centre has 4 basement levels.
(a)
Zhenqi parked her car at Level 2 and took the lift to the highest level. If the lift
travelled up by 7 levels, find the highest level of the shopping centre.
(b)
There are two lifts located at Lift Lobby A of the shopping centre. For every two levels
that Lift 1 travels, Lift 2 travels three levels. If Lift 1 is now at the highest level and
Lift 2 at the lowest level, find the level that Lift 2 is at when Lift 1 is at Level 1.
(b) ………...………….………... [2]
(a)
0.068% of a number is 85. Find the number.
(b)
String P is 3.8 m long. The length of String Q is 135% of the length of String P and
95% of the length of String R. Find the length of String R.
S
m
6
Answer (a) ………...…..……………….. [1]
ile
T
ut
or
.s
g
5
PRSS_2017_MYE_1E_MATH
Answer (a) ………...…..……………….. [1]
(b) ………...………….……....m [2]
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For
Examiner’s
Use
5
PRSS_2017_MYE_1E_MATH
1
7 The journey of a motorist from Town A to Town B took him 2 hours.
4
(a) If the motorist travelled at an average speed of 10 m/s, calculate the distance between the
two towns in kilometres.
or
.s
g
(b) The motorist arrived at 12 10. Calculate the time he left Town A.
ut
Answer (a) ………...…..………...….km [2]
(b) ………...………….……....h [1]
2 g 3h 6 g h
.
2
4
S
m
(b)
ile
T
8 Simplify
(a) 2 xy 3 yz 5 xy 2 yz ,
Answer (a) ………...…..………...…….. [1]
(b) ………...………….……...... [3]
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For
Examiner’s
Use
6
Jazzy has a job for which the basic rate of pay is $C/hour and the overtime rate of pay is
$24/hour. On a particular day, she works for 12 hours, of which 4 hours are overtime.
(a) Express her pay in terms of C.
(b) Find the value of C if she is paid $180 for that day.
(c) How many hours of overtime must she work in total in order to earn $660 in a 5-day
work week?
or
.s
g
9
PRSS_2017_MYE_1E_MATH
ut
Answer (a) $..……...…..………...…….. [1]
(b) $..……...………….……...... [2]
T
ile
10 It is given that
v
Find the value of v when u = 30, a
u
2ab 2
.
3
3 and b
2 .
S
m
(c) ………...………….……....h [2]
Answer v = ....……...…..………...……[2]
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For
Examiner’s
Use
7
PRSS_2017_MYE_1E_MATH
11 (a) The mass of Xueling, measured to the nearest kg, is 43kg. Find the smallest possible
value of Xueling’s mass.
or
.s
g
(b) In the number 608R32, R represents a digit. Given that 608R32, correct to three significant
figures is 608 000, state the smallest value of the digit R, where R is a prime number.
ut
Answer (a) ....……...…..……........….kg [1]
(b) ....……...………………....... [1]
T
12 Eunice, Megan and Shannon planned to contribute money in the ratio 3 : 2 : 4 respectively to
buy a present for their friend. The cost of the present is $270.
ile
(a) Calculate Megan’s contribution.
(b) (i) If Eunice doubles her planned contribution and Megan halves her planned
contribution, find out how much must Shannon contribute for the present.
S
m
(ii) Hence, write down the new contribution ratio.
Answer (a) $..……...…..………...…….. [1]
(b)(i)$…......………….……...... [2]
(ii)…........:….....….:……..... [2]
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For
Examiner’s
Use
8
PRSS_2017_MYE_1E_MATH
13 The figure below is made up of small rectangles each of length a cm and breadth b cm.
Calculate in terms of a and b, the area of the region not enclosed by ABCD.
a cm
ile
T
ut
or
.s
g
b cm
S
m
Answer ….....……...…….……...….cm2 [2]
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For
Examiner’s
Use
9
PRSS_2017_MYE_1E_MATH
Section 2 [40 marks]
Answer all the questions.
.s
g
14 (a) Expand and simplify 3 (4 12 x) .
Answer (a) ………...…..………...…….. [2]
0.
or
5
2
y 4 3y 1
m
ile
T
ut
(b) Solve
S
(b) ………...…..………...…….. [3]
(c) A faulty watch gains x seconds in one hour. Write down an expression for the number of
minutes it would gain in y days. Give your answer in its simplest form.
(c) ………...…..………...…….. [2]
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For
Examiner’s
Use
10
PRSS_2017_MYE_1E_MATH
For
Examiner’s
Use
15 (a) (i) Solve the inequality, 2(3 x) d 42 2 x .
Answer (a)(i)………….….……...…….. [2]
or
.s
g
(ii) Hence, write down the smallest value of x that satisfies the inequality
2(3 x) d 42 2 x such that x is a perfect square.
(ii) x =…..…………....…….. [1]
ut
(b) Ms Lau went shopping for groceries at the supermarket. She intends to buy two bottles of
juice at $6.15 each, 5 packets of fresh milk at $1.67 each, 2 loaves of bread at $2.49 each
and some fruits.
S
m
ile
T
(i) Estimate the total cost Ms Lau will spend by rounding each of the prices to the
nearest ten cents.
(b)(i) $….....…..………...…….. [1]
(ii) If Ms Lau does not wish to exceed her budget of $30, calculate how much money she
should use to buy fruits.
(ii) $…….....…..……..…….. [1]
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11
PRSS_2017_MYE_1E_MATH
16 (a) (i) It is given that 240 2 4 u 3 u 5 .
Express 2750 as a product of its prime factors, giving your answer in index notation.
.s
g
Answer (a)(i)2750 =…..….……...…….. [1]
or
(ii) Find the smallest positive integer k for which 240k is a multiple of 2750.
(ii)…….…...…..……..…….. [1]
3
2750n is a whole number.
T
ut
(iii) Find the smallest positive integer n for which
(iii)...….…...…..……..…….. [1]
ile
(b) Nabilah bought 2 vanguard sheets each measuring 70 cm by 90 cm. She cut out square
cards of identical size from the vanguard sheets such that there was no wastage.
S
m
(i) Calculate the largest possible length of the side of each square card that she can
cut out.
(b)(i)……....…..….……...…cm [2]
(ii) Find the total number of square cards she cut out such that there was no wastage.
(ii)…….…...…..……..…….. [2]
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For
Examiner’s
Use
12
PRSS_2017_MYE_1E_MATH
17 Hongxiang bought 12 boxes of apples at $60 and each box contains x apples. 15% of the
apples were rotten and could not be sold. He would make a profit of 70% if he sells each
apple at 50 cents.
(a)
Find in terms of x, the total number of apples Hongxiang bought.
Calculate the total sales made from the apples that could be sold.
ut
or
(b)
.s
g
Answer (a) ....…..………...….......apples[1]
(b) $.....…...…..………...…….. [2]
T
Express the profit, in terms of x, as a percentage of the total amount paid for all 12 boxes
of apples, assuming that all the remaining apples are sold.
S
m
ile
(c)
(d)
(c) ………...…..………….…% [2]
Hence, find the number of apples per box.
(d) ………...…..………..apples [2]
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For
Examiner’s
Use
13
18 In the diagram, ABCD is a rectangular field. AD
perimeter of the field ABCD is (24 x 6) m.
PRSS_2017_MYE_1E_MATH
(5 x 9) m, AE
(3 x 12) m, and the
(5 x 9) m
(3 x 12) m
E
D
B
C
ile
T
ut
Find an expression in terms of x for
(a) (i) the length of AB,
or
.s
g
A
(ii) the length of DE.
3
AD , show that 11x = 66.
13
(ii) ……….………...…......m [1]
S
m
(b) Given that DE
Answer (a)(i) ………..…..……….......m [2]
(c) Solve the equation in part (b) to find the value of x.
(b) ………..……..……....….......[2]
(c) ………..…..….……...….......[1]
(d) The shaded region shows the location of a flower bed. Calculate the area of the flower
bed.
(d) ……...…..………...…......m2 [1]
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For
Examiner’s
Use
14
PRSS_2017_MYE_1E_MATH
19 Mr Ding who is an NSman is married with 2 children and his wife is not working. In 2016, he
earned a gross annual income of $85 000. The data for the tax reliefs and the tax rates available
are shown in the tables below.
Tax Rates
$550
7%
$3 350
11.5%
First $40 000
Next $40 000
First $80 000
Next $40 000
$5 000
T
ut
or
Calculate
(a) (i) the amount of tax relief that he is entitled to,
.s
g
Personal
Wife
Each child
CPF contributions
Parent/Handicapped
parent
NSman
Reliefs
$3 000
$2 000
$4 000
$15 000
$11 000
Answer (a)(i) $.............…..……...….......[2]
ile
(ii) his amount of taxable income,
m
(ii) $…….....…..…………… [2]
Mr Ding told his wife he needs to pay a total income tax of $3 350. Showing your
working clearly, explain why his calculation is wrong. State a possible reason for
his error.
S
(b)
(b) …………………………………………………….……….…..………...…….....................
……………………………………………………………………………………………….
……………………………………………………………………………………………[3]
END OF PAPER
238
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For
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.s
g
or
ut
T
ile
m
S
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Solutions 1Exp EM 2017 SA1 Paper
SECTION 1 (40 marks)
1(a)
2M
S
3.142
[B1]
26.6 u 19.9 2
49.6 529
| 2.465861....
[B1/B2]
ut
2.47 [B1]
2
[B1]
x x
x x
100 u 0. 4 7 100
00 u 0.474747... = 47. 4 7
x x
x x
x x
4M
3M
[B1]
100 u 0. 4 7 0. 4 7 = 47.474747… 0.4
0.474747…=
.474
4747…=
= 447
7
ile
3(c)
c)
[B1]
T
2(b)(i)
b)(i)
2(b)(ii)
b)(ii)
3(a)
a)
[B1]
or
3
2.4658
3(b)
b)
9 3.18
.s
g
S
1(b)
b)
2(a)
a)
x
7
22
[B
[B1]
x x
100 u 0. 4 7 0. 4 7 = 47
x x
m
4(a)
a)
99 u 0. 4 7 = 477
x x
47
47
? 0. 4 7
99
9
9
S
[B1]
[B1]
2(m 5n) m(m 5n)
(m 5n)((2 m)
5(a)
a)
5(b)
2M
8 x 2 y 20 xy 3
4 xyy (2 x 5 y 2 )
4(b)
b)
[[B
1]
[B1]
[B1]
2 + 7 = 5
?the highest level is Level 5. [B1]
Number of levels Lift 1 travels= 5 – (1) = 6
Number of levels Lift 2 travels=(6 y 2)u3 =9
Level Lift 2 is at = 4 + 9 = 5
6(a)
0.068
x 85
100
x 125000
3M
[M1] for method to find levels that
L1 and L2 will be at.
[A1]
3M
[B1]
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240
6(b)
7(a)
String Q =
135
(3.8) 5.13 m
100
[M1cao]
String R =
5.13
(100) 5.40 m
95
[A1]
10m/s = 10 y 1000 u 3600 36 km/h
1
[A1]
Therefore distance = 36 u 2
81 km
4
1210 0215 0955 h [B1]
2 xy 3 yz 5 xy 2 yz 7 xy yz [B1]
2 g 3h 6 g h
2
4
2(2 g 3h) 6 g h
[M1cao]
4
4 g 6h 6 g h
[M1]
4
7h 2 g
[A1]
4
$(8C + 96) [B1]
3M
4M
9(a)
a)
9(b)
b)
T
5M
ile
[A1]
660 y 5 $132
8(10.50) 24(OT ) 132
OT 2 or 2 u 5 10
m
9(c)
c)
2(3)(2) 2
v 30 3
22
S
100
[M1]
8C 96 180
8C 84
C $10.50
ut
or
7(b)
b)
8(a)
a)
8(b)
b)
.s
g
[M1] to convert m/s to km/s
11(a)
1(a)
11(b)
1(b)
12(a)
2( )
12(b)(i)
42.5 kg
R=2
[M1]
[M
1]ca
cao
o
[M1]cao
[A
A1]
[A1]
2M
[M1]
[M1] tto
o sub in values
[A1]
2M
[B1]
[B1]
2
u 270 $60 [B1]
9
3
Eunice’s initial contribution
[M1cao]
u 270 $90
9
Eunice’s new contribution 90 u 2 $180
1
$30
Megan’s new contribution 60 u
2
? Shannon’s contribution 270 180 30 $60 [A1]
Megan’s contribution
4M
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241
12(b)(ii)
13
New contribution ratio
180 : 30 : 60
6 : 1 : 2 [B1]
2
Area of one small rectangle = ab cm .
2M
[M1]
There are 12 small rectangles and four half rectangles outside ABCD.
?total area = area of 14 small rectangles = 14ab cm2
14(c)
4(c)
multiply
[M1] for cross multipl
plly
[A
A1]
[A1]
[M
M1]
1
[M1]
ile
1 day – 24 hours
y days – 24y
4 hours
[M1]
T
5
2
0
y 4 3y 1
2
5
y 4 3y 1
5(3 y 1
1)) 2( y 4)
15 y 5 2 y 8
13 y 13
y 1
or
[M1]cao
[A1]
12 x 1
14(b)
4(b)
.s
g
SECTION 2 (40 marks)
3 (4 12 x)
3 4 12 x
ut
14(a)
[A1]
1 hour – x seconds
24y
4 hours – 24xy seconds
m
minutes
Therefore number ooff mi
m
nutess =
2(3 x) d 4
42
2 2x
6 2 x d 42
42 2 x
[M1]
4 x d 36
xd9
[A1]
S
15(a)(i)
5(a)(i)
24 xy
24xy
minutes
60
[A1]
Q14 Total Marks: 7
15(a)(ii)
5( )(ii)
15(b)(i)
x = 9 [B1]
Total cost = 2 u 6.15 + 5 u 1.67 + 2 u 2.49
| 2 u 6.20 + 5 u 1.70 + 2 u 2.50
= 12.40 + 8.50 + 5
= $ 25.90 [B1]
15(b)(ii)
Amount of money = 30 – 25.90 = $ 4.10 [B1]
16(a)(i)
2750
Q15 Total Marks: 5
2 u 5 u11 [B1]
3
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242
16(a)(ii)
LCM 2 4 u 3 u 5 3 u 11
Therefore k 5 2 u 11 275
[B1]
16(a)(iii) n 2 2 u 112 484
[B1]
16(b)(i) 70 = 2 u 5 u 7
[M1] to prime factorise both 70 and 90
90 = 2 u 32 u 5
HCF = 2 u 5 = 10
?largest possible length = 10 cm
[A1]
Number of cards per sheet = (70 y 10) u (90 y 10) = 63
?total number of cards = 63 u 2 = 126
Number of apples in the 12 boxes
[A1]
12x
[B1]
Number of remaining apples that could be sold
5.1x 60
u 100
60
$5.1x
$5
5..1
.1x
[A1]
[A
1]
[M1]
[A1]
ile
?
$(5.1x – 60)
51
x u 0.5
5
[M1]
[M
M1]
T
Profit
51
85
x
u 12 x
5
100
ut
Total sales made from remaining apples
17(c)
7(c)
Q16
Q1
16 Total
Total Marks: 7
or
17(a)
7(a)
17(b)
7(b)
[[M1]]
.s
g
16(b)(ii)
5.1x 60
u
u100
100
60
5.1x 102
x 20
70
[M
M1cao
o]
[M1cao]
m
17(d)
7(d)
?there are 20
20 ap
aapples
pless iinn a bo
box.
x
[A1]
Q17 Total Marks: 7
S
18(a)(i)
8(a)(i)
Length AD
D + BC = 2(5 x 99)) 10 x 18
24 x 6 10 x 18
Length AB =
2
=
18(a)(ii)
18(b)
14 x 12
2
7x 6
Length DE = 5 x 9 3 x 12
3
DE
AD
13
[M1]
[A1]
2 x 3 [B1]
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243
3
(5 x 9)
13
15
27
2x 3
x
13
13
11
66
x
13
13
11x 66
2x 3
66
11
6
.s
g
18(d)
8(d)
11
x
11
x
[A1]
[B1]
ª 7(6) 6 º
Area of 1 small rectangle = «
» u [2(6) 3] 108 m
¬ 3 ¼
or
18(c)
[M1]
Area of flower bed = 6 u 108
648 m2
ut
Amount of taxable income = 85000
850000 33
33000
0
= $522 00
000
0
[M1cao]
[A1]
[M1c
[M
[M1cao]
1cao
ao]
[A1]
[A
A1]
1st $40 000 = $550
m
19(c)
9(c)
T
19(b)
9(b)
Q19
Q1
19 Total
To Marks: 7
15000
Amount of tax relief = 3000 + 2000 + 2(4000) + 150
5 00 + 5000
= $33 000
ile
19(a)
9(a)
[B1]
S
2nd $40 000,
000
0,
7
u (52000
520000 40000
400000)
=
100
$8400
[M1]
Therefore, total
tota
to
t l in
ta
income tax payable = 550 + 840 = $1390
[A1]
Possible reason: he assumed his taxable income was the gross annual income. [B1]
Q19 Total Marks: 7
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244
.s
g
or
ut
T
ile
m
S
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g
or
ut
T
ile
m
S
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or
ut
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ile
m
S
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276
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g
or
ut
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ile
m
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or
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ile
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ile
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ile
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ile
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or
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ile
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or
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ile
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or
ut
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ile
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or
ut
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ile
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or
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ile
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or
ut
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ile
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ile
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or
ut
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ile
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ile
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ut
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ile
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4
3
2.
(b)
(a)
(b)
(c)
(a)
(c)
Qn
1.
(a)
(b)
Ͳ
‫ܣ ׵‬ǣ
‫ܣ‬ǣ ‫ܤ‬ǣ
‫ܤ‬ǣ ‫ ܥ‬െ ʹͲǣ ʹͶǣ ͻ
ʹͲǣǣ ʹͶ
ʹ
ʹͲ
ʹͶǣ
ʹ ǣͻ
ʹͶ
͵
ut
ͷǤͷ
T
ξͳͲͲ
͵
ile
ͲǤͷͶͻ ξ
ξʹ͵
ͷ
ͳͲ͹Ψ െ ̈́ͷ͵ͷ
ͳΨ െ ̈́ͷ
ܲ‫݁ܿ݅ݎ‬
ܲ‫ܶܵܩ݁ݎ݋݂ܾ݁݁ܿ݅ݎ‬
ܾ݂݁‫ ܶܵܩ ݁ݎ݋‬െ ͳͲͲ ൈ ͷ ൌ ̈́ͷͲͲ
̈́ͷͲͲ
ʹͶͲ݉
ʹͶͲ
݉ ‫ͳ ׷‬Ǥ͵
ͳǤ͵݇݉
݇݉
ʹͶͲǣ ͳ͵ͲͲ
ͳʹǣ
ͳʹ ͸ͷ
‫ܣ‬ǣǣ ‫ ܤ‬െ ͷǣ ͸
‫ܣ‬
ͺǣ ͵ െ ‫ܤ‬
ͺǣ
‫ܤ‬ǣǣ ‫ܥ‬
ʹ
͹
Solution
m
S
LCM
CM = ʹଵଵ ൈ ͵ଵ଴ ൈ ͳͳ଼
‫ ݔ‬ൌ ͵ଶ ൈ ͳͳ
ξʹ
െͳͶ
HCF
CF = ͵ସ ൈ ͳͳ଻
͵ǡ Ͳ
23 14
,
5
2
Secondary 1 Express
ction A Marking Scheme
2017 MYE Section
or
A1
M1
B1
A1
M1
B1
B1
B1
B2
Marks
B1
B1
.s
g
Guidance
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293
8
7.
6
5
(b)
(a)
(b)
(c)
(b)
(a)
Qn
ଷ଴
Rate
ate of increase of Temperature = ଵଶ ൌ ʹǤͷιȀŠ”
Temperature
emperature difference = ͳ͵ െ ሺെͳʹሻ ൌ ʹͷι
ʹͷ
ܶ݅݉݁ ‫ ݊݁݇ܽݐ‬ൌ
ൌ ͳͲ݄‫ݏݎ‬
ͳͲ ݄‫ݏݎ‬
ܶ݅݉݁‫݊݁݇ܽݐ‬
ʹǤͷ
ܶ݅݉݁ ൌ ͳͲͲͲ݄‫ݏݎ‬
3p 2
2q
q 2 p 10q p 12q
a 2b b c 2(c a)
ൌ ܽ െ ʹܾ ൅ ܾ ൅ ܿ െ ʹܿ ൅ ʹܽ
ൌ ͵ܽ െ ܾ െ ܿ
‫ ݔ‬ͷ‫ ݔ‬൅ ͳ
൅
͹
͵
͵‫ ݔ‬͹ሺͷ‫ ݔ‬൅ ͳ
ͳሻሻ
ൌ
൅
ʹ
ʹͳ
ʹͳ
͵‫ ݔ‬൅ ͵ͷ‫ݔ‬
͵ͷ
ͷ‫ ݔ‬൅ ͹ ͵ͺ
͵ͺ‫ݔ‬
‫ݔ‬൅͹
ൌ
ൌ
ʹͳ
ʹͳ
ut
T
ile
724
= 0.300305... | 0.300 (3 s.f.)
3.2 (8.24 5.32)
Temp
emp Difference = ͳͺ െ ሺെͳʹሻ ൌ ͵Ͳι
2
3
m
Solution
ͳ͵‫ݏݐ݅݊ݑ‬
ͳ͵
‫ ݏݐ݅݊ݑ‬െ ‫ݏݐ݊ܽݏݏ݅݋ݎܥ‬
ͳͲ
‫ ݏݐ݅݊ݑ‬െ ‫ݐ݅ݑݎܨ‬
ܶܽ‫ݏݐݎ‬
ͳͲ‫ݏݐ݅݊ݑ‬
‫ݏݐݎܽܶݐ݅ݑݎܨ‬
ʹ͵
‫ ݏݐ݅݊ݑ‬െ ͷ͹ͷ
ʹ͵‫ݏݐ݅݊ݑ‬
ͳ
‫ ݐ݅݊ݑ‬ൌ ʹͷ
ͳ‫ݐ݅݊ݑ‬
‫ ݏݐ݊ܽݏݏ݅݋ݎܥ ݂݋‬ൌ ʹͷ ൈ ͳ͵ ൌ ͵ʹͷ
ܰ‫݋‬Ǥ ‫ݏݐ݊ܽݏݏ݅݋ݎܥ݂݋‬
‫ ݏݐݎܽݐ ݐ݅ݑݎܨ ݂݋‬ൌ ʹͷ ൈ ͳͲ ൌ ʹͷͲ
ܰ‫݋‬Ǥ ‫ݏݐݎܽݐݐ݅ݑݎܨ݂݋‬
S
Secondary 1 Express
ction A Marking Scheme
2017 MYE Section
or
M1A1
M1
M1
A1
B1
B
B1
B1
B1
B
1
B1
B
1
B11
B
1
B1
Marks
.s
g
Guidance
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12
11
10
(a)
(b)
(bii)
(bi)
(a)
(b)
Qn
9
(a)
ut
T
ile
m
ଵ
ͳ
ʹʹ
‫ݏݐ݊ܽݎ݀ܽݑݍ݂݋ܽ݁ݎܣ‬
‫ܽ݁ݎܣ‬
‫ ݏݏݐ݊ܽݎ݀ܽݑݍ ݂݋‬ൌ ʹ ൈ ൈ ͹ଶ ൈ
ൌ ͹͹
͹͹ ଶ
Ͷ
͹
݄ܵܽ݀݁݀
݀ ‫ܽ݁ݎܣ‬
݁ܽ ൌ ͻͺ
ͺ െ ͹͹ ൌ ʹͳ
݄ܵܽ݀݁݀‫ܽ݁ݎܣ‬
ʹͳ ଶ
Volume
olume of container = ͳͲͲ ൈ ͷͲ ൈ ͷͲ ൌ ʹͷ
ʹͷͲͲ
ʹͷͲͲͲͲ
ͲͲͲͲ ଷ
No.
o. of containers that ccan
an
n ffit
it int
into
ntoo tr
truck
ruckk
଺଴଴
ଶ଴଴
ଷ଴଴
= ଵ଴଴ ൈ ହ଴ ൈ ହ଴ ൌ ͳͶ
ͳͶͶ
ͶͶ ‘
‘–ƒ‹‡”•
–ƒ‹
–
ƒ ‡‡”•
Area
rea of rectangle = ͹ ൈ ͳͶ ൌ ͻͺ
ͻͺ ଶ
‫݁ܿ݊݁ܪ‬ǡ ‫݄݁ݏ‬
‫͵͵݈݈݁ݏݐݏݑ݄݉݁ݏ‬Ͷ‫ݐݏ݈ܽ݁ݐܽݏ݈݄݁݁ݓ݊݅݌‬Ǥ
݉‫͵͵ ݈݈݁ݏ ݐݏݑ‬Ͷ ‫ݏ݈݄݁݁ݓ݊݅݌‬
݈ ܽ‫ݏ݈ܽ݁݁ ݐ‬
ܽ‫ݐݐݏ‬Ǥ
̈́ହ଴
How
ow many pinwheels to sell
seell = ̈́଴Ǥଵହ ൌ ͵͵͵ ଷ
Profit
ofit made = ̈́ͲǤͷͲ െ ̈́ͲǤ͵ͷ ൌ ̈́ͲǤͳͷ
Solution
ͷ
ܽ ൌ ͳǤͷ ൊ ൌ ͳǤͺ
ͳǤͺȀŠ
ȀŠ
͸
ܾ ൌ ͲǤͷ݄‫ ݏݎ‬ൈ ʹͷ ൌ ͳʹǤͷ

ͳʹǤͷ
ܿ ൌ ͺ ൊ ͳͲ ൌ ͲǤͺ݄‫ݏݎ‬
ͳǤͷ ൅ ͳʹǤͷ ൅ ͺ
ʹʹ
‹†›
‹†› ᇱ ••ƒ˜‡”ƒ‰‡•’‡‡†
ƒ˜‡”ƒ‰‡ •’‡‡† ൌ
ൌ
ൎ ͳͲǤ͵
ͳͲǤ͵ȀŠሺ͵‫ݏ‬Ǥ
ȀŠ ሺ͵‫ݏ‬Ǥ ݂Ǥ ሻ
ʹ
ͷ
ʹ
൅
ͲǤͷ
൅
ͲǤͺ
ͳͷ
͸
ͳͲ
‫ݎ݁݌ܽ݌݁݊݋݂݋ݐݏ݋ܥ‬
‫ݐݏ݋ܥ‬
‫ ݎ݁݌ܽ݌ ݁݊݋ ݂݋‬ൌ
ൌ ̈́ͲǤʹͲ
ͷͲ
ͷ
‫݊݅݌݁݊݋݂݋ݐݏ݋ܥ‬
‫ ݊݅݌ ݁݊݋ ݂݋ ݐݏ݋ܥ‬ൌ
ൌ ̈́ͲǤͲͷ
ͳͲͲ
ͷ
‫ݐݏ݋ܥ‬
‫ ݓܽݎݐݏ ܿ݅ݐݏ݈ܽ݌ ݁݊݋ ݂݋‬ൌ
ൌ ̈́ͲǤͳͲ
‫ݓܽݎݐݏܿ݅ݐݏ݈ܽ݌݁݊݋݂݋ݐݏ݋ܥ‬
ͷͲ
‫݁ܿ݊݁ܪ‬ǡ ‫݈݄݁݁ݓ݊݅݌ͳ݂݋ݐݏ݋݈ܿܽݐ݋ݐ‬
‫ ݈݄݁݁ݓ݊݅݌ ͳ ݂݋ ݐݏ݋ܿ ݈ܽݐ݋ݐ‬ൌ ̈́ͲǤʹͲ ൅ ̈́ͲǤͲͷ ൅ ̈́ͲǤͳͲ ൌ ̈́ͲǤ͵ͷ
ͷ
S
Secondary 1 Express
ction A Marking Scheme
2017 MYE Section
M1A1
B1
M1A1
M1
Guidance
.s
g
Students need to show rounded
rounde answer
Don’t accept 15 cents
Don’t
Don’
Do
n’t accept 35 cents – 1 mark
mar for working
or
B1
B1
M1A1
B1
Marks
B1
B1
B1
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4
3
2.
‫ݎ݁ݒ݋ݐ݂݈݁ݐ݊ݑ݋݉ܣ‬
‫ݐ݊ݑ݋݉ܣ‬
݈݂݁‫ݒ݋ݐ‬
‫ ݎ݁ݒ‬ൌ ̈́ͻͺͳͲͳ െ ̈́ʹͷͲͲͲ ൌ ̈́
̈́͹͵ͳͲͳ
͹͵ͳͲ
͹͵
ͳͲͳ
ܶ‫݀݁ݎݎݑܿ݊݅ݐݏ݁ݎ݁ݐ݈݊݅ܽݐ݋‬
ܶ‫ ݀݁ݎݎݑܿ݊݅ ݐݏ݁ݎ݁ݐ݊݅ ݈ܽݐ݋‬ൌ ሺʹǤͷΨ ൈ ͹͵ͳͲͳሻ ൈ ͷ ൌ ̈́ͻͳ͵͹Ǥ͸ʹͷ
̈́ͻͳ
ͻͳ͵͹
͵͹Ǥ͸ʹ
͸ʹͷ
ͷ
̈́͹͵ͳͲͳ ൅ ͻͳ͵͹Ǥ͸ʹͷ
‫ ݐ݈݊݁݉ܽݐݏ݊ܫ ݕ݈݄ݐ݊݋ܯ‬ൌ
ൌ ̈́ͳ͵͹ͲǤ͸Ͷ
̈́ͳ͵
ͳ͵͹Ͳ
͹ Ǥ͸Ͷ ൎ ̈́
̈́ͳ͵͹ͳ
ͳ͵͹ͳ
ͳ͵
͹ͳ
‫ݐ݈݊݁݉ܽݐݏ݊ܫݕ݈݄ݐ݊݋ܯ‬
͸Ͳ
(b)
(d)
(a)
(b)
(c)
Sister’s
ster’s age
ge = x 12
Father’s
ther’s ageൌ ʹሺ‫ ݔ‬൅ ͳʹሻ ൌ ʹ‫ ݔ‬൅ ʹͶ
Sum
um of agesൌ ‫ ݔ‬൅ ‫ ݔ‬൅ ͳʹ ൅ ʹሺ‫ݔ‬
ʹሺ‫ ݔ‬൅ ͳʹሻ
ͳʹ
ʹሻ
ൌ Ͷ‫ݔ‬
Ͷ‫ ݔ‬൅ ͵͸
Erica’s
ica’s age = 12, let ‫ ݔ‬ൌ ͳʹǡ
ͳʹǡ
‫ݎ݄݁ݐܽܨ‬
‫ݐܽܨ‬
‫ܽܨ‬
‫ ݎݎ݄݁ݐ‬ᇱ ‫݁݃ܽݏݏ‬
ܽ݃݁݁ ൌ ʹሺͳʹሻ
ܽ݃
ʹሺͳʹሻ ൅ ʹͶ
ൌ Ͷͺ‫݈݀݋ݏݎܽ݁ݕ‬
Ͷͺ
ͺ ‫݁ݕ‬
‫݈݀݋ ݏݎܽ݁ݕ‬
‫݀݁݊ݎܽ݁݊݋݅ݏݏ݅݉݉݋ܥ‬
‫݊݋݅ݏݏ݅݉݉݋ܥ‬
݁ܽ‫ ݀݁݊ݎ‬ൌ ̈́ͶͺͲͲͲ ൈ ͵Ψ
Ψൌ̈́
̈́ͳͶͶͲ
ͳͶͶͲ
ͳͶ
ͶͲ
݈݈ܵ݁݅݊݃‫ݖݖܽܬ݂݋݁ܿ݅ݎ݌‬ሺ‫ܧܱܥݐݑ݋݄ݐ݅ݓ‬ሻ
݈݈ܵ݁݅݊݃
‫ ݖݖܽܬ ݂݋ ݁ܿ݅ݎ݌‬ሺ‫ܧܱܥ ݐݑ݋݄ݐ݅ݓ‬ሻ ൌ ͻͺͳͲͳ െ ͷͲͳͲͳ
ͳ ൌ ̈́ͶͺͲͲͲ
‫ ܯܥܮ‬ൌ ʹଶ ൈ ͵ ൈ ͷ ൈ ͹ ൌ ͶʹͲ‫ݏݎܽ݁ݕ‬
ͶʹͲ ‫ݏݎܽ݁ݕ‬
‫݁ܿ݊݁ܪ‬ǡ ‫͵ʹݎܽ݁ݕ݄݁ݐ݈݈݅ݓ݈݊݃݅ܽݏݐ݈݁݊ܽ݌݄݁ݐ݁݉݅ݐݐݔ݄݁݊݁ݐ‬ͷʹ
‫݁ݕ ݄݁ݐ ݈݈݅ݓ ݈݊݃݅ܽ ݏݐ݈݁݊ܽ݌ ݄݁ݐ ݁݉݅ݐ ݐݔ݁݊ ݄݁ݐ‬
‫͵ʹ ݎܽ ݕ‬ͷʹ
(a)
M1A1
A1
B1
B1
M1
A1
M1
M
A1
A
M1
A1
M1
M1
.s
g
Guidance
Accept either answer
or
B1
B
1
B1
B
1
B1
B
1
B1
B1
Marks
B1
B1
B1
ut
T
ile
m
S
Solution
‫݁ܿ݊݁ܪ‬ǡ
݁݊ܿ݁ǡ ‫݉ܿʹͳݏܾ݅݁ݑ݄݂ܿܿܽ݁݋݄ݐ݈݃݊݁ݐݏ݁݃ݎ݈݄ܽ݁ݐ‬.
‫݉ܿ ʹͳ ݏ݅ ܾ݁ݑܿ ݄ܿܽ݁ ݂݋ ݄ݐ݈݃݊݁ ݐݏ݁݃ݎ݈ܽ ݄݁ݐ‬.
ͻ͵͸ ʹͷʹ ͳ͵ʹ
ܶ‫ݐݑܾܿ݁݊ܽܿݏܾ݁ݑ݂ܿ݋ݎܾ݁݉ݑ݈݊ܽݐ݋‬
‫ ݐݑܿ ܾ݁ ݊ܽܿ ݏܾ݁ݑܿ ݂݋ ݎܾ݁݉ݑ݊ ݈ܽݐ݋‬ൌ
ൈ
ൈ
ͳʹ
ͳʹ
ͳʹ
ൌ ͳͺͲͳͺܿ‫ݏܾ݁ݑ‬
ͳͺͲͳͺ ܿ‫ݏܾ݁ݑ‬
ͳʹ ൌ ʹଶ ൈ ͵
͵Ͳ ൌ ʹ ൈ ͵ ൈ ͷ
ͺͶ ൌ ʹଶ ൈ ͵ ൈ ͹
ଶ
ͻ͵͸
͵͸ ൌ ʹ ൈ ͵ ൈ ͳ͵
ଶ
ଶ
ͷʹ ൌ ʹ ൈ ͵ ൈ ͹
ʹͷʹ
͵ʹ ൌ ʹଶ ൈ ͵
͵
ͳ͵ʹ
ൈ ͳͳ
ଶ
ൌ ʹ ൈ ͵ ൌ ͳʹ
ͳʹ 
ଷ
(b)
(a)
(c)
(b)
Qn
1.
(a)
Secondary 1 Express
ction B Marking Scheme
2017 MYE Section
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296
8
7
6
(b)
(a)
(b)
(a)
(b)
(a)
(b)
Qn
5
(a)
T
ile
m
M1A1
M1
M
1A1
A1
A1
A1
M1
M1A1
Marks
A1
M1
M1A1
M1A1
or
A
A1
M1
A1
M1
ut
Solution
ͷ‫ݏݐ݅݊ݑ‬
ͷ
‫ ݏݐ݅݊ݑ‬െ ʹͲͲ
ʹͲͲŽ
Ž
ͳ
‫ ݐ݅݊ݑ‬െ ͶͲ
ͳ‫ݐ݅݊ݑ‬
‫ ݀݁݀݁݁݊ ݈݇݅ܯ‬ൌ ͵ ൈ ͶͲ ൌ ͳʹͲŽ
ͳʹͲ Ž
‫݈݀݁݀݁݁݊݇݅ܯ‬
ʹͲ݉‫݀݁݁݊ݏ݂݂݊݅ݑ‬ͶͲͲ݈݉‫ݎݑ݋݈݂݂݋‬
ʹͲ
݉‫ ݀݁݁݊ ݏ݂݂݊݅ݑ‬ͶͲͲ ݈݉ ‫ݎݑ݋݈݂ ݂݋‬
ͶͲͲ
‫݁ܿ݊݁ܪ‬ǡ ͷͲ݉‫݀݁݁݊ݏ݂݂݊݅ݑ‬
ͷͲ ݉‫ ݀݁݁݊ ݏ݂݂݊݅ݑ‬ൌ
ൈ ͷͲ ൌ ͳͲͲͲ
ͳͲͲͲ݈݉‫ݎݑ݋݈݂݂݋‬Ǥ
݈݉ ‫ݎݑ݋݈݂ ݂݋‬Ǥ
ʹͲ
ͳͲͲͲ
‫ݎ݋ܨ‬
ͳͲͲͲ ݈݉ ‫ݎݑ݋݈݂ ݂݋‬ǡ ݈݉݅݇
݊݁݁݀݁݀ ൌ
ൈ ͵ ൌ ͸ͲͲ݈݉
͸ͲͲ ݈݉
‫ݎݑ݋݈݂݂݋݈݉ͲͲͲͳݎ݋ܨ‬ǡ
݈݉݅݇݊݁݁݀݁݀
ͷ
Selling
lling price of the vacuum cleaner for Shop A
ͺͷ
ͻͲ
ൌ ̈́ͺͲͲ ൈ
ൈ
ൌ ̈́͸ͳʹ
ͳͲͲ ͳͲͲ
Selling
lling price of VC for Shop B
͹ͷ
ൌ ̈́ͺͲͲ ൈ
ൌ ̈́͸ͲͲ
ͳͲͲ
Since
nce Shop B is cheaper, Mr Sim should buy from Shop B.
Since
nce S$1 to 0.71 USD
̈́͵͸ͲͲ ൌ ͵͸ͲͲ ൈ ͲǤ͹ͳ ൌ ʹͷͷ͸
ʹͷͷ͸
ence, Mr Sim got ʹͷͷ͸
Ǥ
Hence,
ʹͷͷ͸Ǥ
‫ ݎ݁ݒ݋ݐ݂݁ܮ‬ൌ ͺͲͲܷܵ‫ܦ‬
ͺͲͲ
ͺͲ
Ͳ
‫݁ܿ݊݁ܪ‬ǡ ܽ݉‫ܾ݇ܿܽݐ݋݄݃݁ܦܩ݂ܵ݋ݐ݊ݑ݋‬
ܽ݉‫ ܾ݇ܿܽ ݐ݋݃ ݄݁ ܦܩܵ ݂݋ ݐ݊ݑ݋‬ൌ
ൌ ܵ̈́ͳͳʹ͸
ܵ̈́ͳͳ
ͳͳʹ͸
ʹ͸
Ͳ
Ǥ͹ͳ
͹ͳ
ͲǤ͹ͳ
Total
otal intere
interest
rest accumulated
ͲͲͲ ൈ ͺǤͷΨ ൈ Ͷ ൌ ̈́ͶͲͺͲ
ͳʹͲͲͲ
mount he have to pay back
k ൌ ̈́ͳʹͲͲͲ
̈́ͳʹ
ͳ ͲͲͲ ൅ ̈́
ͶͲͺͲ
ͶͲ
ͺͲ ൌ ̈́
̈́ͳ͸ͲͺͲ
Amount
̈́ͶͲͺͲ
̈́̈́ͳ͸ͲͺͲ
‫ݐ݊݁݉ݐݏ݁ݒ݊ܫ‬
‫ݐݏ݁ݒ݊ܫ‬
‫ ݐݐ݊݁݉ݐ‬ൌ ̈́͵ͷͲͲͲ
̈́͵ͷ
͵ͷͲͲ
ͲͲͲ
Ͳ
‫݁ݎ݁ݐ݊ܫ‬
‫ܽ݁ ݐݏ݁ݎ‬
ܽ‫݊ݎ‬
݊݁݀ ൌ ̈́ͳ͸ͺͲͲ
̈́ͳ͸
ͳ ͺͲͲ
‫݀݁݊ݎܽ݁ݐݏ݁ݎ݁ݐ݊ܫ‬
ͳ͸ͺͲ
ͳ͸
ͺ Ͳ
ͳ͸ͺͲͲ
‫݁݌ ݐݏ݁݁ݎ݁ݐ݊ܫ‬
‫݁ݕ ݎݎ݁݌‬
‫ ݎܽ ݕ‬ൌ
ൌ ̈́ʹͳͲͲ
‫ݎܽ݁ݕݎ݁݌ݐݏ݁ݎ݁ݐ݊ܫ‬
ͺ
ʹ
ʹͳ
ʹͳͲͲ
ͲͲ
‫ݐݏ݁ݎ݁ݐ݊ܫ‬
‫݁ݐܽݎ‬
‫ܽݎ‬
‫ ݁ݐ‬ൌ
ൈ ͳͲͲΨ ൌ ͸Ψ
‫݁ݐܽݎݐݏ݁ݎ݁ݐ݊ܫ‬
͵ͷͲͲͲ
S
Secondary 1 Express
ction B Marking Scheme
2017 MYE Section
.s
g
Guidance
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297
(b)
Qn
9
(a)
ile
m
or
Mark
Marks
ks
B1
B1
B1
ut
T
Solution
‫݈݂݂݀݁݅݋݄ݐ݈݈ܾ݃݊݁݁݅ݏݏ݋݌ݐݏ݁ݐܽ݁ݎܩ‬
‫ݐݏ݁ݐܽ݁ݎܩ‬
‫ ݈݂݀݁݅ ݂݋ ݄ݐ݈݃݊݁ ݈ܾ݁݅ݏݏ݋݌‬ൌ ͳͲͷǤͶ݉
ͳͲͷ
ͷǤͶ
Ͷ݉
‫ݐݏ݁ݐܽ݁ݎܩ‬
‫ ݈݂݀݁݅ ݂݋ ݄ݐ݀ܽ݁ݎܾ ݈ܾ݁݅ݏݏ݋݌‬ൌ ͹ͲǤͶ݉
͹Ͳ
ͲǤͶ ݉
‫݈݂݂݀݁݅݋݄ݐ݀ܽ݁ݎܾ݈ܾ݁݅ݏݏ݋݌ݐݏ݁ݐܽ݁ݎܩ‬
‫ݎ݁ݐ݁݉݅ݎ݁݌݈ܾ݁݅ݏݏ݋݌ݐݏ݁ݐܽ݁ݎܩ‬
‫ݐݏ݁ݐܽ݁ݎܩ‬
‫ ݎ݁ݐ݁݉݅ݎ݁݌ ݈ܾ݁݅ݏݏ݋݌‬ൌ ʹሺͳͲͷǤͶሻ ൅ ʹሺ͹ͲǤͶሻ
ʹሺሺ͹Ͳ
͹ͲǤͶሻ ൌ ͵ͷͳǤ͸
͵ͷ
͵
ͷͳǤ͸ 
S
Secondary 1 Express
2017 MYE Section B Marking Scheme
.s
g
Guidance
.s
g
or
ut
T
ile
m
S
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298
Register No.
Class
Name :
Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School
yS
chool Bendemeer
Ben
Bendemeer Secondary
School
Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School
Secon
con
cco
oonnddar
daar
ary S
chhho
ccho
oooll Ben
Bendemeer Secondary
School
Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School
Seeco
ccon
oonnddar
daar
ary S
cho
cch
hho
oooll Ben
B
Bendemeer Secondary
School
Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School
Seeccco
Se
oon
nddar
arry S
cho
cho
hool
ol B
Ben
Be
e
Bendemeer Secondary
School
Bendemeer
Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School
Seeco
S
coon
ndda
dar
ar
ary S
ch
cho
hhoool
ol B
en
Bendemeer Secondary
School
Bendemeer
Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School
ecoonnd
dar
da
ar
ary S
cho
cch
hhooooll B
en
Bendemeer S
Secondary
School
Bendemeer
Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School
Se
eco
con
oon
ondar
ndda
dar
aarry
ry S
cho
cch
hhooooll Be
B
en
Bendemeer S
Secondary
School
Bendemeer
Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School
S
eccon
co
oonnddar
daar
ary S
cch
cho
h ol
ho
ol B
en
Bendemeer Se
Secondary
School
Bendemeer
Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School
S
ecco
con
oonnddar
daar
ary S
cho
ch
hoooll B
Ben
Be
e
Bendemeer Se
Secondary
School
Bendemeer
Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School
ecco
con
oonnda
ddar
ar
ary S
ch
ccho
hho
oooll B
en
Bendemeer Se
Secondary
School
Bendemeer
Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School
nda
ddar
ar
ary S
cho
cch
hhoool
o Ben
Bendemeer Secon
Secondary
School
Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School
Bendemeer Secondary School Ben
Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School
Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School
:
:
:
5 Oct 2017
1 hour
50 Marks
ut
READ THESE INSTRUCTIONS FIRST
or
DATE
DURATION
TOTAL
.s
g
BENDEMEER SECONDARY SCHOOL
2017 END OF YEAR EXAMINATION
SECONDARY 1 EXPRESS
Mathematics Paper 1
T
Write your name, class and register number on all the work you hand in.
Write in dark blue or black pen on both sides of the paper.
You may use a 2B pencil for any diagrams or graphs.
Do not use staples, paper clips, highlighters, glue or correction fluid/tape.
S
m
ile
Answer all questions.
Write your answers in the spaces provided on the question paper.
All the diagrams in this paper are not drawn to scale.
If working is needed for any question, it must be shown with the answer.
Omission of essential working will result in loss of marks.
The use of an approved scientific calculator is expected, where appropriate.
If the degree of accuracy is not specified in the question, and if the answer is not exact, give
the answer to three significant figures. Give answers in degrees to one decimal place.
For S , use either your calculator value or 3.142, unless the question requires the answer in
terms of S .
At the end of the examination, fasten all your work securely together.
The number of marks is given in brackets [ ] at the end of each question or part question.
FOR EXAMINER’S USE
50
This document consists of 9 printed pages including this cover page.
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25
Answer all the questions.
1
For
Examiner’s
Use
Arrange the following numbers in ascending order.
x
x
x
x x
6
, 0.4 6 5
13
.s
g
0. 4 6 5, 0.46 5,
Answer:
[2]
______________________________________________________________________
(b)
900
1500
ut
(i)
(ii)
or
(a) Using prime factorisation, express the following two numbers as a product
of its prime factors. Leave your answer in index notation.
Hence or otherwise, find the
HCF of 900 and 1500
LCM of 900 and 1500
S
m
ile
(i)
(ii)
T
2
Answer:
2(a)(i) ………………………. [2]
2(a)(ii) ………...……………. [2]
2(b)(i) ………………………. [1]
2(b)(ii) ……………………… [1]
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26
Evaluate the following, and show your working clearly.
(a)
3 42 y 2 3 8 u 2 8
(b)
ª 2 § 1 ·º 6 § 4
3·
«1 3 ¨ 6 ¸» y 7 u ¨1 5 2 10 ¸
©
¹¼
©
¹
¬
For
Examiner’s
Use
ile
T
ut
or
.s
g
3
Answer:
3(a) ………………………. [2]
Nana bought 5 chocolate blocks and 3 bottles of carbonated drinks from a
supermarket. The price of a chocolate block is $3.95 and that of a bottle of
carbonated drink is $2.05. By estimating the price of each item, calculate the
estimated total price of Nana’s purchase.
S
4
m
3(b) ………………………. [2]
______________________________________________________________________
Answer:
$
…………………………
[2]
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27
5
Given the formula x
For
Examiner’s
Use
or
.s
g
and c = –3.
b b 2 4ac
, find the value of x when a = –4, b = 8
2a
Answer:
………………………. [2]
______________________________________________________________________
(a)
S
m
ile
(b)
4g 3 2 g 1
7
3
9 s 4t 3s 2t s 5t
5
2
3
ut
Express each of the following as a single fraction in its simplest form.
T
6
Answer:
6(a) …………………………… [2]
6(b) …………………………… [2]
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28
7
(a)
Expand and simplify (2 – b)(-3a) + 5(6ab – 2a + 3)
(b)
Factorise the following completely
25bx + 35by
8mn – 4m – 2n + 1
ut
or
.s
g
(i)
(ii)
For
Examiner’s
Use
7(a) ………………………… [2]
7(b)(i) ………………………… [1]
ile
T
Answer:
7(b)(ii) ………………………… [2]
______________________________________________________________________
Three numbers x, y and 36 have an average of 30.
Five numbers w, x, y, z and 36 have an average of 40.
What is the average of w and z?
S
m
8
Answer:
………………………… [3]
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29
Given that 3x and 6y are complementary angles, find the value of x + 2y.
For
Examiner’s
Use
.s
g
9
Answer:
………………………… [2]
______________________________________________________________________
Three of the exterior angles of a polygon with n sides are 60q, 45q and 75q.
The remaining exterior angles are each 30q. Calculate the value of n.
or
(a)
ile
T
ut
10
A
F
130q
120q
2w
B
2w
S
m
(b) ABCDEF is a hexagon. Find the value of w.
E
140q
2w
D
C
10(a) ………………………… [2]
Answer:
10(b) ………………………… [3]
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30
Zilong suffered a loss of 20% when his watch was sold at $80. How much should
he have sold his watch if he wanted to make a gain of 20%?
For
Examiner’s
Use
.s
g
11
ut
Karrie, Layla & Miya buy a present for their friend. The present costs $270 and it
is shared by Karrie, Layla & Miya in the ratio 3: 2 : 4.
(a)
Calculate the amount Karrie needs to contribute.
(b)
(i) If Layla doubles the amount she needs to contribute
and Karrie halves her amount, how much must Miya
contribute?
(ii) Hence, write down the new ratio of the amount that Karrie, Layla &
Miya need to contribute.
S
m
ile
T
12
or
$
Answer:
…………………………
[2]
______________________________________________________________________
$
12(a) …………………………
[1]
Answer:
$
12(b)(i) ………………………
[2]
12(b)(ii) ……………………... [1]
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31
If
k 21
, find the largest possible value of k such that k is a prime number.
5 4
For
Examiner’s
Use
or
.s
g
13
Line V
Line W
S
m
(a)
(b)
T
Write down the equation of the following graphs.
ile
14
ut
Answer:
………………………… [2]
______________________________________________________________________
y
Line W
x
Line V
14(a) ………………………… [1]
Answer:
14(b) ………………………… [2]
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32
15
A group of Singaporeans were surveyed to determine which countries they would
like to visit the most. Their choices were represented on a pie chart as given
below.
(a)
(b)
Find the value of w.
Hence, calculate the percentage of the group who would like to visit Japan
most.
If 40 adults would like to visit USA most, find the total number of adults
surveyed.
S
m
ile
T
ut
or
.s
g
(c)
For
Examiner’s
Use
Answer:
15(a) ………………………… [2]
15(b) ………………………… [1]
15(c) ………………………… [1]
- End of Paper -
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33
Register No.
Class
Name :
Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School
yS
chool Bendemeer
Ben
Bendemeer Secondary
School
Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School
Secon
con
cco
oonnddar
daar
ary S
chhho
ccho
oooll Ben
Bendemeer Secondary
School
Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School
Seeco
ccon
oonnddar
daar
ary S
cho
cch
hho
oooll Ben
B
Bendemeer Secondary
School
Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School
Seeccco
Se
oon
nddar
arry S
cho
cho
hool
ol B
Ben
Be
e
Bendemeer Secondary
School
Bendemeer
Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School
Seeco
S
coon
ndda
dar
ar
ary S
ch
cho
hhoool
ol B
en
Bendemeer Secondary
School
Bendemeer
Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School
ecoonnd
dar
da
ar
ary S
cho
cch
hhooooll B
en
Bendemeer S
Secondary
School
Bendemeer
Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School
Se
eco
con
oon
ondar
ndda
dar
aarry
ry S
cho
cch
hhooooll Be
B
en
Bendemeer S
Secondary
School
Bendemeer
Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School
S
eccon
co
oonnddar
daar
ary S
cch
cho
h ol
ho
ol B
en
Bendemeer Se
Secondary
School
Bendemeer
Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School
S
ecco
con
oonnddar
daar
ary S
cho
ch
hoooll B
Ben
Be
e
Bendemeer Se
Secondary
School
Bendemeer
Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School
ecco
con
oonnda
ddar
ar
ary S
ch
ccho
hho
oooll B
en
Bendemeer Se
Secondary
School
Bendemeer
Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School
nda
ddar
ar
ary S
cho
cch
hhoool
o Ben
Bendemeer Secon
Secondary
School
Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School
Bendemeer Secondary School Ben
Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School
Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School
:
:
:
10 Oct 2017
1 hour 30 minutes
50 Marks
ut
READ THESE INSTRUCTIONS FIRST
or
DATE
DURATION
TOTAL
.s
g
BENDEMEER SECONDARY SCHOOL
2017 END OF YEAR EXAMINATION
SECONDARY 1 EXPRESS
Mathematics Paper 2
T
Write your name, class and register number on all the work you hand in.
Write in dark blue or black pen on both sides of the paper.
You may use a 2B pencil for any diagrams or graphs.
Do not use staples, paper clips, highlighters, glue or correction fluid/tape.
S
m
ile
Answer all questions.
Write your answers in the spaces provided on the question paper.
All the diagrams in this paper are not drawn to scale.
If working is needed for any question, it must be shown with the answer.
Omission of essential working will result in loss of marks.
The use of an approved scientific calculator is expected, where appropriate.
If the degree of accuracy is not specified in the question, and if the answer is not exact, give
the answer to three significant figures. Give answers in degrees to one decimal place.
For S , use either your calculator value or 3.142, unless the question requires the answer in
terms of S .
At the end of the examination, fasten all your work securely together.
The number of marks is given in brackets [ ] at the end of each question or part question.
FOR EXAMINER’S USE
50
This document consists of 9 printed pages including this cover page.
Need a home tutor? Visit smiletutor.sg
34
Answer all the questions.
A sequence of patterns formed by dots is as shown.
Pattern 2
Pattern 3
Number of dots = 1
Number of dots = 5
Number of dots = 9
(a)
(b)
Draw the 4th pattern of the sequence in the above box.
State the total number of dots required, in terms of n, to form the nth
pattern?
Pattern P requires 333 dots. What is the value of ‘P’?
[1]
m
ile
T
ut
(c)
Pattern 4
.s
g
Pattern 1
or
1
For
Examiner’s
Use
Answer:
1(b) ………………………… [1]
S
1(c) ………………………… [1]
______________________________________________________________________
2
(a) Factorise xy – yz.
(b) Using the answer in (a), find the exact value of the following without the use
of calculator.
3165 × 876543 – 876543 × 3155
Answer:
2(a) ………………………… [1]
2(b) ………………………… [1]
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35
3
Franco went to a fast-food restaurant and saw the following sign.
Burger o $2x each
For
Examiner’s
Use
Fries o $2.00 each
Drink o $(x+1) each
He bought 5 burgers, 5x fries, 3 drinks and 6 sundaes.
(a)
Write down, in the expanded form, the amount Franco paid for the
following items, in terms of x,
or
(i) burger
(ii) fries
(iii) drinks
ut
Find the cost of each burger if Franco paid $58 for all the items.
S
m
ile
T
(b)
.s
g
Sundae o $1.50 each
Answer:
3(a)(i) ……………………… [1]
3(a)(ii) ……………………... [1]
3(a)(iii) …………………….. [1]
3(b) ………………………... [2]
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36
4
ଵ
Tigreal spent x hours per day to revise for his examinations. He spent of his
଺
ଵ
ଵ
revision time on Geography, of his remaining revision time on English, of the
ହ
ସ
remaining revision time after English on Biology and then spent the last 40
minutes on Mathematics.
For
Examiner’s
Use
(i) Biology
(ii) Mathematics
(b)
Hence, find the value of x.
ut
or
(a)
.s
g
Giving each answer in its simplest form, find an expression, in terms of x, for the
time Tigreal spent revising for
4(a)(i) ……………………… [1]
4(a)(ii) ……………………... [1]
ile
T
Answer:
4(b) ………………………... [1]
______________________________________________________________________
Freya drives a distance of 150 km at a speed of 90 km/h. After resting for 20
mins, she took another 2.5 h to complete the remaining 245 km of the journey.
Find Freya’s average speed for the whole journey.
S
m
5
Answer:
………………………… [3]
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37
In the figure, AF // BE, ‘FJG = 115q and ‘KLM = 120q. Find the following
angles, giving reasons for each answer
(a)
(b)
(c)
For
Examiner’s
Use
angle x
angle y
angle z
F
E
115q
J
K
H
M
x
y
120q
z
L
B
C
S
m
ile
T
ut
A
D
or
G
.s
g
6
Answer:
6(a) ………………………… [1]
6(b) ………………………… [1]
6(c) ………………………… [1]
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38
In the figure, ABCD is a trapezium. Given that DA is parallel to GF, BA is parallel
to CD, CG = CF, ‘DAG = 78°, ‘FGC = 43° and ‘BFE = 35°, show that AG is
parallel to EF.
[3]
E
A
For
Examiner’s
Use
B
35q
78q
.s
g
7
F
43q
D
C
S
m
ile
T
ut
or
G
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39
8
ABCD is a square of side 10 cm. P, Q, R and S are midpoints of AB, BC, CD and
AD respectively. The figure is drawn using 4 equal semicircles and 4 equal
quadrants of circles. Calculate
S
A
(a) the area of the shaded region
(b) the perimeter of the shaded region
For
Examiner’s
Use
D
.s
g
(Take S to be 3.14)
R
Q
C
S
m
ile
T
ut
B
or
P
Answer:
8(a) ………………………… [4]
8(b) ………………………… [4]
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40
9
During the ancient days in China, the coins were used for transactions. A typical
coin has a circular cross-section area with a square hole. It has an uniform
thickness of 2 mm and its outermost diameter is 25 mm. The square hole is 5 mm
by 5 mm. Find its
(a)
(b)
For
Examiner’s
Use
volume
total surface area
.s
g
(Take S to be 3.14, and round off your answers to the nearest integer)
25 mm
S
m
ile
T
ut
or
5mm
Answer:
9(a) ………………………… [4]
9(b) ………………………… [4]
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41
10
The marked price, inclusive of 7% GST, of a LCD television was $2675. Harley
bought the television during the recent COMEX exhibition and received a 5%
discount.
Calculate the marked price before GST.
Find the original GST amount.
Find the selling price, before GST, of the LCD television.
Find the GST amount after the discount.
ut
or
.s
g
(a)
(b)
(c)
(d)
For
Examiner’s
Use
10(a) ………………………… [1]
10(b) ………………………… [1]
10(c) ………………………… [1]
ile
T
Answer:
10(d) ………………………… [1]
______________________________________________________________________
Answer the WHOLE of this question on a graph paper
m
11
Given that y = 1 – 3x, copy and complete the following table.
x
-3
y
10
S
(a)
-2
-1
1
2
[2]
3
-2
(b)
Using a scale of 2 cm to represent 1 unit on the x-axis and 2 cm to represent
2 units on the y-axis, draw the graph of y = 1 – 3x for values of x from -3 to
3.
[3]
(c)
Using your graph, find the value of
(i) y when x = 1.5
(ii) x when y = 1
[1]
[1]
(d)
Hence, or otherwise, find the gradient of the graph.
[1]
- End of Paper -
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42
.s
g
or
ut
T
ile
m
S
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43
PAPER 1
MARKING SCHEME
.
Answer all the questions.
1
For
Examiner’s
Use
Arrange the following numbers in ascending order.
x
x
x
0. 4 6 5, 0.46 5,
x x
6
, 0.4 6 5
13
.s
g
[B2] – 0.5 for ea ch correct order
x
x
x
x x
6
, 0. 4 6 5, 0.46 5, 0.4 6 5
13
Answer:
[2]
[ ]
[2
______________________________________________________________________
________________________________________________________________
_______
__
(i)
(ii)
(b)
900
1500
or
numbers
Using prime factorisation, express the following two number
rs as a product
produ
duct
du
ct
of its prime factors. Leave your answer in index notation.
ut
(a)
Hence or otherwise, find the
HCF of 900 and 1500
LCM of 900 and 1500
ile
(i)
(ii)
T
2
Prime fa ctor
ctoriza
riz
i a tion for 900 [M1]
reee or ddivision
re
ivision method
} fa ctorr ttree
Prime fa ctoriza tion for 1500 [M1]
m
900 = 22 × 32 × 52
1500 = 22 × 3 × 53
[A1]
[A1]
[A11]
LCM of 900
0 & 150
500 = 22 × 32 × 53
= 4500
[A11]
S
HCF of 900
900 & 1500
50 0 = 22 × 3 × 52
= 3300
00
22 × 32 × 52
2(a)(i) ……………………….
[2]
Answer:
22 × 3 × 53
2(a)(ii) ………...……………. [2]
300
2(b)(i) ………………………. [1]
4500
2(b)(ii) ………………………
[1]
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44
3
Evaluate the following, and show your working clearly.
(a)
3 42 y 2 3 8 u 2 8
(b)
ª 2 § 1 ·º 6 § 4
3·
«1 3 ¨ 6 ¸» y 7 u ¨1 5 2 10 ¸
©
¹¼
¹
©
¬
= 3 + 16 y 2 + 2 ×(-6)
= 3 + 8 + (-12)
= -1
ut
T
[M1]
[A1]
ile
7
8
or
[M11]
[A1]
ª 2 § 1 ·º 6 § 4
3·
«1 3 ¨ 6 ¸» y 7 u ¨1 5 2 10 ¸
¹
©
¹¼
©
¬
3
6
1
·
§
= y u¨ ¸
2 7 © 2¹
7
= u §¨ 1 ·¸
4 © 2¹
=
.s
g
3 42 y 2 3 8 u 2 8
For
Examiner’s
Use
–1
1
3(a)
3(a
(a)) ……………………….
[2]
7
8
3(b) ……………………….
[2]
______________________________________________________________________
________________________
_ __
_ __________
____
____
__________________________________
chocolate
Nana bought 5 cho
hocolatee bblocks
lock
lo
ckss and
and 3 bottles of carbonated drinks from a
supermarket.. The
he pprice
rice
ce of
of a ch
choc
chocolate
o olate block is $3.95 and that of a bottle of
carbonated ddrink
rink
ri
nk is
is $2.05.
$2.0
$2
05. By estimating the price of each item, calculate the
estimated total
tota
tall price
pric
pr
icee of Nana’s purchase.
S
4
m
Answer:
A
An
swerr:
Estima ted cost of chocola te block | $4.00
} [M1]
Estima ted cost of ca rbona ted drink | $2.00
Tota l price | $4.00 × 5 + $2.00 × 3
[A1]
= $26.00
Answer:
26
$
…………………………
[2]
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45
5
Given the formula x
and c = –3.
x
b b 2 4ac
, find the value of x when a = –4, b = 8
2a
8 82 4 4 3
2 4
For
Examiner’s
Use
[M1]
.s
g
8 64 48
8
8 16
8
8 4 1
8
2
[A1]
(a)
ile
(b)
4g 3 2 g 1
7
3
9 s 4t 3s 2t s 5t
5
2
3
ut
Express each of the following as a single fraction in it
its
simplest
ts ssi
im
mp
ple
lesstt form.
for
orm
m..
T
6
or
1
……………………….
Answer:
………
………
…2……
… ……
…. [2
[2]]
______________________________________________________________________
____________________________________________________
__
__
__
_____
____
____
___________
S
m
4g 3 2 g 1
7
3
9s 4t 3s 2t s 5t
5
2
3
3 4 g 3 14 g 1
21
2
1
12 g 9 14
14 g 14
4
21
2
1
2g 5
21
2
1
[M1]
[A1]
6 9s 4t 15 3s 2t 10 s 5t
30
54 s 24t 45s 30t 10 s 50t
30
109s 44t
30
[M1]
[A1]
2g 5
21
6(a) ……………………………
[2]
Answer:
109 s 44t
30
6(b) …………………………… [2]
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46
7
(a)
Expand and simplify (2 – b)(-3a) + 5(6ab – 2a + 3)
(b)
Factorise the following completely
(i)
(ii)
For
Examiner’s
Use
25bx + 35by
8mn – 4m – 2n + 1
25bxx + 35by = 5b (5x + 7y)
[M1]
[A1]
.s
g
(2 – b )(-3a ) + 5(6a b – 2a + 3) = -6a +3a b + 30 a b – 10 a + 15
= 33a b – 16a + 15
or
[A1]
8mn
n – 4m – 2n + 1 = 4m (2n – 1) – (2n – 1)
= (2n – 1)(4m – 1)
ut
[M1]
[A1
1]
a b – 16a……
+ 15
7(a) …………………………
… 33
……
………………
…………
[[2]
2]
T
Answer:
An
5b (5x + 7y)
7(b)(i) …………………………
………
……………………… [1]
Three numbers x, y and 36 have an average
aver
av
erag
agee of 30.
30.
Five numbers w, x, y, z and 36 have aan
average
n av
averag
ge of 40.
What
Wh
hat is the average of w aand
nd z??
m
8
ile
( n – 1)(4m – 1)
(2
7(b)(ii)
7(b)
b)(i
(ii)
i) …………………………
………
……………………… [2]
______________________________________________________________________
_______________________________________________
_ __
____
_ ____________________
[B1]
w + x + y + z + 36 = 40 × 5
w + x + y + z = 200 – 36
w +54 + z = 164
w + z = 164 – 54
w + z = 110
[B1]
Avera ge of w & z = 110 y 2 = 55
[B1]
S
x + y + 36 = 30 × 3 = 90
x + y = 90 – 36
x + y = 54
Answer:
55
………………………… [3]
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47
9
Given that 3x and 6y are complementary angles, find the value of x + 2y.
[M1]
[A1]
.s
g
3x +6y = 90
3(x + 2y) = 90
x + 2y = 30
For
Examiner’s
Use
x +2
+ 2y = 30
Answer:
…………………………
………………………
……… [2]
[2
______________________________________________________________________
________________________________________________________________
________
(a)
Three of the exterior angles of a polygon with n sides are 60q,
60
0q, 45
45qq and
and 75q.
75q.
The remaining exterior angles are each 30q. Calculate the value
valu
va
luee of n.
or
10
0
ile
T
ut
Sum of a ll ext. ‘s = 360q
Sum of rema ining ext. ‘s = 360q - 60q - 45q - 75q
75
5q
= 180q
[B1]
No. of rema ining ext. ‘s = 180q y 30q = 6
n = 6 +3 = 9
[B1]
m
w..
(b) ABCDEF
F iiss a hexagon. Find thee value
valu
va
lue of w
A
F
1 0q
13
130q
2w
2w
S
B
120q
E
140q
2w
Sum of a ll int. ‘s = (6 – 2) × 180q = 720q
+ 120q +2
+ 2w +1
130q +1
+ 140q +
+2
2w +2
+ 2w = 720q
390q + 6w = 720q
w = 55q
[B1] C
D
[B1]
[B1]
9
10(a) ………………………… [2]
Answer:
55°
10(b) …………………………
[3]
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48
11
Zilong suffered a loss of 20% when his watch was sold at $80. How much should
he have sold his watch if he wanted to make a gain of 20%?
[B1]
[B1]
.s
g
80% o $80
1% o $1
120% o $120
For
Examiner’s
Use
ut
Karrie, Layla & Miya buy a present for their friend. The presen
present
en
nt costs
cco
osstts $270
$2 aand
nd iitt
is shared by Karrie, Layla & Miya in the ratio 3: 2 : 4.
(a)
Calculate the amount Karrie needs to contribute.
(b)
(i) If Layla doubles the amount she needs to contribute
contrribute
and Karrie halves her amount, how much mustt Miya
contribute?
(ii) Hence, write down the new rratio
amount
Karrie,
atio of
at
of th
tthee amou
unt tthat
hatt Ka
ha
K
rrie, Layla &
Miya need to contribute.
ile
T
122
or
120
$
Answer:
…………………………
…………………
…………
… [2]
[2]
______________________________________________________________________
_________________________________________________________
____
____
___________
Tota l pa rts = 3 + 2 + 4 = 9 pa rts
m
9 pa rts = $270
1pa rt = $30
3 pa rts = $900
[A1]
[A1
[B1]
Miya ’s new contribution = $270 - $120 - $45
= $105
[B1]
S
origina
La yla ’s or
orig
igin
inaa l ccontribution
ontr
on
trib
b ut
utio
i n : 2 pa rts o $60
contribution
La yla ’s ne
new
w co
cont
n riibu
buti
tion = $60 × 2 = $120
Ka rrie’s new
ew contribution
con
ontr
trib
ibution = $90 y 2 = $45
Ka rrie : La yla : Miya
45 : 120 : 105
3:8:7
[A1]
$
90
12(a) …………………………
[1]
Answer:
105
$
12(b)(i) ………………………
[2]
3:8:7
12(b)(ii) ……………………... [1]
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49
13
If
k 21
, find the largest possible value of k such that k is a prime number.
5 4
k
21
u5
4
For
Examiner’s
Use
[B1]
.s
g
k < 26.25
[B1]
or
la rgest possible va lue of k , such tha t k is a prime number = 23
Write down the equation of the following graphs.
Line V
Line W
m
ile
(a)
(b)
T
14
4
ut
23
23
Answer:
…………………………
……
……
……
……
……
……
………
………
… [2]
[2]
______________________________________________________________________
_____________________________________________________
___
__
__
_______
____
__
_________
__
y
Line W
x
S
Line V
Line W:
Gra dient = –1
y-intercept = 1
equa tion:
y = –x + 1
[B1]
[B1]
x = –1
14(a) ………………………… [1]
Answer:
y = –x + 1
14(b) ………………………… [2]
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50
15
A group of Singaporeans were surveyed to determine which countries they would
like to visit the most. Their choices were represented on a pie chart as given
below.
(a)
(b)
Find the value of w.
Hence, calculate the percentage of the group who would like to visit Japan
most.
If 40 adults would like to visit USA most, find the total number of adults
surveyed.
T
ut
or
.s
g
(c)
For
Examiner’s
Use
ile
3w + 80q + w + 120q = 360q
4w + 200q = 360q
w = 40q
[B1]
[B1
[B1]
3w = 3 × 40q = 120q
(120/360) × 100% = 33.3%
m
[A1]
S
80q o 40
10q o 5
360q o 5 × 36 = 180 a dults
[A1]
40°
15(a)
15( ) ………………………… [2]
Answer:
A
33.3%
15(b) ………………………… [1]
180
15(c) …………………………
[1]
- End of Paper -
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51
PAPER 2
MARKING SCHEME
Answer all the questions.
A sequence of patterns formed by dots is as shown.
Pattern 1
Pattern 2
Pattern 3
Number of dots = 1
Number of dots = 5
Number of dots = 9
Draw the 4th pattern of the sequence in the above box.
State the total number of dots required, in terms of n, to form
m th
thee nth
pattern?
Pattern P requires 333 dots. What is the value of ‘P’?
[1]
ut
(c)
.s
g
(a)
(b)
Pattern 4
or
1
For
Examiner’s
Use
ile
T
dots.
The difference between ea ch pa ttern is 4 dot
ott s.
T1
=1
= 4(1) – 3
T2
=5
= 4(2) – 3
T3
=9
= 4(3) – 3
T4
= 4(4) – 3
= 13
[A1]
Tn
= 4n – 3
4p – 3 = 333
= 336
4p
= 84
p
m
Tp =
[A11]
[[A
4n – 3
1(b) ………………………… [1]
Answer:
An
S
84
1(c) ………………………… [1]
______________________________________________________________________
______________
___
____
____
_ __
___
_ ______________________________________________
2
(a) Factorise xy – yz.
(b) Using the answer in (a), find the exact value of the following without the use
of calculator.
xy – yz = y (x – z)
3165 × 876543 – 876543 × 3155
[A1]
x = 3165, y = 876543, z = 3155
3165 × 876543 – 876543 × 3155
= 876543 (3165 – 3155)
Answer:
= 876543 (10)
= 8765430
[A1]
y (x – z)
2(a) ………………………… [1]
8 765 430
2(b) ………………………… [1]
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52
3
Franco went to a fast-food restaurant and saw the following sign.
Burger o $2x each
For
Examiner’s
Use
Fries o $2.00 each
Drink o $(x+1) each
He bought 5 burgers, 5x fries, 3 drinks and 6 sundaes.
(a)
Write down, in the expanded form, the amount Franco paid for the
he
following items, in terms of x,
or
(i) burger
(ii) fries
(iii) drinks
ut
Find the cost of each burger if Franco paid $58
the
$558 fo
ffor
or al
aall
ll tth
he items.
iitteem
ms.
5 × 2x = 10 x
[A1]
Fries:
T
(b)
.s
g
Sundae o $1.50 each
5x × 2 = 10 x
[A1]
Drinks:
Drinks
ks:
3 × (x + 1) = 3x +
+3
3
[A1
[A
A1]
ile
Burger:
[B1]
S
m
10 x + 10 x + 3x + 3 + 6 × 1.50
50 = 558
8
23x + 12 = 558
8
23x = 466
x =2
Eaa ch bburger
urge
ur
gerr co
cost
costs
stss = 2x = 2 × 2 = $4
Answer:
[B1]
10 x
3(a)(i) ………………………
[1]
10 x
3(a)(ii) ……………………...
[1]
3x + 3
3(a)(iii) ……………………..
[1]
$4
3(b) ………………………...
[2]
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53
4
Tigreal spent x hours per day to revise for his examinations. He spent of his
revision time on Geography, of his remaining revision time on English, of the
remaining revision time after English on Biology and then spent the last 40
minutes on Mathematics.
For
Examiner’s
Use
(a)
(i) Biology
(ii) Mathematics
(b)
Hence, find the value of x.
Time spent on Geogra ph = h
Time spent on English =
ut
= h
or
Let x be the tota l time spent for the study period.
Time spent on Biology =
T
= h
Time spent on Ma thema tics =
[A1]
= h
[A1
[A1]
h
4(a)(i)
4(a
(a)(
)(i)
i) ………………………
……………………… [1]
Answer:
An
Answer
er:
ile
Given =
.s
g
Giving each answer in its simplest form, find an expression, in terms of x, for the
time Tigreal spent revising for
h
4(a)(ii)
4(
4(a)
a)(ii) ……………………... [1]
1 h
4(b) ………………………... [1]
______________________________________________________________________
______________________
___
_______
_ __
____
____
____
_ ________________________________
Freya drives a distance
dis
ista
tance of 1150
50 kkm
m at a speed of 90 km/h. After resting for 20
mins, she took another
anoth
her 2.5
2.5 h ttoo complete the remaining 245 km of the journey.
Find Freya’s
Freya
ya’s
’s average
ave
vera
rage
ge speed
spe
peed
ed
d for the whole journey.
S
5
[A1]
m
=1 h
Tota l distaa nce
nce ttra
ra ve
velled = 150 + 245 = 395 km
Time ta ken for first pa rt of journey =
Time spent on resting =
[B1]
= h
= h
Tota l time ta ken = + + 2.5 = h
[B1]
Avera ge speed for the whole journey =
=
Answer:
km/h
[B1]
km/h
………………………… [3]
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54
In the figure, AF // BE, ‘FJG = 115q and ‘KLM = 120q. Find the following
angles, giving reasons for each answer
(a)
(b)
(c)
For
Examiner’s
Use
angle x
angle y
angle z
F
E
115q
115
J
K
H
M
x
y
120q
z
L
A
C
ut
B
D
or
G
.s
g
6
x = 115°
[A1]
T
(vert. opp. ‘s)
y = x = 115°
[A1]
ile
(corr. ‘s, // lines)
z = 180° – 120°
[A1]
[A1
S
m
(int. ‘s, // lines)
z = 60°
Minus
M
inuss 1m ffor
or not sta ting properties used
Answer:
115q
6(a) ………………………… [1]
115q
6(b) …………………………
[1]
60q
6(c) …………………………
[1]
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55
7
In the figure, ABCD is a trapezium. Given that DA is parallel to GF, BA is parallel
to CD, CG = CF, ‘DAG = 78°, ‘FGC = 43° and ‘BFE = 35°, show that AG is
parallel to EF.
[3]
E
A
For
Examiner’s
Use
B
35q
78q
.s
g
F
43q
D
‘AGF = ‘DAG = 78° (a lt. ‘s, // lines)
C
or
G
ut
ngle)
‘CFG = ‘CGF = 43° (ba se a ngles of isoceles tria ng
glee )
T
‘BFE +‘EFG +‘CFG = 180° (‘s on a st. line)
35° + ‘EFG +43° = 180°
‘EFG = 102°
[M2]
[M2
M]
[A1]
S
m
ile
‘AGF +‘EFG = 78° + 102° = 180°
Therefore, ‘AGF & ‘EFG must be inte
interior
e rior
o a ngless of ppaa ra
ra llel
l
lines, a nd the pa ra llel lines a re AG
G a nd
nd E
EF
F.
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56
8
ABCD is a square of side 10 cm. P, Q, R and S are midpoints of AB, BC, CD and
AD respectively. The figure is drawn using 4 equal semicircles and 4 equal
quadrants of circles. Calculate
S
A
(a) the area of the shaded region
(b) the perimeter of the shaded region
For
Examiner’s
Use
D
.s
g
(Take S to be 3.14)
R
Q
ut
B
or
P
[B1]
[B2]
[B1]
ile
T
Area of sha ded region
= a rea of 4 qua dra nts – a rea of 4 semi-circles
= [(3.14 ×5
× 52) y 4] × 4 – [(3.14 × 2.52) y 2] × 4
= 78.5 – 39.25
= 39.25 cm 2
C
S
m
Perimeter of sha ded region
= circumference of 4 qua dr
ra nts
nts + cir
rcu
cumf
mferen
e ce of 4 semi-circles [B1]
dra
circumference
+ 4 × 5 cm
m
[B2]
= [(3.14 × 10) y 4] × 4 + [[(3.1
(3.1
(3
.14 × 5) y 2] × 4 + 20
= 31.4 + 31.44 + 20
[B1]
= 82.8 cm
Answer:
39.25 cm 2
8(a) ………………………… [4]
82.8 cm
8(b) ………………………… [4]
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57
9
During the ancient days in China, the coins were used for transactions. A typical
coin has a circular cross-section area with a square hole. It has an uniform
thickness of 2 mm and its outermost diameter is 25 mm. The square hole is 5 mm
by 5 mm. Find its
(a)
(b)
For
Examiner’s
Use
volume
total surface area
.s
g
(Take S to be 3.14, and round off your answers to the nearest integer)
ut
= volume of cylinder – volumee ooff ccu
u bo
b oid
id
cuboid
2
= 3.14 × (25 y 2) × 2 – 5 × 5 × 2
= 981.25 – 50
= 931.25 mm 3
est integer)
| 931mm 3 (rounding off to nea rrest
T
Volume of coin
255 m
mm
m
or
5mm
[B1]
= surfa ccee a rea
rea of cy
cyli
lind
nder
er – a rrea
ea of two squa res [B1]
cylinder
ea ooff sides of cub
uboi
oid
d
+ a rea
cuboid
(25 y 2)2 × 2 + 3.
3.14 ×
×25
= 3.14 × (25
25 × 2 – 5 × 5 × 2
[B2]
+5 ×4 ×2
= (981
81.25
.25 + 157)) – 50 + 40
= 1128.25
28.2
28
.25
5 mm
m 2
m m 2 (rounding off to nea rest integer)
| 1128 mm
[B1]
S
m
ile
Tota l surfa ce a rea of coin
[B1
[B1]
[B2]
[B2
B2]]
Answer:
931 mm 3
9(a) ………………………… [4]
1128 mm 2
9(b) …………………………
[4]
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58
The marked price, inclusive of 7% GST, of a LCD television was $2675. Harley
bought the television during the recent COMEX exhibition and received a 5%
discount.
107% o $2675
100% o $2500
[A1]
GST = $2675 – $2500 = $175
[A1]
00%
100
% o $2500
95% o $2375
[A1]
GST
= 7% × $2375
= $166.25
.s
g
Calculate the marked price before GST.
Find the original GST amount.
Find the selling price, before GST, of the LCD television.
Find the GST amount after the discount.
or
(a)
(b)
(c)
(d)
For
Examiner’s
Use
[A1]
ut
10
$2500
$2500
$2
0
10(a) …………………………
…………………
………
……
……… [1
[1]
$175………
10(b) …………………………
………………
………… [1]
10(c)) …………………………
…………
……
… $2375
……………… [1]
ile
T
Answer:
$166.25
66 25
10(d)
10(d
10
(d)) …………………………
[1]
______________________________________________________________________
____________________________________
____
____
____
_ __
____
__________________________
Answer the WHOLE of this question
quest
stio
ion
n on
o a graph
graph paper
m
11
Given thatt y = 1 – 3x, copy
c py aand
co
nd ccomplete
omplete the following table.
x
--33
y
10
S
(a)
--2
2
-1
1
2
[2]
3
-2
(b)
Using a scale
sccal
a e of 2 cm to represent 1 unit on the x-axis and 2 cm to represent
2 units on the y-axis, draw the graph of y = 1 – 3x for values of x from -3 to
3.
[3]
3
(c)
Using your graph, find the value of
(i) y when x = 1.5
(ii) x when y = 1
[1]
[1]
(d)
Hence, or otherwise, find the gradient of the graph.
[1]
- End of Paper -
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59
.s
g
or
ut
T
ile
m
S
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60
.s
g
or
ut
T
ile
m
S
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61
Class
Index Number
Name
BUKIT MERAH SECONDARY SCHOOL
.s
g
END OF YEAR EXAMINATION 2017
SECONDARY 1 EXPRESS
MATHEMATICS
READ THESE INSTRUCTIONS FIRST
ut
Candidates answer on the Question Paper.
No additional material is required.
5 October 2017
1 hour 15 minutes
or
Paper 1
4048/01
T
Write your name, class and index number on all the work you hand in.
Write in dark blue or black pen on both sides of the paper.
You may use a pencil for any diagram or graphs.
Do not use staples, paper clips, highlighters, glue or correction fluid.
m
ile
Answer all questions.
If working is needed for any question it must be shown with the answer.
Omission of essential working will 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 the answer
to three significant figures. Give the answers in degrees to one decimal place.
For ߨ, use either your calculator value or 3.142, unless the question requires the answer in terms of ߨ.
S
At the end of the examination, fasten all your work securely together.
The number of marks is given in brackets [ ] at the end of each question or part question.
The total number of marks for this paper is 50.
For Examiner’s Use
Part A
(Algebra
Component)
Part B
Calculator Model:
Total
This document consists of 12 printed pages, including this cover page.
Setter: Yvonne Lee
[Turn over
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62
2
Part A – Answer all questions
Simplify
(a)
a u 3b a ,
(b)
x 2 y 2x ,
(c)
4 z 3 2 5z
.
3
4
S
m
ile
T
ut
or
.s
g
1
Answer (a)
……………….……………
[1]
(b)
……………….……………
[2]
(c)
……………….……………
[2]
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Yvonne Lee/BMSS/2017/1E/P1/EOY
63
2
3
Factorise
(a)
v w v( w v) .
or
.s
g
(b)
3 p 2 q 12 pq 6 pq 2 ,
…………………..…………
[1]
(b)
…………………..…………
[1]
(a) Solve the inequality 4 x ! 8 and illustrate your solution on the number line below.
S
m
ile
3
T
ut
Answer (a)
[2]
Answer (a)
-4
-3
-2
-1
0
1
2
3
(b) Hence, write down the largest integer value of x which satisfies 4 x ! 8 .
Answer (b)
x
……………..………… [1]
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Yvonne Lee/BMSS/2017/1E/P1/EOY
64
Solve
(a)
2 3c 1 3 2 c
(b)
f 2
1
5
0
f 1
2
S
m
ile
T
ut
or
.s
g
4
4
Answer (a)
c
……………..…………
[2]
(b)
f
...…………..…………
[3]
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Yvonne Lee/BMSS/2017/1E/P1/EOY
65
5
Part B – Answer all questions
(a) Express 0.28 as a fraction in its simplest form.
Answer (a)
13.6 1.482
S
, correct your answer to
2 significant figures,
(ii)
3 decimal places.
T
ut
(i)
[1]
or
(b) Evaluate
……………………………..
.s
g
5
(i)
………………………
[1]
(ii)
………………………
[1]
2
§ 1· 3 § 2·
Without using a calculator, evaluate ¨1 ¸ y ¨ ¸ . Show your workings clearly.
© 2¹ 7 © 3¹
S
m
6
ile
Answer (b)
Answer …………………………………...
[3]
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Yvonne Lee/BMSS/2017/1E/P1/EOY
66
7
When written as a product of their prime factors,
6
p
23 u 39 ,
q
2 u 32 u 5 ,
r
22 u 3 u 7 .
Find
(a) the value of the cube root of p ,
.s
g
(b) the LCM of p , q and r , giving your answer as the product of its prime factors,
S
m
ile
T
ut
or
(c) the greatest number that will divide p , q and r exactly.
Answer (a)
…………………..…………
[1]
(b)
LCM = ...…………………..
[1]
(c)
……………………………..
[1]
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Yvonne Lee/BMSS/2017/1E/P1/EOY
67
8
7
(a) Apple juice, peach juice and lemonade were used to make a fruit punch in the ratio 5 : 3 : 7
respectively. Ali used 2.8 litres of lemonade.
How much apple juice did he use?
.s
g
(i)
...………..………..... l
[1]
How much fruit punch did he make altogether?
ile
T
ut
(ii)
(i)
or
Answer (a)
Answer (a)
(ii)
…...……..……...….. l
[1]
m
(b) Baba makes a fruit punch using mango juice, orange juice and lemonade.
The ratio of mango juice : orange juice is 2 : 3 .
S
The ratio of orange juice : lemonade is 4 : 3 .
Find the ratio of mango juice : orange juice : lemonade.
Answer (b)
……..… : ….…... : ……….
[1]
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Yvonne Lee/BMSS/2017/1E/P1/EOY
68
9
8
(a) Express 3 centimetres as a percentage of 6 metres.
Answer (a)
………………..……...… %
[1]
or
.s
g
(b) Express 24 m/s into km/h.
Answer (b)
………………..…….. km/h
ut
10 In the diagram, ABCD is a trapezium in which AD 13 cm, AB 10 cm, BC
‘DAB 90q . E and F are points on AD and AB respectively such that AE
[1]
20 cm and
6 cm and AF
8 cm.
S
m
ile
T
Find the area of the shaded region EFBC.
Answer …………………………….... cm2
[3]
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Yvonne Lee/BMSS/2017/1E/P1/EOY
69
.s
g
11 Mrs Lee bought 2 books during a sale.
9
Calculate
(a) the total amount she paid for both books,
S
m
ile
T
ut
or
(b) the total amount of GST.
Answer (a)
$ …………………………...
[2]
(b)
$ …………………………...
[2]
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Yvonne Lee/BMSS/2017/1E/P1/EOY
70
10
12 Given the following sequence,
.s
g
1 1 1
6 3 2
1 1 1
12 4 3
1 1 1
20 5 4
1 1 1
30 6 5
#
1 1
1
p 12 11
or
find
(a) the 5th line of sequence,
ut
(b) the value of p ,
S
m
ile
T
(c) the value of 1 1 , showing your workings clearly.
98 99
Answer (a)
…………………..…………
[1]
(b)
p
...…………..…………
[1]
(c)
…………………..…………
[2]
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71
11
13 In the diagram, UTR is a straight line and TQR is an isosceles triangle such that QT
that PQ // RS , ‘UTQ 155q and ‘PQT
90q , find
‘TRS .
or
(b)
S
m
ile
T
ut
‘TQR ,
.s
g
155o
(a)
QR . Given
Answer (a)
‘TQR
............................q
[2]
(b)
‘TRS
.............................q
[2]
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Yvonne Lee/BMSS/2017/1E/P1/EOY
72
12
14
(a) Complete the following table for the equation y
0
x
4
1
x.
2
4
[2]
8
y
4
1
x for 0 d x d 8 on the grid provided below.
2
[2]
S
m
ile
T
ut
or
.s
g
(b) Draw the graph of y
(c) Draw a straight line y 3 on the same grid.
[1]
(d) Write down the coordinates of the point of intersection of the two lines.
Answer (d)
( .................. , .................... )
[1]
End of paper
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Yvonne Lee/BMSS/2017/1E/P1/EOY
73
Class
Index Number
Name
BUKIT MERAH SECONDARY SCHOOL
.s
g
END OF YEAR EXAMINATION 2017
SECONDARY 1 EXPRESS
MATHEMATICS
READ THESE INSTRUCTIONS FIRST
ut
Additional Materials: Writing paper (5 sheets)
Cover Page (1 sheet)
10 October 2017
1 hour 30 minutes
or
Paper 2
4048/02
T
Write your name, class and index number on all the work you hand in.
Write in dark blue or black pen on both sides of the paper.
You may use a pencil for any diagram or graphs.
Do not use staples, paper clips, highlighters, glue or correction fluid.
m
ile
Answer all questions.
If working is needed for any question it must be shown with the answer.
Omission of essential working will 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 the answer
to three significant figures. Give the answers in degrees to one decimal place.
For ߨ, use either your calculator value or 3.142, unless the question requires the answer in terms of ߨ.
S
At the end of the examination, fasten all your work securely together.
The number of marks is given in brackets [ ] at the end of each question or part question.
The total number of marks for this paper is 60.
For Examiner’s Use
Part A
(Algebra
Component)
Part B
Calculator Model:
Total
This document consists of 7 printed pages, including this cover page.
Setter: Yvonne Lee
[Turn over
Need a home tutor? Visit smiletutor.sg
74
2
Part A – Answer all questions
1
(a) Solve
x 3 2x 4
1.
4
5
[3]
(b) If a 3 , b 2 and c 5 , evaluate
a 4 b 2c ,
[1]
(ii)
ac 2 b 3 .
[1]
.s
g
(i)
(c) Soil costs x cents per kilogram.
or
Peter paid y dollars for some soil.
(a) Find the interior angle of a regular 15-sided polygon.
[2]
[2]
T
2
ut
Find an expression, in terms of x and y, for the number of kilograms of soil that Peter bought.
(b) An n-sided polygon has 2 interior angles measuring 100q each and the remaining
ile
interior angles are qq each.
[2]
S
m
Find an expression for q in terms of n.
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Yvonne Lee/BMSS/2017/1E/P2/EOY
75
3
Part B – Answer all questions
3
In a sewing kit, there are blue, green and red buttons.
1
4
of the buttons are blue and
of the
5
7
remainder are green. The rest are red buttons.
(a) the fraction of red buttons in the sewing kit,
[2]
(b) the ratio of blue buttons to green buttons to red buttons,
[1]
(c) the total number of buttons if there are 80 green buttons in the sewing kit.
[2]
(a) The cash price of a new car is $90 500.
or
4
.s
g
Find
ut
David buys the car under the hire purchase scheme as shown below.
Hire Purchase Scheme
a deposit of 20% of cash price
x
simple interest of 2% per year over 3 years
x
repayment to be made monthly
ile
T
x
Calculate
the total amount of interest payable,
[3]
(ii)
the monthly instalment paid by David.
[2]
m
(i)
(b) A bag costs 1 850 000 Korean Won (KRW). The conversion rate between Singapore dollars
S
and Korean Won is SGD1 = KRW815.79.
Calculate the price of the bag in Singapore dollars.
[2]
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Yvonne Lee/BMSS/2017/1E/P2/EOY
76
4
5
A cylindrical block of metal has radius 10 cm and height 30 cm.
(a) Calculate its volume, leaving your answer in terms of S .
[1]
The block of metal is then melted and recast into 6 similar rods of height 15 cm.
(b) Show that the radius of the base area of one such rod is 5.77 cm, correct to 3 significant
[2]
.s
g
figures.
The diagram shows the cross-sectional view of a box holding the 6 rods. The box is in the shape
ut
or
of a cuboid and the rods just fit into the box.
[3]
S
m
ile
T
(c) Calculate the volume of empty space in the box.
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Yvonne Lee/BMSS/2017/1E/P2/EOY
77
5
(a)
Calculate the gradient of AB.
(ii)
Write down the equation of BC.
(iii)
Find the area of 'ABC .
ut
(i)
or
.s
g
6
the value of y when x
3
,
4
[2]
(ii)
the value of x when y
1 .
[1]
ile
(i)
m
Hence, explain why 7 , 1 does not lie on the line.
(a) Calculate the total surface area of the prism below.
[2]
[3]
S
7
[1]
1
x 2 . Find
3
T
(b) The equation of a function is y
[1]
(b) Mr Lee took 30 mins to drive from Jurong to Changi at an average speed of 72 km/h. He took
the same route (but in the opposite direction) at an average speed of 5 km/h faster for
his return trip. Find his average speed for the round trip correct to the nearest km/h.
[4]
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Yvonne Lee/BMSS/2017/1E/P2/EOY
78
6
The pie chart shows how a box of sweets was shared among Alex, Bryan and Clement.
or
(a) Find the fraction of the sweets that Alex received.
.s
g
8
[1]
(c) If Bryan received 345 sweets, how many sweets were there in the box?
[2]
ut
(b) If Clement received 22.5% of the sweets, find x.
In the diagram, the shape is made up of trapezium ABFG, rectangle BCEF and semicircle CDE.
S
m
ile
T
9
[1]
Find
(a) its perimeter,
[3]
(b) its area.
[4]
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79
7
10 Mrs Lee would like to dine at the Big Signboard Thai Restaurant. Below shows the pricing of the
food items she would like to order. There is a service charge of 10% and GST of 7% but no service
charge is imposed for takeout.
Big Signboard Thai Restaurant
$13.50
Green papaya salad
$7.90
Green curry
$10.90
Thai fish cake
$6.70
Chendol
$4.30
or
.s
g
Pineapple rice
(a)
How much more must Mrs Lee pay if she were to dine in instead of takeout?
(b)
If Mrs Lee has only $50, suggest on which is a better option for her. Support your answer with
ut
relevant workings.
[4]
[2]
S
m
ile
T
End of paper
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80
.s
g
or
ut
T
ile
m
S
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81
BMSS 1Exp End-Of-Year Examination 2017
(Mathematics P1) – Marking Scheme
c
2
a
b
x 2 y 4x
5x 2 y
4 z 3 2 5z
3
4
16 z 9 2 5 z
12
16 z 18 45 z
12
61z 18
12
3 pq p 4 2q
v w 1 v
a
M1
a
x 3
B
B1
B1
1, B1
B1,
2 3c 1 3 2 c 0
6c 2 6 3c 0
8
2
or
c 2 or
3
3
f 2
f 1
11
5
2
f 7 f 1
5
2
2 f 7 5 f 1
2 f 14 5 f 5
f 3
M1
A1
S
b
5
a
bi
7
25
1.9 (2 s.f.)
bii
1.906 (3 decimal places)
B1 ffor
or correct
inequality
B1 for correct
illustration on
number line
B1
m
4
common
den
de
nominator
denominator
A1
B
B1
ile
b
Remarks
M1
A1
T
3
Marks
B1
.s
g
b
Solution
3ab a
or
Qn
a
ut
1
correct
expansion
M1
fraction=fraction
M1
cross-multiply
A1
B1
B1
B1
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82
6
c
8
ai
aii
.s
g
y to u
B1
B
B1
B
1
B1
B1
B1
mango : orange
2:3
8 : 12
ile
b
HCF 22u 3
6
7 parts Æ 2.8l
1 part Æ 0.4l
5 parts Æ 2l
15 parts Æ 6l
M1
or
b
removing the
brackets
B1
ut
a
M1
A1
T
7
2
3 § 2·
§ 1·
¨1 ¸ y ¨ ¸
© 2¹ 7 © 3¹
9 3 2
y 4 7 3
9 7 2
u 4 3 3
21 2
4 3
63 8
12
55
7
4
or
12
12
3 p
2 u 33
54
LCM 2 3 u 39 u 5 u 7
m
orange : lemonade
4:3
12 : 9
a
S
9
? mango : oran
orange
ange
ge : llemonade
emon
em
o ade 8 : 12 : 9
3
u 100
100% 0.
0.5%
5%
60
600
00
24 m Æ 1 s
0 m Æ 60 s
1440
86400 m Æ 1 h
86.4 km Æ 1 h
b
B1
B1
B1
2
? 86.4 km/h or 86 km/h
5
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83
10
Divide shaded diagram into 2 parts by drawing a line
perpendicular to BC through E.
area of shaded triangle
1
2 10 6 36 cm2
2
1
u 14 u 10
2
70 cm2
12
a
b
GST
1
1
1
99 u 98 99 98
1
1
1
98 99 99 u 98
1
9702
2
‘QTR 1800q 155
155q
255q
m
c
7
u 30.60
107
$2
1 1 1
42 7 6
p 132
70
u 18 18
100
$30.60
a
S
13
‘QRT
T
b
M1
‘QRS
M1
M
1
A
A1
A1
A1
M1
A1
(adj ‘s on a str. line)
‘QTR
QTR 25q
‘TQR 25q 25q
‘TQR
‘PQR 90q 130q
‘PQR
area of
trapezium
ABCD 165 cm2
[M1]
area of ' AEF
24 cm2
area of ' EDC
35 cm2 [M1]
area
are
ar
ea of shaded
ea
re
egi
gion EFBC
region
165 24 35
165
1106
06 cm2 [A1]
A1
A
ut
b
total amount paid
T
a
A1
ile
11
M1
or
area of shaded region EFBC 36 70
106 cm2
M1
.s
g
area of shaded trapezium
accept
alternative
method:
180q
130q
360q
140q
‘PQR 140q
M1
(base ‘s of isos. tri)
( ‘ sum of tri)
A1
( ‘s at a pt)
M1
(alt ‘s , PQ // RS )
‘TRS 140q 25q
115q
A1
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84
14
a
B2
minus 1m for
every wrong /
missing answer
Refer to b
d
(2, 3)
ile
c
T
ut
or
.s
g
b
B1
S
m
B1
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85
BMSS 1Exp End-Of-Year Examination 2017
(Mathematics P2) – Marking Scheme
3 4> 2 2 5 @
bii
3 5 2
c
$ y 100 y cents
2
3
Marks
1
M1
1
1
M1
20
2
11
x 3 or
3
3
51
a
A1
A1
83
x cents Æ 1 kg
§1·
1 cent Æ ¨ ¸ kg
© x¹
§ 100 y ·
100y cents Æ ¨
¸ kg
© x ¹
15 2 u 1800q
interior
o angle
15
156q
n 2 u q 100 100 n 2 u 18
180
1
0
n 2 q 20
2
200
0 180
180
0n 36
360
3
0
1180
80n 560
q
n2
4 4
u
fraction
frac
fr
acti
tion
on of
of green
gree
gr
eenn bu
but
buttons
ttons
7 5
16
35
1 16
fraction of red buttons 1 5 35
12
35
1 16 12
7 : 16 : 12
: :
5 35 35
16 parts Æ 80
1 part Æ 5
35 parts Æ 175
80
amount borrowed
u 90500
100
a
S
3
b
c
4
ai
cross-multiply
A1
m
b
LHS into a
single fraction
A1
ile
2
Remarks
or
bi
Solution
.s
g
x 3 2x 4
4
5
5 x 3 4 2x 4
20
3 x 31
20
3 x 31
ut
Qn
a
T
1
M
M1
A1
M1
A1
M1
A1
M1
A1
A1
M1
A1
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$72400
total interest 72400 u
aii
M1
2
u3
100
M1
A1
$4344
total amount payable 72400 4344
$76744
76744
36
$2131.78
1850000
price in SGD
815.79
$2267.74
2
volume S 10 30
3000S cm3
2
6 u Sr 15 3000S
r 5.7735 cm
rej. -5.7735
5.77 (shown)
length 5.7735 u 6 34.641 cm
breadth 5.7735 u 4 23.094 cm
M1
monthly instalment
b
c
.s
g
a
A1
B1
or
5
M1
M1
A
A1
ut
b
A1
empty space (cross sectional))
34.641 23.094 6 S 5.7735
171.681 cm2
2
@
ile
T
>
M1
accept
alternative
method:
A1
vol. of box
34.641u 23.094
u15
11999.99 cm3
[M1]
S
m
6881u 155
emptyy space in box 171.681
2575.2220
20
25800 cm3 (3
(3 s.f.)
s.f.
s.
f.))
M1
M
6
ai
gradient
aii
x 6
a
iii
area
bi
y
B1
3
4
empty space
11999.99
3000S
2580 cm3 [A1]
B1
M1
1
u 3u 8
2
12 units2
3
1§ 3·
¨ ¸2 1
4
3© 4¹
A1
B1
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87
7
a
1
1 x 2
3
x 9
B1
B1
when y 1 , x 9 and not 7.
base area 15 u 3 3 u 3
54 cm2
M1
perimeter of base 3 3 3 3 9 3 15 3
42 cm
42 10
area of lateral faces 42u
420 cm2
A1
M
M1
1
2
36 km
distance from Jurong to Changi 72 u
ut
b
420 2 u 54
528 cm2
M1
or
S.A.
.s
g
bii
36
77
36 36
1 36
2 77
7744.4416
16 km
kkm/h
m/h
7744 km
km/h
m/h
(nearest
(nea
(n
eare
rest
st km/h)
km/h)
T
time taken for return trip
a
7
12
22
5
2..5
x
u 360
36
60
100
10
00
81
8 q
fraction
frac
cti
tion
on of
of sw
sweets Bryan received
360
0 21
2
210
0 81
360
23
120
c
no. of sweets in a box
9
a
BC
FE
55 12 11
32 cm
A1
B1
S
b
M1
B1
210
360
m
8
ile
average speed for the round trip
M
M1
M1
120
u 345
23
1800
A1
M1
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length of arc CE
perimeter 40 15 32 34.558 32 15
169 cm (3 s.f.)
1
40 22 12 372 cm2
area of trapezium
2
M1
area of rectangle 22 u 32 704 cm2
M1
area of semicircle
a
1
2
u S 11
2
190.07 cm2
A1
M1
1 .07 1270 cm2 (3 s.f.)
area 372 7044 190
Dine in
10.90 6.70 4.30
cost of food 13.50 7.90 1
$43.30
A1
or
10
M1
.s
g
b
1
u 2S 11
2
34.558 cm
M
M1
ut
43.3300
cost of food including service charge 1.1u 43
$47.6633
T
cost of food including servi
service
vice charge and GST
1.07 u 47.63
$50.96
M1
M1
amount 50.96 46.33
$4.6633
A1
50 $50
50.96
96 $0.96 , Mrs Lee does not have
Since $50
enough
money
en
nou
ough
gh m
oney
on
ey too dine
din in with the purchase of the food
items.
item
em
ms.
s I would
wouuld su
sug
suggest
ggest that she takeout her purchase.
M1
m
ile
Takeout
cost of
of food including GST 1.0077 u 433.3300
$4466.3333
S
b
A1
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.s
g
or
ut
T
ile
m
S
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90
East Spring Secondary School
J
Towards Excellence and Success
Name : _____________________________________________________ (
)
Class : Sec 1-___
Second Semester Examination 2017
4016/1
.s
g
Mathematics
Paper 1
Secondary 1 Express
1 hour
7.45 am – 8.45 am
Additional materials:
Nil
INSTRUCTIONS TO CANDIDATES
or
Monday 9th Oct 2017
T
Answer All questions.
ut
Write your name, class and register number in the spaces provided on the paper/answer
booklet.
ile
All necessary working must be shown.
Omission of essential working will result in loss of marks.
ELECTRONIC CALCULATORS CAN BE USED IN THIS PAPER.
m
INFORMATION FOR CANDIDATES
The number of mark is given in brackets [
] at the end of each question or part question.
You should not spend too much time on any one question.
S
The total marks for this paper is 40.
If the degree of accuracy is not specified in the question and if the answer in not exact, the
answer should be given to three significant figures. Answers in degrees should be given to
one decimal place.
For π, use either your calculator value or 3.142 unless the question requires the answer in
terms of π.
MARKS:
40
This question paper consists of 8 printed pages including the cover page.
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East Spring Secondary School
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Do It Right. Always
S1Ex Maths Paper 1
2017 2SE
Mathematical Formulae
Compound Interest
r ⎞
⎛
Total amount = P⎜ 1 +
⎟
⎝ 100 ⎠
.s
g
Mensuration
n
Curve surface area of a cone = πrl
Surface area of a sphere = 4πr 2
or
1 2
πr h
3
4
Volume of a sphere = πr 3
3
1
Volume of triangle ABC = absin C
2
Arc length = rθ , where θ is in radians
T
ut
Volume of a cone =
ile
Area of sector =
1 2
r θ where θ is in radians
2
S
m
Trigonemetry
a
b
c
=
=
sin A sin B sinC
a 2 = b 2 + c 2 − 2bc cos A
Statistics
Mean =
∑ fx
∑f
Standard derivation =
∑ fx
∑f
2
⎛
fx ⎞
−⎜∑ ⎟
⎜∑f ⎟
⎠
⎝
2
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S1Ex Maths Paper 1
2017 2SE
Answer all questions.
1.
Without using a calculator, estimate each of the following.
(a)
√
+√
.s
g
(b)
×
Use your calculator to find the value of
[2]
(b)
_______________
[2]
√
.
× .
. Give your answer
.
Ans:
_______________
[2]
___________ m/s
[2]
___________ m3
[2]
Express each of the following in the respective units.
m
3.
ile
T
ut
correct to 4 significant figures.
_______________
or
2.
Ans: (a)
(a)
km/h to m/s
S
(b) 2 400 000 cm3 to m3
Ans: (a)
(b)
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East Spring Secondary School
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4.
S1Ex Maths Paper 1
2017 2SE
Consider the following number sequence.
− ,− ,
,
,
,…
(a) Write down the next two terms for the following sequence.
(b) Express
Find the 100th term.
ut
or
.s
g
(c)
in terms of .
5.
ile
T
Ans: (a)
_____
_____
[1]
(b)
_______________
[1]
(c)
_______________
[2]
3 drones can deliver 9 packages in 2 hours. Assuming that the packages are
identical and the drones work at the same rate, how long will it take 5 drones to
S
m
deliver 30 packages?
Ans: _____________ hours
[2]
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East Spring Secondary School
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6.
S1Ex Maths Paper 1
2017 2SE
Clare needs to pack 108 chocolate chip cookies, 162 oatmeal cookies and 54
macadamia nut cookies into identical boxes so that each type of cookies is equally
distributed. Find
(a) the largest number of boxes that can be packed,
ut
or
.s
g
(b) the total number of cookies in each box.
Ans: (a) ___________boxes
[2]
Expand and simplify each of the following.
ile
7.
T
(b) ___________cookies [1]
(a)
+
+
−
−
S
m
(b)
−
Ans: (a) _______________
[2]
(b) _______________
[2]
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East Spring Secondary School
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8.
S1Ex Maths Paper 1
2017 2SE
Factorise each of the following expressions completely.
(a)
−
+
.s
g
(b)
−
[1]
(b) _______________
[1]
or
9.
Ans: (a) _______________
For the following figure, consisting of a trapezium and a circle, find the area of
ut
the shaded region, where O is the centre of the circle.
5 cm
O
26 cm
S
m
ile
T
18 cm
Ans: _______________ cm2
[3]
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East Spring Secondary School
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10.
S1Ex Maths Paper 1
2017 2SE
In the given diagram, AB is parallel to CD and CG is parallel to BF,
∠ABF = 46° and ∠GCE = 108° .
B
A
.s
g
D
C
or
E
F
G
∠CED
(b)
∠CDB
(c)
reflex ∠DCG
S
m
ile
T
(a)
ut
State with reasons clearly, find the value of the following.
Ans: (a) ______________°
[2]
(b) ______________°
[2]
(c)
[3]
______________°
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11.
S1Ex Maths Paper 1
2017 2SE
The sum of the interior angles of a regular polygon is 1080°. Find the size
or
.s
g
of one exterior angle.
ut
Ans: ___________________
[3]
12. Emma and Rupert each conduct a survey among 100 people to find out their
T
most commonly used form of transportation. The information they gathered is
ile
shown in the table below.
Rupert
Car
67
9
Public Transport
26
71
Walking
7
20
m
Emma
Give two reasons to account for the differences in their results.
[2]
Reason 1:
S
Ans:
_________________________________________________________
_________________________________________________________
_________________________________________________________
_________________________________________________________
Reason 2:
_________________________________________________________
_________________________________________________________
_________________________________________________________
_________________________________________________________
– End of paper –
2SE 2017 1E MATHS P1
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East Spring Secondary School
J
Towards Excellence and Success
Name : _____________________________________________________ (
)
Class : Sec 1-___
Second Semester Examination 2017
.s
g
Secondary 1 Express
4016/2
Mathematics
Paper 2
1 hour 15 minutes
10.05 am – 11.20 am
or
Monday 2nd October 2017
ut
Additional materials:
3 sheets of writing paper , 1 sheet of blank paper and 1 sheet of graph paper
READ THESE INSTRUCTIONS FIRST
ile
T
Write your Name and Index Number on all the work you hand in.
Write in dark blue or black pen.
You may use a pencil for any diagrams or graphs.
Do not use staples, paper clips, highlighters, glue or correction fluid.
S
m
Answer all questions.
If working is needed for any question, it must be shown with the answer.
Omission of essential working will result in loss of marks.
You are expected to use an electronic calculator to evaluate explicit numerical
expressions. If the degree of accuracy is not specified in the question, and if the answer is
not, give the exact answer to three significant figures. Give answers in degrees to one
decimal place.
For π, use either your calculator value or 3⋅142, unless the question requires the answer
in term of π.
At the end of the examination, fasten all your work securely together.
The number of marks is given in brackets [ ] at the end of each question or part question.
The total number of marks for this paper is 50.
MARKS:
50
This question paper consists of 6 printed pages including the cover page.
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146
S
m
ile
T
ut
or
.s
g
East Spring Secondary School
Mathematics Department
Do It Right. Always
2SE 2017 1E MATHS P2
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East Spring Secondary School
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(a) Solve the following equations.
(i)
− 13x − 3 + 5 x = 5
[2]
(ii)
5x x + 2
−
=5
2
3
[3]
Solve the inequality 32 + 3 x ≤ 23 .
[2]
Hence, find the biggest possible value of x if x is an even number.
[1]
(b) (i)
(ii)
2.
.s
g
1.
Nathiel walks from home at a speed of 60 m/min to school at 0630 in the
morning to school. After walking for 12 minutes he stopped by 7-eleven for 5
or
minutes to buy some snacks. Nathiel then continues to walk at the same
speed for another 8 minutes before reaching school.
[2]
ut
(a) Express Nathiel’s walking speed in km/h.
(b) What is the distance, in metres, of the school from his home?
[1]
(c)
[2]
What is the average speed, in m/min, of the whole journey?
T
(d) Allen cycles at a speed of 12 km/h from home which is 4 km away from [2]
school. He leaves home at 0640 in the morning. Who will reach school
3.
ile
first, Nathiel or Allen?
The diagram below is made up of a square, a regular pentagon and a regular
m
polygon of n sides. ABCDE shows part of the n-sided polygon.
K
S
L
M
Find
(a) ∠BCM
[2]
(b) the interior angle of n-sided polygon ∠BCD
[2]
(c)
the number of sides n
2SE 2017 1E MATHS P2
[2]
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4.
(a) The tickets to Thomas & Friends the Musical were sold at $30, $50 and
$100. The number of $30-tickets sold was thrice the number of $50tickets. The number of $100-tickets sold was 100 less than the number
of $50-tickets. The number of $50-tickets sold was x. The total number
of the tickets sold were 2605.
Write down an expression, in terms of x, for the total number of
[1]
.s
g
(i)
tickets sold.
(ii)
Hence, find the value of x.
(iii)
The following year, the tickets to Thomas & Friends the Musical
[1]
[2]
price for each ticket.
or
were sold at $33, $55 and $110. Find the percentage increase in
ut
(b) Selina Kyle, a cat burglar broke into Wayne Enterprise and stole a [2]
diamond pendant worth 12 million dollars. She then sells the diamond
pendant at 240% of the original value on the black market. Find the
The price of My Melody figurine toy in the month of October was $m. [2]
ile
(c)
T
price of the diamond pendant on the black market.
During a toy fair in November, the price increased by 25%. After the
toy fair, the sales of the figurine dropped by 25% in March. After the
m
sales, did the price of the figurine dropped back to its original price?
S
Explain your answer.
2SE 2017 1E MATHS P2
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5.
The figure below shows a rectangular children’s swimming pool that is 15 m
long, 8 m wide and 0.9 m deep. On one end of the pool, along the width, a flight
.s
g
of three steps is built. Each step is 0.3 m in height and 0.4 m in width.
Find the
(a) depth of the swimming pool,
[1]
(b) volume of water needed to fill the pool
[3]
(c)
[2]
ut
total surface area of the water in contact with the sides of the pool.
T
6.
or
0.9
Answer the whole of this question on the graph paper provided.
ile
Given the equation y = 2 x ,
0
0
4
a
8
16
m
x
y
(a) Find the value of a.
[1]
(b) Using a scale of 2 cm to represent 1 unit on the x-axis and 1 cm to [3]
S
represent 1 unit on the y-axis, draw the graph of y = 2 x for 0 ≤ x ≤ 8 .
(c)
From the graph, find the value of x when y = 5 .
[1]
(d)
Find the gradient of the graph.
[1]
2SE 2017 1E MATHS P2
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7.
Answer the whole of this question on the blank paper provided.
Indiana Jeromes was looking for a treasure chest buried in a field ABCD.
His father Benry decided to help him map out the dimensions of the field
ABCD. The dimensions are as follow. AB = 9 cm, BC = 4 cm, AD = 7 cm,
∠ABC = 60° and ∠BAD = 90°
(b) (i)
Draw the angle bisector of ∠BAD ,
[4]
.s
g
(a) Construct the quadrilateral field ABCD on your writing paper
[2]
(ii)
Draw the perpendicular bisector of AB.
(iii)
The treasure chest is located at the intersection of the 2 [1]
[2]
S
m
ile
T
ut
measure the length of BT.
or
bisectors. Label the location of the treasure chest as T and
– END OF PAPER –
Please check your work.
2SE 2017 1E MATHS P2
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.s
g
or
ut
T
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m
S
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S1Ex Maths Paper 1
2017 2SE
MARK SCHEME
√
+√
× .
.
=√
=
.
3(a)
/ℎ =
=
(b)
×
+
≈
=
+√
=
M1
A1
M1
A1
×
M1
= 5.3396859…
.s
g
2
√
≈
=
A1
= 5.340
ℎ
/
=
=
= .
4(a)
19, 24
(b)
T1 = 5(1) – 11 = -6
÷
M1
1
÷
÷
A1
1
M1
A1
B1
Tn = 5n – 11
B1
T100 = 5(100) – 11
M1
m
(c)
ile
T
T2 = 5(2) – 11 = -1
×
×
×
or
(b)
×
ut
1(a)
= 489
Drones
e
3
5
5
S
5
A1 ECF
Pack
Pa
Packages
ckag
ages
e
9
15
30
Hours
2
2
4
M1
Answer : 4
6(a)
(b)
2
3
3
3
108
54
18
6
2
A1
162
81
27
9
3
54
27
9
3
1
M1
HCF = 54
Total number of cookies in each box = 2 + 3 + 1 = 6
A1
B1
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9
East Spring Secondary School
Mathematics Department
Do It Right. Always
9
10
−
−
+
=
+
+
+
−
−
=
+
=
M1
+
+
A1
−
−
M1
A1
−
=
B1
B1
− +
Area of Circle =
=
Area of trapezium =
Area of shaded region =
M1
M1
= .
×
=
− . ≈
or
8(a)
(b)
=
−
A1
1
B
ut
(b)
=
−
.s
g
7(a)
S1Ex Maths Paper 1
2017 2SE
A
ile
T
D
m
C
S
(b) ∠
11
(alt
(al
altt ∠ ,
=∠
=
°
(c) ∠
=
=
=
=∠
=
reflex ∠
°−∠
°− °
°
°
//
M1
A1
=
=
(int ∠ ,
(alt ∠ ,
°−
°
Sum of int. angles = −
°=
− ×
°
°
− =
°
= +
=
2SE 2017 1E MATHS P1
Deduct one
mark
overall if no
reasons
given.
F
G
(a) ∠
E
//
M1
A1
//
M1
M1
A1
° (∠
×
°
M1
M1
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10
East Spring Secondary School
Mathematics Department
Do It Right. Always
12
1 ext. angle =
=
S1Ex Maths Paper 1
2017 2SE
°
A1
°
Location: Emma conducted her survey near an office while
Rupert was near a school/interchange.
S
m
ile
T
ut
or
.s
g
People surveyed: Emma chose mostly working adults to survey
while Rupert chose students.
B1 for each
correct
reason, up
to B2
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155
11
East Spring Secondary School
Mathematics Department
Do It Right. Always
MARK SCHEME
1(a)(i)
− 8x = 8
M1
A1
x = −1
.s
g
M1
M1
1
or
(b)(i)
15 x 2 x + 4
−
=5
6
6
15 x − 2 x − 4
=5
6
13x = 4 = 30
13x = 34
8
x=2
13
(or 2.62)
ut
(a)(ii)
3x ≤ −9
-4
2(a)
60m/min
3600m/hr
3.6 km/hr
(b)
12+8 = 20
20 x 60
=1200m
ile
(b)(ii)
T
x ≤ −3
m
(d)
M1
A1
1
B1
M1
A1
B1
M1
1200
12 + 5 + 8
= 48m / m
min
in
A1
S
(c)
A1
1
4
12
= 20 min
i
60 ×
M1
0640 + 20 = 0700
3
Nathiel reached first
(5-2)180
=540
A1
M1
540/5
A1
=108
2SE 2017 1E MATHS P2
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(b)
360 – 108 – 90
=162
(c)
180 – 162
=18
360/18
=20
M1
A1
3 x + x + x − 100
.s
g
4(a)
M1
A1
B1
5 x − 100
(iii)
3
× 100%
30
= 10%
10% same throughout
240
× 12
100
= 28.8million
or 28800000
ile
Nov toy price = 1.25m
After discount
=0.75 (1.25m)
0.9375m
It became cheaper
A1
M1
A1
M1
A1
m
(c)
M1
T
b)
B1
or
5 x − 100 = 2605
x = 541
ut
(ii)
0.9m
B1
(ii)
Volume
e off step
steps
epss in
nw
water
ater
at
er
= 0.3x
3x 0.4x
0.4
.4xx 3 x 8
2.88
M1
Volume off wa
water
w
ter
(13.8 x 8 x 0.9) – 2.88
=102.24
=102 24
M1
A1
S
5(a))
iii)
Accept other ways:
1m for calculation of water above steps
1m for calculation of cuboid pool excluding steps
1m for final ans
Surface are
(14.6 x8) + 2(14.6 x 0.9- 0.3 x 0.4x 3) + 2(0.9 x 8)
=157 (3sf)
2SE 2017 1E MATHS P2
M1
A1
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6a)
a=8
B1
d)
2
ut
(c)
1m for correct plot with label
1m for correct scale x axis
1m for correct scale y axis
x = 2 .5
or
.s
g
(b)
B1
1
S
m
ile
T
7(a)
B1
B1
2SE 2017 1E MATHS P2
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.s
g
or
ut
T
ile
m
S
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159
EAST VIEW SECONDARY SCHOOL
SECOND SEMESTRAL EXAMINATION 2017
SECONDARY ONE EXPRESS
CANDIDATE NAME
CLASS
INDEX NUMBER
MATHEMATICS
.s
g
4048/02
Paper 2
11 October 2017
Total Marks: 50
1 Hours 15 Minutes
READ THESE INSTRUCTIONS FIRST
or
Additional Materials: Writing Paper (4 sheets) and Graph Paper (1 sheet)
ile
Answer all questions.
T
ut
Write your name, class and index number on all your answer sheets to be handed in.
Write in dark blue or black pen.
You may use a soft pencil for any diagrams, graphs or rough working.
Do not use staples, paper clips, highlighters, glue or correction fluid.
S
m
If working is needed for any question it must be shown with the answer.
Omission of essential working will 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
the answer to three significant figures. Give answers in degrees to one decimal place.
For S, use either your calculator value or 3.142, unless the question requires the answer in
terms of S.
At the end of the examination, fasten all your work securely together.
The number of marks is given in brackets [ ] at the end of each question or part question.
For Examiner’s Use
This paper consists of 6 printed pages (including the cover page)
50
Setter: Mdm Humairah
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170
2
Mathematical Formulae
Compound interest
r ·
§
Total amount = P ¨1 ¸
© 100 ¹
.s
g
Mensuration
n
Curved surface area of a cone = S rl
Surface area of a sphere = 4S r 2
1 2
Sr h
3
or
Volume of a cone =
Volume of a sphere =
4 3
Sr
3
1
absin C
2
ut
Area of triangle ABC
Arc length = rT, where T is in radians
T
1 2
r T , where T is in radians
2
m
Trigonometry
ile
Sector area =
a
sin A
a2
b
sin B
c
sin C
b 2 c 2 2bc cos A
S
Statistics
Mean =
¦ fx
¦f
Standard deviation =
¦ fx
¦f
2
§ ¦ fx ·
¨
¨ ¦ f ¸¸
©
¹
2
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171
3
Answer all the questions.
(a) Sarah buys the car on hire purchase. She pays a deposit of one fifth of the cash
price. She then pays $1300 monthly for 10 years. What is the total amount that
Sarah pays for the car?
[3]
(b) The original value of the car is its cash price of $175 000. Each year the value of
the car decreases by 10% of its value at the start of the year. At the end of three
years, Sarah decides to sell the car. Calculate the overall percentage reduction in
the value of the car compared with its original value.
[3]
Marcus, Ali and Tan shared a sum of money in the ratio 11 : 4 : 1.
(a) Given that Ali received $4.80 more than Tan, find the sum of money shared by the
three of them.
[2]
(b) Marcus distributed part of his money equally to Ali and Tan and was left with
$2.60. Find the new ratio of Marcus’s money to Ali’s money to Tan’s money.
[3]
S
m
ile
T
ut
or
2
The cash price of a new car is $175 000.
.s
g
1
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172
4
There are 16 adults and 10 children going to the Singapore Flyer. You are required to
book taxis for them. Below is the taxi seating capacity given to you. At least one adult
must accompany the children.
ut
or
.s
g
3
Source: https://www.cdgtaxi.com.sg/commuters_seating_capacity.mvn?cid=256
(b)
There is a change of number of people going to the Singapore Flyer. An additional
4 adults and 2 children would like to go too. How many more taxis do you need to
[2]
book?
[3]
ile
T
What is the minimum number of taxis you need? Show all your working clearly.
m
Two different sizes of cylindrical fruit cans are shown below. The small can has a
diameter of 12 cm and a height of 13 cm. The prices of the fruit cans are given on the
respective cans.
S
4
(a)
LARGE
SMALL
$18.80
13 cm
$4.80
11 310 cm3
12 cm
(a)
Find the volume of the small can.
(b)
Which size of canned fruit gives the better value? Show all the working clearly of
[3]
can.
(c)
What is the maximum number of small cans that can fit into a rectangular
packaging of size 72 cm by 24 cm and height of 39 cm?
[3]
[2]
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173
5
(a) Express the number of apples in term of k.
[1]
(b) Express the number of oranges in term of k.
[1]
(c)
[3]
If there are a total of 35 fruits in the box, how many peaches are there in the box?
[3]
(e)
[2]
.s
g
(d) If the cost of a peach, an apple and an orange is $1.10, $0.20 and $0.50
respectively, what is the cost of one box of fruits?
How many numbers of boxes of fruits can May purchase with $42?
An aeroplane travelled a distance of 1130 km from Singapore to Jakarta. For the first x
hour of its journey, the aeroplane travelled at a constant speed of 350 km/h. The speed
x
of the aeroplane was increased by 80 km/h for the remaining hour of its journey.
2
ut
6
There are 2(k – 3) peaches in a box. There are 3 more apples than peaches and twice as
many oranges as peaches in the same box.
or
5
T
(a) Write down the total distance travelled for the first x hour of its journey, in terms
of x.
(b) Write down the distance travelled by the aeroplane in the remaining
(c)
ile
journey, in terms of x.
x
hour of its
2
[1]
[2]
[3]
(d) Find the average speed, in km/h, for the whole journey, correct to 2 decimal
places.
[2]
S
m
Find the value of x. Hence, find the total time, in hours, taken for the whole
journey.
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174
6
7
Answer the whole of this question on a sheet of graph paper.
The variables x and y are connected by the equation
y 2 2x .
Some corresponding values of x and y, are given in the table below.
2
1
0
y
p
4
2
1
2
.s
g
x
q
2
Calculate the value of p and of q.
(b)
Using a scale of 2 cm to 1 unit for the y-axis and 4 cm to 1 unit for the x-axis, draw
the graph y 2 2 x for 2 d x d 2 .
[3]
(c)
Using your graph, find the value of x when y
(d)
On the same axes, draw the line x = 1.5 . Find the coordinates of the point of
[2]
intersection of the two lines.
or
(a)
[1]
T
ut
3.5 .
[2]
S
m
ile
--- End of Paper ---
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175
.s
g
or
ut
T
ile
m
S
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176
3
Answer all the questions.
1
(a)
Consider the following numbers.
64,
2
, 121,
5
1.2,
79,
2
.s
g
Write down the prime number.
Answer (a)
By rounding each number to 1 significant figure, estimat
estimate
atte th
thee vvalue
aluee of
or
(b)
79
………………………
[1]
251.76
.
22.65
.65 3.295
ile
T
300
[ M 1]
33
ut
You must show your working clearly.
Answer
A
nswer (b)
ns
50
………………………
[2]
2
m
_________________________________________________________________________________
___________________________________
_____________________________________________
The first four terms
ter
erms
m of
of a sequence
seequ
q en
ence
ce are
are 12,
12, 15, 18, 21 ……
he 6th term.
term
te
m.
Write down the
S
(a)
Answer (a)
(b)
27
6th term = ………………
[1]
i down
d
h generall term, Tn for
f the
h sequence.
Write
the
3n + 9
[1]
Answer (b)
Tn = …….....……………..
_________________________________________________________________________________
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177
4
3
When written as the product of their prime factors,
p
23 u 3n ,
q 52 u133 ,
r
23 u 5 u 7 2 .
the value of the n if the cube root of p is 2 u 32 ,
or
(a)
.s
g
Find
Answer (a)
[1]
rimee ffactors,
prod
pr
oduc
od
du
ucct of
of iits
tss pprime
acto
ac
tors
to
r,
rs
the LCM of q and r, giving your answer as the product
An
nswer (b)
Answer
23 u 52 u 7 2 u133
………………………
[1]
5
………………………
[1]
the greatest
st nnumber
umbe
um
b r th
hat w
illl di
divide q and r exactly.
that
will
S
m
(c)
ile
T
ut
(b)
6
n = ……………………
……………
…………
……
………
……
Answer (c)
_________________________________________________________________________________
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178
5
4
(a)
Jordan took two tests.
In a second test, Jordan scored 18 marks.
The second test mark is an improvement of 20% of the first test mark.
Find Jordan’s first test mark.
.s
g
[ M 1]
or
18
1.2
[2]
Convert 56 m/s to km/h.
ile
T
(b)
115
5 …… marks
………
……
……………………
…………
…………
ut
Answer (a)
m
Answer (b)
[1]
Giv
ven that
tha
h t the
th
he ra
rate
te of
of ex
eexchange
change between Euro and Singapore dollars is €1 = S$1.59.
Given
S
(c)
201.6
…………………… km/h
Find
nd
d tthe
he amount
amo
moun
u t of Euro dollars one can receive from S$300.
Give your answer to 2 decimal places.
Answer (c)
188.70
…………………… Euros
[1]
_________________________________________________________________________________
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179
6
5
Given that x
b b 2 4ac
,
2a
find the value of x when a = 4, b = –2 and c = –3. Give your answer to 3 decimal places.
2
2 4 4 3
2 4
[ M 1]
.s
g
x
2 1.151
or
= ………..…………………..
Answerr x =
……
………
……
……
……
..……
……
…..
[2]
_________________________________________________________________________________
_____________________________________________________
____
____
___
______
___
____
____
_________
6
nd ‘CEF
nd
42q aand
CE
C
EF
136q .
m
ile
T
ut
In the diagram below, AB // CD // EF. ‘ABC
‘ABC
Find
‘BCD ,
S
(a)
(b)
(c)
Answer (a)
42
‘BCD = ………………
[1]
Answer (b)
44
‘DCE = ………………
[1]
o
‘DCE ,
o
the reflex ‘BCE .
Answer (c)
reflex ‘BCE
o
274
…..………
[1]
_________________________________________________________________________________
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180
7
7
In the trapezium ABCD, AB // DC, AD is perpendicular to DC, AB = 14 cm, BC = 18 cm,
CD = 26 cm and AD = 15 cm.
14 cm
A
B
D
Find the area of trapezium ABCD.
> M 1@
T
ut
1
14 26 15
2
C
or
26 cm
.s
g
18 cm
15 cm
300
8
ile
An
Answer
nsw
swer
e ………………………… cm2 [2]
_________________________________________________________________________________
______________________________________
_ ________
____
____
____
____________________________
Solve solution
l tiion on
on a number
nu
line.
2
2 x 10 d 4 and show the solu
S
m
22 x d 6
xx d 3 [ M 11]]
x t 3 [ M 11]]
x t 3
[A1]
x
–3
0
[3]
_________________________________________________________________________________
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181
8
9
(a)
Using the line segment given below, AC, construct a triangle ABC, such that
ile
T
ut
or
.s
g
BC = 10 cm and ‘BAC = 40°.
C
[2]
m
A
S
On the same diagram,
m
(b)
cons
construct
nstr
truc
uctt thee angle
a gle bisector of ‘ACB.
an
[1]
(c)
construc
construct
uctt the perpendicular bisector of AC.
[1]
_________________________________________________________________________________
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182
9
10
(a)
Factorise 8cd – 2cd 2 completely.
2cd ( 4 – d )
Answer (a) ..…………….....……………….. [1]
Simplify
S
p y 3 – 3(2x
( – 3)) .
.s
g
(b)
3 6 x 9 [ M 1]
1122 – 66x
x
Simplify
2x 1 x 3
.
3
2
ut
(c)
or
Answer (b) ..…………….....………………..
..…………
………
……
….....…
……………….. [2]
T
4 x 2 3x 9
[ M 1]
6
ile
x 11
6
m
Answer
A
An
swer
sw
e (c) ..………..............................…….. [2]
_________________________________________________________________________________
________________________________
_ __
____
____
____
_________
_ ________________________________
S
11 (a)
2
x2 x5 4 x4
Simplify
Simpliify
completely.
u
2
2x2 x 4
x5
x2 2 x4
u
x2
x5
[ M 1]
2 x2 x4
x2 x 5
Answer (a) ..…………….....……………….. [2]
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183
10
(b)
Simplify
8x2
2x2
y
completely.
2
5 x7
x7 x7
2
x7 x7
8x2
u
5 x7
2 x2
[ M 1]
.s
g
4 x7 x7
5
Answer (b) ..…………….....………………..
[2]
_________________________________________________________________________________
____________________________________________________________
___
_ ____
_____________
or
Express 35 m2 in cm2.
ut
12 (a)
350
3
50 00
000
00
(b)
T
…….
… ....…………… cm2 [1]
Answer (a) ..…………
..…………….....……………
The ratios of a : b and a : c are given
g ven below.
gi
ile
a : b = 2:3
a : c = 3:5
S
m
Find the ratio
rat
a io off a : b : c.
c.
6 : 9 : 10
[B2]
Answer (b) ...……… : ..….…… : ..…….… [2]
_________________________________________________________________________________
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184
11
13 The diagram below shows a straight line.
y
16
14
12
8
6
4
2
4
6
8
100 12 14 16
1
x
or
2
Find the gradient of this straight line.
(b)
( )
(b
T
ut
(a)
ile
0
.s
g
10
00.5
5
Answer
Answ
An
wer
e (a)
(a) gradient = .....………………..
mx c , where m is
S
m
Write down the equation
equ
q ation
n of tthis
hiss straight
hi
straig
i ht line in the form y
the gradient
grad
a ientt ooff th
the li
line,
ine
ne,, and
and c is its y-intercept.
[1]
0.5x + 8
Answer (b) y = .....………….............……..
[1]
_________________________________________________________________________________
End of Paper
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185
EAST VIEW SECONDARY SCHOOL
SECOND SEMESTRAL EXAMINATION 2017
SECONDARY ONE EXPRESS
CANDIDATE NAME
MARKING SCHEME
CLASS
INDEX NUMBER
.s
g
MATHEMATICS
Paper 2
4048/02
13 Octoberr 2017
201
Total
otal Marks: 50
1 Hour
Hours
urs 15 Minutes
ur
Minute
ut
READ THESE INSTRUCTIONS FIRST
or
Additional Materials: Writing Paper (4 sheets) and Graph Paper (1 sheet)
she
heet
et))
et
ile
Answer all questions.
T
Write your name, class and index number on all your answer
an
nsw
we
err sheets
sh
he
eet
ets to
o be
be handed
ha
and
nded
ed in.
Write in dark blue or black pen.
diag
rough
working
You may use a soft pencil for any diagrams,
gra
r ms, graphs or rou
o gh working.
g.
Do not use staples, paper clips, highlighters, glue or correction
corre
r ction fluid.
S
m
Iff working is needed for any question it must
mus
ustt be shown
sho
hown
wn
n with the answer.
Omission of essential working will result
resul
ultt in loss
loss
s of marks.
Calculators
Calculat
attors should be used
ussed
e where
whe
h re
ea
appropriate.
ppro
pp
ro
opr
pria
i te.
Iff the degree of accuracy
give
accurrac
acyy is not specified
spe
peci
cifi
fied
ed in the question, and if the answer is not exact, giv
the
figures.
he answer to three significant
sign
si
gnifican
antt fi
figu
gure
res.
s Give answers in degrees to one decimal place.
For
or S, use either your
you
ourr calculator
calc
ca
lcul
ulat
ator
or value
value or 3.142, unless the question requires the answer in
i
erms of S.
terms
At the end of the examination,
exxam
amin
ination, fasten all your work securely together.
The
he number of marks is given in brackets [ ] at the end of each question or part question.
For Examiner’s Use
This paper consists of 6 printed pages (including the cover page)
50
Setter: Mdm Humairah
Need a home tutor? Visit smiletutor.sg
186
2
Mathematical Formulae
Compound interest
r ·
§
Total amount = P ¨1 ¸
© 100 ¹
.s
g
Mensuration
n
Curved surface area of a cone = S rl
Surface area of a sphere = 4S r 2
1 2
Sr h
3
or
Volume of a cone =
Volume of a sphere =
4 3
Sr
3
1
absin
ab C
2
ut
Area of triangle ABC
Arc lengthh = rT, where T is inn radians
T
1 2
n ra
radi
radians
d ans
r T , where T is in
2
m
Trigonometry
ile
Sector area =
a
sin
si
nA
a2
b
sin
in B
c
sin C
b 2 c 2 2bc cos A
S
Statistics
Mean =
¦ fx
¦f
Standard deviation =
¦ fx
¦f
2
§ ¦ fx ·
¨
¨ ¦ f ¸¸
©
¹
2
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187
3
Answer all the questions.
(a) Sarah buys the car on hire purchase. She pays a deposit of one fifth of the cash
price. She then pays $1300 monthly for 10 years. What is the total amount that
Sarah pays for the car?
[3]
(b) The original value of the car is its cash price of $175 000. Each year the value of
the car decreases by 10% of its value at the start of the year. At the end of three
yyears,, Sarah decides to sell the car. Calculate the overall ppercentage
g reduction in
the value of the car compared with its original value.
[3]
Answer
1
Deposit = $175000 u = $35000
5
Total monthly for 10 years = $1300 u 12 u 10 $156000
Total amount that Sarah pays for the car
$35000 $156000 $191000
Mark
Marker
Mark
Ma
r er Report
[M1]
1]
[M1]
[M
1]
ut
or
S/N
1(a)
The cash price of a new car is $175 000.
.s
g
1
[M1]
[M1]
[A1]
S
m
ile
T
1(b) At first year = $175000
At second year = $175000 u 0.9 $157500
At third year = $157500 u 0.9 $14
41750
141750
Reduction price = $175000 $141750 $33250
33250
Percentage reduction =
u 100% 1
199%
175000
[A1]
[[A
A1]
1]
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188
4
Marcus, Ali and Tan shared a sum of money in the ratio 11 : 4 : 1.
(a) Given that Ali received $4.80 more than Tan, find the sum of money shared by the
three of them.
[2]
(b) Marcus distributed part of his money equally to Ali and Tan and was left with
$2.60. Find the new ratio of Marcus’s money to Ali’s money to Tan’s money.
[3]
S/N
2(a) Marcus : Ali : Tan
11
: 4 :1
Answer
4-1 = 3
3 units = $4.80
1 unit = $4.80 y 3 $1.60
11+4+1 = 16
16 units = $1.60 u 16 $25.60
Mark
Marker Report
p
.s
g
2
or
1]
[M1]
[A1]
[[A
A1]
1]
2(b) At first,
ile
T
Marcus = $1.60 u 11 $17.60
$17.60 $2.60 $15.00
$15.00 y 2 $7.50
ut
The sum of money shared by the three of them is $25.60.
$25.
5 60
5.
60.
Ali and Tan received $7.50 each.
Ali = ($1.60 u 4) $7.50 $13.90
Tan = $1.60 $7.50 $9.10
Marcus : Ali : Ta
Tan
n
2.60 : 13.90 : 9.10
26
: 139
: 991
1
[M1]
m
[M1]
S
[A1]
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189
5
There are 16 adults and 10 children going to the Singapore Flyer. You are required to
book taxis for them. Below is the taxi seating capacity given to you. At least one adult
must accompany the children.
ut
or
.s
g
3
What is the minimum number of taxis you need? Show
ow all you
your
ur working
wo
clearly.
(b)
There is a change of number of peopl
people
ple going
going too the
the Singapore
Sing
Si
ngapore Flyer. 4 adults and 2
children would like to go too. How
How m
many
a y more
an
moree taxis
tax
axiis do
d you need to book?
[2]
ile
T
(a)
m
S/N
Answer
Mark
er
3(a) Note: We cannot take one child oonly
nly
nl
y as w
wee do not know
how
ho
ow the seating capacity
capa
paciity ffor
o onee child
or
chi
hild
ld tto
o how many adults.
Child cannot go
o al
aalone
onee mu
m
must
st be
be accompany
acco
ac
comp
mpan
any by an adult.
S
Child
4
4
2
0
0
0
10
Adul
Ad
Adult
ultt
1
1
3
4
4
3
16
Taxi
1
1
1
1
1
1
6
[3]
Marker Report
[B3]
or
6 is the minimum number of taxi needed.
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190
6
Adult
3
3
3
3
3
1
16
Taxi
1
1
1
1
1
1
6
6 is the minimum number of taxi needed.
or
Taxi
1
1
1
1
1
1
6
or
Adult
3
3
3
3
2
2
16
ut
Child
2
2
2
2
1
1
10
.s
g
Child
2
2
2
2
2
0
10
Adult
1
1
3
4
4
4
3
20
Taxi
Ta
x
1
1
1
1
1
1
1
7
Adult
3
3
3
3
3
3
2
20
Taxi
1
1
1
1
1
1
1
7
ile
Child
4
4
2
0
0
0
2
12
S
m
3(b)
T
6 is the minimum number of taxi needed.
neeed
e ed.
[B2]
7–6=1
1 more taxi needed.
need
eded
ed.
or
Child
2
2
2
2
2
2
0
12
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7–6=1
191
7
1 more taxi needed.
Child
2
2
2
2
2
2
0
12
Adult
3
3
3
3
3
3
2
20
Taxi
1
1
1
1
1
1
1
7
S
m
ile
T
ut
or
7–6=1
1 more taxi needed.
.s
g
or
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192
8
4
Two different sizes of cylindrical fruit cans are shown below. The small can has a diameter of
12 cm and a height of 13 cm. The prices of the fruit cans are given on the respective cans.
LARGE
SMALL
$18.80
13 cm
11 310 cm3
.s
g
$4.80
12 cm
(a)
Find the volume of the small can.
(b)
working
Which size of canned fruit gives the better value? Show all thee wo
work
rkin
rk
ing
in
g clearly of
[3]
can.
(c)
What is the maximum number of small cans that
thaat can
can fit
ca
fit iin
fi
nto a rectangular
rec
ecta
tang
ta
gular
into
[3]
packaging of size 72 cm by 24 cm and height of 339
9 cm
ccm?
m?
ut
or
[2]
[M1]
4(b) Small can per cm
c 3 = $4.80 y 1470.265
26
65 $$0
0.003264717
0032
3264
6471
7 7
71
3
Large can per cm = $18.80
80 y 11310
11310 $0
$0.001662245
0016
00
1662
6 24
62
245
5
[M1]
[M1]
La
arge can gives the better value based
bas
ased
ed
d oon
n per cm3.
Large
[A1]
T
Answer
S/N
4(a) Volume of the small can = S u r 2 u h
= S u (6) 2 u 13
= 1470.265 cm3
= 1470 cm3
Mark
Mark
k
Marker
Mark
Ma
rker Report
rk
m
ile
[A1]
[B2]
6×2×3 = 36
[A1]
S
4(c) 72 y 122 6
24 y 12
2 2
39 y 13
13 3
36 cans is the maximum number to fit into a rectangular
packaging.
k i
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193
9
There are 2(k – 3) peaches in a box. There are 3 more apples than peaches and twice as
many oranges as peaches in the same box.
(a) Express the number of apples in term of k.
[1]
(b) Express the number of oranges in term of k.
[1]
(c)
[3]
If there are a total of 35 fruits in the box, how many peaches are there in the box?
[3]
(e)
[2]
.s
g
( ) If the cost of a ppeach,, an apple
pp and an orange
g is $1.10,, $0.20 and $0.50
(d)
respectively, what is the cost of one box of fruits?
How many numbers of boxes of fruits can May purchase with $42??
S/N
Answer
5(a) peaches = 2(k 33)) 2k 6
apples = 2(k 3) 3 2k 6 3 2k 3
5(b) oranges = 2(2k 6)
35
[B1]
[[B
B1
1]]
[M1]
k
k
ile
T
12)
5(c) (2k 6) (2k 3) (4k 12)
2k 6 2k 3 4k 12 35
8k 21 35
8k 35 21
8k 56
Marker
Marker Report
[B1]
[B
B1]]
ut
4k 12
Mark
rk
k
or
5
56 y 8
7
2( 7 ) 6
8
[A1]
2(7) 3 11
[M1]
m
peaches
peeaches = 2k 6
5(d) apples = 2k 3
[M1]
S
oranges = 4k 112
2
4(7) 1122 16
[M1]
total cost for oone
ne bbox
ox
= 8(1.10) 11(0.20
20) 16(0.50)
5(e)
$42.00 y $19.00
2
$19.00
[A1]
[M1]
4
19
2 number of boxes that May is able to purchase with $42.
[A1]
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194
10
6
An aeroplane travelled a distance of 1130 km from Singapore to Jakarta. For the first x
hour of its journey, the aeroplane travelled at a constant speed of 350 km/h. The speed
x
of the aeroplane was increased by 80 km/h for the remaining hour of its journey.
2
(a) Write down the total distance travelled for the first x hour of its journey, in terms
of x.
terms of x.
n for th
the whole
Find the value of x. Hence, find the total time, in hours, taken
journey.
or
(c)
x
hour of its journey, in
2
.s
g
(b) Write down the distance travelled by the aeroplane in the
(d) Find the average speed, in km/h, for the whole journey,
journ
ney
ey,, correct
corr
co
rrrect to
rre
o 2 ddecimal
ecim
ec
imal
im
places.
Answer
ut
S/N
6(a) First part of journey
T
Speed = 350 km/h
Time taken = x hour
ile
Total distance travelled = 350x km
Mark
Ma
M
arrk
k
[1]
[2]
[3]
[2]
Marker
Mark
Ma
rker
rk
err Report
[B1]
6(b) Second part of jjourney
ourney
m
Speed = 350 + 80 = 430 km/h
Time taken = x/2 hour
travelled
Total distance tra
rave
vell
lled = 430
430 u
215 x km
S
11
130
6(c) 350 x 215 x 1130
565 x 1130
0
x 2
1
x
2
[M1]
x
1
x
2
1
2 (2)
2
[A1]
[M1]
[M1]
3
Total time taken for the whole journey = 3 hours
6(d) Average speed for the whole journey
1130
3
2
376 km/h
3
= 376.67 km/h
[A1]
[M1]
[A1]
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11
7
Answer the whole of this question on a sheet of graph paper.
The variables x and y are connected by the equation
y 2 2x .
Some corresponding values of x and y, are given in the table below.
2
1
0
1
2
y
p
4
2
q
2
.s
g
x
Calculate the value of p and of q.
(b)
Using a scale of 2 cm to 1 unit for the y-axis and 4 cm to 1 unit forr the
x-axis,
th x-ax
ax
axis,
x draw
the graph y 2 2 x for 2 d x d 2 .
[3]
(c)
Using your graph, find the value of x when y
(d)
On the same axes, draw the line x = 1.5 . Find the
th
he coordinates
coo
co
orrd
diina
nattes off tthe
he ppoint
o nt of
oi
[2]
intersection of the two lines.
or
(a)
[1]
ut
3.5 .
[2]
S
m
ile
T
--- End of Paper ---
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196
.s
g
or
ut
T
ile
m
S
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197
JUNYUAN SECONDARY SCHOOL
END OF YEAR EXAMINATION 2017
SECONDARY ONE EXPRESS
CANDIDATE NAME
INDEX NUMBER
.s
g
CLASS
MATHEMATICS
9 October 2017
Candidates answer on the Question Paper.
ut
READ THESE INSTRUCTIONS FIRST
1 hour
or
Paper 1
4048/01
ile
Answer all questions.
T
Write your name, class and index number on all the work you hand in.
Write in dark blue or black pen.
You may use an HB pencil for any diagrams or graphs.
Do not use paper clips, highlighters, glue or correction fluid.
If working is needed for any question it must be shown with the answer.
Omission of essential working will result in loss of marks.
m
The use of calculator is not allowed for this paper.
S
At the end of the examination, fasten all your work securely together.
The number of marks is given in brackets [ ] at the end of each question or part question.
The total of the marks for this paper is 50.
For Examiner’s Use
This document consists of 12 printed pages (including the Cover Sheet).
[Turn over
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198
2
Mathematical Formulae
Compound interest
r ·
§
Total amount = P ¨1 ¸
© 100 ¹
n
.s
g
Mensuration
Curved surface area of a cone = Srl
Surface area of a sphere = 4Sr2
Volume of a cone = 1 Sr2h
3
or
Volume of a sphere = 4 Sr3
3
1
ab sin C
2
ut
Area of triangle ABC =
Arc length = rT, where T is in radians
1 2
r T, where T is in radians
2
Trigonometry
ile
T
Sector area =
m
a
b
c
=
=
sin A sin B
sin C
a2 = b2 + c2 2bc cos A
S
Statistics
Mean =
¦ fx
¦f
Standard deviation =
¦ fx
¦f
2
§ ¦ fx ·
¸
¨
¨¦f ¸
©
¹
2
1E Math P1 2017 EOY
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199
3
1
The numbers 540 and 7056, written as a product of their prime factors, are
540
2 2 u 3a u 5
and
7056
2 4 u 32 u 7 2 .
Find
the value of a,
.s
g
(a)
2
7056 .
Answer ...............................................[1]
m
Factorise completely 4ax 12by 16ay 3bx .
S
2
ile
T
ut
(b)
or
Answer a = ........................................ [1]
Answer ............................................... [2]
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200
4
3
(a)
Express
23
% as a decimal.
100
Answer .............................................. [1]
Arrange the following in ascending order.
1
4
0.4 2
44%
or
0.4
.s
g
(b)
A Singapore twenty-cents coin has a diameter of 21 mm.
A British five-pence coin has a diameter of 18 mm.
Shannon placed one row of twenty-cent coins and one row of five-pence coins on the table as
shown below.
.
. .
.
.
. .
.
S
m
ile
T
4
ut
Answer ......... . .......... , ......... , ......... [2]
smallest
largest
Finding the minimum number of coins in each row such that the two rows are of the same length.
Answer ............... twenty-cents coins
.................. five-pence coins [3]
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201
5
Keith keeps track of his monthly business profits and losses over a period of five months given in
the table below.
Month
April
May
June
July
August
Find his total losses from April to August.
or
(a)
Profit
í$2800
í$1200
$900
$1500
$1000
.s
g
5
Answer $.............................................[1]
ut
If he makes a total profit of $2000 from April to September, what is his profit for September?
6
ile
T
(b)
Answer $.............................................[2]
Mr Tan is presently 4 times as old as his son Kenneth.
If Kenneth is x years old now, write down Mr Tan’s age in terms of x.
S
m
(a)
(b)
Answer .............................. years old [1]
In 20 years’ time, Mr Tan will be 2 times as old as Kenneth.
Form an equation in x, and hence find Mr Tan’s age in 20 years’ time?
Answer .............................. years old [2]
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202
6
7
The figure below shows a trapezium PQST.
14 cm
O
Q
2 cm
T
R
A
B
PT is the diameter of a circle with centre O.
PT = 14 cm, QA = BS = 2 cm.
S
or
22
.
7
2 cm
S
m
ile
T
ut
Find the area of the shaded region. Take S
.s
g
P
Answer ...................................... cm2 [3]
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203
7
1
h to cycle from her house to the library at a speed of 12 km/h.
3
Upon reaching the library, she suddenly remembered that she has forgotten to feed her cat.
She rushed home at double the speed which she cycled from her house to the library.
Emilia took
(a)
Find the distance between Emilia’s house and the library.
.s
g
8
Answer ....................................... km [1]
Find the average speed for Emilia’s entire journey.
ut
or
(b)
Solve the inequality 3 x 16 t 5 x 24 .
ile
(a)
m
9
T
Answer .................................... km/h [2]
S
Answer .............................................. [2]
(b)
Hence, write down
(i)
the smallest odd number,
Answer .............................................. [1]
(ii)
the smallest prime number.
Answer .............................................. [1]
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204
8
10
At a bakery, the prices of a plain waffle and a peanut butter waffle are in the ratio 5 : 6.
Given that the prices of a plain waffle and a chocolate waffle are in the ratio 3 : 4, find the
ratio of the price of a peanut butter waffle to the price of a chocolate waffle.
Give your answer in the simplest form.
ut
or
.s
g
(a)
Answer ..................... : ...................... [2]
The difference in price between the plain waffle and the peanut butter waffle is $0.30.
T
(b)
S
m
ile
Find the price of a peanut butter waffle.
Answer $.............................................[2]
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205
9
(a)
Solve the equation 4 x 5 3(3 2 x) .
3n m 2n m
.
4
3
T
Simplify
Answer x = ........................................ [2]
S
m
ile
(b)
ut
or
.s
g
11
Answer .............................................. [2]
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206
10
12
(a)
Find the value of x in the diagram shown below.
x°
100°
135°
.s
g
85°
or
70°
Answer x = ........................................ [2]
In the diagram, lines AB, DE and FCG are parallel.
‘ABC 84q and ‘BCD 39q .
C
T
F
ut
(b)
ile
39°
A
G
D
84°
3x°
E
S
m
B
Find the value of x, stating all reasons clearly.
Answer x = ........................................ [3]
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207
11
The birth weight of a newborn baby girl is 2 800 g.
During the first year, her weight increases by 480 g every month.
(a)
Write down her weight when she is
(i)
1 month old,
.s
g
13
Answer ........................................... g [1]
2 months old.
or
(ii)
Answer ........................................... g [1]
ut
Find an expression for her weight when she is n months old.
Answer ........................................... g [1]
If the girl weighs 8.0 kg when she is m months old, find the value of m.
S
m
(c)
ile
T
(b)
Answer m = ....................................... [1]
(d)
Explain why the expression in (b) is not used to find the weight of the girl when she is
10 years old.
Answer...............................................................................................................................
............................................................................................................................ [1]
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208
12
14
In the diagram below, the points A and B DUH í DQG UHVSHFWLYHO\
Answer (b) and (c)
y
.s
g
6
B
4
0
2
4
6
ut
2
or
2
x
T
A
2
AB
Find the gradient of the line AB.
m
(a)
ile
4
Answer .............................................. [1]
On the same diagram, draw the lines y = 2 and x = 6.
(c)
Point C is the point of intersection between the lines y = 2 and x = 6.
S
(b)
Mark and label point C on the diagram.
(d)
[2]
[1]
Hence, calculate the area of triangle ABC .
End of Paper
Answer ..................................... unit2 [2]
1E Math P1 2017 EOY
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209
JUNYUAN SECONDARY SCHOOL
END OF YEAR EXAMINATION 2017
SECONDARY ONE EXPRESS
CANDIDATE NAME
INDEX NUMBER
.s
g
CLASS
MATHEMATICS
4048/02
Paper 2
13 October 2017
Additional Materials: Writing paper (6 sheets)
Graph paper (1 sheet)
1 String
ut
READ THESE INSTRUCTIONS FIRST
or
1 hour 30 minutes
T
Write your name, class and index number on all the work you hand in.
Write in dark blue or black pen on both sides of the paper.
You may use an HB pencil for any diagrams or graphs.
Do not use paper clips, highlighters, glue or correction fluid.
m
ile
Answer all questions.
If working is needed for any question it must be shown with the answer.
Omission of essential working will result in loss of marks.
The use of an approved scientific calculator is expected, where appropriate.
If the degree of accuracy is not specified in the question, and if the answer is not exact, give the
answer to three significant figures. Give answers in degrees to one decimal place.
For S, use either your calculator value or 3.142, unless the question requires the answer in
terms of S.
S
At the end of the examination, fasten all your work securely together.
The number of marks is given in brackets [ ] at the end of each question or part question.
The total number of marks for this paper is 50.
Hand in your question paper and answer scripts SEPARATELY.
This document consists of 6 printed pages (including the Cover Sheet).
[Turn Over
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210
2
Mathematical Formulae
Compound interest
r ·
§
Total amount = P¨1 ¸
© 100 ¹
n
Mensuration
.s
g
Curved surface area of a cone = Srl
Surface area of a sphere = 4Sr2
Volume of a cone =
1 2
Sr h
3
4 3
Sr
3
or
Volume of a sphere =
1
ab sin C
2
ut
Area of triangle ABC =
Arc length = Uș, where ș is in radians
1 2
r T , where ș is in radians
2
ile
Trigonometry
T
Sector area =
a
sin A
m
a2
b
sin B
c
sin C
b 2 c 2 2bc cos A
S
Statistics
Mean =
¦ fx
¦f
Standard deviation =
1E Math P2 2017 EOY
¦ fx 2 § ¦ fx ·
¸¸
¨¨
¦f
©¦f ¹
2
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211
3
2
(a)
Express 1296 as a product of its prime factors.
[1]
(b)
Find the largest integer, which is both a factor of 1296 and 672.
[2]
The diagram below shows a 5-sided polygon.
AB is parallel to DE, and AE is parallel to BC.
‘BAE 4 xq , ‘BCD 134q and ‘CDE (5 x 18)q .
Find the value of x.
B
[3]
C
(5x + 18)° D
4x°
The diagram shows a sequence of figures formed by matchsticks, where n is the figure
number.
S
m
3
E
ile
T
A
ut
or
134°
.s
g
1
n=1
n=2
n=3
(a)
Draw the figure for n = 4.
[1]
(b)
If Tn is the number of matchsticks in the nth figure, state T1 , T2 , T3 and T4 .
[2]
(c)
Hence, or otherwise, find the general term Tn in terms of n.
[1]
(d)
Explain why 99 could not be a possible number for Tn .
[1]
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212
4
4
2 , b
1
and c
2
27
, evaluate b 2 3a 3 3 c .
64
(a)
Given that a
(b)
(i)
Solve the inequality 3x 1 d
(ii)
Illustrate your solution in (b)(i) on a number line.
[1]
3x 7
.
2
[3]
[1]
(iii) Find the smallest value of x 2 .
.s
g
A stack of ten $1 coins forms a cylinder of base diameter x cm and height 2.5 cm.
or
5
[1]
ut
2.5 cm
x cm
If the volume of the stack is 11.9 cm3, find x.
(b)
Find the total surface area of the stack.
(c)
If six more of the identical $1 coins are added to the stack, find the percentage increase
of the total surface area of the stack.
[3]
T
[2]
ile
[2]
m
In a chemical reaction, the volume V cm3 of a crystal at time t minutes is given by the function
4V 3t 8 for 0 d t d 8 .
The table below shows some corresponding values of t and V.
t / min
0
1
2
3
4
5
6
7
8
V / cm3
2
2.75
3.5
4.25
5
5.75
6.5
7.25
8
S
6
(a)
(a)
Using a scale of 2 cm to 1 unit on both t- and V-axes, draw the graph of 4V
for 0 d t d 8 .
(b)
Using your graph, find the time that the volume of the crystal is 5.5 cm3.
[1]
(c)
(i)
Find the gradient of the graph.
[2]
(ii)
Suggest a physical meaning of the gradient in this graph.
[1]
(d)
Suggest what the V-intercept represents in this graph.
3t 8
[2]
[1]
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5
7
The picture below shows the national flag of Bahamas.
ABCD is a rectangle, CDRQ and ABPS are identical trapeziums and ADT is an equilateral
triangle.
D
C
R
Q
T
P
S
B
The ratio of AB to BC is 3 : 2, BP =
It is given that AB = 54 cm.
.s
g
A
4
1
BC and QR = CD.
3
5
Find the lengths of BC, BP and QR.
(b)
Find the area of CDRQ.
(c)
Find the ratio of the area of CDRQ to the area of the flag.
[2]
(d)
If the area of PQRTS is 216 cm2, find the height of the triangle ADT.
[2]
[3]
[1]
S
m
ile
T
ut
or
(a)
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6
The table below shows the pricing of three taxi companies in Singapore.
GrabCar Economy
Basic fare: $3.00
Every kilometer or less: $0.80
Uber X
Basic fare: $3.00
Every kilometer or less: $0.45
Per minute: $0.20
(a)
1km or less: $3.20
Every 400 m thereafter or less up to 10 km: $0.22
Every 300 m thereafter or less up to 10 km: $0.22
Every 45 seconds of waiting or less: $0.22
or
ComfortDelGro
.s
g
8
Mrs Lim travels from home to work every morning. The distance between her home
and work is 6.4 km.
Michael leaves his house at 0837 and travels by Uber X to Changi Airport, which is
15.5 km away from his house.
(ii)
Find how much Michael has to pay for his trip.
[1]
ComfortDelGro imposes peak period surcharges as follows.
S
m
(c)
If he arrives at the airport at 0902, find the average speed at which Michael
[2]
travels, in km/h.
ile
(i)
T
(b)
ut
Find how much Mrs Lim pays every morning if she were to travel by GrabCar
[1]
Economy.
Monday to Friday
0600 – 0929
Monday to Sunday &
Public Holidays
1600 – 2359
25 % of metered fare
Find how much Michael in (b) has to pay if he were to travel by ComfortDelGro to
Changi Airport.
[2]
(d)
(e)
Khairul wishes to travel from Tampines MRT to ION Orchard, which is 16 km away.
The average speed a taxi travels is 80 km/h during non-peak period.
Find which taxi company Khairul should choose for the cheapest fare.
[4]
State any assumption(s) made in your calculations in (d).
[1]
End of Paper
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215
.s
g
or
ut
T
ile
m
S
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216
Junyuan Secondary Secondary School
End of Year 2017
Secondary 1 Express
Marking Scheme
3
(a)
a=3
22×3×7 = 84
4ax 16ay 12by 3bx
4ax 3bx 16ay 12by
4a( x 4 y ) 3b(4 y x)
or x(4a 3b) 4 y (4a 3b)
4a( x 4 y ) 3b( x 4 y )
( x 4 y )(4
)(4a 3b)
( x 4 y )(4
)(4a 3b)
0.0023
(b)
1
0.4
44%
4
21 = 3×7
18 = 2×32
LCM = 2×32×7 = 126
126
6 twenty cents coins
21
126
7 five pence coins
18
0.4 2
(a)
2800 (1200) 900 15
15000 10
11000
00 $60
6000
Total
To
ota
t l loss = $600
2000 (600)
$2600
Profit for Se
S
Sep
p = $260
$2600
00
4x
m
(b)
T
(a)
ile
5
6
(a)
S
(b)
7
M1
A1
M1
A1
B22
B
ut
4
B1
B1
.s
g
2
(a)
(b)
(a)
or
1
20 2( x 20
20)
4 x 20
20 2 x 40
4 x 20
20
2 x 20
x 100
? 20 years time 4(10) 20 60 years old
Area of trapezium PQST
1
= u 14 18 u 7
2
= 112 cm².
Area of semi-circle PRT
1 22
= u u 72
2 7
= 77 cm².
Area of shaded region
= 112 77 = 35 cm2
$Q\PLVWDNHíP
$Q\
$Q
\PL
\
PLVVWDNHíP
PL
M1
M
((LCM)
LCM)
LC
M
A
A1
A1
B1
M1
A1
Follow through from
(a)
B1
M1
A1
M1
M1
A1
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217
8
(a)
B1
1
Distance = 12 u = 4km
3
Return speed = 24 km/h
(b)
Time taken for return journey =
4u 2
1 1
6 3
= 16 km / h
4
1
hr = hr
24
6
M1
Speed =
10 (a)
11 (a)
ile
2 x 14
x 7
S
12 (a)
(b)
13 (a)(i) 2800 + 480 = 3280g
(a)(ii) 3280 + 480 = 3760g
(b)
2800 + 480n
M1
M
A1
A1
M
M1
A1
A
M1
A1
3n m 2n m
4
3
9n 3m 8n 4m
=
12
nm
=
.
12
Sum of interior
int
nter
erio
iorr angles
angl
an
gles of pentagon
= (5
( – 2)×180q
2)×
)×18
1800q
540o
= 540
135
13
35 100
100 85
8 70 180 x 540
540
0 570 x
x = 30q
‘BCG
‘ CG 84 q (alternate
( lt
t angles,
l parallel
ll l li
lines))
‘DCG 84 39 45 q
‘CDE 180 45 (interior angles, parallel lines)
= 135q
3x 135 360 (angles at a pt)
x = 75
m
(b)
B1
B11
P : PB : C
5:6
:4
3
15 : 18 : 20
9 : 10
1 unit Æ $0.30
6 units Æ $1.80
4x 5 9 6x
(b)
.s
g
(b)
(c)
M1
A1
or
8x t 8
x t1
1
2
ut
(a)
T
9
A1
M1
A1
M1
A1
M1
D
Deduct
d t 1mark
1
k if any
reason is not provided
M1
A1
B1
B1
B1
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(c)
2800 + 480(m) = 8000
m = 10.3 (3 s.f)
The expression should only be used to find his weight
for the first year. It is unrealistic to say that the weight
of the girl still increases by 480 g every month at age
of 10.
(d)
14 (a)
B1
B1
4
0
4
6
\ í
[B
[B1]
1]
C
ut
í
2
or
-22
.s
g
x=6 [B1]
T
By drawing a suitable triangle under the straight line.
lliine
ne.
6
gradient =
1
6
1
u 6 u 6 units 2
2
=18 units2
ile
(d)
-Correctly
indicated
B1 -C
B
-Cor
orre
r ctly in
C
B1
B
1
M1
S
m
A1
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219
Junyuan Secondary School
End-of-Year Examinations 2017
Mathematics Paper 2
Marking Key
Secondary One Express
(a)
1296
(b)
672 25 u 3 u 7
HCF 2 4 u 3
.s
g
[M1]
or
48
‘ABC ‘AED
A
(180 4 x )q (int. ‘s, AB // DE, BC // AE)
Sum of int. angles of pentagon (5 2) u 180q
540q
2(180 4 x ) 4 x 5 x 18 134 520
x 28q
2
(b)
6
11
16
21
5n 1
5n 1 999
n z in
integer
intege
er
S
(d)
4
(a)
(b)(i)
1
27
( )2 3
3(( 2)3 3
2
64
3x 7
3x 1 d
2
6 x 2 d 3x 7
25
[M
1]
[M1]
[A1]
[A
A1]
[B1]
[B
B1]
[B2]
[SC1] for 2 or 3 corre
correct
answers
[M1]
3 x d 9
(b)(ii)
[A1]
[M1]
[M
1]
[B1]
Accept
Tn 6 5( n 1)
[B1]
Accept any logical
reasoning for n must be
an integer
[B1]
m
(c)
T1
T2
T3
T4
Tn
ut
(a)
T
3
[B1]
2 4 u 34
ile
1
[A1]
x d 3
[B1]
௅5
௅4
௅3
(b)(iii) 9
[B1]
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220
(b)
(c)
Sr h 11.9
r 1.2309 cm
x ( 2)(1.2309)
2.46 cm (3 s.f.)
surface area 2Sr 2 2Srh
[M1]
[A1]
2S (1.2309) 2 2S (1.2309)( 2.5)
9.52 19.335
[M1]
28.9 cm 2
[A1]
2.5
10
0.25 cm
increase in surface area ( 2.4618)(S )(0.25)(6)
height of one $1 coin
11.601 cm 2
11.601
u 100%
28.88
40.2% (3 s.f.)
ut
increase in percentage
(a)
[[M1]
[M
1]
[M1]
1]
[A1]
[ 1]]
[A
S
m
ile
T
6
2
2
.s
g
(a)
or
5
(b)
(c)(i)
By calculation: 4.67 min (3 s.f.)
Therefore, accept 4.6, 4.65 and 4.7 min only.
gradient
[B1]
[M1] Correct coordinates substituted
into formula
[A1]
y 2 y1
x 2 x1
3
4
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The initial volume of the crystal is 2 cm3.
2
( )(54)
3
36 cm
1
BP ( )(36)
3
12 cm
BC
QR
(b)
(c)
4
( )(54)
5
43.2 cm
1944 cm 2
(a)
(b)(i)
(b)(ii)
(c)
[B1]
[B
1]
[B1]
[M1]
[A1]
5561
61.6 cm 2
[M1]
1
u basee u height
h ig
he
ght 561.6
561.
56
1.6
6
2
height
1123.2
3 u he
36
heig
ight 11
1123
2 .2
heig
he
height
ight
h 31.2 cm
$3.00
00 $0.8800(7) $8.60
0837 Æ 0902: 25 minutes
15.5
Speed
25/60
37.2 km/h
$3.00 $0.45(16) $0.20( 25)
S
8
[B1]
[B
1]
583
83.2 : 1944
583.2
3 : 10
Area of ADT (54)(36) (583
8 .2)(
83
)( 2) 216
216
m
(d)
1
( 43.2 54)(12)
2
583.2 cm 2
(54)(36)
ile
CDRQ : flag
[B1]
Accept “initial volume
of crystal”, “volume of
crystal at the
beginning/start”.
[B1]
Area of CDRQ
Area of flag
[B1]
.s
g
(a)
3
cm3.
4
or
7
Every minute, the volume of the crystal increases by
ut
(d)
3
T
(c)(ii)
Fare without surcharge
Fare with surcharge
[A1]
[B1]
[M1]
[A1]
$15.20
$3.20 $0.22(
$12.00
($12.00)(1.25)
$15.00
[B1]
4500
10000
)
) $0.22(
300
400
[M1]
[A1]
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.s
g
or
ut
T
ile
m
S
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223
4
GrabCar
$3.00 (16)($0.80) $15.80
16
Time taken
80
0.2 h
12 min
Uber X $3.00 (16)($0.45) (12)($0.20) $12.60
5100
10000
)($0.22)
)($0.22) (
ComfortDelGro $3.20 (
300
400
$12.44
From above, ComfortDelGro offers the cheapest fare.
Assume there is smooth traffic / no jam / no waiting of traffic
light.
[B1]
[B1]
[B1]
[B1]
Accept any logical
answer.
S
m
ile
T
ut
(e)
or
.s
g
(d)
Accept answer t $15 if
student consider
waiting time at $0.22
per minute.
[B1]
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REGENT SECONDARY SCHOOL
END OF YEAR EXAMINATION (SA2) 2017
SECONDARY ONE (EXPRESS)
NAME: _______________________________________
INDEX NUMBER: ________
CLASS: ________
SETTER : Ms Jacintha
_________________________________________________________________________
MATHEMATICS
4048/01
.s
g
9th October 2017
READ THESE INSTRUCTIONS FIRST
or
Paper 1
1 hour 15 mins
Candidates answer on the Question Paper.
_________________________________________________________________________
ut
Write your class, index number and name on all the work you hand in.
Write in dark blue or black pen.
You may use a pencil for any diagrams or graphs.
Do not use staples, paper clips, highlighters, glue or correction fluid.
ile
T
Answer all questions.
If working is needed for any question it must be shown with the answer.
Omission of essential working will result in loss of marks.
The use of an approved scientific calculator is expected, where appropriate.
If the degree of accuracy is not specified in the question, and if the answer is not exact, give
the answer to three significant figures. Give your answers in degrees to one decimal place.
For ʌ , use either your calculator value or 3.142, unless the question requires the answer in
terms of ʌ .
m
At the end of the examination, fasten all your work securely together.
The number of marks is given in brackets [ ] at the end of each question or part question.
The total of the marks for this paper is 50.
S
TARGET
50
PARENT’S SIGNATURE
_________________________________________________________________________
This document consists of 10 printed pages.
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246
2
For
Examiner’s
Use
Answer all questions.
1 Express
(a)
For
Examiner’s
Use
33% as a fraction in its lowest terms,
Answer (a)…………………………………..
15
1
as a percentage.
4
.s
g
(b)
[1]
or
Answer (b)…………………………………..
[1]
56.89 104.2
.
3
61.76 3.99
Answer …………………………………..
[2]
Consider the following numbers,
m
3
ile
T
ut
2 By rounding off each term to 1 significant figure,estimate the value of
3
x x x
125 , 0. 51 6 , 8 , S
Write down all the
(a) irrational number(s).
49
, S
7
Answer (a)………………………………….. [1]
(b)
integer(s).
Answer (b)………………………………….. [1]
(c)
perfect cube(s).
Answer (c)………………………………….. [1]
Regent Secondary School
2017 End of Year Examination (SA2) Sec 1 Express Paper 1
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3
For
Examiner’s
Use
4
(a)
Write a simplified algebraic expression for the statement “ Cube root of the
product of w and x.’
Express
b 5 2b 3
as a single fraction.
3
5
5
ile
T
ut
or
(b)
.s
g
Answer (a) ……………….……….. [1]
Answer (b) ………..……………….. [3]
A sum of money was divided between Amy and Daniel in the ratio 5 : 12. After
S
m
Amy spent $22, the ratio became 3 : 16. Find the amount of money Amy had at first.
Answer $………………..……….. [3]
Regent Secondary School
2017 End of Year Examination (SA2) Sec 1 Express Paper 1
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248
For
Examiner’s
Use
4
6
The number 1888 can be expressed as 2a × b, where a and b are integers.
For
Examiner’s
Use
(a) Find the value of a and of b.
.s
g
For
Examiner’s
Use
or
Answer (a) a = …………………………. [1]
b = ………………………….
[1]
m
ile
T
ut
(b) Given that x = 23 × 5 × 7, evaluate the highest common factor of 1888 and x.
Answer (b) .………………………………….. [1]
S
(c) Find the smallest integer n such that 1888n is a perfect square.
Answer (c) n = .…………………………………..
Regent Secondary School
2017 End of Year Examination (SA2) Sec 1 Express Paper 1
[1]
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249
5
7
A man ran 2.4 km in 16 minutes. He then walked a further 900 m at an average speed
of 4 km/h. Calculate
(a)
his speed, in km/h, in the first 16 minutes,
.s
g
For
Examiner’s
Use
Answer (a)………………………..km/h [2]
the time, in minutes, he took to walk,
ut
or
(b)
his average speed, in m/s, for the whole distance travelled.
m
ile
(c)
T
Answer (b)……………………..minutes [2]
S
Answer (c)…………………………..m/s [2]
8
If a
2
1
and b
4
0.75 , find the ratio of a : b.
Answer ….…………………………… [2]
Regent Secondary School
2017 End of Year Examination (SA2) Sec 1 Express Paper 1
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250
For
Examiner’s
Use
6
9
(a) Factorise completely
(i)
For
Examiner’s
Use
6c 2 4cd
.s
g
For
Examiner’s
Use
Answer (a)(i) …..……………………….. [1]
ile
T
ut
or
(ii) 4 pq 2 p 2 10 p
m
Answer (a)(ii) ……………………….. [2]
S
(b) Expand and simplify 3 (2 x 2 4) .
Answer (b)……………………………….. [2]
Regent Secondary School
2017 End of Year Examination (SA2) Sec 1 Express Paper 1
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7
10
Solve the following equations.
For
Examiner’s
Use
(a) x 3 2 x 1 .
.s
g
For
Examiner’s
Use
Answer x = ………………………..
3
.
x2
or
2
x
ile
T
ut
(b)
[2]
m
x9
3
Answer x = ……………………….. [2]
3 .
S
(c) 2 Answer x = ………………………. [3]
Regent Secondary School
2017 End of Year Examination (SA2) Sec 1 Express Paper 1
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252
8
11
(a) Solve 3q ! 6 and illustrate the solution on a number line in the space given
below.
.s
g
For
Examiner’s
Use
or
Answer (a) ………………………………….. [2]
T
ut
(b) Find the smallest integer value q that satisfies the inequality 4q 1 ! 6 .
In the diagram below, BCEF is a square with an area of 36 cm2 and GF = 4cm.
Calculate the area of parallelogram BDEG.
S
m
12
ile
Answer (b) ………………………………….. [2]
Answer ……….……………………..cm2 [2]
Regent Secondary School
2017 End of Year Examination (SA2) Sec 1 Express Paper 1
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253
For
Examiner’s
Use
9
For
Examiner’s
Use
13
Find the value of x in the figure below, showing your working clearly.
State the properties and angles where possible.
For
Examiner’s
Use
x
D
C
o
B
A
P
Q
o
45
S
m
ile
T
ut
or
F
.s
g
275
o
Regent Secondary School
2017 End of Year Examination (SA2) Sec 1 Express Paper 1
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10
Answer ……………………………….. [3]
For
Examiner’s
Use
14
In the closed cylinder below, the diameter of the cross-section is 18 cm. Given that
its total surface area is 702S cm2, calculate the height, h, of the cylinder.
S
m
ile
T
ut
or
h cm
.s
g
18cm
Answer h = ……………………………. [3]
Have you checked your work?
END OF PAPER
Regent Secondary School
2017 End of Year Examination (SA2) Sec 1 Express Paper 1
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255
For
Examiner’s
Use
REGENT SECONDARY SCHOOL
END OF YEAR EXAMINATION (SA2) 2017
SECONDARY ONE (EXPRESS)
NAME: _______________________________________
INDEX NUMBER: ________
CLASS: ________
SETTER: Ms Jacintha
_________________________________________________________________________
MATHEMATICS
.s
g
Additional Materials:
4048/02
10 October 2017
Paper 2
th
1 hour 30 minutes
Answer Paper
READ THESE INSTRUCTIONS FIRST
or
_________________________________________________________________________
ut
Write your class, index number and name on all the work you hand in.
Write in dark blue or black pen.
You may use a pencil for any diagrams or graphs.
Do not use staples, paper clips, highlighters, glue or correction fluid.
m
ile
T
Answer all questions.
If working is needed for any question it must be shown with the answer.
Omission of essential working will result in loss of marks.
The use of an approved scientific calculator is expected, where appropriate.
If the degree of accuracy is not specified in the question, and if the answer is not exact, give
the answer to three significant figures. Give your answers in degrees to one decimal place.
For ʌ , use either your calculator value or 3.142, unless the question requires the answer in
terms of ʌ .
S
At the end of the examination, fasten all your work securely together.
The number of marks is given in brackets [ ] at the end of each question or part question.
The total of the marks for this paper is 50.
TARGET
50
PARENT’S SIGNATURE
_________________________________________________________________________
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256
2
Answer all questions.
1
(a)
Find the sum of interior angles of a 12-sided polygon.
(b)
A polygon has 15 sides. Three of its exterior angles are 45D , 46 D and 29 D while
[2]
the twelve remaining exterior angles of the polygon are x D each. Find the value
[2]
The population of Brunei was 422 000 in 2016. This value has been rounded off to the
nearest 1000.
(b)
What is the smallest possible value of the population of Brunei in 2016 ?
(a)
The price of a computer increases from $1300 to $1420. Find the percentage
increase in its price.
(b)
The marked price of a paint art is $6750. There is a discount of 5% for members.
ut
3
What is the largest possible value of the population of Brunei in 2016 ?
or
(a)
Find the selling price for a member after the discount.
ile
(i)
T
2
.s
g
of x.
(ii) Given that there is a GST of 7%, find the total amount payable by the
member, leaving your answer in the nearest cents.
(b)
2 p 5 3q 1
7
4
[2]
[1]
[2]
[2]
Expand and simplify the following expression.
5 4a 5b 3 2a 7b
(c)
[1]
Simplify the following expression.
m
(a)
S
4
[1]
[2]
Factorise the following expression completely.
18 gh 9 g 27 gk
Regent Secondary School
2017 End of Year Examination (SA2) Sec 1 Express Paper 2
[2]
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257
3
A pattern was created using toothpicks. The first three figures are shown below.
Figure 1
Figure 2
Figure 3
(a) How many toothpicks are used in Figure 5?
.s
g
5
or
(b) Write down an expression, in terms of n, for the number of toothpicks in
Figure n.
[1]
The following pictogram illustrates the number of cupcakes sold in a bakery in a
particular week.
MONDAY
ile
TUESDAY
T
6
[1]
ut
(c) Calculate the number of toothpicks in Figure 250.
[1]
WEDNESDAY
THURSDAY
m
FRIDAY
SATURDAY
S
SUNDAY
Each
represents 6 cupcakes.
(a) How many more cupcakes were sold on Monday as compared to Tuesday?
[1]
(b) If each cupcake was sold at $3.50, calculate the total sales amount from the
cupcakes sold in that week.
[2]
(c) Express the ratio of cupcakes sold on weekends to that sold on weekdays.
[1]
Regent Secondary School
2017 End of Year Examination (SA2) Sec 1 Express Paper 2
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4
7
The diagram below shows trapezium ABCD where AD is parallel to BC. ABE is a
straight line, ‘CAB 90q , ‘ADC 115q and ‘ACB 43q .
o
115
43
o
.s
g
x
z
y
or
Stating the reasons clearly, find
(a) x ,
(b) y ,
(a) Draw and label ' ABC such that ‘BAC = 48° , AB = 7.9 cm and AC = 4.8 cm.
T
8
ut
(c) z.
[2]
[2]
[1]
[3]
[1]
(c) Construct the bisector of ‘ABC.
[1]
ile
(b) Construct the perpendicular bisector of AB.
(d) Label the intersection point of the perpendicular bisector of AB and the angle
[2]
S
m
bisector of ‘ABC as M. Measure the distance M from A.
Regent Secondary School
2017 End of Year Examination (SA2) Sec 1 Express Paper 2
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5
9
The bar graph below shows the survey result of a group of Secondary One Students
from Santa Secondary School on their preference of ice-cream flavour.
ut
or
.s
g
No. of students
Favourite Ice-Cream Flavour
[1]
How many more students prefer Mango flavour to Coffee flavour?
(b)
What fraction of the students chose Chocolate flavour as their favourite?
[2]
(c)
What percentage of the students did not choose Vanilla as their favourite
flavour?
[2]
(d)
Jamie observed the bar graph and claimed that the number of students who
ile
T
(a)
m
prefer Chocolate flavour is twice the number of students who prefer Vanilla
[2]
S
flavour. State one way in which the bar graph is misleading Jamie.
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6
10
The diagram below shows a solid prism. The prism has a cross-section of a rightangled triangle.
AB = 6 cm, AC = 8 cm, EF = 10 cm and BE = 17 cm.
E
10 cm
.s
g
17 cm
D
B
F
Calculate,
C
ut
8 cm
A
or
6 cm
the area of the cross-section ABC,
[1]
(b)
the volume of the prism,
[1]
(c)
the total surface area of the prism.
(d)
A cylindrical container with radius 10 cm is filled with some water.
T
(a)
ile
[2]
Ten such solid prisms were dropped into the container, causing the water level to
m
rise. Assuming that there is no water flowing out of the container, calculate the
[3]
S
increase in the water level in the container.
Have you checked your work?
END OF PAPER
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7
Answer x = ………………………..
x9
3
3
[1]
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or
.s
g
(e) 2 ile
T
Answer x = ……………………….
S
m
[2]
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8
(a) Solve 3q ! 6 and illustrate the solution on a number line in the space given
below.
ut
10
S
m
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T
For
Examiner’s
Use
or
.s
g
[3]
Answer (a) ………………………………….. [2]
(b) Find the smallest integer value q that satisfies the inequality 4q 1 ! 6 .
Answer (b) ………………………………….. [2]
Regent Secondary School
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263
For
Examiner’s
Use
9
In the diagram below, BCEF is a square with an area of 36 cm2. What is the area of
parallelogram BDEG?
Answer ……….……………………..cm2 [2]
Find the value of x in the figure below.
S
m
ile
T
12
ut
or
.s
g
11
Regent Secondary School
2017 End of Year Examination (SA2) Sec 1 Express Paper 2
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264
ut
or
.s
g
10
o
Answer ………………………………..
In the cylinder below, the diameter of the cross-section is 18 cm. Given that its total
surface area is 702S cm2, calculate the height, h, of the cylinder.
T
13
S
m
ile
For
Examiner’s
Use
[3]
Regent Secondary School
2017 End of Year Examination (SA2) Sec 1 Express Paper 2
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For
Examiner’s
Use
S
m
ile
T
ut
or
.s
g
11
Answer …………………………………. [3]
Have you checked your work?
END OF PAPER
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2017 End of Year Examination (SA2) Sec 1 Express Paper 2
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.s
g
or
ut
T
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m
S
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267
33
B
Ma ks
%
B
60 100
M
3
a
Wo ki g
50
4
60 4
= .
A
S
3
B
125 ,8,
Ma ke s epo t
Well do e
Ma stude ts put
. % i stead.
Co
o
istake :
Stude ts did ot
esti ate a d o l
ou ded off the fi al
a s e to
o ssf.
f
Badl do
o e. Stude
Sttud
ude ts
or
Q
a
7 MARKING SCHEME
.s
g
E EOY PAPER
49
7
B
3
wx
T
a
ut
B
ile
b 5 2b 3
3
5
5(b 5) 3(2b 3)
15
15
5b 25 6b 9
15
b 16
15
M
A
m
S
:
:
= :
= :
M
– =
a
M
Majo
o it
it of stude ts got
a ko l .
istake :
Co
o
b 5 2b 3
3
5
5(b 5) 3(2b 3)
15
15
5b 25 6b 9
15
b 34
15
Well do e.
M
u its Æ $
u it Æ $
u its Æ
=$
=
a=
=
A
B
B
Well do e
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268
B
B
2.4
16
( )
60
9km / h
900 y 1000
u 60
4
13.5 min s
2400 900
(16 u 60) (13.5 u 60)
1.86m / s
9
: 0.75
4
9:3
2 p (2
(2q p 5)
M
A
M
ut
A
B
M
m
3 2x 2 4
A
2 x 2 1
x 3 2x 1
2x x 3 1
x 2
M
A
S
2
3
x x2
3 x 2(
2( x 2)
3x 2 x 4
x 4
x9
2
3
3
6 x9
3
3
15 x 9
x 24
did
.
M
A
3 (2
( 2 x 2 4)
a
Badl do e. Ma
ot di ide
or
A
ile
aii
3 :1
6c 2 4cd
2c(3c 2d )
or
2c(3c 2d )
A
T
ai
M
.s
g
a
Ma stude ts left the
a s e as
Well do e.
Stude ts ho got this
o g did ot o e t
the ti e to hou s.
M
Well do e. O e a k
as gi e fo the p
fa to ised out o e tl .
Ma
a aged to get
2
3 2 x 4 ut si plified it
o gl .
Well do e.
Stude ts had a issue
si plif i g afte ossultipli atio .
A
x9
5
3
15 x 9
x
M
24
M
Badl do e. Stude ts did
ot ha ge the sig of
afte aki g o
o
de o i ato o the left.
A
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269
a
q 2
B
Badl do e. Stude ts
e e a le to sol e the
i e ualit ut ould ot
illust ate it o the
u e li e o e tl .
Well do e.
B
-
-
4q 1 ! 6
q ! 1.75
q 2
M
A
Le gth of s ua e =
A ea =
=
36
A
45q(corr ‘s )
360 275
85q(‘s at a pt
p)
‘XBC
85 45
40q
M
T
ut
ABX
‘A
‘ABC
ile
‘BCY 40q
40q(alt ‘s )
x 180 40
220q
2(S u 9 u 9) 2 u S u 9 u h
162S 18
1 Sh
Well do e..
or
D a a li e BX th ough B
P odu e the li e DC to Y
M
6cm
.s
g
-
7002S
702
ak
fo a
o e t
easo s
A
M
702S
M
A
S
m
18Sh 540S
h 30cm
m
A e age.
P ese tatio of o ki g
fo this uestio as
do e adl .
Ma
e e e ed the
fo ulas o gl .
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E EOY PAPER
Wo ki g
=
i
ii
A
B
B
M
.s
g
1420 1300
u 100
1300
3
9.23% or 9 %
13
6750
u 95
100
$6412.50
6412.50
u 107
100
$6861.38
M
A
A
M
A
2 p 5 3q 1
4
7
4(2 p 5) 7(3q 1)
28
8 p 20 2211q 7
2288
8 p 211q 13
2288
5 4a 5b 3 2a 7b
20a 25b 6a 21b
14a 46
14a
6b
S
A
M
A
18 gh 9 g 27 gk
B
9 g (2h 1 3k )
a
Well do e.
M
m
a
=
T
a
+
ile
a
=
=
+
Ma ke s epo t
Reaso a l do e. So e
stude ts did ot e e e
the fo ula.
Reaso a l do e. So e
stude ts e t to al ulate
su of i te io a gles i stead.
Mostl ell do e
Mostl ell do e
or
+
Ma ks
M
A
ut
Q
a
7 MARKING SCHEME
M a a ded fo fa to isi g o e fa to out
o e tl .
+
Reaso a l do e. So e
stude ts did ot e pa d the
se o d pa t of the uestio
o e tl .
Not ell do e.
e Stude ts a e
ot fa ilia ith fa to isatio .
OR
B
B
Well do e
Reaso a l do e. But a
stude ts did ot si plif thei
a s e s. Co
o e os
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271
a
.s
g
.
.
=$
:
B
M
A
x 180 115 43
M
22 43
65q(vert opp ‘s )
m
ile
z
T
ut
22q(int ‘s )
‘ABC
A
180 90 43
47q(‘s in ')
y 180 47
133q(‘s on strt line)
or
a
B
B
M
A
i lude: + n – o n + n –
.
n–
as pe alised fo
p ese tatio .
Well do e. No e f a a ded.
Well do e.
Well do e. Sa e p ese tatio
e o fo so e stude ts ho
e p essed a s e as $
.
Well do e.
Well do e.
S
a
d
140
360
7
18
280
u 100
360
A
Mi
Mi us
fo
o
easo
i a
of the
pa ts
B
M
A
M
7
77.8% or 77 %
9
The a g aph is isleadi g as its e ti al
a is sta ts f o
i stead of , thus
aki g the u e of stude ts ho p efe
Cho olate fla ou look like it is t i e the
A
B
Well do e. Stude ts ho
ote opp. a gles e e
pe alised. Vertically opposite
is the ke o d to e a a ded
a ks fo easo s. E f allo ed
fo stude ts ho got a
o g.
Well do e
Reaso a l do e. So e
stude ts is al ulated total
as
.
Reaso a l do e. So e
stude ts e p essed a s e as
e u i g de i al a d as
a ked fo a u a .
Badl do e. A fe stude ts i
the hole oho t got full
edit.
as a a ded fo
e tio i g that the g aph
sta ted at ,
fo sho i g
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272
a
u e of stude ts ho p efe Va illa
fla ou he it is o l a diffe e e of .
1
u6u8
2
24cm 2
24 u 17
2
408cm
Vol (24 u 2) (17 u 10) (17 u 6) (17 u 8)
d
456cm
Volume of 10 prisms
408 u 10
4080
S (10) 2
13.0cm((3
3sf )
A
M
A
Reaso a l do e.
Reaso a l do e.
M
4080cm 3
or
M
A
S
m
ile
T
ut
Increase
A
.s
g
2
e ide e of ot ha i g t i e
the u e s.
Reaso a l do e.
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.s
g
or
ut
T
ile
m
S
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