Download Candidate Name Class Index Number

1
JUNYUAN SECONDARY SCHOOL
MID YEAR EXAMINATION 2014
SECONDARY ONE EXPRESS
CANDIDATE NAME
CLASS
1
E
INDEX NUMBER
MATHEMATICS
15 MAY 2014
2 hours
READ THESE INSTRUCTIONS FIRST
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 or graphs.
Do not use paper clips, highlighters, glue or correction fluid.
Answer all the questions in this paper.
Show all your working on the same page as the rest of 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 exact, give
the answer to three significant figures. Give answers in degrees to one decimal place.
For , use either your calculator value or 3.142, unless the question requires the answer in
terms of .
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.
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2
Answer all questions.
3
Represent the numbers  , 2.7, -3 and 0.5 on a number line.
2
1
Answer:
3.15,
Given the numbers -3.15,
2

22
, 3.2,
7
(a) .......as shown in answer space.................. [2]
 2 
2
,
 1
3
, 7,
(a) write down the irrational number(s),
(b) arrange them in descending order.
Answer:
(a).................................................................. [1]
(b).................................................................. [2]
3
(a) Take  to be
22
7
17 2 3
7
9
, evaluate
giving your answer in decimal
3 17.95  1.292
correct to 5 significant figures.
(b) A number is approximated to 3 significant figures and its value is given as 91400.
What is the largest integer it could have been?
Answer:
(a).................................................................. [2]
(b).................................................................. [1]
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3
4
On a certain morning, the temperature in London was – 12 OC, the temperature in Hong
Kong was 8 OC and the temperature in Singapore was 26 OC.
(a)
Find the difference in temperature between London and Singapore.
(b)
The temperature in Beijing was mid-way between the temperatures of London
and Hong Kong. What was the temperature of Beijing that morning?
Answer:
(a).................................................................. [1]
(b).................................................................. [2]
5
(a)
Compute 45  3871  3871 35 without using a calculator. Show your working
clearly.
(b)
Factorise the following completely,
(i)
2 x 2 y 3 z  8xy 2 z 3 ,
(ii)
3 x( y  2)  4(2  y ) .
Answer:
(a) .................................................................. [1]
(b)(i).................................................................. [1]
(ii).................................................................. [1]
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4
6
Showing your working clearly, evaluate
(a)
5  (4)2  (3)3  2  (9) ,
(b)
1
3
 1
1   5  1
2
4
 2
.
1

1 
4

2
Answer:
(a).................................................................. [2]
(b).................................................................. [3]
7
An advertisement signboard has 3 different coloured neon lights that flash at different
intervals. The blue neon light flashes every 20 seconds, the orange neon light flashes
every 36 seconds and the green neon light flashes every 55 seconds. If all 3 neon lights
flash together at 15 45, find the next time that they will flash together again.
Answer:
........................................................................ [3]
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5
8
Furby is 11 years older than her brother. If her brother is x years old, how old was
Furby 6 years ago?
Answer:
9
(a)
.................................................................. [2]
Using a calculator, evaluate
(i)
3
599   7.84   2.465 , correct to 4 significant figures.
3
3
(ii)
3
(b)
5
0.39   
 9  , correct to 3 decimal places.
 1
  5   0.591
 3
Elsa buys 3 files at 49 cents each and 5 pens at $1.99 each at the school
bookshop. The shopkeeper asks for $12.42. Show using estimation that the
shopkeeper has made a mistake.
Answer:
(a)(i)............................................................... [1]
(ii)................................................................ [2]
(b)................................................................ [2]
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6
10
Express
2( x  1) 1  2 x

as a single fraction in its simplest form.
3
6
….................................................................. [3]
Answer:
11
In the diagram below, AB is parallel to CD. PAC and PBD are straight lines. Calculate
the values of
(a)
x,
(b)
y.
P
y
A
B
x
46o
24o
52
C
Answer:
D
(a) x = ........................................................ [2]
(b) y = ......................................................... [3]
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12
(a)
(b)
Given that a  3 , b  2 , and c  1 , find the value of a  b 2  c 3 .
Given that x  2 , y  8 and z  4 , find the value of
Answer:
6 x  3z
.
y
(a).................................................................. [2]
(b).................................................................. [2]
13
(a)
Express 126 as the product of its prime factors, giving your answer in index
form.
(b)
Find the smallest positive integer value of n for which 126n is a multiple of 35.
(c)
The lowest common multiple of 6, 14 and x is 126. Find the 2 possible values of
x which are odd numbers.
Answer:
(a) ................................................................. [2]
(b) ................................................................. [2]
(c) ................................................................. [2]
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8
14
Solve the following equations.
(a)
3(5m  2)  6  2(4  5m) ,
(b)
3
4

k  2 3k
Answer:
(a).................................................................. [2]
(b).................................................................. [2]
15
(a)
Subtract the sum of (2 x 2  7 x  4) and (5 x  7) from the product of 4 and
( x 2  3 x) .
(b)
Solve the equation
x 1 x  2 x

 .
3
4
2
Answer:
(a).................................................................. [4]
(b).................................................................. [3]
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16
The lines AB and CDE are parallel. CDB = 125 and DBE = 102. Giving your
reasons, find the values of
x
A
B
y
125
C
(a)
x,
(b)
y,
(c)
z.
D
Answer:
102
z
E
(a) x =............................................................... [1]
(b) y = .............................................................. [1]
(c) z = .............................................................. [2]
17
Simplify
(a)
2a  3b  a  8a  2b ,
(b)
(3 p  2q)  (q  3 p) .
Answer:
(a)................................................................... [1]
(b)................................................................... [2]
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18
(a)
The sum of three consecutive odd numbers is 237. By forming an algebraic
equation, find the largest odd number.
(b)
Given that 343000  2 x  5 y 7 z ,
(i)
find the values of x, y and z.
(ii)
Hence, determine the cube root of 343 000.
Answer:
(a) .................................................................... [3]
(b)(i) ................................................................... [2]
(ii) ...................................................................[1]
19
3 ropes of different lengths, 240 cm, 318 cm and 426 cm are to be cut into equal lengths
with no remainder.
(a)
What is the greatest possible length of each piece of rope?
(b)
Hence, find the total number of pieces of ropes that can be obtained.
Answer:
(a).................................................................... [2]
(b).................................................................... [1]
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20
The figure shows a rectangle ABCD where AB is 2 y  8 cm. X is a point on the length
DC such that DX is  y  7 cm and the perimeter of rectangle is 60 cm.
(a)
(b)
Expressing in term of y, find the length of
(i)
AD,
(ii)
XC.
Hence, find the area of ABCD if y  3.8 cm.
2 y  8 cm
A
D
 y  7cm
Answer:
B
C
X
(a)(i) AD = ....................................................cm [2]
(ii) XC = ....................................................cm [2]
(b)
....................................................cm [2]
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