The Chinese High School
Mathematics Learning And Research Centre
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Singapore Mathematical Olympiad
for Primary Schools 2001
First Round
2 hours
(150 marks )
Instructions to Participants
Attempt as many questions as you can.
Neither mathematical tables nor calculators may be used.
Write your answers in the answer boxes on the separate answer sheet provided.
Working may be shown in the space below each question.
Marks are awarded for correct answers only.
This question paper consists of 16 printed pages ( including this page )
Number of correct answers for Q1 to Q10 :
Number of correct answers for Q11 to Q20 :
Number of correct answers for Q20 to Q30 :
Marks ( 4 ) :
Marks ( 5 ) :
Marks ( 6 ) :
Total Marks for First Round :
1.
Find the value of
0.1 + 0.11 + 0.111 + . . . . + 0.1111111111 .
2.
Find the missing number in the box.
3.
Find the missing number in the following number sequence.
1, 4, 10, 22, 46, _____, 190 , . . .
4.
If numbers are arranged in 3 rows A, B and C according to the following
table, which row will contain the number 1000 ?
A
1,
6,
7,
12,
13,
18,
19,
. . . .
2,
5,
8,
11,
14,
17,
20,
. . . .
3,
4,
9,
10,
15,
16,
21,
. . . .
5.
How many 5-digit numbers are multiples of 5 and 8 ?
6.
John started from a point A, walked 10 m forwards and then turned
right. Again he walked 10 m forwards and then turned
right. He
continued walking in this manner and finally returned to the starting point A.
How many metres did he walk altogether ?
7.
What fraction of the figure is shaded ?
8.
How many triangles are there in the figure ?
9.
Between 12 oclock and 1 oclock, at what time will the hour hand and
minute hand make an angle of
?
10.
The rectangle ABCD of perimeter 68 cm can be divided into 7 identical
rectangles as shown in the diagram. Find the area of the rectangle ABCD.
11.
Find the smallest number such that
(i)
(ii)
(iii)
12.
it leaves a remainder 2 when divided by 3 ;
it leaves a remainder 3 when divided by 5 ;
it leaves a remainder 5 when divided by 7 .
The sum of two numbers is 168. The sum of
of the smaller number
and
of the greater number is 76. Find the difference between the two
numbers.
13.
There are 325 pupils in a school choir at first. If the number of boys
increases by 25 and the number of girls decreases by 5%, the number of
pupils in the choir will become 341. How many boys are there in the choir at
first ?
14.
Mr Tan drove from Town A to Town B at a constant speed of
. He
then drove back from Town B to Town A at a constant speed of
.
The total time taken for the whole journey was 5.5 h. Find the distance
between the two towns.
=, E =5
15.
Which one of the following is the missing figure ?
(A)
(B)
(C)
(D)
16.
Which two of the following solid figures can be fitted together to form a
cuboid ?
17.
In how many different ways can you walk from A to B in the direction
or
, without passing through P and Q ?
18.
In the figure, ABCD is a square and EFGC is a rectangle. The area of the
rectangle is
the square.
. Given that
, find the length of one side of
19.
The diagram shows a circle and 2 quarter circles in a square. Find the area
of the shaded region. ( Take
.)
20.
The area of rectangle ABCD is
ADF are
AEF.
21.
and
. The areas of triangles ABE and
respectively. Find the area of the triangle
A rectangular paper has a circular hole on it as shown. Draw a straight line
to divide the paper into two parts of equal area..
22. What is the 2001th number in the following number sequence ?
23.
There are 25 rows of seats in a hall, each row having 30 seats. If there are
680 people seated in the hall, at least how many rows have an equal number
of people each ?
24. In the following columns, A, B, C and X are whole numbers. Find the value
of X.
A
B
B
B
C
38
25.
A
A
B
B
C
36
A
A
A
B
C
34
A
B
C
C
C
28
A
B
C
X
There were 9 cards numbered 1 to 9. Four people A, B, C and D each
collected two of them.
A said :
B said :
C said :
D said :
The sum of my numbers is 6.
The difference between my numbers is 5.
The product of my numbers is 18.
One of my numbers is twice the other.
What is the number on the remaining card ?
26. Minghua poured out
of the water in a container.
In the second pouring, he poured out
of the remaining water ;
In the third pouring, he poured out
of the remaining water ;
In the forth pouring, he poured out
and so on.
of the remaining water ;
After how many times of pouring will the remaining water be exactly
the original amount of water ?
27.
of
A bus was scheduled to travel from Town X to Town Y at constant
speed
. If the speed of the bus was increased by 20%, it could
arrive at Town Y 1 hour ahead of schedule.
Instead, if the bus travelled the first 120 km at
was increased by 25%, it could arrive at Town Y
schedule. Find the distance between the two towns.
and then the speed
hours ahead of
28. The diagram shows three circles A, B and C.
of the circle A is shaded,
of the circle B is shaded,
of the circle C is shaded.
If the total area of A and B is equal to
the area of A to the area of B.
of the area of C, find the ratio of
29. Given that m =
find the sum of the digits in the value of
30.
,
.
Each side of a pentagon ABCDE is coloured by one of the three colours :
red, yellow or blue. In how many different ways can we colour the 5 sides
of the pentagon such that any two adjacent sides have different colours ?
Singapore Mathematical Olympiad for Primary Schools 2001
First Round Answers Sheet
Answers
Answers
For markers use only
1.0987654321
17
48
345
18
8 cm
94
19
129 cm2
Row C
20
9 cm2
2250
100 m
Questions 11 to 20
each carries 5 marks
21
The line drawn must pass through the centre of the circle and of the rectangle.
15
22
12.20
23
10
280 cm2
24
20
25
Questions 1 to 10
each carries 4 marks
For markers use only
11
68
26
12
27
360 km
13
145
28
3:1
14
140 km
29
18009
15
16
B and C
30
30
Questions 21 to 30
each carries 6 marks
