South East Asia Mathematics Competition

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South East Asia Mathematics Competition
SHA TIN COLLEGE
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M
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A
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South East Asia
Mathematics Competitions
Plus...
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The English Schools Foundation Hong Kong
Click when ready...
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Individual Competition Part 1
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Trial Question How many prime numbers are there
between 90 and 110?
A) 4 B) 5 C) 7 D) 23 E) 61
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Everything OK?
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START
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1. A bag contains 20 red sweets, 20 blue
sweets, 20 yellow sweets and 20 green sweets.
How many sweets would a blindfolded person
have to eat to be certain of eating at least one
sweet of each colour ?
A) 4 B) 5 C) 7 D) 23 E) 61
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2. A person walks from A to B along the lines
shown. How many different paths are there that
are exactly 6 units long ?
A) 23 B) 39 C) 42 D) 45 E) 46
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3. If the distance between consecutive fence
posts is 5 metres, how many posts would be
needed to build a fence around a triangular
region with sides 20m, 20m and 30m ? A) 11
B) 13 C) 14 D) 15 E) 17
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4. Thirty two teams enter a competition, the
teams are paired randomly with each other in
each round, the winning team goes forward to the
next round. How many matches must be played
before we get a winner ? A 16 B 31 C
32 D 64 E 496
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5. A triangle has sides of length 5cm, 5cm, and
6cm. What is its area, in cm2 ?   A 12 B
15 C 18 D 20 E 30
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6. If and , then
equals A ?1 B ?5 C D
1 E 2



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7. The number 56665 is a palindrome, it reads the
same forwards and backwards. The next palindrome
will be 56765. What will the 8th palindrome be
after 56765 ? A 56865 B 57065 C 57475 D
57575 E 58085
123454321
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8. In the diagram you see a quarter-circle. A
semi-circle is drawn with XY as the
diameter. What is the ratio ? A
B 1 C D E
X
Y
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9. How many blocks are missing in this
cube? (Assume that all unseen blocks are
present) A 64 B 27 C 25 D 24 E 23
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10. The area of the triangle that is bounded
by y 2x, y 6 and y 6 ? x is A 1 B
1½ C 2 D 2½ E 3
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11. It is actually impossible, but assuming that
you could tear a playing card in half, put the
two pieces together and tear again (getting
four), put them together and tear again and so on
52 times and then piled up the pieces,
approximately how high would the stack be ? A
5cm B 50cm C 1m D 100m E From
the Earth to the Sun
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12. How many squares are there in this
diagram ?   A) 23 B) 39 C) 42 D)
45 E) 46
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13. Rearranging the digits of the number 579
produces different numbers. The sum of all
such numbers, including 579, is A) 4662 B)
4065 C) 3705 D) 3687 E) 3303
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14. The area of a circle is 36?cm2. The
circumference, in cm is A 6? B 18? C
12?? D 12? E 18??
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15. 5 boys and 5 girls sit around a circular
table so that boys and girls alternate. How
many different seating arrangements are there?
A) 1440 B) 2880 C) 7200 D) 14400 E)
28800
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16. A square floor is tiled with square tiles
and there are 125 tiles on the diagonals. How
many tiles are in the room? A) 125 B)
961 C) 2566 D) 3844 E) 15625
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17. How many terms of this series are needed
to make a sum greater than 2½ ? A)
24 B) 22 C) 20 D) 18
E) 16
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18. Tom eats twice as many caterpillars as
Jennifer, but Jennifer eats three times as many
caterpillars as David. Tom eats 40 caterpillars
more than David, how many caterpillars does
Jennifer eat? A) 8 B) 24 C) 36 D) 48
E) 60
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19. Give the next number in the sequence
2 17 82 257 626 A) 1027 B) 1297 C)
1513 D) 2027 E) 2107
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20. Three vertices of a triangle are A (?5 ,
6) , B (1 , 10) and C (3 , 20). M is the
midpoint of AB. What is t he length of MC ? A
21 B 19 C 16 D 13 E 10
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21. What is the maximum number of 70? angles in
a heptagon? A) 2 B) 3 C) 4 D) 5
E) 6
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22. In a game of NIM two people take it in
turns to take 1,2,3,4 or 5 matches from the
centre pile. The person to take the last match
is the winner. In order to win, how many matches
should you need to take on your first go ?
A 1 B 2 C 3 D 4 E 5
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23. In the diagram, if AD CD CB, and ?A is
40?, then find ?DCB.   A) 40? B) 35?
C) 25 ? D) 20 ? E) 10 ?
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24. Steve has a set of 100 cards numbered
consecutively from 1 to 100. He forms pairs of
cards which have a sum of 50, such as 12 and 38.
How many such pairs can he form ? A)
20 B) 24 C) 25 D) 49 E) 50
38
12
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25. In an art class students are taught to
shape a 1 ounce bag of clay into a small
statue. During this process some clay is
unused. For every five statues made there is
enough clay to make one extra statue. If a
student is presented with 25 ounces of clay,
what is the maximum number of statues that they
can sculpt ? A 25 B 30 C 31 D
50 E 51
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OK! Time for a BREAK...
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Ready for Part 2 ?
Click when ready...
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Individual Competition Part 2
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26. Which of the following is midway between
and ? A) B) C)
D) E)
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27. An unusual die has its six faces labelled
1, 2, 3, 5, 7, 9. If two such dice are
rolled, and the numbers rolled added
together, then how many different sums are
possible ? A) 36 B) 16 C) 15 D)
14 E) 13
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28. The sum of the acute angles at A, B, C, D
and E is A) 150 B) 200 C) 240
D) 180 E) 360
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29. 4 boys take a French test and get an
average of 4 marks. 6 girls take the same test
and get an average of 6. What is the average for
all 10 children? A) 4.8 B) 5.0 C)
5.2 D) 5.4 E) 5.6
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30. A large box measures 1.7 m by 1.2 m by 1.5
m. It is to be packed with smaller boxes each
measuring 15 cm by 20 cm by 20 cm. What is the
greatest number of small boxes that can be
fitted into the larger box? A) 510 B)
480 C) 462 D) 448 E) 424
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31. In the diagram, the value of y is
A) 85 B) 40 C) 36 D) 30
E) 20
3y?
20?
y?
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32. If x is an integer, how many integer values
of y will there be for A) 0 B) 1 C)
2 D) 3 E) More than 3
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33. A medium size jet has a wingspan of about
40 metres. An albatross is a bird with a
wingspan of about 4 metres. If the jet is flying
at 100m on a sunny day, at what height would the
albatross have to fly to cast a shadow of about
equal size ? A 10m B 100m C
400m D 1000m E None of the these.
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34. A five digit number 1 uses the digits
1, 2, 3, 4, 5 once only and is divisible by 4.
How many such numbers are there?   A)
0 B) 3 C) 6 D) 12 E) 24
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35. Mr Tung owns a piece of land. The exact
shape of this land is shown here. The perimeter
of the land in kilometres is exactly equal to
the area of the land in square kilometres.
What is the perimeter of his land in km ? A
25.2 B 28 C 31.36 D 33.6 E 42
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36. In a chess league, each of the
competitors plays each of the others once.
If there are 300 games altogether, how many
competitors are there ? A) 24 B) 25 C)
30 D) 32 E) 40
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37. is equal to   A) B)
C) D) 1 E)
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38. Thirty equally spaced points on the
circumference of a circle are labelled in order
with the integers 1 to 30. What number is
diametrically opposite 7 ?   A) 7 B)
21 C) 22 D) 23 E) 24
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39. What is the total number of digits needed
to number the pages of a book from 1 to 250
inclusive ? A) 637 B) 639 C) 640 D)
642 E) 643
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40. Which of these four dice is different from
the other three ?   A First B Second C
Third D Fourth E All dice the same
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41. When 324 is divided by 5 the
remainder is A 0 B 1 C 2 D 3 E 4
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42. What is the difference between one hundred
millionths and one hundred millionth ?   A)
0 B) C) D) 1000 E) 100 000 000
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43. The greatest value of is
A 5 B 3 C 1 D 0 E ?1
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44. A whole number is called an ascending
number if each digit in the number is greater
than the digit on its left. 1679 is an example
of an ascending number. How many ascending
numbers are there between 4000 and 5000 ? A)
7 B) 8 C) 9 D) 10 E) 11  
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45. The largest divisor of 723 , other than
itself, is A 29.35 B 28.36 C
28.35 D 25.35 E 26.36
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46. If then equals
  A) B) C) D) E)
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47. What is the next term in this sequence of
numbers? 1, 1, 2, 5, 29, .. A) 866 B)
145 C) 107 D) 73 E) 53
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50. If x and y are integers and x gt y, the
number of integers between (but not including)
x and y is A x ? y B x y C x ? y
? 1 D x y ? 1 E x ? y 1
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ALL OVER !
Bye Bye