Welcome to

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Welcome to
The Alice Smith School
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M
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South East Asia
Mathematics Competitions
Plus...
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Team Competition Part 1
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You have 5 minutes to answer each problem.
Good Luck
Click when ready...
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Trial Question 1 Find the area of the region
formed by the solution of this system of
inequalities. x 3y gt 2 x y lt 4 x - 3y gt - 4
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Everything OK?
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Trial Question 2 Given the following data 16,
14, 30, 14, 18, 19, 24, 13, 14 Find
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Everything OK?
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1. What is the Highest Common Factor of 215280,
290472 6683040 ?
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2. The two circles are identical, and have
radius x. The quadrilaterals are squares. What is
the sum of the purple shaded areas in terms of x
?
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3. A thick cylindrical pipe fits exactly in a
box. The radius of the hole in the pipe is 2cm.
The width and height of the box are both 8cm.The
box is 5 times as long as it is wide. Find in
terms of ? the volume of water that could be
contained in the box (inside and outside the
pipe).
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4. Three rollers, each of radius 1, are mounted
from their centres to the vertices of a
triangular frame with sides 4, 6 7.
A belt fits tightly around the rollers. Find the
length of the belt.
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5. A box 9cm by 5cm by 4cm is covered by 6
plastic sheets, each covering completely one
face. What are the dimensions of the smallest
rectangle from which all 6 sheets can be cut?
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6. The digits 1, 1, 2, 2, 3 and 3 can be
arranged as a six digit number in which the 1s
are separated by one digit, the 2s are separated
by two digits, and the 3s are separated by 3
digits. Find the sum of all such six-digit
numbers.
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7. Consider the graphs of the two equations a)
xy 12 b) y 2x - 10 Which graph
comes closer to the origin, and what is its
distance from the origin? Give the distance in
the form p?q, where p and q are integers.
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8. There are four pairs of positive integers
(x,y), such that x2 - y2 105 Find them.
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OK! Time for a BREAK...
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Team Competition Part 2
Click when ready...
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9. Given that the coordinates of the triangle
ABC are A(3,1) B(1,1)
C(-2,3), find the coordinates of the triangle
ABC which is the image of ABC after
rotating it about (0,0) through an angle of 90º
anti-clockwise.
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10. The grid can be filled up using only the
letters A, B, C, D and E, so that each letter
appears just once in each row, column and
diagonal. Fill up the empty squares.
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11. Three fair six-sided dice A, B and C are
numbered A 1,1,2,2,3,3 B
4,4,5,5,6,6 C 7,7,8,8,9,9 The
three dice are rolled once. Find the probability
of obtaining a total which is an odd number.
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12. In a circle of radius 1 unit, two congruent
circles are drawn tangent to the large circle and
passing through its centre.
Then each smaller circle is sub-divided
similarly. The process goes on indefinitely.
What is the sum of the areas of all the circles?
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13. a?b ab . a?b ab . .
ab a-b and
a?b ab .
a-b Find the value of
(a?b) ? (a?b), if a 10 and b -2.
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14. All the angles except one in a convex
polygon add up to 3315º. How many sides does the
polygon have?
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A2
A3
15. How many triangles with vertices at the
marked points A1, A2,.,A10 can be drawn?
A4
A5
A1
A6
A10
A9
A8
A7
Note that the order of the vertices does not
change the triangle.
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That's all folks!