South East Asia Mathematics Competition

1
South East Asia Mathematics Competition
GARDEN INTERNATIONAL SCHOOL MALAYSIA, ALICE
SMITH, ELC
2
M
S
E
A
C
3
South East Asia
Mathematics Competitions
Plus...
4
Team Competition Part 1
5
Rules for Team Competition

• Answer the question on the RED ANSWER SHEET THEN
• Hold up your TEAM NUMBER CARD so that order
  recorders can see your team number KEEP HELD UP
  until.
• Runners take your red sheet to markers
• With remaining time work on your 2nd attempt
  (Blue Sheet)
• Runners will collect these at the end of question
  time.
• Bonus marks 4 for 1st, 3 for 2nd, 2 for 3rd

6
Rules for Bonus Round

• Fill in the BONUS ROUND QUIZ in any spare time
  you haveit does not count towards the team
  competition
• Place upside down on your table during break
• Runners will collect in at the end
• 1 mark per correct answer
• Prize for 1st winning team

7
Trial Question There are 2 painters. David can
paint a wall in 6 minutes, and Joanne can paint a
wall in 3 minutes. How long would it take
to paint the wall if
they worked together ?
You now have 30 seconds left
10
9
8
7
6
5
4
3
2
1
STOP
8
START
9
1. What is the last digit of 91997?
You now have 30 seconds left
10
9
8
7
6
5
4
3
2
1
STOP
10
2. A census-taker knocks on a door and asks the
woman inside how many children she has and how
old they are. I have three daughters, their ages
are whole numbers, and the product of their ages
is 36, says the woman. Thats not enough
information, responds the census-taker. Id
tell you the sum of their ages, but youd still
be stumped. I wish youd tell me something
more. Okay my oldest daughter Jasmine likes
cats.   What are the ages of the three
daughters?
You now have 30 seconds left
10
9
8
7
6
5
4
3
2
1
STOP
11
3. A 4-digit number p is formed from the digits
5,6,7,8 and 9. Without repetition. If p is
divisible by 3,5 and 7, find the maximum value of
p.
You now have 30 seconds left
10
9
8
7
6
5
4
3
2
1
STOP
12
4. Write as a fraction in lowest terms.
You now have 30 seconds left
10
9
8
7
6
5
4
3
2
1
STOP
13
5. The radius of the two smallest circles is
one-sixth that of the largest circle. The
radius of the middle-sized circle is double that
of the small circles. What fraction of the
large circle is shaded?
You now have 30 seconds left
10
9
8
7
6
5
4
3
2
1
STOP
14
6. Given that x represents the sum of all the
even integers from 1 to 200 and y represents
the sum of all the odd integers from 1 to 200,
evaluate x - y.
You now have 30 seconds left
10
9
8
7
6
5
4
3
2
1
STOP
15

• As shown in the diagram, in a 5x4x4 cuboid, there
  are 3 holes of dimension 2x1x4, 2x1x5 and 3x1x4.
  What is the remaining volume?

You now have 30 seconds left
10
9
8
7
6
5
4
3
2
1
STOP
16
8. A function f has the property for
all positive integers n. Given that is
non- zero, what is the value of
?
You now have 30 seconds left
10
9
8
7
6
5
4
3
2
1
STOP
17
9. A tennis club has n left- handed players and
2n right-handed players, but in total ther are
fewer than 20 players. At last summers
tournament, in which every player in the club
played every other player exactly once, no
matches were drawn and the ratio of the number of
matches won by left-handed players to the number
of matches won by the right-handed players was
34. What is the value of n ?
You now have 30 seconds left
10
9
8
7
6
5
4
3
2
1
STOP
18
10. Adding 1 to which variable would
increase T by the most?
where
You now have 30 seconds left
10
9
8
7
6
5
4
3
2
1
STOP
19
OK! Time for a BREAK...
20
Ready for Part 2 ?
Click when ready...
21
Team Competition Part 2
22
11.
You now have 30 seconds left
10
9
8
7
6
5
4
3
2
1
STOP
23

• When the mean, median, and mode of the list
• 10,2,5,2,4,2,x
• are arranged in increasing order, they form a
  non-constant arithmetic progression. What is the
  sum of all possible real values of x?

You now have 30 seconds left
10
9
8
7
6
5
4
3
2
1
STOP
24
13. Nine squares are arranged as shown. If
square A has area 1cm2 and square B has area 81
cm2 then the area, in square centimetres, of
square I is
You now have 30 seconds left
10
9
8
7
6
5
4
3
2
1
STOP
25
14. A circle of radius 6 has an isosceles
triangle PQR inscribed in it, where PQPR. A
second circle touches the first circle and the
mid-point of the base QR of the triangle as
shown. The side PQ has length 4v5. The radius
of the smaller circle is
P
R
Q
You now have 30 seconds left
10
9
8
7
6
5
4
3
2
1
STOP
26
15. What is the product of the real roots of the
equation
You now have 30 seconds left
10
9
8
7
6
5
4
3
2
1
STOP
27
16. Four different positive integers a,b,c,d
satisfy the following relations
Find d.
You now have 30 seconds left
10
9
8
7
6
5
4
3
2
1
STOP
28
17. A square XABD of side length 1 is drawn
inside a circle with diameter XY of length 2. The
point A lies on the circumference of the circle.
Another square YCBE is drawn. What is the ratio
of the area of square XABD to area of square
YCBE? In the form 1 n
You now have 30 seconds left
10
9
8
7
6
5
4
3
2
1
STOP
29
18. A square with sides of length 1 is divided
into two congruent trapezia and a pentagon, which
have equal areas, by joining the centre of the
square with points on three of the sides, as
shown. Find x, the length of the longer parallel
side of each trapezium.
x
You now have 30 seconds left
10
9
8
7
6
5
4
3
2
1
STOP
30
19. In the xy-plane, what is the length of the
shortest path from (0,0) to (12,16) that does not
go inside the circle (x 6)2 (y 8)2
25?
You now have 30 seconds left
10
9
8
7
6
5
4
3
2
1
STOP
31

• The figure on the right shows two parallel lines
  L1 and L2. Line L1 is a tangent to circles C1
  and C3, line L2 is a tangent to the circles C2
  and C3 and the three circles
  touch as shown.
  Circles C1 and C2 have
  radius s and t respectively.
  What is the radius of
  circle C3 ?

L1
L2
C2
C1
C3
You now have 30 seconds left
10
9
8
7
6
5
4
3
2
1
STOP
32
ALL OVER !
BYE BYE