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 have…it 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 STOP 1 10 9 8 7 6 5 4 3 2

8. START

9. 1. What is the last digit of 91997? You now have 30 seconds left STOP 1 10 9 8 7 6 5 4 3 2

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. “That’s not enough information”, responds the census-taker. “I’d tell you the sum of their ages, but you’d still be stumped.” “I wish you’d 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 STOP 1 10 9 8 7 6 5 4 3 2

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 STOP 1 10 9 8 7 6 5 4 3 2

12. 4. Write as a fraction in lowest terms. You now have 30 seconds left STOP 1 10 9 8 7 6 5 4 3 2

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 STOP 1 10 9 8 7 6 5 4 3 2

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 STOP 1 10 9 8 7 6 5 4 3 2

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 STOP 1 10 9 8 7 6 5 4 3 2

16. f ( 2002 ) 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 STOP 1 10 9 8 5 7 4 6 2 3

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 summer’s 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 3:4. What is the value of n ? You now have 30 seconds left STOP 1 10 9 8 7 6 5 4 3 2

18. 10. Adding 1 to which variable would increase T by the most? where You now have 30 seconds left STOP 1 10 9 8 7 6 5 4 3 2

19. OK! Time for a BREAK...

20. Ready for Part 2 ? Click when ready...

21. Team Competition Part 2

22. A 74 cents B 80 cents C ? cents D 79 cents 11. You now have 30 seconds left STOP 1 3 4 5 6 7 8 9 10 2

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 STOP 1 10 9 8 7 6 5 4 3 2

24. D I E C F A H B G 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 STOP 1 3 4 5 6 7 8 9 10 2

25. 14. A circle of radius 6 has an isosceles triangle PQR inscribed in it, where PQ=PR. 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 4√5. The radius of the smaller circle is P R Q You now have 30 seconds left STOP 1 10 9 8 7 6 5 4 3 2

26. 15. What is the product of the real roots of the equation You now have 30 seconds left STOP 1 10 9 8 7 6 5 4 3 2

27. , , 16. Four different positive integers a,b,c,d satisfy the following relations : Find d. You now have 30 seconds left STOP 1 10 9 8 7 6 5 4 3 2

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 STOP 1 10 9 8 7 6 5 4 3 2

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 STOP 1 10 9 8 7 6 5 4 3 2

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 STOP 1 10 9 8 7 6 5 4 3 2

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 STOP 1 4 6 2 7 8 9 10 5 3

32. ALL OVER ! BYE BYE