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Mathematics Competitions South East Asia Mathematics Competitions Plus...

Individual Competition Part 1

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Trial Question I have a cube and a square-based pyramid. What is the total number of faces, edges and vertices? A) 40 B) 42 C) 44 D) 46 E) 48 You now have 30 seconds left STOP 1 3 2 4 9 10 8 7 6 5

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1. Simplify (22)7 A) 10242 B) 163842 C) 128 D) 1024 E) 16384 STOP 1 You now have 30 seconds left STOP 1 4 3 2 5 10 9 8 7 6

3. Reflection in the line x = -1 2. The line y = x + 1 undergoes the following transformations: 1. Reflection in the x-axis, then… 2. Rotation of +90º about (0,0), then... 3. Reflection in the line x = -1 The final image line is: A) y = x - 1 B) y = x + 3 C) y = -x + 1 D) y = -x - 1 E) y = -x - 3 You now have 30 seconds left STOP 1 4 3 2 5 10 9 8 7 6

3. Solution A contains 45% salt. Solution B contains 54% salt. A and B are mixed in the ratio 2:1. What is the percentage of salt in the mixture? A) 99% B) 48% C) 33% D) 49.5% E) 72% You now have 30 seconds left STOP 1 4 3 2 5 10 9 8 7 6

4. If a T-shirt is sold for $40, 20% is lost 4. If a T-shirt is sold for $40, 20% is lost. What is the percentage gain or loss if it is sold for $45? A) loss of 5% B) gain of 5% C) gain of 10% D) loss of 10% E) no gain or loss You now have 30 seconds left STOP 1 4 3 2 5 10 9 8 7 6

What is the largest of the three numbers? 5. Three whole numbers, when added two at a time, give sums of 39, 48 and 51. What is the largest of the three numbers? A) 21 B) 30 C) 18 D) 28 E) 14 You now have 30 seconds left STOP 1 4 3 2 5 10 9 8 7 6

The area of triangle DOC is 4 square units. 6. ABCD is a square. The area of triangle DOC is 4 square units. The perimeter of triangle DOC is: A B C D O A) 8 B) 82 C) 42 D) 8 + 22 E) 4 + 42 You now have 30 seconds left STOP 1 3 2 4 9 10 8 7 6 5

7. Calculate 2001 - 2000 + 1999 - … + 3 - 2 + 1 A) 999 B) 1000 C) 1001 D) 2001 E) none of these You now have 30 seconds left STOP 1 4 3 2 5 10 9 8 7 6

8. How many different triangles have sides 6, 7 and N, where N is a whole number? A) 9 B) 13 C) 10 D) 11 E) 12 You now have 30 seconds left STOP 1 4 3 2 5 10 9 8 7 6

9. Given that y is 3 times the sum of twice x plus the square of x, what values of x will make y = 9? A) x = 3, x = -3 B) x = 3, x = -1 C) x = 1, x = 0 D) x = 3, x = 0 E) x = 1, x = -3 You now have 30 seconds left STOP 1 4 3 2 5 10 9 8 7 6

10. Simplify A) 10 B) 15 C) 9 D) 5 E) 2 STOP 1 3 2 5 9 10 8 7 6 4 You now have 30 seconds left STOP 1 3 2 5 9 10 8 7 6 4

What is the probability that the ball is not white? 11. I pick a ball at random from a bag containing 5 white, 2 blue, 1 red and 3 green balls. What is the probability that the ball is not white? A) 5/11 B) 2/11 C) 4/11 D) 8/121 E) 6/11 You now have 30 seconds left STOP 1 4 3 2 5 10 9 8 7 6

12. The mean height of the boys in class T1 was 162cm. When Tom, who is 165cm tall, joined the class, the new mean became 162.2cm. How many boys are now in T1? A) 11 B) 12 C) 13 D) 14 E) 15 You now have 30 seconds left STOP 1 4 3 2 5 10 9 8 7 6

At what time will the water be 144cm high? h (cm) 13. The graph shows the change in height, h, of the water level in a pool against time. At what time will the water be 144cm high? 200 179 0 3 time (min) A) 4 min B) 5 min C) 8 min D) 10 min E) 12 min You now have 30 seconds left STOP 1 3 8 9 10 7 6 4 5 2

14. How many whole numbers are perfect squares with four digits? A) 32 B) 99 C) 67 D) 68 E) 9801 You now have 30 seconds left STOP 1 4 3 2 5 10 9 8 7 6

15. If A) 7/2 B) 5/2 C)3/2 D) 1/2 E) -1/2 STOP 1 3 2 5 9 10 8 7 6 4 You now have 30 seconds left STOP 1 3 2 5 9 10 8 7 6 4

find the value of x + y, where x and y are positive integers. 16. If 2x.3y = 432, find the value of x + y, where x and y are positive integers. A) 3 B) 7 C) 12 D) 72 E) none of these You now have 30 seconds left STOP 1 4 3 2 5 10 9 8 7 6

Find 52 17. ab = a2 - (a - b)2 A) 4 B) 1 C) 74 D) 34 E) 16 STOP 1 4 You now have 30 seconds left STOP 1 4 3 2 5 10 9 8 7 6

what is the average of x, y and z? A) (p + q + r)/3 B) (p + q + r)/2 18. If p is the average of x and y, q is the average of y and z, and r is the average of x and z, then what is the average of x, y and z? A) (p + q + r)/3 B) (p + q + r)/2 C) 2(p + q + r)/3 D) p + q + r E) 3(p + q + r)/2 You now have 30 seconds left STOP 1 4 3 2 5 10 9 8 7 6

19. If f(x) = 5x + 6, then f(x) < 16 if and only if A) x = 2 B) x < 2 C) x > 2 D) -2 < x < 2 E) 0 < x < 2 You now have 30 seconds left STOP 1 4 3 2 5 10 9 8 7 6

Each letter in the subtraction above represents a single digit. 20. 7 a b c . - d 1 2 8 . c d 6 5 Each letter in the subtraction above represents a single digit. The letters in order a, b, c, d are A) 4,9,3,6 B) 3,4,9,5 C) 4,3,9,5 D) 4,9,3,5 E) 5,9,3,4 You now have 30 seconds left STOP 1 4 3 2 5 10 9 8 7 6

21. Simplify A) x + 1 B) 3x + 2 C) 2x + 1 . 2x + 1 2x + 1 3x + 2 D) x + 2 E) none of these You now have 30 seconds left STOP 1 4 3 2 5 10 9 8 7 6

22. When two distinct circles and three distinct lines intersect each other, the maximum number of points of intersection is: A) 14 B) 15 C) 21 D) 19 E) 17 You now have 30 seconds left STOP 1 4 3 2 5 10 9 8 7 6

and xy = 7 23. If x2 + y2 = 8 then (x + y)2 = A) 14 B) 16 C) 22 D) 30 E) 49 You now have 30 seconds left STOP 1 4 3 2 5 10 9 8 7 6

24. If a watch is set at 2pm and loses minutes every two hours, what will it read, on the following day, when it is actually 2pm? A) 1.30 B) 1.36 C) 1.40 D) 1.42 E) 1.51 You now have 30 seconds left STOP 1 4 3 2 5 10 9 8 7 6

25. A square ABCD contains an equilateral triangle ABF. The size of the angle CFD , in degrees, is A) 120 B) 150 C) 75 D) 90 E) 180 You now have 30 seconds left STOP 1 4 3 2 5 10 9 8 7 6

OK! Time for a BREAK...