3. M C S E A

6. You have 5 minutes to answer each problem. Click when ready... Good Luck

7. You now have 1 minute left 10987654321STOP Trial Question 1 Find the area of the region formed by the solution of this system of inequalities. x + 3y > 2 x + y < 4 x - 3y > - 4

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9. You now have 1 minute left 10987654321STOP Trial Question 2 Given the following data: 16, 14, 30, 14, 18, 19, 24, 13, 14 Find

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11. You now have 1 minute left 10987654321STOP 1. What is the Highest Common Factor of: 215280, 290472 & 6683040 ?

12. You now have 1 minute left 10987654321STOP 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 ?

13. You now have 1 minute left 10987654321STOP 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).

14. You now have 1 minute left 10987654321STOP 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. 4 7 6

15. You now have 1 minute left 10987654321STOP 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?

16. You now have 1 minute left 10987654321STOP 6. The digits 1, 1, 2, 2, 3 and 3 can be arranged as a six digit number in which the 1’s are separated by one digit, the 2’s are separated by two digits, and the 3’s are separated by 3 digits. Find the sum of all such six-digit numbers.

17. You now have 1 minute left 10987654321STOP 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.

18. You now have 1 minute left 10987654321STOP 8. There are four pairs of positive integers (x,y), such that x 2 - y 2 = 105 Find them.

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21. You now have 1 minute left 10987654321STOP 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 A’B’C’ which is the image of ABC after rotating it about (0,0) through an angle of 90º anti-clockwise.

22. You now have 1 minute left 10987654321STOP 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. D EDC B

23. You now have 1 minute left 10987654321STOP 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.

24. You now have 1 minute left 10987654321STOP 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?

25. You now have 1 minute left 10987654321STOP 13. a  b = ab. a b = ab.. a+b a-b and a b = a+b. a-b Find the value of (a  b) (a b), if a = 10 and b = -2.

26. You now have 1 minute left 10987654321STOP 14. All the angles except one in a convex polygon add up to 3315º. How many sides does the polygon have?

27. You now have 1 minute left 10987654321STOP 15. How many triangles with vertices at the marked points A 1, A 2,….,A 10 can be drawn? Note that the order of the vertices does not change the triangle. A1A1 A2A2 A3A3 A4 A4 A 10 A6 A6 A5 A5 A9A9 A8A8 A7A7