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Team roundThis round will last for approximately 2 hours. There will be no break. If you wish to leave for a toilet break or to get some water then you may do so at any time, but the competition will be ongoing.

• There will be 15 questions.

• Each question has a time limit, given before the question is shown.

• Answer on white paper and hand in when the time is up.

• Hand in an answer on coloured paper for bonus marks. Raise your hand with the paper in your hand for collection.

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You have 8 minutes forthe next question.

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1.How many squares are in this picture?

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2. Complete the final row in the table below.

n    

10 10 + 5 + 1 = 16

20 20 + 10 + 2 = 32

30 30 + 15 + 3 = 48

  =1760

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3. The pentagon below is constructed by drawing an equilateral triangle on each side of a right angled triangle with an angle of 30 degrees and the length of the hypotenuse is 12cm. What is the area of the pentagon?

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A circle is drawn through A and D so that it is tangent to BC, as shown. What is the radius of the circle?

4. A square has sides of length 16 cm.

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5. Find the volume of a regular tetrahedron with an edge of 1 cm.

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6. A man is walking across a railroad bridge that goes from point A to point B. He starts at point A, and when he is of the way across the bridge, he hears a train approaching. The train's speed is 60 mph (miles per hour).The man can run fast enough so that if he turns and runs back toward point A, he will meet the train at A, and if he runs forward toward point B, the train will overtake him at B.How fast can the man run?

3

8

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7. ( 2) means the square root of 2 rounded to the nearest integer. 

Find,

(2) + (3) + (5) + (7) + ……… + (23) + (29)

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8. The numbers 1, 2, 3, 4, 5, and 6 are printed on cards and arranged to form a 6-digit number.

Find the probability that the number is divisible by 3 or 7.

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9. Which is the first term in the fibonacci series to be a multiple of 10?

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10. A new monument is to be made in the shape of a cuboid.Only three of the faces are to be decorated.To allow for this:one face has to have an area of 48 square metres;another to have an area of 72 square metres;and another of 96 square metres.

What will be the volume of the monument?

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11.If S A V E + M O R E = M O N E Y

give the value of SOME.

No letter has the same number.

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12. ABCD is a rectangle and point E lies on AB. The triangle DEC has angle DEC = 90 degrees, DE = 3 cm, EC = 4 cm.

Find the length of AD.

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13.Study the grid below.

9 7 5 3 1

19 17 15 13 11

29 27 25 23 21

39 37 35 33 31

49 47 45 43 41

Find the sum of the diagonal of a 10x10 grid.

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14. Lost Lake Road lies 300 yards north of Vanda's house and runs straight east and west. Art lives 600 yards south of Lost Lake Road and 1200 yards down the road from Vanda. Neither Art nor Vanda has a phone. Art's carrier pigeon just arrived at Vanda's screeching loudly with an emergency message from Art. He has fallen and broken his leg at home. Vanda decides to ride her dirt bike from her home to Lost Lake Road to try to flag down a passing motorist with a cell phone so that an ambulance can be sent to pick up Art. Vanda wants to ride in a straight line to Lost Lake Road, and then go straight from that point to Art's house.Where must Vanda hit Lost Lake Road (in the 1200 yard stretch) to make the distance she travels the

shortest?

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15. can be simplified to give by simply cancelling out the 6 in the numerator with the 6 in the denominator. Find one more example in the form where .

16

64

1

4

a

ba b