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ISMTF Junior Mathematics Competition 2006 Team Event British School of Paris Team Number score Trial Round 1. 2006 has 3 prime factors: p1 , p2 , p3 Calculate p1 + p2 + p3 2. Find the perimeter of this quarter circle. Write your answer in the form a + b 4 cm 3. How many terms are there in the simplified expansion of : (a + b + c) (b + c + d) Write one answer only in each of the boxes below. Ring the question number that your answer refers to. Ring the question number Write your answer here 1 2 3 1 2 3 1 2 3 ISMTF Junior Mathematics Competition 2006 Team Event British School of Paris Team Number score Round 1 1. The sum of three consecutive prime numbers is 121. Calculate the product of these three primes. 2. Find the sum of: 1602 - 1502 + 1402 - 1302 + ……………………….. + 202 - 102 3. A regular octagon of sides 2 cm is made by cutting the corners of a square. area of square area of octagon Calculate the ratio: a b c Express the answer in the form Write one answer only in each of the boxes below. Ring the question number that your answer refers to. Ring the question number Write your answer here 1 2 3 1 2 3 1 2 3 ISMTF Junior Mathematics Competition 2006 Team Event British School of Paris Team Number score Round 2 1. The task is to reduce a given integer to the smallest integer possible using simple calculations. As an example, to reduce 71: 71 - 1 = 70 Each of the single digits can be used only once. 70 7 = 10 Each simple calculation involves one operation ( + - x ) with one single digit number. 10 5 = 2 2 - 2 = 0 Using this strategy (method), reduce 106 down to an integer less than 20 Show your steps in the table (the solution starts with…. 8 ) operation result 2. 8 125 000 What is the largest integer that may be reduced to 1 for the task described above ? 3. A square based pyramid with all its edges of length 4 cm is cut parallel to its base to give two parts of equal volume. How far down, measured vertically from the top towards the horizontal base, is the cut made ? Write your answer as a power of 2. Write one answer only in each of the boxes below. Ring the question number that your answer refers to. Ring the question number Write your answer here 1 2 3 1 2 3 1 2 3 ISMTF Junior Mathematics Competition 2006 Team Event British School of Paris Team Number score Round 3 1. 5 x - 5 x 2 = 120 5 . Solve for x. 1 2. If the pattern of 90o triangles is continued, how many triangles are needed for the hypotenuse to be greater than 10 ? 1 2 3 3. Calculate the area of the largest equilateral triangle that fits inside a square of area 1 m2. Write your answer in the form of a b c , where a, b and c are integers. Write one answer only in each of the boxes below. Ring the question number that your answer refers to. Ring the question number Write your answer here 1 2 3 1 2 3 1 2 3 ISMTF Junior Mathematics Competition 2006 Team Event British School of Paris Team Number score Round 4 1. A cube of volume 3 cm3 is placed on top of a cube of volume 15 cm3. Finally, a cube of volume cm3 is placed on top of the 3 cm3 cube. What is the height of the stack of three cubes ? 4 2. 3 A rectangular card measuring 4 by 3 can be folded lengthways to form an open cylinder and widthways to form a different open cylinder. Find the difference in volume of the two cylinders. 3. Find the sum of two numbers whose difference, sum and product are in the ratio 1 : 5 : 24 Write one answer only in each of the boxes below. Ring the question number that your answer refers to. Ring the question number Write your answer here 1 2 3 1 2 3 1 2 3 ISMTF Junior Mathematics Competition 2006 Team Event British School of Paris Team Number score Round 5 1. A cube of volume 1 m3 sits tightly inside a sphere. Calculate the volume of the sphere. Give your answer as a multiple of . 2. If n is the 2nd of 3 consecutive perfect squares, find in terms of n the difference between the 1st and 3rd perfect squares. 3. A STOP sign 0.5 metres high is fixed to a lamp post such that the bottom of the sign is 2 metres up from the ground as shown. lamp lamp post STOP sign 0.5m high The lamp casts a shadow of the sign on the ground that is 0.3 metres wide and 0.5 metres from the bottom of the lamp post. 2.0m How high is the lamp post ? ground 0.3m 0.5m Write one answer only in each of the boxes below. Ring the question number that your answer refers to. Ring the question number Write your answer here 1 2 3 1 2 3 1 2 3 ISMTF Junior Mathematics Competition 2006 Team Event British School of Paris Team Number score Round 6 1. Find the 4th root of the 3rd root of the square root of 4 to the power of factorial 3. 4 3 4 3! 2. D C A B 10m H G 15m E F 20m A spider is in the top corner A of a rectangular room 20m long, 15m wide and 10m high. It spots a tasty meal in the furthest corner of the room at G. What is the shortest distance the spider could travel along the surface of the room to claim its prize ? 3. By completing the magic square, find the product of the two numbers found in the shaded cells. 3 20 14 1 9 21 13 16 8 25 24 11 18 10 17 12 Write one answer only in each of the boxes below. Ring the question number that your answer refers to. Ring the question number Write your answer here 1 2 3 1 2 3 1 2 3 ISMTF Junior Mathematics Competition 2006 Team Event British School of Paris Answers Trial Round 1. 78 2. 2 + 8 3. 8 Round 1 1. 65231 2. 13600 3. 1 2 2 Round 2 1. 17 2. 725 760 3. 2 3. 2 3 3 3. 20 3. 4 72 3. 506 7 6 Round 3 1. 3½ 2. 7 Round 4 1. 4½ 2. 32 Round 5 1. 3 2 2. 4 n Round 6 1. 2 2. 5 41 ISMTF Junior Mathematics Competition 2006 Team Event British School of Paris