Team Round.

Team Round

Team Round This round will last for approximately 60 minutes – there is no break! There are 18 questions of varying difficulty. Each question has a time limit in which to complete it.

For each question that is answered correctly you get the:
time allowed in minutes × 2 marks. Only answers are required – it is not necessary to show any working out.

Once the time limit is up you must hand in the correct piece of white paper with the answer filled in where indicated. You have 18 answer sheets – one for each question. Each answer sheet also gives the question number and your team name and team number..

Each team also has 6 sheets of joker paper - each is an opportunity to gain bonus marks.
If you have answered a question correctly within the joker time allowed you can write your answer on the pink paper and then hold this paper up to be collected. If you have answered the question correctly you will gain 5 bonus marks plus the marks for the question. But remember – you only have six of these attempts for bonus marks.

Are there any questions?

You have 1 minute for question 1. Joker time: 30 secs

Team Round Question 1 Two numbers differ by 8 and have a sum 88. What is the ratio of the larger number to the smaller in its simplest form? 00 20 21 19 17 22 16 18 25 27 28 26 15 24 23 12 04 05 03 02 00 01 06 07 29 13 11 10 08 09 14 32 51 52 50 49 47 48 53 54 58 59 57 56 55 30 46 36 37 35 34 31 33 45 38 43 44 39 42 41 40 Time: 60 secs Joker: 30 secs No more joker

Please hand in your answer.

Team Round Question 2 What is the area of the triangle shown here? 3y y 30 00 20 21 19 18 16 17 22 25 27 28 26 15 24 23 12 04 05 03 02 00 01 06 07 29 13 11 10 08 09 14 32 51 52 50 49 47 48 53 54 58 59 57 56 55 30 46 36 37 35 34 31 33 45 38 43 44 39 42 41 40 Time: 60 secs Joker: 30 secs No more joker

You have 2 minutes for question 3. Joker time: 50 secs

Team Round Question 3 Three positive integers a, b and c, where a < b < c, are such that their median is 11, their mean is 9 and their range is 10. Find the value of a. 01 20 21 19 17 22 16 18 25 27 28 26 15 24 23 12 04 05 03 02 00 01 06 07 29 13 11 10 08 09 14 32 51 52 50 49 47 48 53 54 58 59 57 56 55 30 46 36 37 35 34 31 33 45 38 43 44 39 42 41 40 Time: 2 mins Joker: 50 secs No more joker

Team Round Question 3 Three positive integers a, b and c, where a < b < c, are such that their median is 11, their mean is 9 and their range is 10. Find the value of a. 00 20 21 19 17 22 16 18 25 27 28 26 15 24 23 12 04 05 03 02 00 01 06 07 29 13 11 10 08 09 14 32 51 52 50 49 47 48 53 54 58 59 57 56 55 30 46 36 37 35 34 31 33 45 38 43 44 39 42 41 40 Time: 2 mins Joker: 50 secs No more joker

Question 4 Team Round A straight line AE divides the rectangle ABCD into two parts whose areas are in the ratio 1 : 7. Find the ratio of the lengths AE : ED A E D C B 00 20 21 19 18 16 17 22 25 27 28 26 15 24 23 12 04 05 03 02 00 01 06 07 29 13 11 10 08 09 14 32 51 52 50 49 47 48 53 54 58 59 57 56 55 30 46 36 37 35 34 31 33 45 38 43 44 39 42 41 40 Time: 60 secs Joker: 30 secs No more joker

You have 2 minutes for question 5. Joker time: 1 min

Team Round Question 5 You are given six numbers 3, _, _, _, _, 80. Each number in the sequence is the sequence after the first two is formed by adding all the previous terms? What is the sum of the four missing numbers? 01 20 21 19 17 22 16 18 25 27 28 26 15 24 23 12 04 05 03 02 00 01 06 07 29 13 11 10 08 09 14 32 51 52 50 49 47 48 53 54 58 59 57 56 55 46 45 36 37 35 34 31 33 30 38 43 44 39 42 41 40 Time: 2 mins Joker: 1 mins

Team Round Question 5 You are given six numbers 3, _, _, _, _, 80. Each number in the sequence is the sequence after the first two is formed by adding all the previous terms? What is the sum of the four missing numbers? 00 19 20 18 15 21 16 17 24 26 27 25 14 23 22 12 04 05 03 02 00 01 06 07 11 28 10 09 08 13 30 50 51 49 48 46 47 52 53 58 59 57 56 54 55 29 45 35 36 34 33 31 32 44 37 42 43 38 41 39 40 Time: 2 mins Joker: 1 mins No more joker

Question 6 Team Round The area of the shaded triangle is 5 square units. What is the area of the un-shaded trapezium? 3 4 01 19 21 20 16 22 17 18 25 27 28 26 15 24 23 12 04 05 03 02 00 01 06 07 29 13 11 10 08 09 14 32 51 52 50 49 47 48 53 54 58 59 57 56 55 46 45 36 37 35 34 31 33 30 38 43 44 39 42 41 40 Time: 2 mins Joker: 1 min

Question 6 Team Round The area of the shaded triangle is 5 square units. What is the area of the un-shaded trapezium? 3 4 00 19 20 18 15 21 16 17 24 26 27 25 14 23 22 11 04 05 03 02 00 01 06 07 28 12 10 09 08 13 29 50 51 49 48 46 47 52 53 58 59 57 56 54 55 30 45 35 36 34 33 31 32 44 37 42 43 38 41 39 40 Time: 2 mins Joker: 1 min No more joker

Question 7 I need to buy 12 DVD’s for my film collection. They normally cost 450 Baht each, but a number of shops have “special offers”. Which of these is the best deal? A: Pay only three quarters of the normal price! B: Buy two – get one free! C: Two for the price of four! D: One fifth off all prices! E: 30% price cut Team Round 01 21 20 19 17 16 22 18 25 27 28 26 15 24 23 12 04 05 03 02 00 01 06 07 29 13 11 10 08 09 14 32 51 52 50 49 47 48 53 54 58 59 57 56 55 46 45 36 37 35 34 31 33 30 38 43 44 39 42 41 40 Time: 2 mins Joker: 1 mins

Question 7 I need to buy 12 DVD’s for my film collection. They normally cost 450 Baht each, but a number of shops have “special offers”. Which of these is the best deal? A: Pay only three quarters of the normal price! B: Buy two – get one free! C: Two for the price of four! D: One fifth off all prices! E: 30% price cut Team Round 00 19 20 18 15 21 16 17 24 26 27 25 14 23 22 11 04 05 03 02 00 01 06 07 28 12 10 09 08 13 29 50 51 49 48 46 47 52 53 58 59 57 56 54 55 45 44 34 35 33 32 30 31 36 37 42 43 41 40 38 39 Time: 2 mins Joker: 1 mins No more joker

You have 3 minutes for question 8. Joker time: 2 mins

Question 8 Team Round The diagram shows two concentric circles of radii r and 2r respectively. What is the ratio of the total shaded area to the total unshaded area? 02 20 21 19 17 22 16 18 25 27 28 26 15 24 23 12 04 05 03 02 00 01 06 07 29 13 11 10 08 09 14 32 51 52 50 49 47 48 53 54 58 59 57 56 55 46 45 36 37 35 34 31 33 30 38 43 44 39 42 41 40 Time: 3 mins Joker: 2 mins

Question 8 Team Round The diagram shows two concentric circles of radii r and 2r respectively. What is the ratio of the total shaded area to the total unshaded area? 01 19 20 18 15 21 16 17 24 26 27 25 14 23 22 11 04 05 03 02 00 01 06 07 28 12 10 09 08 13 29 50 51 49 48 46 47 52 53 58 59 57 56 54 55 45 44 34 35 33 32 30 31 36 37 42 43 41 40 38 39 Time: 3 mins Joker: 2 mins

Question 8 Team Round The diagram shows two concentric circles of radii r and 2r respectively. What is the ratio of the total shaded area to the total unshaded area? 00 19 20 18 15 21 16 17 24 26 27 25 14 23 22 11 04 05 03 02 00 01 06 07 28 12 10 09 08 13 29 50 51 49 48 46 47 52 53 58 59 57 56 54 55 45 44 34 35 33 32 30 31 36 37 42 43 41 40 38 39 Time: 3 mins Joker: 2 mins No more joker

You have 3 minutes for question 9. Joker time: 1 min 30 s

Question 9 Team Round The first two scales shown are perfectly balanced. How many squares will be needed on the right of the third scales so that the scales balance? ? 02 19 21 20 16 22 17 18 25 27 28 26 15 24 23 12 04 05 03 02 00 01 06 07 29 13 11 10 08 09 14 32 51 52 50 49 47 48 53 54 58 59 57 56 55 46 45 36 37 35 34 31 33 30 38 43 44 39 42 41 40 Time: 3 mins Joker: 1 min 30 s

Question 9 Team Round The first two scales shown are perfectly balanced. How many squares will be needed on the right of the third scales so that the scales balance? ? 01 20 21 19 16 22 17 18 25 27 28 26 15 24 23 12 04 05 03 02 00 01 06 07 29 13 11 10 08 09 14 31 51 52 50 49 47 48 53 54 58 59 57 56 55 30 46 36 37 35 34 32 33 45 38 43 44 39 42 41 40 Time: 3 mins Joker: 1 min 30 s No more joker

Question 9 Team Round The first two scales shown are perfectly balanced. How many squares will be needed on the right of the third scales so that the scales balance? ? 00 20 21 19 16 22 17 18 25 27 28 26 15 24 23 12 04 05 03 02 00 01 06 07 29 13 11 10 08 09 14 31 51 52 50 49 47 48 53 54 58 59 57 56 55 30 46 36 37 35 34 32 33 45 38 43 44 39 42 41 40 Time: 3 mins Joker: 1 min 30 s No more joker

Question 10 Team Round In the right-angled triangle ABC, DB = 12 cm, DC = 15 cm and AD = BC. What is the area of triangle ACD? A B D C 01 20 21 19 18 17 16 22 25 27 28 26 15 24 23 12 04 05 03 02 00 01 06 07 29 13 11 10 08 09 14 33 51 52 50 49 47 48 53 54 58 59 57 56 55 46 45 36 37 35 34 31 32 30 38 43 44 39 42 41 40 Time: 2 mins Joker: 1 min

Question 10 Team Round In the right-angled triangle ABC, DB = 12 cm, DC = 15 cm and AD = BC. What is the area of triangle ACD? A B D C 00 19 20 18 15 21 16 17 24 26 27 25 14 23 22 11 04 05 03 02 00 01 06 07 28 12 10 09 08 13 29 50 51 49 48 46 47 52 53 58 59 57 56 54 55 30 45 35 36 34 33 31 32 44 37 42 43 38 41 39 40 Time: 2 mins Joker: 1 min No more joker

Question 11 Team Round Jill runs around a circular track taking 80 seconds for each lap. Jack runs in the opposite direction and meets Jill every 30 seconds. How long does Jack take for each lap? 02 20 21 19 17 22 16 18 25 27 28 26 15 24 23 12 04 05 03 02 00 01 06 07 29 13 11 10 08 09 14 32 51 52 50 49 47 48 53 54 58 59 57 56 55 46 45 36 37 35 34 31 33 30 38 43 44 39 42 41 40 Time: 3 mins Joker: 2 mins

Question 11 Team Round Jill runs around a circular track taking 80 seconds for each lap. Jack runs in the opposite direction and meets Jill every 30 seconds. How long does jack take for each lap? 01 19 20 18 15 21 16 17 24 26 27 25 14 23 22 12 04 05 03 02 00 01 06 07 11 28 10 09 08 13 30 50 51 49 48 46 47 52 53 58 59 57 56 54 55 29 45 35 36 34 33 31 32 44 37 42 43 38 41 40 39 Time: 3 mins Joker: 2 mins

Question 11 Team Round Jill runs around a circular track taking 80 seconds for each lap. Jack runs in the opposite direction and meets Jill every 30 seconds. How long does jack take for each lap? 00 19 20 18 15 21 16 17 24 26 27 25 14 23 22 12 04 05 03 02 00 01 06 07 11 28 10 09 08 13 30 50 51 49 48 46 47 52 53 58 59 57 56 54 55 29 45 35 36 34 33 31 32 44 37 42 43 38 41 39 40 Time: 3 mins Joker: 2 mins No more joker

You have 3 minutes for question 12. Joker time: 1 min 30s

Question 12 Team Round ABCDEF is a regular hexagon of area 360. What is the area of the kite-shaped figure ABCE? A E D C B F 02 20 21 19 18 17 16 22 25 27 28 26 15 24 23 12 04 05 03 02 00 01 06 07 29 13 11 10 08 09 14 33 51 52 50 49 47 48 53 54 58 59 57 56 55 46 45 36 37 35 34 31 32 30 38 43 44 39 42 41 40 Time: 3 mins Joker: 1 min 30 s

Question 12 Team Round ABCDEF is a regular hexagon of area 360. What is the area of the kite-shaped figure ABCE? A E D C B F 01 19 20 18 15 21 16 17 24 26 27 25 14 23 22 11 04 05 03 02 00 01 06 07 28 12 10 09 08 13 29 50 51 49 48 46 47 52 53 58 59 57 56 54 55 30 45 35 36 34 33 31 32 44 37 42 43 38 41 39 40 Time: 3 mins Joker: 1 min 30 s No more joker

Question 12 Team Round ABCDEF is a regular hexagon of area 360. What is the area of the kite-shaped figure ABCE? A E D C B F 00 19 20 18 15 21 16 17 24 26 27 25 14 23 22 11 04 05 03 02 00 01 06 07 28 12 10 09 08 13 29 50 51 49 48 46 47 52 53 58 59 57 56 54 55 30 45 35 36 34 33 31 32 44 37 42 43 38 41 39 40 Time: 3 mins Joker: 1 min 30 s No more joker

Question 13 Team Round The curve y = x2 - 6x +13 is rotated through 180° about the origin. What is the equation of the new curve in the form y = ax2 + bx + c? 03 20 21 19 17 22 16 18 25 27 28 26 15 24 23 12 04 05 03 02 00 01 06 07 29 13 11 10 08 09 14 32 51 52 50 49 47 48 53 54 58 59 57 56 55 46 45 36 37 35 34 31 33 30 38 43 44 39 42 41 40 Time: 4 mins Joker: 2 mins

Question 13 Team Round The curve y = x2 - 6x +13 is rotated through 180° about the origin. What is the equation of the new curve in the form y = ax2 + bx + c? 02 19 20 18 15 21 16 17 24 26 27 25 14 23 22 12 04 05 03 02 00 01 06 07 11 28 10 09 08 13 30 50 51 49 48 46 47 52 53 58 59 57 56 54 55 29 45 35 36 34 33 31 32 44 37 42 43 38 41 40 39 Time: 4 mins Joker: 2 mins

Question 13 Team Round The curve y = x2 - 6x +13 is rotated through 180° about the origin. What is the equation of the new curve in the form y = ax2 + bx + c? 01 19 20 18 15 21 16 17 24 26 27 25 14 23 22 12 04 05 03 02 00 01 06 07 11 28 10 09 08 13 30 50 51 49 48 46 47 52 53 58 59 57 56 54 55 29 45 35 36 34 33 31 32 44 37 42 43 38 41 39 40 Time: 4 mins Joker: 2 mins No more joker

Question 13 Team Round The curve y = x2 - 6x +13 is rotated through 180° about the origin. What is the equation of the new curve in the form y = ax2 + bx + c? 00 19 20 18 15 21 16 17 24 26 27 25 14 23 22 11 04 05 03 02 00 01 06 07 28 12 10 09 08 13 29 50 51 49 48 46 47 52 53 58 59 57 56 54 55 45 44 34 35 33 32 30 31 36 37 42 43 41 40 38 39 Time: 4 mins Joker: 2 mins No more joker

Question 14 Team Round Pinkie and Perky are each given a 100g chocolate bar. They start eating their chocolate at the same time, but Pinkie eats hers three times as fast as Perky. When Perky has two times as much as has Pinkie, what faction of the chocolate bar has Pinkie eaten? 03 21 20 19 17 16 22 18 25 27 28 26 15 24 23 12 04 05 03 02 00 01 06 07 29 13 11 10 08 09 14 32 51 52 50 49 47 48 53 54 58 59 57 56 55 46 45 36 37 35 34 31 33 30 38 43 44 39 42 41 40 Time: 4 mins Joker: 2 mins

Question 14 Team Round Pinkie and Perky are each given a 100g chocolate bar. They start eating their chocolate at the same time, but Pinkie eats hers three times as fast as Perky. When Perky has two times as much as has Pinkie, what faction of the chocolate bar has Pinkie eaten? 02 21 20 19 17 16 22 18 25 27 28 26 15 24 23 12 04 05 03 02 00 01 06 07 29 13 11 10 08 09 14 32 51 52 50 49 47 48 53 54 58 59 57 56 55 46 45 36 37 35 34 31 33 30 38 43 44 39 42 41 40 Time: 4 mins Joker: 2 mins

Question 14 Team Round Pinkie and Perky are each given a 100g chocolate bar. They start eating their chocolate at the same time, but Pinkie eats hers three times as fast as Perky. When Perky has two times as much as has Pinkie, what faction of the chocolate bar has Pinkie eaten? 01 21 20 19 17 16 22 18 25 27 28 26 15 24 23 12 04 05 03 02 00 01 06 07 29 13 11 10 08 09 14 32 51 52 50 49 47 48 53 54 58 59 57 56 55 30 46 36 37 35 34 31 33 45 38 43 44 39 42 41 40 Time: 4 mins Joker: 2 mins No more joker

Question 14 Team Round Pinkie and Perky are each given a 100g chocolate bar. They start eating their chocolate at the same time, but Pinkie eats hers three times as fast as Perky. When Perky has two times as much as has Pinkie, what fraction of the chocolate bar has Pinkie eaten? 00 20 21 19 18 22 16 17 25 28 29 27 26 24 15 23 13 04 05 03 02 00 01 06 07 12 30 11 10 08 09 14 33 51 52 50 49 47 48 53 54 58 59 57 56 55 31 46 36 37 35 34 32 45 38 43 44 39 42 41 40 Time: 4 mins Joker: 2 mins No more joker

Question 15 Team Round In the diagram, AB, CB and XY are tangents to the circle with centre O and What is the size of O C A B X Y 03 20 21 19 18 17 16 22 26 27 28 15 25 24 23 11 04 05 03 02 00 01 06 07 12 13 29 10 08 09 14 33 51 52 50 49 47 48 53 54 58 59 57 56 55 46 45 36 37 35 34 31 32 30 38 43 44 39 42 41 40 Time: 4 mins Joker: 2 mins

Question 15 Team Round In the diagram, AB, CB and XY are tangents to the circle with centre O and What is the size of O C A B X Y 02 18 19 17 14 20 15 16 24 25 26 13 23 22 21 09 03 04 02 01 00 05 06 10 11 27 08 07 12 28 49 50 51 48 47 45 46 52 53 58 59 57 56 54 55 44 43 33 34 32 31 29 30 35 36 41 42 40 39 37 38 Time: 4 mins Joker: 2 mins

Question 15 Team Round In the diagram, AB, CB and XY are tangents to the circle with centre O and What is the size of O C A B X Y 01 18 19 17 14 20 15 16 24 25 26 13 23 22 21 09 03 04 02 01 00 05 06 10 11 27 08 07 12 28 50 51 49 48 46 47 52 53 58 59 57 56 54 55 45 44 33 34 32 31 29 30 35 36 42 43 41 40 37 38 39 Time: 4 mins Joker: 2 mins No more joker

Question 15 Team Round In the diagram, AB, CB and XY are tangents to the circle with centre O and What is the size of O C A B X Y 00 18 19 17 14 20 15 16 24 25 26 13 23 22 21 09 03 04 02 01 00 05 06 10 11 27 08 07 12 28 50 51 49 48 46 47 52 53 58 59 57 56 54 55 45 44 33 34 32 31 29 30 35 36 41 42 43 40 39 37 38 Time: 4 mins Joker: 2 mins No more joker

You have 3 minutes for question 16. Joker time: 1 min 30s

Question 16 Team Round In a sponsored “Animal Sprint” the cheetah ran at 80 km/hr while the snail slimed along at 30 hr/km. The cheetah kept going for 24 seconds. Roughly how long would the snail take to cover the same distance? 02 20 21 19 17 22 16 18 25 27 28 26 15 24 23 12 04 05 03 02 00 01 06 07 29 13 11 10 08 09 14 32 51 52 50 49 47 48 53 54 58 59 57 56 55 46 45 36 37 35 34 31 33 30 38 43 44 39 42 41 40 Time: 3 mins Joker: 1 min 30 s

Question 16 Team Round In a sponsored “Animal Sprint” the cheetah ran at 80 km/hr while the snail slimed along at 30 hr/km. The cheetah kept going for 24 seconds. Roughly how long would the snail take to cover the same distance? 01 20 21 19 17 16 22 18 25 27 28 26 15 24 23 12 04 05 03 02 00 01 06 07 29 13 11 10 08 09 14 31 51 52 50 49 47 48 53 54 58 59 57 56 55 30 46 36 37 35 34 32 33 45 38 43 44 39 42 41 40 Time: 3 mins Joker: 1 min 30 s No more joker

Question 16 Team Round In a sponsored “Animal Sprint” the cheetah ran at 80 km/hr while the snail slimed along at 30 hr/km. The cheetah kept going for 24 seconds. Roughly how long would the snail take to cover the same distance? 00 20 21 19 17 16 22 18 25 27 28 26 15 24 23 12 04 05 03 02 00 01 06 07 29 13 11 10 08 09 14 31 51 52 50 49 47 48 53 54 58 59 57 56 55 30 46 36 37 35 34 32 33 45 38 43 44 39 42 41 40 Time: 3 mins Joker: 1 min 30 s No more joker

You have 5 minutes for question 17. Joker time: 2 mins 30s

Team Round Question 17 What is the radius of the shaded semicircle in the right-angled triangle? 2 04 20 21 19 18 17 16 22 25 27 28 26 15 24 23 12 04 05 03 02 00 01 06 07 29 13 11 10 08 09 14 33 51 52 50 49 47 48 53 54 58 59 57 56 55 46 45 36 37 35 34 31 32 30 38 43 44 39 42 41 40 Time: 5 mins Joker: 2 min 30 s

Team Round Question 17 What is the radius of the shaded semicircle in the right-angled triangle? 2 03 19 20 18 15 21 16 17 24 26 27 25 14 23 22 11 04 05 03 02 00 01 06 07 28 12 10 09 08 13 30 50 51 49 48 46 47 52 53 58 59 57 56 54 55 29 45 35 36 34 33 31 32 44 37 42 43 38 41 40 39 Time: 5 mins Joker: 2 min 30 s

Team Round Question 17 What is the radius of the shaded semicircle in the right-angled triangle? 2 02 19 20 18 15 21 16 17 24 26 27 25 14 23 22 11 04 05 03 02 00 01 06 07 28 12 10 09 08 13 29 50 51 49 48 46 47 52 53 58 59 57 56 54 55 30 45 35 36 34 33 31 32 44 37 42 43 38 41 39 40 Time: 5 mins Joker: 2 min 30 s No more joker

Team Round Question 18 What is the sum to infinity of the convergent series 05 20 21 19 17 22 16 18 25 27 28 26 15 24 23 12 04 05 03 02 00 01 06 07 29 13 11 10 08 09 14 32 51 52 50 49 47 48 53 54 58 59 57 56 55 46 45 36 37 35 34 31 33 30 38 43 44 39 42 41 40 Time: 6 mins Joker: 4 mins

Team Round Question 18 What is the sum to infinity of the convergent series 01 19 18 20 15 21 16 17 24 26 27 25 14 23 22 11 04 05 03 02 00 01 06 07 28 12 10 09 08 13 29 50 51 49 48 46 47 52 53 58 59 57 56 54 55 45 44 34 35 33 32 30 31 36 37 42 43 41 40 38 39 Time: 6 mins Joker: 4 mins No more joker

Team Round Question 18 What is the sum to infinity of the convergent series 00 19 18 20 15 21 16 17 24 26 27 25 14 23 22 11 04 05 03 02 00 01 06 07 28 12 10 09 08 13 29 50 51 49 48 46 47 52 53 58 59 57 56 54 55 45 44 34 35 33 32 30 31 36 37 42 43 41 40 38 39 Time: 6 mins Joker: 4 mins No more joker

Time to breathe a sigh of relief, and to get ready for the gala dinner at the hotel.
We thank you and hope you have enjoyed this round

Team Round The end

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