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MATHEMATICS TEAM CHALLENGE 2014 TEAM EVENT: Junior Secondary (Calculators are allowed) Please write answers on the answer sheet. Time: 45 minutes Total: 150 points_ T1. (10 points) A soccer team has six reserves sitting on the bench and their shirts are numbered consecutively. During the second half, one of the reserves is called into play and this reduces the total of their shirt numbers by one-seventh. What was the number of the player called into play, if the shirt numbers of the six reserves were between 12 and 21? T2. (20 points) The smallest Pythagorean triple consisting of positive integers is [3, 4, 5]. This is a Pythagorean triple since 32 + 42 = 52. How many sets of triples are there if each set consists of positive integers less than 45? T3. (10 points) Replace the letters with numerals (0 – 9) to make the equation work. Each letter represents a different numeral. What is the numerical value of HANAH? HHA = HANAH T4. (10 points) In the year 2014, a woman adds the year she was born to the year her son was born, then adds her current age and her son’s current age. What number does she come up with? T5. (15 points) What is the next number in the sequence? 18, 65, 61, 37, 58,___ T6. (20 points) A FIFA World Cup football squad consists of 23 players. Only 11 players are allowed on the field at any one time, and a coach needs to select one goalkeeper, three defenders, four midfielders and three attackers. How many possible team combinations are available to a coach if his squad consists of three goalkeepers, six defenders, eight midfielders and six attackers? T7. (20 points) At 7:00 am Mike noticed that his odometer displayed the palindromic number 13131. [A palindromic number is the same forwards and backwards] Mike decided to pull over and have a rest when his odometer displayed the next palindromic number that was also divisible by 11. At what time did Mike pull over if his average speed during the trip was 100 km/h? T8. (15 points) A jet covers 160 kilometres in the time that another jet moving 200 km/h faster covers 200 kilometres. What is the speed of the slower jet? T9. (15 points) In how many ways can five persons be seated in a row so that a certain two of them are not next to each other? T10. (15 points) Three darts are thrown at the target shown below. Assume that each of the darts lands within one of the rings or within the bull’s eye. How many different totals are possible? School Name:_____________________________ Team 1: Team 2: 2014 MATHS TEAM CHALLENGE JUNIOR SECONDARY TEAM EVENT ANSWER SHEET Question T1. (10 points) Answers Points T2. (20 points) T3. (10 points) T4. (10 points) T5. (15 points) T6. (20 points) T7. (20 points) T8. (15 points) T9. (15 points) T10. (15 points) Total /150 2014 MATHS TEAM CHALLENGE JUNIOR SECONDARY TEAM EVENT ANSWER SHEET Question T1. (10 points) Answers 15 T2. (20 points) 17 T3. (10 points) 14641 T4. (10 points) 4028 T5. (15 points) 89 T6. (20 points) 84,000 T7. (20 points) 10:00 am T8. (15 points) 800 km/hour T9. (15 points) 72 ways T10. (15 points) 10 totals Points