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Mathletics 2013

Mathletics 2013. Seniors – Grades 7 & 8 Session 2. Logic. TV & Entertainment. 40. 10. 20. 30. 50. 40. 10. 20. 30. 50. Cartoons. Environment. 40. 40. 10. 20. 30. 50. 10. 20. 30. 50. Q1. Mario’s Obstacles. O = 3M + 18 O = number of obstacles

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Mathletics 2013

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  1. Mathletics 2013 Seniors – Grades 7 & 8 Session 2

  2. Logic TV & Entertainment 40 10 20 30 50 40 10 20 30 50 Cartoons Environment 40 40 10 20 30 50 10 20 30 50

  3. Q1. Mario’s Obstacles O = 3M + 18 O = number of obstacles M= number of Monsters Mario has killed. If Mario has killed 4 monsters, what is O ? Answer

  4. Q2. Amazing Race • 22 Episodes recorded • Rory watches 2 episodes every 3 days • How many days to complete 22 episodes ? Answer

  5. Q3. Juno Awards • In 2011, 1.8 million watched • Increased by 10% in 2012 • Decreased by 10% as compared to 2012 in 2013. • How many people watched in 2013 ? Answer

  6. Q4. Disney’s Jessie • 2009 premiere aired on Sept 11th • June 11 2009 was a Thursday. • What day of the week was Sept 11th 2009. Answer

  7. Q5. Wizards’ Party Alex wants to organize a party. She has two options for food: Buffet: $24/guest + 2 waitpersons Catered: $30/guest + 8 waitpersons Each waitperson charges $50. She has two options for music: DJ: $80/h Band: $325 There are 50 guests, and the party lasts 4 hours. What is the cheapest option? A) Buffet & DJ C) Catered & DJ B) Buffet & Band D) Catered & Band Answer

  8. Q1. Robbery! • Diamond stolen. • Jack: I did not do that. • Mike: Jerry is the criminal. • Jim: Mike stolen the diamond. • Jerry: I am not criminal. • One of the four suspects was lying. • Who is the criminal ? Answer

  9. Q2. Coke Cans • Coca Cola launched a sales promotion. • If you buy 2 cans of Coca Cola, you can get one for free when you return the two empty cans. • The price is one dollar per can. • You have $20 • How many cans can you get? Answer

  10. Q3. Teacher Age • Principal is 50 to 70 years old • Teacher’s age is 5/9 of Principal • Teacher’s age is divisible by 2. • Assume both ages are integer numbers • How old is teacher ? Answer

  11. Q4. Lighter Ball • There are 12 balls • One is lighter than the rest • How many times do you have to weigh to find the lighter ball ? Answer

  12. Q5 Containers • 5 & 6 Litre Containers • How many litres total are needed to measure 2 litres • Fill-Pour Measurement: Fill the container fully with 6 litres of water and pour into the 5-litre container, the water left in the 6-litre container is 1 litre. • Continue this method… 5 Litres 6 Litres Answer

  13. Q1. Dexter’s Experiment • Dexter is doing a science experiment and needs 200 mL of water. • He needs to mix this in a huge vat with 2 mL of dye and 7 full cans of his super-secret glue formula (which each hold 125 mL). • He wants to transfer all of the solution into 0.25 L bottles for easier transportation. • How many bottles does he need? Answer

  14. Q2. Ninja Turtle Pizza • The Ninja Turtles love pizza. The local pizza parlour makes large pizzas that are 10 slices to a (pizza) pie. • They can also top them so that, if you wanted, you could get different toppings on each slice. • The first slice Donatello ordered had one topping on it. • On the next four slices, Michelangelo had 2 toppings. • Raphael then ordered 3 toppings on the next seven slices. • How many pizzas in total to get to 7 toppings on a slice if they continue to order like this? 3 toppings 2 toppings 1 topping Answer

  15. Q3. Scooby-Doo’s Sign 13 nails • Shaggy and Scooby-Doo painted a new rectangular sign with a multicolour design. • They then tacked it up on a wall using nails spaced 5 cm apart, making sure they had exactly one nail in each of the four corners. • If they used 13 nails on the left side, and 90 nails in total, how big was the sign? Answer in square centimetres. Shaggy and Scooby-Doo Adventure Sign! Answer

  16. Q4. Jetsons’ Aerocar Trip • The Jetsons are planning a trip in their aerocar to visit the famous Astro Tower in Sun City. It is 1632 km away from their home in Orbit City. • Their aerocar uses 2 L of fuel for every 8 km, and the tank only holds 10 L of fuel. • How many times will they have to fill up their tank? (Note: A partial fill is still considered a fill.) Answer

  17. Q5. Flintstone Record Room • Fred Flintstone is building a new cylindrical room to store his record collection. • The room must have an inner diameter of 10 ft. • It also has to be 12 ft tall. • To make sure his pet Dino doesn’t accidentally knock anything over, the walls must be 2 ft thick. • If he also put a roof of the same thickness as the walls on top of the structure, how much stone does he need in total to build the new room? Round answers to the nearest ft3. Answer

  18. Q1. Hot & Cool Days Tuesday’s high temperature was 4° C warmer than that of Monday’s. Wednesday’s high temperature was 6°C cooler than that of Monday’s. If Tuesday’s high temperature was 22°C, what was Wednesday’s high temperature? (A) 20°C (B) 24°C (C) 12°C (D) 32°C (E) 16°C Answer

  19. Q2. Tree Planting Steve plants ten trees every three minutes. If he continues planting at the same rate, how long will it take him to plant 2500 trees? (A) 1 ¼ h (B) 3 h (C) 5 h (D) 10 h (E) 12 ½ h Answer

  20. Q3. Recycling Truck • Your community is very environmentally friendly and each home recycles enough materials each week to fill two recycling bins.   • If a recycling truck works 10 hours in one day and can stop at 60 houses in one hour, how many recycling bins can they collect in one day? Answer

  21. Q4. Compost Program • Your community is considering a compost program for food waste. • Community has a population of 73,000 people • Each person creates 25.4kg of waste each week. Of this waste, 10% is food waste. • How much food waste is created per week that could be diverted from the landfill (mass in kg)? Answer

  22. Q5. Snow Fall • Snow is falling at a rate of 1 mm every 6 minutes. • A one metre cubic box is placed in the open to collect the snow. • Snow fell for 1 hour • If one cubic meter of snow weighs 500 Kg, what is the weight of snow collected after 1 hour ? 1m 1m 1m Answer

  23. Mario’s Obstacles Answer: 30 obstacles O = 3 * M + 18 M = 4 Therefore O = 3 * 4 + 18 = 30 Main Page

  24. Amazing Race Answer: 33 days 2/3=22/n, n=number of days n=22*3/2 n=66/2 n=33 Main Page

  25. Juno Awards Answer: D (1.782 million) 10% increase from 1.8 million is 1.8+(10*1.8/100) =1.98 10% decrease from 1.98 is 1.98 - (10*1.98/100) = 1.782 million Main Page

  26. Disney’s Jessie Answer: A Number of days from June 11 to Sep 11 is 92. If you divide 92 by 7 (92/7)gives a remainder of 1. So September 10 is a Thursday and September 11 2009 is a Friday. Main Page

  27. Wizards’ Party Answer: A (Buffet & DJ) Solution: Food: Buffet: $24/guest X 50 guests + 2 waitpersons X $50 = $1200+$100 = $1300 Catered: $30/guest X 50 guests + 8 waitpersons X $50 = $1500+$400 = $1900 Music: DJ: $80/h X 4 hours = $320 Band: $325 Main Page

  28. Robbery Answer: B (Mike) • Mike and Jim’s statement are conflicting. Either one of them is saying the truth. If Jim is lying, Mike is saying the truth which means Jerry is lying (which is not possible). So Mike is lying and all others are saying the truth. • Mike is the criminal Main Page

  29. Coke Cans Answer: 39 Cans Main Page

  30. Teacher’s Age Answer: 30 years • Both principal and teacher's ages are integers. • There are only two numbers between 50 and 70 that can be divided by 9, which are 54 and 63 (since teacher’s age is 5/9 of principal). The age of the principal can be either 54 or 63. • Therefore the teacher may be 30 years old or 35 years old. • Because the teacher's age is evenly divisible by 2, the answer is 30 years old. Main Page

  31. Lighter Ball Answer: 3 times • Balance 6 balls on one side and 6 on the other side. Put the heavier 6 balls away. • Using the 6 lighter balls, balance three Balls on each side. Take lighter 3 balls. • Choose any two of the lighter three balls, put one in each side. • If they are balanced, the one left out is the lighter ball. If they are not balanced, you can pick out the lighter ball. Main Page

  32. Containers Answer: 12 litres • Fill B full (6 L), pour into A, then there is 1 L of water left in B. Empty A and pour the water from B to A. (So you have 1 L in A and nothing in B.) • Fill B full (6 L), pour into A until A is full. This means that 5-1=4 L of water have been poured into A. And then there 6-4=2 L of water left in B. So you need 12 L total to measure 2 L of water with these pails. Main Page

  33. Dexter’s Experiment Answer: 5 Solution: • Total amount of liquid = water + dye + glue= (200 + 2 + 7*125) = 1077 mL • Volume of a bottle = 0.25 L*1000 = 250 mL • Number of bottles = 1077/250 = 4.3 (round up) = 5 bottles Note: You can’t have only part of a bottle! You either use it or you don’t. So the correct answer is 5. Main Page

  34. Ninja Turtle Pizza Answer: 7 Solution: • Sequence: • Total number of slices: 1 + 4 + 7 + 10 + 13 + 16 + 19 = 70 • Total number of pizzas: slices/10 = 70/10 = 7 Main Page

  35. Scooby-Doo’s Sign Answer: 9900 cm2 Solution: • There are 13 nails per side, so this means there are 12 spaces (between nails) on each side. 12 x 5 = 60 cm • On top and bottom (not including the corners), there are 90 – (2*13) = 64 nails  64 / 2 = 32 nails on top edge • If the corners are included, there are 32+ 2 = 34 nails on the top, and 33 spaces between the nails. 33 x 5 = 165 cm • Area = length x width = 165 cm x 60 cm = 9900 cm2 Main Page

  36. Jetsons’ Aerocar Trip Answer: 41 Solution: • Amount of fuel used = 1632 km * (2 L / 8 km) = 408 L • Number of fill-ups = 408 L / 10 L = 40.8 (round up)  41 Main Page

  37. Flintstone Record Room (1) Answer: 1212 ft3 Solution: • The volume of the walls can be calculated by taking the bigger cylinder (outer wall) and subtracting the smaller cylinder shape (inner room). • Let r be the radius of the inner room,and R be the radius of the outer part of the wall. • V room = πr2h = (3.14)(5)2(12) = 942 ft3 • V outer wall = πR2h = (3.14) (7)2(12) = 1846 ft3 • V walls = V outer wall – V room = 1846 – 942 = 904 ft3 Continued…

  38. Flintstone Record Room (2) • The roof is also a cylinder, with a radius that is the same as the outer wall. Its height is the thickness of the wall (i.e. 2 ft). • V roof = πR2h = (3.14) (7)2(2) = 308 ft3 • V total = V walls + V roof = 904 + 308 = 1212 ft3 Main Page

  39. Hot and Cold Days Answer: C (12°C) If Tuesday’s temperature was 22°C then Monday’s high temperature was 18°C. Wednesday’s temperature was 12°C since it was 6°C cooler than that of Monday’s high temperature. Main Page

  40. Tree Planting Answer: E (12 ½ hours) Since Steve plants ten trees every three minutes, he plants one tree every 3/10 minute. In order to plant 2500 trees, he will need 3/10 minute/tree × 2500 tree = 750 minutes There are 60 minutes in an hour, so 750/60 = 12 ½ hours. Main Page

  41. Recycling Truck Answer: 1200 bins 2 bins/house x 60 houses/hour x 10 hours/day = 1200 bins Main Page

  42. Compost Program Answer: 185,420 kg 73,000 people 25.4 kg/person/week 10% of it is food waste So total is 73,000 X 25.4 X 10/100 = 185,420 kg food waste per week for compost Main Page

  43. Snowfall Answer: 5 kg Since 1 mm of snow falls every 6 minutes, 10 mm would have fallen after 60 minutes (1 hr) 10 mm = 0.01 m Total volume of box = 1 X 1 X 1 = 1 m3 Volume of snow after 1 hr = 1 X 1 X 0.01 m = 0.01 m3 Weight of 1 m3 of snow = 500 kg Therefore, weight of 0.01 m3 of snow = 500 X 0.01 = 5 kg Main Page

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