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The Lion

The Lion. Team Competition. Welcome to the team competition. This is the event where using all your teammates to optimize your time will be essential. Each question will have a different allotment of time and each question varies in difficulty.

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The Lion

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  1. The Lion Team Competition

  2. Welcome to the team competition. This is the event where using all your teammates to optimize your time will be essential. • Each question will have a different allotment of time and each question varies in difficulty. • For each question you may score 2 points. One point for a speed answer and a second point for your final answer. (Note: to get the speed answer point it must be same correct answer as your final answer.) • Let’s do a practice question!

  3. Practice question time: Speed answer: 2 minutes Final Answer: 3 minutes

  4. Practice question In Circle Land, all rules of mathematics are the same as we know them except numbers are shown in the following way: Calculate the following expression and provide the answer as they would in Circle Land?

  5. Practice question In Circle Land, all rules of mathematics are the same as we know them except numbers are shown in the following way: Calculate the following expression and provide the answer as they would in Circle Land? STOP 1 10 9 8 7 6 5 4 3 2

  6. Answers in!!!!!!

  7. Practice question answer

  8. Now for the real thing. Good luck.

  9. Question #1 time: Speed answer: 3 minutes Final Answer: 4 minutes

  10. Question #1 In the diagram, ABCD is a square with area 25 cm2 . If PQCD is a rhombus with area 20 cm2. What is the area of the shaded region?

  11. Question #1 In the diagram, ABCD is a square with area 25 cm2 . If PQCD is a rhombus with area 20 cm2. What is the area of the shaded region? STOP 1 10 9 8 7 6 5 4 3 2

  12. Answers in!!!!!!

  13. Question #2 time: Speed answer: 4.5 minutes Final Answer: 6 minutes

  14. Question #2 A hat contains n slips of paper. The slips of paper are numbered with consecutive even integers from 2 to 2n. Consider the situation where there are six slips of paper (n = 6), in the hat, two students, Tarang and Joon, will each choose three slips from the hat and sum their total. In this situation (when n=6) it is impossible for them to have the same total. If more slips of paper are added to the hat, what is the smallest value of n > 6 so that Tarang and Joon can each choose half of the slips and obtain the same total?

  15. Question #2 A hat contains n slips of paper. The slips of paper are numbered with consecutive even integers from 2 to 2n. Consider the situation where there are six slips of paper (n = 6), in the hat, two students, Tarang and Joon, will each choose three slips from the hat and sum their total. In this situation (when n=6) it is impossible for them to have the same total. If more slips of paper are added to the hat, what is the smallest value of n > 6 so that Tarang and Joon can each choose half of the slips and obtain the same total? STOP 1 10 9 8 7 6 5 4 3 2

  16. Answers in!!!!!!

  17. Question #3 time: Speed answer: 2 minutes Final Answer: 3 minutes

  18. Question #3 The Fryer Foundation is giving out four types of prizes, valued at $5, $25, $125 and $625. There are two ways in which the Foundation could give away prizes totaling $880 while making sure to give away at least one and at most six of each prize. Determine the two ways this can be done.

  19. Question #3 The Fryer Foundation is giving out four types of prizes, valued at $5, $25, $125 and $625. There are two ways in which the Foundation could give away prizes totaling $880 while making sure to give away at least one and at most six of each prize. Determine the two ways this can be done. STOP 1 10 9 8 7 6 5 4 3 2

  20. Answers in!!!!!!

  21. Question #4 time: Speed answer: 2 minutes Final Answer: 3 minutes

  22. Question #4 A Nakamoto triangle is a right-angled triangle with integer side lengths which are in the ratio 3 : 4 : 5. (For example, a triangle with side lengths 9, 12 and 15 is a Nakamoto triangle.) There are three Nakamoto triangles that have a side length of 60. Find the combined area of these three triangles.

  23. Question #4 A Nakamoto triangle is a right-angled triangle with integer side lengths which are in the ratio 3 : 4 : 5. (For example, a triangle with side lengths 9, 12 and 15 is a Nakamoto triangle.) There are three Nakamoto triangles that have a side length of 60. Find the combined area of these three triangles. STOP 1 10 9 8 7 6 5 4 3 2

  24. Answers in!!!!!!

  25. Question #5 time: Speed answer: 3.5 minutes Final Answer: 5 minutes

  26. Question #5 • Let s be the number of positive integers from 1 to 100, inclusive, that do not contain the digit 7. • Let t be the number of positive integers from 101 to 300, inclusive, that do not contain the digit 2. • Let f be the number of positive integers from 3901 to 5000, inclusive, that do not contain the digit 4. Determine the value of s+t+f.

  27. Question #5 • Let s be the number of positive integers from 1 to 100, inclusive, that do not contain the digit 7. • Let t be the number of positive integers from 101 to 300, inclusive, that do not contain the digit 2. • Let f be the number of positive integers from 3901 to 5000, inclusive, that do not contain the digit 4. Determine the value of s+t+f. STOP 1 10 9 8 7 6 5 4 3 2

  28. Answers in!!!!!!

  29. Question #6 time: Speed answer: 3 minutes Final Answer: 4 minutes

  30. Question #6 Amanda has the following grades on her Calculus tests this past year. She can’t remember her grade on her Parametrics test but she does remember that her worst test was Applications of Integration. She took her Polar test today but has no idea how she did on it. What is the difference between her highest possible average for the year and her lowest possible average?

  31. Question #6 Amanda has the following grades on her Calculus tests this past year. She can’t remember her grade on her Parametrics test but she does remember that her worst test was Applications of Integration. She took her Polar test today but has no idea how she did on it. What is the difference between her highest possible average for the year and her lowest possible average? STOP 1 10 9 8 7 6 5 4 3 2

  32. Answers in!!!!!!

  33. Question #7 time: Speed answer: 4.5 minutes Final Answer: 6 minutes

  34. Question #7 The odd positive integers are arranged in rows in the triangular pattern, as shown. Determine the row where the number 1001 occurs.

  35. Question #7 The odd positive integers are arranged in rows in the triangular pattern, as shown. Determine the row where the number 1001 occurs. STOP 1 10 9 8 7 6 5 4 3 2

  36. Answers in!!!!!!

  37. Question #8 time: Speed answer: 2 minutes Final Answer: 3 minutes

  38. Question #8 Dmitri has a collection of identical cubes. Each cube is labeled with the integers 1 to 6 as shown in the following net: (This net can be folded to make a cube.) He forms a pyramid by stacking layers of the cubes on a table, as shown, with the bottom layer being a 7 by 7 square of cubes. • Let a be the total number of blocks used. • When all the visible numbers are added up, let b be the smallest possible total. • When all the visible numbers are added from a bird’s eye view, let c be the largest possible sum. Determine the value of a+b+c.

  39. Question #8 Dmitri has a collection of identical cubes. Each cube is labeled with the integers 1 to 6 as shown in the following net: (This net can be folded to make a cube.) He forms a pyramid by stacking layers of the cubes on a table, as shown, with the bottom layer being a 7 by 7 square of cubes. • Let a be the total number of blocks used. • When all the visible numbers are added up, let b be the smallest possible total. • When all the visible numbers are added from a bird’s eye view, let c be the largest possible sum. Determine the value of a+b+c. STOP 1 10 9 8 7 6 5 4 3 2

  40. Answers in!!!!!!

  41. Question #9 time: Speed answer: 3 minutes Final Answer: 4 minutes

  42. Question #9 A number is Beprisque if it is the only natural number between a prime number and a perfect square (e.g. 10 is Beprisque but 12 is not). Find the sum of the first five Beprisque numbers (including 10).

  43. Question #9 A number is Beprisque if it is the only natural number between a prime number and a perfect square (e.g. 10 is Beprisque but 12 is not). Find the sum of the first five Beprisque numbers (including 10). STOP 1 10 9 8 7 6 5 4 3 2

  44. Answers in!!!!!!

  45. Question #10 time: Speed answer: 4 minutes Final Answer: 6 minutes

  46. Lumba River Fishing Felix’s House Kitty’s House Question #10 Felix the cat, wants to give fresh fish to his girlfriend Kitty, as her birthday present. To do this Felix has to walk to the Lumba River, catch a bucket of fish and walk to Kitty’s house. The Lumba River is located 105m north of Felix’s house, and runs straight east and west. Kitty’s house is located 195m south of the Lumba River. If the distance between Felix’s house and Kitty’s house is 410m, what is the shortest route that Felix can take from his house to the river and finally to Kitty’s house?

  47. Lumba River Fishing Felix’s House Kitty’s House Question #10 Felix the cat, wants to give fresh fish to his girlfriend Kitty, as her birthday present. To do this Felix has to walk to the Lumba River, catch a bucket of fish and walk to Kitty’s house. The Lumba River is located 105m north of Felix’s house, and runs straight east and west. Kitty’s house is located 195m south of the Lumba River. If the distance between Felix’s house and Kitty’s house is 410m, what is the shortest route that Felix can take from his house to the river and finally to Kitty’s house? STOP 1 2 3 4 9 6 7 10 5 8

  48. Answers in!!!!!!

  49. Question #11 time: Speed answer: 3 minutes Final Answer: 4 minutes

  50. 7m 5m 4m Question #11 In a large grassy field there is a rectangular barn of dimensions 11m x 5m. There are 2 horses and a llama tied to ropes, the ropes are attached to the barn at points A, B and C. The rope at point A is 7 m long, the rope at point B is 4 m long and the rope at point C is 5 m long. Based upon the length of the rope, in terms of p, determine the area of grass that the animals will be able to reach. BARN

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