Скачать с ютуб AMC 2022 ( Senior) Questions 1-30 в хорошем качестве

AMC 2022 ( Senior) Questions 1-30

In this video, I will answer questions 1 to 30 from AUSTRALIAN MATHEMATICS COMPETITION 11-12 in great detail. Contact me to book lessons: https://www.youtube.com/@math-with-Al... AMC 2022 Intermediate Solutions    • 2022 Australian Mathematics Competition AM...   AMC 2022 Senior Solutions    • AMC 2022  ( Senior)  Questions 1-30   AMC 2022 Junior Solutions    • Australian Mathematics Competition Junior ...   AMC 2021 Intermediate Solutions    • AUSTRALIAN MATHEMATICS COMPETITION  (AMC) ...   let me know if you need help with other tests. hope you find it helpful :) 22. In the two equations ax − b = c and dy + e = f, each of the letters a, b, c, d, e, and f is replaced by a different digit from 1 to 9. When the two equations are solved for x and y, the lowest possible value of x+ y is 23. A semicircle is inscribed in a right-angled isosceles triangle and a square is inscribed in the semicircle as shown. What is the ratio of the area of the square to the area of the triangle? 24. In the grid shown, the numbers 1 to 8 are placed so that when joined in ascending order they make a trail. The trail moves from one square to an adjacent square but does not move diagonally. In how many ways can the numbers 1 to 8 be placed in the grid to give such a trail? 25. When I cycled around the lake yesterday, my children Sally and Wally decided to ride the same route in the opposite direction. We all set off at the same time, from the same point, and finished at that same spot. We each rode at our own steady speed. It took me 77 minutes. Sally and I passed each other, waving, exactly 42 minutes after we started. Precisely 2 minutes later, Wally and I passed each other, puffing. To the nearest minute, how much longer did Wally take than Sally to ride around the lake? 26. Horton has a regular hexagon of area 60. For each choice of three vertices of the hexagon, he writes down the area of the triangle with these three vertices. What is the sum of the 20 areas that Horton writes down? 7. An even square number is multiplied by an odd cube greater than 1, resulting in a fourth power. If the fourth power is as small as possible, what is the sum of the square and the cube? 8. In an infinite sequence, the first two terms are 2 and 6, and apart from the first term, each term is one less than the average of its two neighbours. What is the largest term less than 1000? 29. Wasteful Wayne takes one sheet of paper with ‘My Document’ printed on it. He runs it through the photocopier to make two copies which he then stamps with his ‘COPY’ stamp. Wayne then takes the original and the two copies, runs all three through the photocopier to make two copies of each, stamps the six new copies with his ‘COPY’ stamp, and adds them to the top of the pile. He repeats this process by making two copies of each sheet of paper in his existing pile, stamping the new copies, then adding them to the pile. So the pile triples in size each time. After Wayne has done this eight times in total, the pile is 6561 sheets high. How many sheets have exactly 2 ‘COPY’ stamps on them?