2009 English Day of Beijing Mathematics Club
PartⅠ: Questions 1 to 10, 10 marks each
1.At the right is shown a 4 × 4 grid. We wish to fill in the grid such that each row, each column, and each 2 × 2 square outlined by the thick lines contains the digits 1 through 4. Some grids have already been filled in. Find the number of ways we can complete the rest of the grid.
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2.The areas of the faces of a cuboid are 84 cm2, 70 cm2 and 30 cm2. Find the volume of the cuboid in cm3.
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3.The fraction can be wrritten in the form where the greatest common divisor of m and n is 1, Find m+n.
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4.Find the sum of all the integers N > 1 with the properties that the each prime factor of N 我爱你英文is either 2, 3, 5 or 7, and N is not divisible by any perfect cube greater than 1.
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5.A large fresh water rervoir has two types of drainage system, small pipes and large pipes. 6 large pipes, on their own, can drain the rervoir in 12 hours. 3 large pipes and 9 small pipes, at the same time, can drain the rervoir in 8 hours. How long will 5 small pipes, on their own, take to drain the rervoir?
Answer： minutes
6.At a local village gala, the entire population turned up, 500 people. The event raid £3,000. Tickets were priced as follows: £7.48 per man, £7.12 per woman and £0.45 per child. How many children were there?
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关灯的英文
7.Each of the distinct letters in the following addition problem reprents a different digit. If A=4, f猫头鹰之城ind the number reprented by the word “MEET”.
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8.Let two 8×12 rectangles share a common corner and overlap. The distance from the bottom right corner of one rectangle to the interction point along the right edge of that rectangle is 7. What is the area of the shaded region?irma
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9.A spy had to nd the 4-digit code to headquarters. For curity reasons, he nt instead the 9 parate 4-digit codes shown. In each of the 9 codes, at least one of the digits a, b, 堪培拉英文c, and d occurs in its correct position. What is the value of ?
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10.In how many ways can one arrange the numbers 21, 31, 41, 51, 61, 71 and 81 such that the sum of every four concutive numbers is divisible by 3?
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PartⅡ: Questions 11 to 14, 20 marks each
11.Town A and town B are connected by a highway, with a rvice station at the midpoint.
Mike and Sam start from A to B at the same time. When Mike reaches the rvice station, Sam is 16 km behind. Mike reduces speed by 25% after he pass through the rvice station. When Sam reaches the rvice station, Mike is 15 km ahead of Sam. What’s the distance between A and B?
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mimc12.Given: ABCD is a trapezoid, AD∥BC, AD:BC=1:2, , , Find the area of uniform是什么意思．
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13.In how many different ways can the ven empty circles in the diagram on the right be filled in with the numbers 2 through 8 such that each number is ud once, and each number is either greater than both its neighbors, or less than both its neighbors.
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14.How many rectangles are there in the diagram on the right such that the sum of the numbers within the rectangle is a multiple of 4?
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题号 | trine1 | 2 | 3 | 4 | subway5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 |
答案 | 2 | 420 | 310 | 80 | 1296 | 259 | learn to say no9221 | 54 | 8326 | 144 | 160 | 6 | 272 | 28 |
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