Mathematical Olympiad of junior high school mathematics grade one ① 99 and 3 / 5 × 100 and 2 / 5 ② 998×1002-999×1001

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• 1. In order to encourage water saving, a city has made the following regulations on the charging standard of tap water: the part of water consumption no more than 10 tons per month is charged as 0.45 yuan / ton, while the part of water consumption no more than 20 tons is charged as 0.8 yuan / ton; the part of water consumption more than 20 tons is charged as 1.5 yuan / ton; in a month, a household pays 7.10 yuan more than B household, and B household pays 3.75 yuan more than C household, How much does the third household pay for water in that month? (tap water is charged according to the whole ton) The teacher seems to say that we should use functions
• 2. For real numbers x and y, define a new operation, X * y = ax + BX + cxy, where a, B and C are constants. If 1 * 2 = 3, 2 * 3 = 4 and there is a non-zero constant D, such that for any x, there is always x * d = x, then the value of D is? A、3 B、4 C、5 D、6
• 3. ① The following calculation is correct: a (- 3x) ^ 2 = - 9x ^ 2 b. (- 3x) ^ 2 = 9x ^ 2 C. (- 3) ^ 2 = - 6x ^ 2 D (- 3x) ^ 2 = 6x ^ 2 ② The result of calculating a (- 2A) ^ 3 · (a ^ 2) ^ 5 is () (to simplify) ③ If (x ^ 3Y ^ n) ^ 2 = x ^ 6 y ^ 8, then n equals () ④ Given 2 ^ x = A.2 ^ y = B. find the value of (2 ^ x + y) + (2 ^ 3x + 2Y) ⑤ Given x ^ n = 2. Y ^ n = 3, find the value of (x ^ 2Y) ^ 2n
• 4. Solve the equations 2s+3t=-1,t=4s-1 2b-4b=-1,2s+b=4 2m+3n=3m-2n=3 0.2x +0.3y=0.2 ,0.4x +0.1y=0.4
• 5. Observe the following: From 2 & # 178; × 5 & # 178; = 4 × 25 = 100, （2×5）²＝10²＝100, We can get 2 & # 178; × 5 & # 178; = (2 × 5) &# 178; From 2 & # 179; × 5 & # 179; = 8 × 125 = 1000, (2 × 5) &# 179; = 10 & # 179; = 1000, We can get 2 & # 179; × 5 & # 179; = 10 & # 179 Please write two similar formulas according to the above data characteristics. What rules do you find?
• 6. In the square BX + CZ of equation y = ax, when x = 1, y = 0. When x = - 1, y = - 2. When x = 2, y = 8. Find the value of ABC The sum of ABC three numbers is 18. Given that a is 1 more than B, and the sum of B and C is 4 more than a, then what are ABC respectively
• 7. x/2+x/6+x/12+x/20+x/30+x/42+x/56=7/8 Where x is unknown, finding x is simple
• 8. In the forest, the hound found a rabbit running 20 meters in front of him, and immediately caught up with him. The hound had a big step. It ran 5 steps, and the rabbit had to run 9 steps, but the rabbit was fast. When the hound ran 2 steps, the rabbit could run 3 steps. How far could the hound run to catch up with the hare?
• 9. In the first quadrant of the image with inverse scale function y = K / X (k > o), point m.n passes through point m as me, perpendicular to Y-axis and E, and point n as NF, perpendicular to x-axis and F. the perpendicular feet are e and f respectively
• 10. If P = | 1-2x | + | 1-3x | + | 1-4x | +. + | 1-10x |, for any allowable value of X in a certain range, is the fixed value, then the fixed value is?
• 11. If the solution of {ax + by = C, LX + my = n is {x = 2, y = 1, then the solution of {4ax + 3By = 2c, 4lx + 3My = 2n is_______ . It's OK to have a specific process, or a general process, x = 1, y = 2 / 3, but I don't understand the problem of binary linear equations. I hope you can answer it enthusiastically,
• 12. Observe the following formulas: 1 × 3 = 22-1, 3 × 5 = 42-1, 5 × 7 = 62-1 Please use the equation containing n (n is a positive integer) to express the law you found______ ．
• 13. Mathematical Olympiad problem of one variable linear equation to be solved in detail A middle school enrolled 750 students last year. This year, the number of boys increased by one sixth and the number of girls decreased by one fifth. This year, 710 students were enrolled. How many boys and girls are enrolled this year?
• 14. (percentage problem) requires detailed explanation process (does not accept ternary linear equation solution) A has two containers with different concentrations of alcohol solution are 10 liters and 20 liters respectively. Now take out the same volume of solution from two containers and pour it into each other's containers. After mixing, the concentration of alcohol solution in two containers is equal. What is the volume of solution taken out?
• 15. Mathematical Olympiad problems must be solved by linear equation of one variable The son said, "my age is nine years younger than half of my father's age." the father said, "my age is three times more than my son's age, three years older." Q: how old are my son and father You have to solve it with equations
• 16. A. B is 496 kilometers away. Car a goes from a to B at 32 kilometers an hour. Half an hour after car a leaves, car B goes from B to a at twice the speed of car A. how many hours after car B leaves, do the two cars meet? The number of watermelons from the fruit shop is twice that of the brandy melons. If you buy 40 brandy melons and 50 watermelons every day, there will be 360 watermelons left when the brandy melons are sold out in a few days. How many watermelons and brandy melons are delivered from the fruit shop?
• 17. This year, the combined age of the two sisters is 55 years old. Once upon a time, the elder sister's age was that of the younger sister this year. At that time, the elder sister's age was just twice that of the younger sister. How old are the two sisters this year?
• 18. There is a long-distance bus running at a fixed speed between city a and city B. if the speed is 6 kilometers per hour faster than the original speed, it can arrive 20 minutes earlier. If the speed is 5 kilometers per hour slower than the original speed, it will be 24 minutes late. How many kilometers is the distance between city a and city B?
• 19. Given a + B + C = 0, find the value of a (1b + 1c) + B (1c + 1a) + C (1a + 1b)
• 20. Known x1, X2, X3 , xn can only take one of - 2, 0, 1, and satisfy X1 + x2 + +xn=-17，x12+x22+… +Xn2 = 37, find x13 + x23 + +The value of xn3