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The most difficult problem in junior one mathematics.
1. given A = 200 1x+2002, B = 200 1x+2003, C = 200 1x+2004, the polynomial a * a+b * b+c-a.

2. Let A, B and C be rational numbers, then at least one of X, Y and Z has a value ().

A. greater than 0 b. equal to 0 c. not greater than 0 d. less than 0.

3. A supermarket offers the following preferential schemes: (1) There is no discount if the shopping amount does not exceed 200 yuan; (2) Enjoy a 10% discount for shopping in 200 yuan but not more than 600 yuan; (3) Anyone who shops in 600 yuan will enjoy a 20% discount. Xiao Ming's mother paid 168 yuan and 423 yuan respectively for the two purchases. If Xiaoming's mother buys goods with the same value as the last two times in the supermarket at one time, Xiaoming's mother should pay () yuan.

560.40 C.5 10.40 D.472.80

4. If both A and B are positive numbers and satisfy12345 = (11+a) (11-b), can the relationship between A and B be determined? If yes, write down the reasoning process, if not, explain the reasons.

Solution:

5. The password on the password box is a set of three digits, and the digits on each digit can be selected from 10 digits from 0 to 9. When someone randomly presses a three-digit number when unpacking, the probability of just unpacking is only _ _ _ _. If this person doesn't remember the last digit of the password correctly, then the probability that he presses the last digit of the password at will on the basis of dialing the first two digits of the password is _ _ _ _ _ _.

6. The probability of two consecutive dice being divisible by 3 ()

A.B. C. D。

7. Choose any two numbers from 0 to 9 10, and the probability that the sum of these two numbers equals 8 is _ _ _ _.

8. There are seven white balls and three black balls in a pocket. These balls are exactly the same except the color. Find the probability that two balls are black balls. When two coins are thrown on the ground, the probability of one positive and one negative is _ _ _ _ _; When three coins are thrown on the ground, the probability of a head and two tails is _ _ _ _ _; When four coins are thrown on the ground, the probability of two heads and two tails is _ _ _ _.

9. The passenger train runs between Harbin and Station A, stopping at five stations along the way, so it is necessary to arrange () different tickets between Harbin and Station A. ..

2 1 D.42

10. Xiaoming and Xiao Bin play a ball-touching game: put seven white balls and three black balls in one pocket. These balls are exactly the same except for the different colors. Everyone touches three balls. Of the three balls touched, the white ball won. Before touching the ball, choose the scheme: (1) Touch one ball at a time, write down its color, put it back and mix it evenly, and then touch the next ball. Do you think the two schemes have the same probability of winning? Which scheme do you choose?