2. The circumference of a rectangle is 100cm, and the diagonal length is x. Try to express the area of a rectangle as a function of X. ..
Xiaoming and Xiaoli play games together. Xiao Ming said that if he lost a game, he would give Xiaoli two pieces of candy; Xiaoli said that if she lost a game, she would give Xiaoming three pieces of candy. It is stipulated that every game must be lost and won. After 30 games, Xiao Ming has as much sugar in his hand as at the beginning of the game. How many games did Xiaoming win?
4. Continue according to the law of "AABBBCCCCAABBBCCCC". What is the 2003rd letter?
5. Throw three one-dollar coins at the same time. If at least one coin is up, what is the probability that at least one coin is up?
6. There are 20 white balls and 30 black balls in a bag. Just grab four balls and don't put them back. What is the probability that 1 white ball, 1 black ball, 1 black ball and 1 white ball will win in turn?
7. The square difference between two consecutive odd numbers is 128. Find the product of these two odd numbers.
8. A positive integer with three digits is exactly 32 times the sum of its digits. Find this number.
9. If the radius of a circle is increased by 2 cm, its area will be doubled. Find the radius of this circle.
10. Compare the sizes of 23000 and 32000 without a calculator or computer.
1 1.s and t are two sets. S has two more elements than T, and set S has 96 more subsets than set T. Find the number of elements in set S.
12. A math club with 25 members will form a delegation to attend the meeting of the school student union. Every member of the club can be a member of the delegation, but the delegation must have at least 1 person. There are several ways to form a delegation.
13. Five consecutive integers form a set, and the sum of squares of three small integers is equal to the sum of squares of the other two large integers. Find the set of all possible values of these five integers.
14: Li Bai is walking in the street, carrying a pot to buy wine.
Double it when you meet a store, and have a drink when you see flowers.
I met shops and flowers three times and drank all the wine in the pot.
How much wine is there in the hip flask?
Can you establish an equation to find out how many barrels there are in the hip flask?
15: There is a strange island where there are two kinds of people, those who tell the truth and those who lie. Every word of a truthful person is true, and every word of a liar is a lie.
One day, when Wang Daming visited the island, he met three residents, A, B and C, and asked them curiously whether they were liars or honest people.
A said, "Both B and C are liars."
B said, "I never lie."
C said, "B is a liar."
Wang Daming thought about it, and then he found that some of the three people in his dream were lying, you know?
Mr. Huang, Mr. Lan and Mr. Bai have lunch together. One is wearing a yellow tie, one is wearing a blue tie, and the other is wearing a white collar.
"Have you noticed," said the gentleman in the blue tie, "that although the color of our tie happens to be the surname of three of us, none of us has the same color as his own surname?"
"ah! You are absolutely right! " Mr. Huang sighed. Excuse me, what color are the ties of these three gentlemen?
17: Xiaoming and Zhang are both students. Teacher Zhang's birthday is the n day of M month. Both of them know that Teacher Zhang's birthday is one of the following 10 groups. Teacher Zhang tells Xiao Ming the value of m and Xiao Yong the value of n. Teacher Zhang asked them if they knew when his birthday was.
March 4th March 5th March 8th June 4th June 7th.
September1September 5th 65438+February1February 2nd 65438+February 8th.
Xiao Ming said: If I don't know, Xiao Yong certainly doesn't know.
Xiao Yong said: I didn't know at first, but now I know.
Xiao Ming said: Oh, I know that, too.
Please infer when teacher Zhang's birthday is from the above conversation.
Answers and analysis:
1.0.02
Solution: Let this number be X and move the decimal point to the right by 4 digits, which is equivalent to expanding this number to 10000 times. Therefore,
3. 12 game
Solution: Suppose Xiaoming wins X games. Because every game has to be decided, Xiaoli won 30-x games, Xiaoming got 3 sweets and Xiaoli got 2 (30-X) sweets. Xiao Li got 2 (30-x) pieces of sugar from Xiao Ming, which means Xiao Ming had 2 (30-x) pieces of sugar at first, so.
3x=2(30 times)
X= 12 (field)
4.B
Solution: There are 9 letters in AABBB CCCCC. The serial number of the last C in AABBB CCCCC arranged according to this rule must be 9, 18, 27, 36 and so on.
Since 2003 =9×222+5,
So the 2003rd letter is the 5th letter B in "AABBBCCCC".
5. Solution: When you throw three one-dollar coins at the same time, there are eight possible situations. In one case, the tails of three coins are facing up at the same time, which is irrelevant. In the other seven cases, * * * has six cases, because at least one coin is facing up, excluding the case where three coins are facing up at the same time. Therefore, if three one-dollar coins are thrown at the same time, if at least one coin is upside down, then the probability of at least two tails facing up is 3/4.
6. It is approximately equal to 0.0598.
7. 1023
Solution: Let these two consecutive odd numbers be x and x+2 respectively. According to the meaning of the question, we can get.
128=(x+2)2—x2，
x=3 1，x+2=33，
3 1×33= 1023。
8.576
Solution: let this three-digit number be n, and the sum of the digits on each digit is s. According to the meaning of the question, you can get.
N=32S .
Because the difference between a number and the sum of its numbers is a multiple of 9, and
3 1S=32S-S，
So 3 1S is a multiple of 9, so S is a multiple of 9. Therefore, n must be a multiple of 32× 9 = 288. Since 4× 288 = 1 152, n may be equal to 288, 576 and 864, and the sum of the three possible situations is 18. therefore
N=32× 18=576 .
10.23000 8 1000，
So 23 thousand < 32 thousand.
1 1 .7
Solution: Let set S have n elements, then set T has n-2 elements, so set S has 2n subsets and set T has 2n-2 subsets. According to the meaning of the question, you must
96 = 2n-2n-2 = 2n-2(4- 1)= 2n-2×3，
2n-2=32，
n=7 .
12. 1∶3
13.3355443 1
Solution: There are 225 possibilities to form a delegation with 25 club members, which may include the case that the delegation has no members.
14. Solution: Suppose there is X fighting wine, then,
2[2(2X- 1)- 1]- 1 = 0
The solution is X=7/8 (barrel)
15 solution:
1. If A is telling the truth, then B and C are liars, and C is telling the truth. So what A said is a lie.
2.A tells a lie, and then B and C are the people who tell the truth, but the result is that B tells the truth and C tells the lie.
So A tells a lie, B tells the truth, and C tells a lie.
16. Solution: Mr. Huang wears a white-collar belt.
Mr. Bai is wearing a blue tie.
Mr. Lan is wearing a yellow tie.
Mr Huang Can doesn't want to wear a yellow tie, because then his tie will be the same color as his last name. He can't wear a blue tie either, because this color tie has been put on by the gentleman who asked him questions. So Mr. Huang must be wearing a white collar.
In this way, the remaining blue tie and yellow tie were tied by Mr. Bai and Mr. Lan respectively.
16. The answer is September 1.