1. There are two roads from A to B, four roads from B to C, three roads from A to C without B, and three different roads from A to C. 。
2. There are three, five and two "three good students" in Class A, Class B and Class C respectively. Now we have to choose two "miyoshi students" from different classes to attend the "miyoshi student congress". * * * There are different selection methods.
3. Choose two students from A, B and C to participate in the activities on a certain day, one of them will participate in the activities in the morning and the other will participate in the activities in the afternoon. There are different ways to choose.
4. Take out three letters at a time from the four letters A, B, C and D and arrange them in a row. * * * There are different arrangements.
5. If four of the six volunteers are selected to engage in four different jobs: translation, tour guide, shopping guide and cleaning, three will be selected.
6. There are five railway stations, A, B, C, D and E * * *, all of which have shuttle buses. I need to prepare an inter-station train ticket.
7. There are 14 teams participating in the national football league in a certain year, and each team has to play a game with the other team at home and away.
8. Numbers 1, 2, 3, 4, 5, 6 can form a positive integer, and there are no duplicate numbers.
9. The number of10 can form a three-digit number from 0 to 9, and there is no duplicate sign.
10.( 1) There are five different books, and three books are selected for three students, each 1. * * * There are different selection methods;
(2) There are five different books, so buy three books for three students, each 1 book.
1 1. It is planned to exhibit 10 different paintings, including watercolor painting 1 painting, 4 oil paintings and 5 Chinese paintings, which are displayed in a row, requiring that the paintings of the same variety must be connected together, so there are different display methods.
12.( 1) continuous arrangement 18 people, with few different arrangements;
(2) Arrange 18 people in two rows, with 9 people in each row, with different arrangement methods;
(3) Arrange 18 people into three rows with 6 people in each row.
13.5 people stand in a row, (1) where A and B must be adjacent and have different arrangements;
(2) A and B cannot be adjacent, so they have different arrangements;
(3) Where A does not stand at the head and B does not stand at the tail, there are different arrangements.
14.5 students and 1 teacher took a group photo. Teachers can't stand at the front or the back. * * * The way to stand is different.
15. Four students and three teachers lined up to take pictures. Teachers can't line up at both ends. Teachers must line up together in different ways.
16. There are 7 parking spaces in the parking lot, and now there are 4 cars to park. If you want to connect three parking spaces, there are several parking methods.
17.7 athletes choose 4 relay teams to participate in the 4× 100 meter race, so there are several arrangements for A and B not to run the middle two bars.
18. A pocket contains 7 white balls and 1 black balls of the same size. (1) Take out three balls from your pocket. * * * There are ways;
(2) Take three balls out of the pocket to make them contain 1 black ball, and take them properly;
(3) Take three balls out of your pocket and make them free of black balls.
19. Four football teams, A, B, C and D, played a round robin match:
(1) * * needs an arena;
(2) There may be champions and runners-up.
20. According to the following conditions, five people are selected from 12, with different methods.
(1) A, B and C must be selected;
(2) Party A, Party B and Party C cannot be elected;
(3) A must be selected, but B and C cannot be selected;
(4) Only one of Party A, Party B and Party C was elected;
(5) A, B and C, with a maximum of two people;
(6) Party A, Party B and Party C were elected at least 1;
2 1. A song and dance troupe has seven actors, three of whom can sing, two can dance, and two can both sing and dance. Now we will choose two of the seven actors, one singing and the other dancing, and go to the countryside to perform.
22. Three boys and two girls were selected from six boys and m-girls to undertake five jobs, A, B, C, D and E, respectively, with different distribution methods.
Mathematics examination papers and answers
I. Multiple-choice questions (this is a small question entitled *** 10, with 4 points for each small question, out of 40 points)
1, the following operation is correct ()
A.4 = 2 B.2-3=-6 C.x2？ x3=x6 D.(-2x)4= 16x4
2. With the improvement of China's comprehensive national strength, the number of people learning Chinese in the world has been increasing in recent years. It is reported that in 2006, the number of students studying Chinese overseas has reached 38.2 million, which is expressed as () by scientific notation, and three significant figures are reserved.
a . 0.382× 10 b . 3.82× 10 c . 38.2× 10d . 382× 10
3. The top view of the regular quadrangle as shown in the figure is ()
4. There is a cross-border activity at the New Year's Day Garden Party: five cards of isosceles trapezoid, parallelogram, isosceles triangle, circle and diamond are randomly placed, and one card is randomly opened with the graphic face down. If the opened graph is axisymmetric and can cross the boundary, then the probability of crossing the boundary at one time is ().
A.B. C. D。
5. As shown in the figure, the diameter CD⊙O passes through the midpoint G of the chord EF, and ∠ EOD = 44.
Then ∠DCF is equal to ()
A.22 B.44 C.46 D.88
6. Three students, A, B and C, took part in the kite competition. The length of the kite line and the angle between the line and the ground are shown in the following table (assuming that the kite line is straight, ignoring the height of the three students), then the kite flown by the three students is ().
Classmates A, B and C
The length of the kite string is 100 m, 100m90m90m.
The angle between this line and the ground is 40 45 60.
A is the highest, B is the highest, C is the lowest, and D and C are the lowest.
7. The state implements the policy of "two exemptions and one subsidy" for students who receive nine-year compulsory education. The table below shows our city.
Part of the situation that a middle school country provides textbook subsidies free of charge.
A total of 789 people
Free subsidy amount per person (RMB) 1 10 90 50
Number of people (persons)
Total free subsidy (RMB) 4,000-26,200 yuan.
If you want to know the data in the blank, let the number of students in grade seven be x and the number of students in grade eight be y,
According to the meaning of the question, the equation is listed as ()
A.b.
C.d。
8. Six equal circles are placed in three forms: A, B and C, so that two adjacent circles are circumscribed, and
As shown in the figure, the connecting lines form a regular hexagon, a parallelogram and a regular triangle respectively, and the center of the circle is
The sum of the areas of the six sectors (shaded parts) on the outside of the connection line is recorded as S, P and Q in turn, and then ().
1 1, factorization: =
12, as shown in the figure, △OP A, △ app a are isosceles right triangles, points p and p are on the image of function y=, and hypotenuse OA and A A are on the horizontal axis, so the coordinate of point a is _ _ _ _ _ _ _ _ _.
13, as shown in the figure, the shaded part is the trademark pattern of a commodity. It is known that the side length of the diamond ABCD is 4 ㎝, ∠ a = 60, the arc BD is the arc with the center and the radius b, and the arc CD is the arc with the center and the radius b, then the area of the trademark pattern is _ _ _ _ _ _ _ _ _.
1 4,65438+10/in 2007, a city has fully implemented rural cooperative medical care, and farmers only take it every year.
Pay 10 yuan to enjoy cooperative medical care. The reimbursement methods for hospitalization expenses are as follows:
Proportion of reimbursement for hospitalization expenses (yuan) (%)
Part not exceeding 3000 yuan 15
3000-4000 Part 25
4000-5000 Part 30
5000- 10000 Part 35
Part 40 of 10000-20000
Part of more than 20,000 45
If someone reimburses 880 yuan's hospitalization expenses, then the hospitalization expenses will be _ _ _ _ _ _ _ _ _ yuan.
Three. (There are ***2 small questions in this question, with 8 points for each small question, with a full score of 16).