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.
Newcomers teach seventh-grade mathematics final exam questions next semester.
(3)
Fill in the blanks
1, point b is on the y axis, above the origin, and 4 units away from the origin, then the coordinate of the point is;
2. If the arithmetic square root of a number is 8, then the cube root of this number is;
Question 4
3. As shown in the figure, BE bisects ∠ABD, CF bisects ∠ACD, and BE and CF intersect at G. If ∠ BDC = 140, ∠ BGC =10, then ∠ A.
4. As shown in the figure, ∠1= _ _ _.
As shown in Figure 7, a quadrilateral steel plate is missing a corner. According to the measurement results marked in the figure, the degree of missing A is _ _ _ _ _ _ _.
6. If the square roots of a positive number X are 2a 3 and 5 a, then A is _ _ _ _ _ _ _.
7. If x+2y+3z = 10 and 4x+3y+2z = 15, the value of x+y+z is _ _ _ _ _ _ _.
8. If 25x2 = 36, then the value of x is _ _ _ _ _ _ _.
9. It is known that AD is the midline on the BC side of ABC, AB= 15cm, AC= 10cm, so the circumference of ABD is _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _.
10. If an external angle of a triangle is equal to twice the internal angle adjacent to it and four times the internal angle not adjacent to it, then the degree of each internal angle of this triangle is _ _ _ _ _ _ _ _ _.
1 1. Given that the sum of the inner and outer angles of a polygon is * * * 2 160, the number of sides of this polygon is _ _ _ _ _ _ _.
12. Move point A down by 3 units, and then move point B( 2 units) to the right to get point B (2,5), and the coordinates of point A are.
13. It is known that every external angle of a polygon is equal, and the sum of internal angles is twice that of external angles, so every external angle of a polygon is equal to 1. Fill in the blanks (1.5 points for each question, * * 15 points).
1: A point outside the straight line is called the distance from the point to the straight line.
2. Axiom of parallel lines.
3. Conditions of parallel lines:
;
.
4. The essence of parallel lines:
;
.
The sum of the external angles of the 5:n polygon is; The sum of internal angles is.
6. An N-polygon starting from a vertex can be a diagonal line, which divides the polygon into two parts.
Triangle.
7. From one of the binary linear equations,
This method is called substitution method for short.
8. Coefficients of the same unknown quantity in two equations
This method is called addition and subtraction for short.
9: For 2x-y=3, we have a formula to indicate that y is:.
10: For four pieces of 10cm, 7cm, 5cm and 3cm, three pieces are selected to form a triangle, and the circumference of the triangle is.
Second, the solution and application
1, as shown in Figure ①, is the rest of the trapezoidal iron sheet. What are the other two corners of the trapezoid? (4 points)
2. As shown in Figure ②, a//b, c and d are cutting lines, 1=80, 5=70. What are the degrees of 2, 3 and 4 respectively? Why? (6 points)
3. In the plane rectangular coordinate system, mark the following points:
Point A is on the Y axis, above the origin, and 2 unit lengths away from the origin;
Point B is on the X axis, on the right side of the origin, and is 1 unit length away from the origin;
Point C is on the X axis and on the right side of the Y axis, and the distance between every two coordinate axes is 2 unit lengths;
Point D is on the X axis, located on the right side of the origin, and 3 unit lengths away from the origin;
Point E is located above the X axis and to the right of the Y axis, 2 unit lengths away from the X axis and 4 unit lengths away from the Y axis.
Connect these points in turn. What do you think it looks like? (8 points)
4. As shown in Figure ③, in the triangle AOB, the coordinates of point A and point B are (2,4) and (6,2) respectively. Find the area of triangle AOB (hint: the area of triangle AOB can be regarded as the area of a rectangle minus the area of some small triangles). (8 points)
5. Calculate the degree of each internal angle of regular pentagon and regular decagon. (5 points)
6. The sum of the internal angles of the polygon is equal to 1260. How many polygons does it have? (5 points)
7. As shown in Figure 4, 1 = 2, 3= 4, A= 100, find the value of x .. (6 points)
8. Solve the following equation as required (***8 points)
( 1) x+2y=9 (2) 2x-y=5
3x-2y=- 1 3x+4y=2
Three, the application of binary linear equations (7 points per question, ***35 points)
1. According to market research, the sales ratio of a disinfectant in large bottles (500g) and small bottles (250g) is 2: 5. A factory produces 22.5 tons of this disinfectant every day. How many bottles should these disinfectants be divided into large bottles and small bottles?
2. Two big harvesters and five small harvesters work for 2 hours to harvest wheat. 6 hectares, 3 big harvesters and 2 small harvesters harvest 8 hectares of wheat in 5 hours. 1 hour 1 NTU harvester and 1 small harvester harvest how many hectares of wheat?
3. The route from city A to city B is 1200km long. It takes 2 hours and 30 minutes for the plane to fly from A to B, and 3 hours and 20 minutes to fly from B to A against the wind. Find the average speed and wind speed of the plane.
4. Make tin cans with tin foil. Each tinplate can be made into 25 boxes or 40 boxes. A box body and two box bottoms form a set of boxes. At present, there are 36 sheets of iron. How many sheets are used to make the box, and how many sheets can make the box and the bottom just match?
5. It is necessary to use 30% and 75% of seed preservatives and 50% of antiperspirant to prepare 18kg preservative. How much do I need to take each of the two potions?