Junior one mathematics

(The whole volume has 3 big questions ***28 small questions; Full score 100, examination time 100 minutes).

The total score of the topic is one two three four five.

score

I. Multiple-choice questions (3 points for each question, 10 ***30 points)

1. Given that the distance from point P on the Y axis to the origin is 5, the coordinate of point P is ().

A. (5,0 0) B. (0 0,5) or (0,5)

C. (0,5 5) D. (5 5,0) or (5,0)

2. A beautiful pattern consists of four equilateral regular polygons at a certain vertex, three of which are regular triangles, regular quadrangles and regular hexagons, and the other is ().

A. regular triangle B. regular quadrangle C. regular pentagon D. regular hexagon

3. As shown in the figure, fold the rectangular piece of paper along EF, where D and C are respectively located. If ∠ EFB = 65, ∠AE is equal to ().

50 years later.

4. Given that the solution of a binary linear equation group is, then this equation group is ()

A.B. C. D。

5. If the solution set of inequality is, the value of is ().

A.4 B.2 C. D

6. Xiaolong and Xiaogang are playing pinball. Xiaolong said to Xiaogang, "Give me half of your beads, and I will have 10". Xiao Gang said, "Give me yours and I will 10". If Xiaogang and Xiaolong have the same number of marbles, they are listed.

A.B. C. D。

6. If the solution of the equation is negative, the value range of is ().

A, b, c, d, no solution

7. The following survey work need to adopt the census method is ().

A. Investigation of water pollution in a section of Huaihe River by environmental protection department B. Investigation of ratings of a TV program being broadcast by TV stations.

C. Investigation on the service life of batteries produced by various manufacturers by quality inspection departments D. Investigation on the scale of enterprises before making work clothes for employees.

9. Tongwen folded a rectangular chess piece twice, as shown in the figure: A and B both fell on DA/, and the crease was DE.

DF, then the degree of ∠EDF is ()

a60 b . 75 c . 90d . 120

10. As shown in the figure, there are five semicircles. The diameters of the four small circles are just on the diameter of the big circle, and the sum of the diameters is equal to the diameter of the big circle. Two bugs start from point A at the same time and climb to point B at the same speed. The beetle moves along the circle of the big circle, and the B bug crawls along the arc of the other four small circles. Then the following conclusion is correct ().

A, A arrives at point B first, B arrives at point B first, C arrives at point B first, and A and B arrive at point B at the same time, which is uncertain.

Fill in the blanks (2 points for each question, 8 questions *** 16 points)

1 1. As shown in the figure, the coordinates of points covered by small hands may be (write only one).

12. As shown in the figure, put the right vertex of the triangle on one side of the ruler, ∠ 1 = 300, ∠ 2 = 500, ∠ 3 = 0.

13. As shown in the figure, after a window is opened, it can be fixed with window hook BC. The geometric principle used here is _ _ _ _ _ _ _ _ _ _ _.

14. It is known that A and B are reciprocal, and then.

15. As shown in the figure, the solution set of inequality is.

16. If the outer angle of a regular polygon is equal to its adjacent inner angle, then it is a polygon.

17.

18. As shown in the figure, from left to right, each small cell is filled with an integer, so that any three adjacent cells are

If the sum of all integers is equal, it can be found that c is equal to 3, then the number in the 2009th cell is.

Three. Problem solving (19, 20, 23, 5 points each, 2 1 6 points, 22 questions, 3 points, * * * 24 points).

19.20.

What is the value of 2 1.a? The values of the solutions x and y of the equation are reciprocal. Find their values.

22. The student union of a school is going to investigate the extracurricular exercise time of the seventh-grade students in the school every day (except for class exercise).

(1) When determining the survey method, classmate A said, "I'll go to 1 class to survey all my classmates"; Student b said, "I went to the stadium to ask my classmates who participated in the exercise"; Student C said, "I went to every class in grade seven of the whole school to randomly investigate a certain number of students." What do you think is the most reasonable investigation method (fill in "a" or "b" or "c");

(2) They collected data by the most reasonable investigation method, and drew a bar chart as shown in figure 1 and a fan chart as shown in figure 2. Please complete these two charts.

(3) If there are 65,438+0,200 students in the seventh grade of our school, please estimate the number of them who exercise less than 20 minutes after class every day (except in class) and make suggestions to the students' union according to the investigation.

23. As the picture shows, there is a beautiful and lovely little goldfish in the square.

(1) If the side length of the square is 1, calculate the area of the small fish.

(2) The small fish moves 3 squares to the left and draws a figure (the steps and processes of drawing are not required).

Iv. Answer questions (5 points for questions 24-25, 6 points for questions 26, *** 16)

24.

25. As shown in the figure, fold the paper △ABC along DE, and the point A falls on the point P. It is known that ∠ 1+∠ 2 = 124, and find the degree of ∠ A. 。

26. In a promotion, a store stipulated that consumers could get a discount when they spent all their money in 200 yuan. A classmate bought a prize for the class and was going to buy six photo albums and some pens. Given each album 15 yuan and each pen 8 yuan, how many can he buy at least to get a discount?

Verb (abbreviation of verb) solving problems (7 points for each question, *** 14 points)

27. In order to attract more tourists during the May Day holiday, a scenic spot launched a group ticket purchase discount fare activity. Ticket prices are as follows:

No more than 30 people, no more than 30 people, but no more than 50 people, no more than 50 people

The ticket price is 2 yuan 1.5 yuan 1 yuan per person.

A total of 60 people from two tour groups A and B of the same travel agency (group A has more people than group B) are going to travel to this scenic spot. If Group A and Group B buy tickets separately, then one group has to pay 98 yuan.

(1) If two groups buy tickets jointly, how much will they save compared with buying tickets separately?

(2) How many people are there in each group?

(3) If there are 12 people in Group A who can't travel for some reason, how can the travel agency buy tickets to save the most money?

28. As shown in figure 1, line segment AB and CD intersect at point O, connecting AD and CB. We call the figure with the shape of 1 the "8" shape. As shown in figure 2, under the condition of figure 1, the bisectors AP and CP of ∠DAB and ∠BCD intersect at point P, while

(1) In the figure 1, please directly write the quantitative relationship between ∠A, ∠B, ∠C and ∠D:;

(2) Look carefully, the number of "8" in Figure 2 is:

(3) In Figure 2, if ∠ d = 400 and ∠ b = 360, try to find ∠P times;

(4) If ∠D and ∠B are arbitrary angles in Figure 2, and other conditions remain unchanged, what is the quantitative relationship between ∠P and ∠D and ∠B? (Just write a conclusion directly)