The reciprocal of 1 is ()

A, B, C, D,

2, the following calculation is correct ()

A, B, C, D,

3. The top view of the geometric figure as shown in the figure is ().

4. The graphics in the following grids are translated from some of their graphics, which is ().

5. It is known that the two solutions of the unary quadratic equation are exactly the base length and waist length of isosceles △ABC, so the circumference of △ABC is () [Source: Z]. xx .k.Com]

A, 13b, 1 1 or 13c, 1 1 D, 12.

6. There are three opaque cards with numbers 3 and 4 on the front respectively. Everything is the same except the numbers. Now, after washing, put their backs up and take them from

If you choose a card (don't put it back) and then choose a card from the remaining cards, the probability that the product of the numbers on two cards is a positive even number is () [Source: Z.xx.k.Com].

A, B, C, D,

7. As shown in the figure, in the right angle △ABC, ∠ BAC = 90 AB = 8, AC = 6°, and DE is the middle vertical line of AB side.

If the vertical foot is D, the intersection BC is at point E, and AE is connected, then the circumference of △ACE is ().

a、 16 B、 15 C、 14 D、 13

8. With the improvement of living standards, Kobayashi's family bought a private car. It took him 15 minutes less to go to school by private car than by bus. Now we know that Xiaolin's home is 8 kilometers away from school, and the average speed of taking a private car is 2.5 times that of taking a bus. If the average speed of taking a bus is x kilometers per hour, the equation can be listed as () according to the meaning of the question.

A, B,

C, D,

9. In diamond ABCD, diagonal AC and BD intersect at point O, AB=5, AC=6, and cross point D..

If the parallel lines of AC intersect the extension lines of BC at point E, the area of △BDE is ()

a、2 2 B、24

Day 48

10, as shown in the figure, it is known that point A is on the image of inverse proportional function y=, and point B is on inverse proportional function.

On the image numbered y= (k≠0), the AB∨X axis passes through point A and point B and works on the X axis respectively.

The vertical line and vertical foot are c and d respectively. If OC= OD, the value of k is ().

a、 10 B、 12

c、 14 D、 16

II. Fill in the blanks (3 points for each question, ***24 points)

1 1, 1 nm = m, the diameter of a particle is 158 nm, and the diameter of a particle _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ m scientific notation.

12, factorization factor _ _ _ _ _ _ _.

13, in a set of data, 1, 2, 2, 3, 4, the mode is _ _ _ _ _ _ _.

14. As shown in the figure, a sector with a radius of 4cm and an arc length of 6πcm is used to enclose the side of a cone.

Then the height of the cone is _ _ _ _ _ _ cm.

15. In an opaque bag, there are six red balls and several green balls. If you put five white balls in this bag (all the balls in the bag are the same except the color) and shake them well, you can find a ball. The probability of touching the red ball is just right, so there are _ _ _ _ _ _ green balls in this bag.

16 as shown in the figure, in □ABCD, the bisector of ∠ABC intersects the edge of AD at point E,

Diagonal AC is at point F. If it is, then _ _ _ _ _.

17 As shown in the figure, in the rectangular ABCD, point P and point Q are the midpoint of the AD side and BC side respectively.

Fold the rectangle ABCD along the straight line passing through point C, so that point B falls on the point on line PQ.

At F, the crease intersects AB at E point and PQ at G point. If BC is 3,

The length of the line segment FG is _ _ _ _ _ _ _.

18, as shown in the figure below, is a set of regular patterns consisting of diamonds and rectangles. 1 The area of the diamond in the graph is S(S is a constant), and the shadow part in the second graph is generated by connecting the midpoint of the diamond and then the midpoint of the rectangle, and so on ... Then the area of the shadow part in the nth graph can be expressed by an algebraic expression containing n (n≥2, n is a positive integer).

Three. Solve the problem (19,10,20, 12, ***22)

19, simplify first and then evaluate:, where.

20. As shown in the figure, △ABC is a schematic diagram of a triangular green space near Xiaojin's home. In order to strengthen his physique, he runs along the three paths AB, BC and CA around the green area every morning (regardless of the width of the path). It is observed that point B is 30 southeast of point A, point C is 60 southeast of point A and point B is 75 northwest of point C, and the distance between them is AC.

(Reference data:)

Iv. Answer (No.265438 +0 12, No.22 12, ***24)

2 1. In order to better enliven the campus cultural life, a middle school plans to revise its own "brilliant" school newspaper. Firstly, a group of students are randomly selected from the whole school to conduct a questionnaire survey, and the topic is "Which section of the school newspaper do you like best" (each student can only choose one). After collecting and sorting out the questionnaire, an incomplete frequency distribution table and fan-shaped statistical chart are drawn below.

(1) Fill in the blank: In the frequency distribution table, a=_______, and b = _ _ _ _ _ _ _.

(2) The degree of the central angle of the "natural exploration" plate in the sector statistical chart is _ _ _ _ _ _ _;

(3) Which section is the most popular among the students who participated in this questionnaire survey? How many people like it?

(4) If the whole school has 1500 students, how many people like the "Campus News" section?

[Source: Xue. Part. Net]

22. A shop buys two kinds of scooters, A and B, which costs 13000 yuan. The number of cars purchased by A is not less than twice that of B, but not more than three times that of B. Now I know that the price of each A car is within 200 yuan and the price of each B car is within 400 yuan, and I have set up a shop to buy X B cars.

(1) What kinds of car purchase schemes are there in the store?

(2) If the store sells all scooters of model A and model B, each selling model A earns a profit, and each selling model B earns a profit. Write down the functional relationship between the total profit y (yuan) of selling these two scooters and the number x (cars) purchased by the store? And find out how many B-cars in the store will get the most profit.

V. Solving problems (full score 12)

23. As shown in the figure, in △ABC, point D is a point on the side of AC, with AD= 10 and DC=8. O with the diameter AD is tangent to the side BC at point e, and AB=BE.

(1) Verification: AB is the tangent of ⊙O;

(2) Make DF∨BC⊙O intersect with point F at point D, and find the length of line DF.

Six, solve the problem ((out 12))

24. A factory produces a brand of eye protection lamps, which are divided into 15 grades according to quality (the higher the grade, the better the quality of the lamps. Second-class products are better than first-class products.

Products). If you sell these eye protection lamps, each first-class product can earn a profit of 2 1 yuan, and each upgrade can earn an extra profit of 1 yuan. The factory can only produce eye protection lamps of the same grade every day, and the number of units produced per grade every day is shown in the following table:

Grade (X) 1 grade, grade 2, grade 3 …

Output (y unit/day) 78 76 74 …

(1) It is known that the daily output y (sets) of eye protection lamps is a linear function of X level. Please write the functional relationship between y and x directly: _ _ _ _ _ _ _;

(2) If the factory sells all the eye protection lamps produced that day, which grade of eye protection lamps should the factory produce in order to get the maximum profit? What is the maximum profit?

Seven, solve the problem (full score 12)

25. It is known that in △ABC, AB=AC. The straight line A passing through point A rotates clockwise around point A from the position coincident with the AC side, and the straight line A and BC intersect at point P (point P is not coincident with point B and point C). The edge MN of △BMN is always on the straight line A (point M is above point N), and BM=BN connects CN.

(1) When ∠ BAC = ∠ MBN = 90,

(1) as shown in Figure A, when = 45, the degree of ∠ANC is _ _ _ _ _ _ _ _;

② As shown in Figure B, does the conclusion in ① change when ≠ 45? Explain the reasons; [Source: Subject Network ZXXK]

(2) As shown in Figure C, when ∠BAC = ∠ MBN ≠ 90, please write the quantitative relationship between ∠ANC and ∠BAC directly without proof.

Eight, solve the problem (full score 14)

26, as shown in the figure, known parabola y=ax? +bx+3 passes through point b (-1, 0) and point c (3,0) and the y axis intersect at point a, and the line segment OB is rotated 90 degrees clockwise around point o, the point corresponding to point b is point m, and the straight line passing through point a intersects with the x axis at point d (4,0). The top and bottom EF of the right-angled trapezoid EFGH coincide with the line segment CD of. The right-angled trapezoid EFGH starts from point D and moves at a constant speed along the direction of ray DA, with the speed of 1 length unit/second. During the exercise, the waist FG and the straight line AD always coincide, and the exercise time is assumed to be t seconds.

(1) Find the analytical expression of this parabola;

(2) When t is what value, the quadrilateral with M, O, H and E as vertices is a special parallelogram;

(3) Let point A be the symmetrical point A' about the parabola symmetry axis, and the straight line HG intersects the symmetry axis at point K. When t is what value, the quadrilateral with vertices A, A', G and K is a parallelogram. Please write the qualified t value directly.