(Time: 120 minutes; Full score: 150)

Huian county Luocheng high school He Yukun Huang Shimin Huian further education school

First, multiple-choice questions (4 points for each small question, ***24 points)

1. The following calculation is correct ()

A. BC? =

2. The following groups of data are known: 3.6, 3.8, 4.2, 4.0, 3.8, 4.0; The following statement is true ()

A. the mode is 3.9b The range is 0.6c. The median is 3.8d. The average value is 4.0.

3. The following four figures are each composed of six identical small squares, and the one that can be folded into a cube is ().

4. Fold a circular piece of paper in half and then fold it in half to get the lower right figure, and then cut it along the dotted line in the figure to get two parts, one of which has a flat figure ().

5. A park plans to build a fountain in the shape of figure (1), but it was later suggested to change it to the shape of figure (2), with the diameter of the outer circle unchanged and the width and height of the fountain edge unchanged. How to treat the construction of fountain edge ()?

A) Figure (1) needs as much material as Figure (2). B) Figure (2) needs more material.

C. The diagram (1) requires a lot of materials. How much material is needed for drawing (1) and drawing (2) is uncertain.

6. As shown on the right, an athlete starts from the point of the semi-circular runway and advances at a constant speed along the arc AB to reach the finish line.

, with time as the independent variable, the area of the sector as a function of the image is roughly ()

Fill in the blanks (3 points for each small question, 36 points for * * *)

The reciprocal of 7 is.

8. Factorization:

9. The diameter of cold virus is 0.00000012m, which is expressed as _ _ _ _ _ _ _ m by scientific notation.

10. A supermarket bought a batch of commodities, and the purchase price of each commodity was one yuan. If it wants to make a profit of 25%, the retail price of each commodity should be set at.

1 1. In order to ensure the successful launch of Shenzhou VI manned spacecraft, the investigation method was adopted for the inspection of important components. (Fill in "general survey" or "spot check")

12. "The sun rises in the west" describes a _ _ _ _ _ _ _ event. (Fill in the blanks with "inevitable", "impossible" and "uncertain")

13. the distance from point P (-4, -7) to the x axis is.

14. If the image of inverse proportional function y= passes through the point (-1, 2), then the image of linear function y =-kx+2 must not pass through the _ _ _ _ quadrant.

15. Connect the midpoints of each side of the diamond in turn, and the quadrilateral obtained must be.

16. As shown in the figure, it is known that AB is the diameter ⊙O, D is the midpoint of chord AC, BC=6cm, then OD=.

17. As shown in the figure, the side length of each small square is 1, the center of the circle is c, and the positional relationship between the circle with radius of 3 and AB is.

A

B

C

Question 16

18. The way of stacking wood in the wood processing plant is shown as follows: According to this rule, the number of wood in the sixth pile can be obtained as follows.

Iii. Answer questions (* *10 small questions, 90 points)

19.(8 points) (π-2007) 0+(-2) 3-|-5 |.

20.(8 points) Simplify before evaluation: (,where x=. (The result is accurate to 0.0 1).

2 1.(8 points) It is known that the quadrilateral ABCD is a square, G is any point on BC (point G does not coincide with B and C), AE⊥DG is in E, and CF⊥DG is in F. 。

Verification: δ aed δ DFC

22.(8 points) In order to study the extracurricular activities of students in a middle school, the Youth League Committee conducted a survey of several students' hobbies from four aspects, such as reading, sports, entertainment and others, and drew the following two incomplete statistical charts according to the survey results (as shown in figure 1, figure 2). Please answer the following questions according to the information provided in the chart:

(1) How many students did Yi * * investigate in this study?

(2) What is the central angle of "others" in the pie chart?

(3) Complete the line chart of frequency distribution.

23.(8 points) In order to solve the problem of shading between buildings, a certain area stipulates that the room spacing between two buildings should be at least 40 meters, and shading is not allowed at noon 12. As shown in the figure, the window sill on the first floor of the old building is 1 m, and a new building will be built 40 meters south of this building. It is known that the sun shines from the south at noon 12 in winter in this area. (The result retains two significant figures)

24.(8 points) If Xiao Qiang invites you to play a game of tossing two coins, the rules of the game are as follows:

Throw two heads and you win 1 point; Throwing other achievements, Xiao Qiang got 1 point; Whoever reaches 10 first wins.

Please answer the following questions:

(1) Are the rules of the game fair to you? Please use the tree diagram to analyze all possible results;

If it is unfair, please modify the rules of the game to make it a fair game.

25.(8 points) As shown in the figure, in the grid paper (the side length of each small square is 1), we call the vertex of each small square a grid, and the graph with the grid as the vertex is called a grid diagram. The ABC in the figure is called lattice △ABC.

(1) If the coordinates of point A and point D are (1, 1) and (0,-1) respectively, please establish a plane rectangular coordinate system in the grid paper and directly write out the coordinates of point B and point C;

(2) According to your knowledge of translation, rotation or axial symmetry, please explain how the "quadrilateral pattern of lattice" in the drawing is obtained through the transformation of "ABC pattern of lattice".

26.(8 points) A residential district plans to purchase and plant 500 saplings, and a sapling company provides the following information:

Data 1: There are three kinds of poplars, lilacs and willows, and the number of poplars and lilacs is required to be equal.

Information 2: As shown in the following table: Suppose the poplar and willow purchased are X and Y plants respectively.

Young poplar lilac willow

Wholesale price of each seedling (yuan) 3 2 3

After two years, the air purification index of each tree seedling was 0.40. 10.2.

(1) is represented by the algebraic expression contained;

(2) If the total cost of purchasing these three kinds of saplings is W yuan, the sum of air purification indexes of these 500 saplings in this community after two years should not be less than 120, and try to find the range of W. 。

27.( 13 points) As shown in the figure, in an isosceles trapezoid, the hypotenuse of an isosceles right triangle coincides with the point, and in a straight line, the isosceles trapezoid remains motionless, and the isosceles right triangle will move to the right at the speed along the straight line until the point coincides with the point.

(1) The shape of the overlapping part of isosceles right triangle and isosceles trapezoid changes constantly during the whole moving process;

(2) Let the area of the overlapping part between the isosceles right triangle and the isosceles trapezoid be the function of sum when the isosceles right triangle moves;

(3) When ① and ② x = 8 (s), find the overlapping area of isosceles right triangle and isosceles trapezoid.

28.( 13 point) As shown in the figure, in the rectangular coordinate system, a circle with a point as the center and a point as the radius intersects the axis at this point, and intersects the axis at this point.

(1) If the parabola passes through two points, find the analytical expression of the parabola and judge whether the point is on the parabola;

(2) Find a point on the parabola symmetry axis in (1) to minimize its circumference;

(3) Let it be a point on the axis of symmetry of the parabola in (1), and whether there is such a point on the parabola that the quadrilateral is a parallelogram. If yes, find out the coordinates of the point; If it does not exist, explain why.

(Revised by the Mathematics Group of Quanzhou Institute of Education)

Reference answer to junior high school mathematics comprehensive exercise (1)

First, multiple-choice questions: 1. d，2。 b，3。 c，4。 c，5。 a，6.c。

Second, fill in the blanks:

7.-2，8.x (x+3) (x-3)，9. 1.2× 10-7， 10。 1.25a， 1 1。 Census,

13.7,14.4,15. Rectangular, 16. 3, 17. Intersection, 18. 28.

Third, answer questions:

19.- 12.

20. Melting tank = 3x+6, and the evaluation material is 10.24.

2 1.AD=DC，∠AED=∠DFC=90？ ,

It is proved again that ∠EAD=∠FDC, ∴ΔAED Δ DFC (AAS).

22.( 1) 100 (2) (3) as shown in the right.

23. Make CE⊥BD after E point C,

You can get, DB ≈ m

In other words, the maximum height of the building is about 100 meter.

24.( 1) Because P (positive, positive) =, the game is unfair (the tree is abbreviated).

(2) changed to: I throw two faces with the same face to win 1 point; Xiao Qiang wins by throwing two different faces 1 point; Whoever arrives first 10 wins. This is fair.

25.( 1)B(- 1，- 1)，C(3，- 1)

(2) Move ABC to the right by 10 units, then move it up by 5 units, and then rotate it clockwise with P (1 1, 4) as the rotation center 1800.

26. Solution: (1) y = 500-2x

(2) From 200 ≤ 250

∵w=3x+2x+3y=5x+3(500-2x)= 1500-x,∴ 1250≤w≤ 1300

27.( 1) isosceles right triangle; isosceles trapezoid

(2) can be divided into the following two situations:

① ②

① When in use, the shape of the overlapping part is an isosceles right triangle (Figure ①).

At this point, if the intersection is made at the point, it will be divided equally.

Ann, ∴ y = s delta ane =? EH= x？ x= x2

② When in use, the shape of the overlapping part is isosceles trapezoid (Figure ②).

At this point, you can get.

Excessive, excessive,

Then,

.

(3)① Timely.

② When =8(s), y = 3x-9 = 3x8-9 = 15.

28( 1) inches, first served.

The coordinates of are the other two points on the parabola,

The analytical formula of parabola can be obtained as follows:

When the point is on a parabola

(2) First, the equation of parabola symmetry axis is as follows

There are points on the axis of symmetry of parabola to minimize the perimeter of parabola.

The length of is a constant value, so we only need to minimize the perimeter.

Link, then the intersection with the axis of symmetry is the point that minimizes the perimeter.

The analytical formula of a straight line can be obtained as follows

The coordinates of the dead center are

(3) Existence, set as a point on the parabola symmetry axis. On the parabola, if the quadrilateral is a parallelogram, then the point is on the left side of the symmetry axis.

Then, a straight line passing through this point intersects the parabola at this point.

Therefore,

So there is a point on the parabola, which makes the quadrilateral a parallelogram.

If you need pictures, please let me know and send you attachments.