First, choose carefully: this big question is ***8 small questions, with 4 points for each small question and 32 points for * * *.

The reciprocal of 1 Yes ()

A. 20 BC11d.

2. Which of the following operations is correct ()

A.B. C. D。

3. It is known that the point p () is in the first quadrant of the plane rectangular coordinate system, so the value range of a can be expressed as () on the number axis.

4. In the parallelogram, equilateral triangle, rhombus, isosceles trapezoid, which is both an axisymmetric figure and a centrally symmetric figure is ().

A. parallelogram B. equilateral triangle C. diamond D. isosceles trapezoid

5. A parabola can be regarded as a parabola obtained by the following transformation ().

A. translate 5 units up. B. translate 5 units down. C. translate 5 units left. D. translate 5 units right.

6. As shown in the figure, a geometric figure has three views, so the shape of the geometric figure is ().

A. cuboid B. triangular prism C. cone D. cube

7. The two sides of an isosceles triangle are 3 and 6 respectively, so its circumference is ().

A.15b.12c.12 or 15D. Not sure.

8. As shown in the figure, in the rectangular ABCD, point E is on the side of AB, and the rectangular ABCD is folded along CE, so that point B falls on point F on the side of AD. If AB=4 and BC=5, the value of tan∠AFE is ().

A.B. C. D。

Second, fill in carefully: this topic is entitled ***8 small questions, with 4 points for each small question and 32 points for * * *)

9. There are 86,400 seconds in a day, which is expressed as _ _ _ _ _ _ _ seconds by scientific notation;

10. The average value of the data is 1, so the median value of this set of data is _ _ _ _ _ _ _.

The radius of 1 1 ⊙ and ⊙ are 3㎝ and 4㎝ respectively. If ⊙ and ⊙ are circumscribed, the center distance is = _ _ _ _ _ _ cm.

12. If the outer angle of a regular polygon is equal to 40, then the polygon is _ _ _ _ _ _ _ _.

13. There are 6 black chess and 1 white chess in the Go box. Just take out a piece. If the probability that it is black is 0, then A = _ _ _ _ _ _ _

14. As shown in the figure, line segments AB and DC respectively represent the heights of two buildings A and B, AB⊥BC and DC⊥BC, and the distance between the two buildings is 30m. If the height of building A is AB = 28m, and the elevation of point D measured at point A is α = 45, then the height of building B is DC = _ _ _.

15. As shown in the figure, a beam of light starts from point A (3,3) and passes through point B (1 0) after being reflected by point C on the Y axis, so the path length of light from point A to point B is _ _ _ _ _ _ _ _.

16. Known function, indicating the corresponding function value, for example,

Then = _ _ _ _ _.

3. Fill in patiently: this big topic is ***9 small questions, and the score is ***86. Write the necessary text explanation, proof process or calculation steps when answering.

17. (Full score for this small question)

Calculation:

18. (Full score for this small question)

Simplified assessment:, in which.

19. (Full score for this small question)

As shown in the figure. At △ABC, D is the midpoint of AB. E is the midpoint of CD.

The intersection point C is the extension line of CF∨AB intersecting AE at point F, connecting BF.

(1)(4 points) Verification: DB = CF

(2)(4 points) If AC = BC, try to judge the shape of BDCF.

And prove your conclusion.

20. (The full score for this short question is 8)

On the occasion of "International No Tobacco Day", Xiao Min conducted a survey on a group of people's three attitudes towards smoking in restaurants (total smoking ban, establishment of smoking room, and others), and drew the survey results as shown in figure 1 and figure 2. Please answer the following questions according to the information in the picture below:

(1)(2 points) Among the respondents, _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

(2)(2 points) The sample size of this sampling survey is _ _ _ _ _ _ _ _ _.

(3 )(2 points) Among the respondents, the number of people who want to establish a smoking room is _ _ _ _ _ _ _ _ _;

(4)(2 points) There are about 3 million people in a city. According to the information in the picture, it is estimated that about _ _ _ _ _ _ _ million people are in favor of smoking in restaurants.

2 1. (Full score for this small question)

As shown in the figure, ∠ c = 90 in Rt△ABC, and O and D are points on AB and BC respectively. ⊙O intersects AB and AC through points A and D respectively at points E and F, and D is the midpoint.

(1)(4 points) Verification: BC is tangent to ⊙O;

②(4 points) When AD =；; When CAD = 30, the length of the solution,

22. (Full score for this small question 10)

As shown in the figure, put the right-angle OABC in the right-angle coordinate system, where O is the coordinate origin. Point a is on the positive semi-axis of the x axis. The point E is the moving point on the AB side (not coincident with the points A and N), and the image of the inverse proportional function passing through the point E intersects the BC side at the point F.

(1)(4 points) If the product of △OAE and △OCF is. The value of the mark k is:

(2)(6 points) If OA = 2.0C = 4. Ask when and where point E will be moved.

Quadrilateral OAEF has the largest area. What is its maximum value?

23. (The full mark of this little question is I0)

According to the market demand, a high-tech company plans to produce two kinds of medical devices, A and B. Some information is as follows:

Data 1: 80 sets of Class A and Class B medical devices were produced.

Information 2: The funds raised by the company for the production of medical devices are not less than 180,000 yuan, but not more than18100,000 yuan, and all the funds raised are used for the production of these two medical devices.

Information 3: The production costs and sales prices of medical devices A and B are as follows:

AB type

Cost (ten thousand yuan/set) 20 25

Price (ten thousand yuan/set) 24 30

According to the above information, answer the following questions:

(1)(6 points) What kinds of production schemes does the company have for these two medical devices? Which production scheme can get the most profit?

(2)(4 points) According to the market survey,-the price of each Class A medical device will increase by 1 10,000 yuan ().

The price of each type A medical equipment will not change. How should the company get the maximum profit?

(Note: profit = selling price cost)

24. (The full score of this short question is 12)

It is known that the symmetry axis of parabola is a straight line, which intersects with X axis at points A and B, and intersects with Y axis at point C, where ai (1, 0) and c (0, 0).

(1)(3 points) Find the analytical formula of parabola;

(2) If point P moves on a parabola (point P is different from point A).

①(4 points) as shown in Figure L. When the area of △PBC is equal to the area of △ABC, find the coordinates of point P;

②(5 points) as shown in Figure 2. When ∠PCB=∠BCA, find the analytical formula of straight line CP.

25. (The full score of this short question is 14)

It is known that the side length of rhombic ABCD is 1. ∠ A DC = 60, and two sides of equilateral△ △AEF intersect DC and CB at points E and F respectively.

(1)(4 points) It is especially found that, as shown in figure 1, if point E and point F are the midpoints of DC and CB sides respectively, it is proved that the intersection point O of diagonal AC and BD of rhombic ABCD is the outer center of equilateral △AEF;

(2) If point E and point F always move on the sides of DC and CB respectively, remember that the outer center of equilateral △AEF is point P. 。

①(4 points) Guess verification: as shown in Figure 2. Guess which straight line the epicenter p of △AEF falls on and prove it;

②(6 points) Extended application: As shown in Figure 3, when the area of △AEF is the smallest, take the intersection point P as a straight line, the intersection point DA at M point, and the extension line of the intersection point DC at N point, and try to judge whether it is a fixed value. If yes, request a fixed value; If not, please explain why.

20 1 1 Putian junior high school graduation examination paper

Mathematical reference answers and grading standards

First, choose an option carefully.

1.C 2。 D 3。 a4。 C 5。 B 6，B 7。 An eight. C

Second, fill in patiently-fill in.

9.I 0. 1 1 I . 7 12，9 13.4 14，58 15，5 16.5 15 1

Third, fill in patiently.

17. solution: original formula =4.

18. Original formula =, where applicable, original formula = 18.

19.( 1) It is proved that (2) the quadrilateral BDCF is rectangular. Simply prove it.

20.( 1) Prove that if OD is connected, OD=OA,

∴∠OAD=∠ODA

D is the midpoint

∴∠OAD=∠CAD

∴∠ODA=∠CAD

∴OD∥AC

And ∵∠ C = 90, ∴∠ ODC = 90, that's BC⊥OD.

∴BC is tangent to⊙ O.

(2) After DE, ∠ ade = 90.

* oad =∠ODA =∠CAD = 30 ,∴∠aod= 120

In Rt△ADE, it is easy to find AE=4,

∴⊙O radius r=2.

∴' s length.

22. solution: (1)∵ points e and f are on the image of the function.

Guess,

∴ ,

∵ ,∴ , 。

(2)∵ Quadrilateral OABC is a rectangle with OA=2 and OC=4.

Settings,

Be =, boyfriend =

∴

∵ ,

∴

=

When? AE = 2.

When point E moves to the midpoint of AB, the area of quadrilateral OA EF is the largest, with the maximum value of 5.

23. Solution: (1) If the company produces X sets of medical devices at clock A, then it produces () sets of medical devices at clock B, according to the meaning of the question.

Solve,

integer

The company has a 3-hour production plan:

Scheme 1: produce 38 A clock instruments and 42 B clock instruments.

Scheme 2: produce 39 A-clock meters and 4 1 B-clock meters.

Scheme 1: produce 40 A-clock meters and 40 B-clock meters.

The company made a profit;

When there is a maximum value.

When 38 sets of A clock tools and 42 sets of B clock tools are produced, the maximum profit is obtained.

(2) According to the meaning of the question,

When, in time, 40 sets of A clock instruments and 40 sets of B clock instruments were produced, and the maximum profit was obtained.

When, that is, when, the profits of the three schemes in (1) are all 4 million yuan;

38 sets of A-clock instruments and 42 sets of B-clock instruments were produced in time to obtain the maximum profit.

24. Solution: (1) Judging from the meaning of the question, you get it.

The analytical formula of parabola is.

(2) order ①, the solution is ∴ b (3,0)

When the point P is above the X axis, as shown in figure 1,

Parallel lines intersecting point a intersect parabola at point p as a straight line BC,

The analytical formula of easy-to-find straight line BC is,

∴ Let the analytical formula of linear AP be,

∫ The straight line AP passes through point A (1, 0) and is obtained by substitution.

∴ The analytical formula of linear AP is

Solve the equation and get

main points

When the point P is below the X axis, as shown in figure 1.

Let a straight line intersect the y axis at a point,

Translate the line BC downward by 2 units and intersect the parabola at this point.

The analytical formula of the straight line is,

Solve the equation and get

∴

To sum up, the coordinates of point P are:

②∵

∴OB=OC,∴∠ OCB=∠OBC=45

Let the analytical formula of straight line CP be

As shown in fig. 2, the cross x axis of CP is extended to point q,

Let ∠OCA=α, then ∠ ACB = 45 α.

Polychlorinated biphenyls = ∠ Basic chemical composition ∴∠PCB=45 α.

∴∠oqc=∠obc-∠pcb=45-(45°α)=α

∴∠OCA=∠OQC

∠∠AOC =∠COQ = 90。

∴Rt△AOC∽Rt△COQ

∴ ,∴ ,∴OQ=9,∴

* ∴ Straight CP crossing point

∴

∴ The analytical formula of straight line CP is.

Other methods are omitted.

25. Solution: (1) Proof: As shown in Figure 1, connect OE and 0F respectively.

∫ The quadrilateral ABCD is a diamond.

∴AC⊥BD, BD and so on ∠ ADC. ao = DC = BC。

∴∠COD=∠COB=∠AOD=90。

∠ADO= ∠ADC= ×60 =30

And f are the midpoint of DC and CB, respectively.

∴OE= CD, OF= BC, AO= AD.

E = of = OA Point O is the outer center of △AEF.

(2)① conjecture: the epicenter P must fall on the straight line DB.

Proof: As shown in Figure 2, connect PE and PA respectively, and make PI⊥CD in I and P J⊥AD in J respectively through P.

∴∠PIE=∠PJD=90，∫∠ADC = 60

∴∠ipj=360-∠pie-∠pjd-∠jdi = 120

∵ Point P is the outer center of the equilateral △AEF, ∴∠ EPA = 120, PE=PA.

∴∠IPJ=∠EPA,∴∠IPE=∠JPA

∴pi=pj ∴△pie≌△pja

Point p is on the bisector of ∠ADC, that is, point p falls on the straight line DB.

② is a fixed value of 2.

When AE⊥DC, the area of △ AEF is the smallest.

At this time, point E and point F are the midpoint of DC and CB respectively.

Connect BD and AC at point P, which is defined by (1).

The available point p is the outer center of △AEF.

Solution 1: As shown in Figure 3, let MN and BC intersect at G point.

Let DM=x, DN = Y (X ≠ 0. Y ≠ O), then CN=

∫ BC ∥∴△ GBP ∽△ MDP. ∴ BG = DM = X.

∴

∵BC∥DA,∴△GBP∽△NDM

∴ ,∴

∴

∴, namely

Other schemes are omitted.