Source: Time: June 2009-13 Author:

10. As shown in Figure 3, it is a quarter circle with one side AB of the equilateral triangle ABC as the radius, and P is any point on it. If AC=5, the maximum circumference of quadrilateral ACBP is

A. 15

Figure 5

Fill in the blanks (***5 small questions, 4 points for each question, out of 20 points. Please fill in the answer in the corresponding position on the answer sheet)

1 1. Decomposition factor: =

12. Please write an integer less than.

13. If known, the value of is

14. as shown in figure 4, AB is the diameter ⊙O, point c is on ⊙O, and OD‖AC. If BD= 1, the length of BC is

Figure 6

15. It is known that a, b, c, d and e are inverse proportional functions (x >；; 0) Five integer points on the image (both horizontal and vertical are integers), which are taken as vertical lines to the horizontal axis or vertical axis, respectively, and the length of the square where the vertical lines are located is taken as the radius to form five olive shapes (shaded parts) as shown in Figure 5, then the sum of the areas of these five olive shapes is (expressed by an algebraic expression containing π).

Third, answer the question (out of 90. Please fill in the answer sheet in the corresponding position)

16. (7 points for each small question, *** 14 points)

(1) calculation: 22-5×+

(2) Simplification: (x-y) (x+y)+(x-y)+(x+y)

17. (8 points for each small question, *** 16 points)

(1) Solving inequality: represents the solution set on the number axis.

(2) It takes 60 hours to sort out a batch of books if one person does it alone. At present, some people spend an hour tidying up, plus 15 people to work with them for another two hours, just finishing tidying up. Assuming everyone's work efficiency is the same, how many people will arrange the ranking first?

18. (in 10)

As shown in fig. 6, it is known that AC bisects ∠BAD, ∠ 1=∠2, which proves that AB=AD.

19. (Full score: 12) The following figure describes the reading time of the students in Class 9 (1) in three stages (morning, noon and evening) during the one-month reading month:

(1) As can be seen from the above statistics, there are students in Class * * * in Grade 9 (1);

(2) In Figure 7- 1, the value of a is;

(3) According to Figure 7- 1 and Figure 7-2, in this reading month activity, the daily reading time of the students in this class (fill in "general increase" or "general decrease");

(4) Through this reading month activity, if the students in this class have initially formed good daily reading habits, referring to the changing trend of the above statistical chart, by the end of the reading month activity, the number of students in this class reading 0.5~ 1 hour every day has increased compared with the initial activity.

20. (Full score 12)

As shown in Figure 8, in a grid composed of small squares with a side length of 1, all three vertices are on the grid points.

Please complete the following questions as required:

(1) Connect the CD with the signature stroke AD BC (D is the grid);

(2) The length of the line segment CD is;

(3) Figure 8

Please choose any acute angle among the three internal angles. If the acute angle you choose is 0, then its corresponding sine function value is 0.

(4) If E is the midpoint of BC, the value of tan∠CAE is

2 1. (in 12)

As shown in Figure 9, the equilateral length is 4, which is the moving point on the side. In h, the intersecting line segments are at points, and the points on the line segments are made. Settings.

(1) Please directly write two line segments equal to those in the drawing (without additional auxiliary lines);

(2) is the moving point on the line segment. When the quadrilateral is a parallelogram, find the area (expressed by the contained algebraic expression);

(3) When the area in (2) is the largest, take E as the center and the radius as a circle, and find out the corresponding value range according to the total number of intersections of E and four sides at this time.

22. (Full score 14)

It is known that the straight line L: y =-x+m (m ≠ 0) intersects the X axis and the Y axis at two points A and B, and points C and M are respectively at.

On line segments OA and AB, OC=2CA, AM=2MB, connect MC, and wind △ACM on point m..

Rotate 180 to get △FEM, then point E is on the Y axis and point F is on the straight line L; Take the EO line

At point n, fold ACM along the line where MN is located, and get △PMG, where P and A are symmetrical points. note:

The hyperbola passing through point F is that the parabola passing through point M with vertex B is, and the parabola passing through point P with vertex M is.

A parabola with vertices is.

(1) As shown in figure 10, when m=6, ① directly write the coordinates of points m and f,

(2) the distinguishing function between seeking and seeking;

(2) When m changes, how does ①Y change with the increase of X on each branch? Please provide a justification for the answer.

(2) If Y exists and decreases with the increase of X, write the range of X. ..

Answer:

First, multiple-choice questions (4 points for each small question, 40 points for * * *)

1.A 2。 B 3。 D 4。 C 5。 D

6. A seven. An eight. B 9。 C 10。 C

Fill in the blanks (4 points for each small question, 20 points for * * *)

1 1.x(x-2)

12. The answer is not unique. Any integer less than or equal to 2 is acceptable, such as 2, 1, etc.

13.5

14.2

15. 13π-26

Third, answer questions.

16.( 1) solution: the original formula = 4- 1+2.

=3+2

= 5.7 points.

(2) Solution: Original formula =

= ...................................... 7 points.

17.( 1) solution: 3x-x > 2

2x>2

X >1.............................. 6 points.

Eight points, eight points, eight points

(2) solution: suppose there are x people to arrange the sorting first, according to the meaning of the question.

............................., 4 points.

Solution, x = 10.

Answer: There are 10 people who arrange the sorting first. ..........................................................................................................................................................

Figure 6

18. Proof: ∫ AC split ∠ bad.

∴∠BAC=∠DAC.

∵∠ 1=∠2

∴∠ABC=∠ADC.

In △ABC and △ADC,

∴△ ABC△ ADC (AAS) ................................. scored 8 points.

∴ ab = ad ....................................10.

(Refer to the above scoring criteria for other different syndromes)

19. (3 points for each small question, *** 12 points)

( 1)50

(2)3

(3) general increase

(4) 15

20. (3 points for each small question, *** 12 points)

(1) as shown in the figure.

2 1. Solution: (1) Choose two ................................................................ from the three line segments Be, PE and BF, and score 2 points.

(2) In Rt△CHE, ∠ Che = 90 ∠ C = 60,

∴EH=

∫PQ = EF = BE = 4-x

∴ .................................. 5 points.

(3)

When x = 2, there is a maximum.

At this time, E, F and P are the midpoint of triangle BC, AB and AC of △ABC respectively, and point C coincides with point Q..

∴ The parallelogram EFPQ is a diamond.

Do ED⊥FP at point D after point E,

∴ED=EH=。

∴, 0 < r when the total number of intersections of⊙ e and four sides is 2.

When the total number of intersections of ⊙E and four sides is four, r =；;

When the total number of intersections of ⊙E and four sides is six, < r < 2；;

When the total number of intersections between e and four sides is three, r = 2；;

When the total number of intersections of ⊙E and four sides is 0, r > 2.

22. Solution: (1)① The coordinates of point M are (2,4) and the coordinates of point F are (-2,8). .......................................................................................................................

(2) According to the meaning of the question, A(m, 0), B(0, m),