Instructions for candidates:

1. This paper is ***4 pages, * * * 5 big questions and 25 small questions, with full marks120; Examination time 120 minutes.

2. The answer sheet is ***6 pages, and the school name, class and name should be filled in carefully at the specified position.

The answers to the questions are written on the answer sheet, and the answers on the test paper are invalid.

After the exam, please return the answer sheet, and the test paper and draft paper can be taken away.

1. Multiple choice questions (Only one of the four alternative answers to the following questions meets the meaning of the question. Please write the letters before the correct answer on the answer sheet; * * * 32 points for this question, 4 points for each small question)

1. The known diameter ⊙O is 3cm, and the distance from point P to the center of the circle O OP=2cm, then point P.

A. External ⊙ O.B.On ⊙ O.C. Internal ⊙ O.D. Uncertainty

2. Among the known △ABC,? C=90？ , AC=6, BC=8, then the value of cosB is

A.0.6 B.0.75 C.0.8 D

3. As shown in the figure, in △ABC, points M and N are on both sides of AB and AC respectively, and MN∨BC, then the following proportional formula is incorrect.

Answer. B.

C.D.

4. In the picture below, which one is centrosymmetric and which one is axisymmetric?

A.B. C. D。

5. Given that the radii of ⊙O 1 and ⊙O2 are 1cm and 4cm respectively, and O 1O2= cm, the positional relationship between ⊙O 1 and ⊙O2 is

A. outside B. outside C. inside D. intersection

6. The image of a quadratic function y=ax2+bx+c is shown in the figure, so the following conclusion is correct.

A.a & gt0，b & gt0，c & gt0b . a & gt； 0，b & gt0，c & lt0

C.a & gt0，b & lt0，c & gt0d . a & gt； 0，b & lt0，c & lt0

7. Among the following propositions, the correct one is

A. Three points on the plane define a circle. B. the circumferential angles of equal arcs are equal.

C. the diameter of the bisecting chord is perpendicular to the chord d. The straight line perpendicular to the radius of a circle is the tangent of the circle.

8. First, translate the parabola y=-x2+4x-3 by 3 units to the left, and then by 2 units to the down, then the analytical formula of the transformed parabola is

a . y =-(x+3)2-2 b . y =-(x+ 1)2- 1

C.y=-x2+x-5 D. None of the first three answers are correct.

II. Fill in the blanks (the score for this question is *** 16, with 4 points for each small question)

9. Given that the ratio of two similar triangles areas is 2∶ 1, the ratio of their perimeters is _ _ _ _.

10. When the inverse proportional function y=, x >; 0, y increases with the increase of x, so the value range of k is _ _ _ _ _ _ _.

1 1. When two people with the same level play badminton, it is stipulated that two games will win, and the probability that Team A will beat Team B is _ _ _ _ _ _ _ _; The probability that Team A will beat Team B 2-0 is _ _ _ _ _.

12. It is known that the diameter AB of ⊙O is 6cm, and the chord CD intersects AB with an included angle of 30? , the intersection m happens to be the bisector of AB, then the length of CD _ _ _ _ _ _ _ _ _ cm.

Iii. Answer the question (30 points for this question, 5 points for each small question)

13. Calculation: cos245? -2tan45？ +tan30？ - sin60？ .

14. It is known that the square MNPQ is inscribed with △ABC (as shown in the figure). If the area of △ABC is 9cm2 and BC=6cm, find the side length of the square.

15. A shopping mall is going to improve the safety performance of the original escalator, and the inclination angle is changed from 30? Reduce it to 25? As shown in the figure, the length of the original stair slope AB is known as 12m. How long does the adjusted staircase occupy the ground CD? (The result is accurate to 0.1m; Reference data: sin250.42, cos 250.95438+0, tan250.47)

16. Known: △ABC,? A is an acute angle, and b and c are respectively? B, is it? The opposite of C.

Prove: the area of △ABC S △ABC= bcsinA.

17. As shown in the figure, △ABC is inscribed in ⊙O, and the diameter BD of chord AC is at point E, AG? BD is at G point, and the extension of AG to BC is at F point. Verification: AB2=BF? BC.

18. The image passing point (-3, 1) of the quadratic function y=ax2-x+ is known.

(1) Find the value of a;

(2) Whether the image of this function intersects with the X axis is judged? If they intersect, request the coordinates of the intersection;

(3) Draw the image of this function. (columns are not required to correspond to numerical tables, but it is required to draw as accurately as possible. )

Iv. Answer questions (20 points for this question, 5 points for each small question)

19. As shown in the figure, in 12? In the grid of 10, the vertices of points O, M and quadrilateral ABCD are all on the grid.

(1) Draw a graph that is symmetrical about the straight line CD and the quadrilateral ABCD;

(2) Translate the quadrilateral ABCD to make its vertex b coincide with the point m, and draw the translated figure;

(3) Rotate the quadrilateral ABCD 90 counterclockwise around the O point? Draw the rotated figure.

20. There are five pieces in the pocket that are all the same except the color. Three of them are red and the others are black.

(1) Randomly draw a piece from the pocket, and the probability of touching the black piece is _ _ _ _ _ _;

(2) Take two pieces out of your pocket at a time and find the probability of different colors. List? Or painting? Tree diagram? ) process

2 1. It is known that the images of function y 1=- x2 and inverse proportional function y2 have an intersection point a (,-1).

(1) Find the analytical expression of function y2;

(2) Draw the image sketches of functions y 1 and y2 in the same rectangular coordinate system;

(3) Answer with the help of images: When the independent variable X is in what range, for the same value of X, there is y 1.

22. The factory has a batch of rectangular iron sheets, 3 meters long and 2 meters wide. In order to make use of this batch of materials, cut the largest round iron sheet ⊙O 1 (as shown in the figure) on each piece, and then cut the round iron sheet ⊙O2 on the remaining iron sheets.

(1) Find the radius of ⊙O 1 and ⊙O2 and the length of r2;

(2) Can you cut another round iron sheet with the same size as ⊙O2 on the remaining iron sheet? Why?

V. Answer questions (22 points for this question, 7 points for questions 23 and 24, and 8 points for question 25)

23. As shown in the figure, in △ABC, AB=AC, and O with the diameter of AB intersects with AC and BC at points M and N, respectively. Take point P on the extension line of AC as? CBP=？ A.

(1) Judge the positional relationship between straight line BP and ⊙O, and prove your conclusion;

(2) If the radius of ⊙O is 1, tan? CBP=0.5, find the length of BC and BP.

24. As shown in the figure, the side length of square paper ABCD is 4, and points M and N are on both sides of AB and CD respectively (where point N does not coincide with point C). Fold the paper in half along the straight line MN, and the point B just falls on the point E on the edge of AD.

(1) Let AE=x and the area of quadrilateral AMND be s, find the resolution function of S about x, and indicate the definition domain of this function;

(2) What is the value of 2)AM and the maximum area of quadrilateral AMND? What is the maximum value?

(3) Can point M be any point on the side of AB? Request the value range of AM.

25. In the rectangular coordinate system xOy, it is known that the image of a quadratic function passes through A (-4,0) and B (0 0,3) and intersects with the positive semi-axis of the X axis at point C, if △AOB∽△BOC (similarity ratio is not 1).

(1) Find the analytic expression of this quadratic function;

(2) Find the radius r of the circumscribed circle of △ABC;

(3) Is there a point M(m, 0) on the line segment AC, so that the circle with the diameter of the line segment BM intersects with the line segment AB at the point n, and the triangle with the vertices of points O, A and N is an isosceles triangle? If it exists, find the value of m; If it does not exist, please explain why.

Reference answer

I. ACCB·DABB

Second, nine. : 1 10.k

Three. 13. The original formula = -2+-?

= -2+-4 points

= -3+ 5 points

14.AE？ BC in e, MQ in f.

By Italy, BC? AE=9cm2，BC=6cm。

? AE=3cm。 ? 1 point

Let MQ= xcm,

∫MQ∨BC，？ △AMQ∽△ABC。 2 points

? .3 points

EF = MN = MQ，？ AF=3-x。

? .4 points

The solution is x=2.

The side length of a square is 2 cm. Five minutes.

15. From the meaning of the question, in Rt△ABC, AC= AB=6 (meters),? 1 point

Also ∵ in Rt△ACD,? D=25？ = Tan? d，？ 3 points

? CD= 12.8 (m).

Answer: The adjusted staircase occupies about 12.8m.5min on the ground.

16. Proof: CD? If AB is greater than d, then S△ABC= AB? CD. 2 points

No matter where point d falls on ray AB,

In Rt△ACD, there is CD=ACsinA. 4 points

AC = b，AB=c，

? S△ABC= AB？ ACsinA

= bcsinA。 5 points

17. Proof: cross ⊙O in extended AF and H.

Diameter BD? Huh? AB⌒ = BH⌒。 2 points

C=？ BAF。 ? 3 points

In △ABF and △CBA,

∵? BAF =？ c，？ ABF=？ CBA，

? △ABF∽△CBA。 4 points

? , that is AB2=BF? BC. 5 points

Evidence 2: Linked advertisements,

∫BD is the diameter, including+? DAG=90？ . 1 point

∵AG？ BD，DAG+？ D=90？ .

BAF =？ Bag =? D. 2 points

Again? C =？ d，

BAF=？ c？ 3 points

18.( 1) Substitution point (-3, 1),

Get 9a+3+ = 1,

? a= -。

(2) intersection? 2 points

From-x2-x+ =0，？ 3 points

Get x=- 1? .

? The coordinates of the intersection point are (-1? ,0).？ 4 points

(3) Give points as appropriate? 5 points

19. Item (1) is allocated 1 minute, and items (2) and (3) are allocated 2 points.

20.⑴ 0.4 ? 2 points

⑵ 0.6 ? 4 points

List (or draw a tree) 5 points correctly.

2 1.( 1) Substitute point A (,-1) into y 1=-, and get? 1= - ,

? a=3。 ? 1 point

Let y2= and substitute it into point A (,-1) to get k=? ,

? y2=？ .2 points

(2) drawing; 3 points

(3) From the image, we know that when X

22.( 1) As shown in the figure, in the rectangular ABCD, AB= 2r 1=2dm, that is, r 1= 1dm. 1.

BC=3dm, ⊙O2 should be tangent to ⊙O 1, BC and CD.

Connect O 1 O2, cross O 1 as a straight line O 1E∨AB, cross O2 as a straight line o 2e∨BC, then o 1E? O2E。

At Rt△O 1 O2E, O 1 O2=r 1+ r2, O 1E= r 1? r2，O2E=BC？ (r 1+ r2)。

By o 1o 22 = o 1e 2+02e 2,

That is, (1+ r2)2 = (1? r2)2+(2？ r2)2。

Solution, r2= 4? 2. Again ∵ R2 < 2,

? r 1= 1dm，r2=(4？ 2 )dm。 3 points

(2) the fourth point

∫R2 =(4？ 2)>； 4? 2? 1.75= (dm)，

Namely r2 & gtDm. , and ∵CD=2dm,

? CD<4 r2, so the required round iron sheet can't be cut any more. 5 points

23.( 1) Tangency. 1 point

Proof: link AN,

∫AB is the diameter,

ANB=90？ .

AB = AC，

BAN=？ A=？ CBP。

Again? Class+? ABN= 180？ -? ANB= 90？ ,

CBP+？ ABN=90？ , which is AB? BP。

∵AB is the diameter⊙ O,

? The straight line BP is tangent to the point ⊙ O.3.

(2) In Rt△ABN, AB=2, tan? Ban = Tan? CBP=0.5，

Can be found, BN=,? BC=。 4 points

Making CDs? BP is in d, then CD∨AB,

In Rt△BCD, CD=, BD=. ? 5 points

Substitute in the above formula and you get =

? CP=。 6 points

? DP=。

? BP=BD+DP=+=。 7 points

24.( 1) According to the meaning of the question, point B and point E are symmetrical about MN, so ME=MB=4-AM.

Then from AM2+AE2=ME2=(4-AM)2, AM=2- is obtained. 1.

As MF? DN is in f, then MF=AB, and? BMF=90？ .

∵MN？ BE，ABE= 90？ -? BMN。

Again? FMN =？ BMF -？ BMN=90？ -? BMN，

FMN=？ Abel.

? Rt△FMN≌Rt△ Abe.

? FN=AE=x，DN=DF+FN=AM+x=2- +x？ 2 points

? S= (AM+DN)？ advertisement

=(2- + )? four

= - +2x+8。 ? 3 points

Where, 0? X & lt4.4 points

⑵∫S =-+2x+8 =-(x-2)2+ 10，

? When x=2, the maximum value of s =10; 5 points

At this point, AM=2-? 22= 1.5 ? 6 points

A: When AM= 1.5, the area of the quadrilateral AMND is the largest, which is 10.

(3) No, 0

25.( 1)∫△AOB∽△BOC (similarity ratio is not 1),

? . And ∵OA=4, OB=3,

? OC=32？ = .？ Point c (,0). 1 point

Let the resolution function of an image passing through points A, B and C be y=ax2+bx+c,

So c= -3, and then what? 2 points

that is

Solution, a=, b=.

? The analytical formula of this function is y = x2+ x-3. 3 points

⑵△ AOB ⑵△ BOC (similarity ratio is not 1),

Bao =? CBO。

Again? ABO+？ Bao =90? ,

ABC=？ ABO+？ CBO=？ ABO+？ Bao =90? .4 points

? AC is the diameter of the circumscribed circle of △ABC.

? r = AC=？ [-(-4)]=.5 points

(3) ∵ point n is on a circle with BM as its diameter,

MNB=90？ .6 points

(1) When AN=ON, point N is on the vertical line of OA.

? Point N 1 is the midpoint of AB and M 1 is the midpoint of AC.

? AM 1= r =, point M 1(-, 0), that is, point m 1=-.7.

② when AN=OA, Rt△AM2N2≌Rt△ABO,

? AM2=AB=5, point M2( 1, 0), that is, m2= 1.

(3) When ON=OA, the point n obviously cannot be on the line segment AB.

To sum up, the point M(m, 0) that satisfies the meaning of the question exists, and there are two solutions:

M=-, or 1. Eight points.

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