mathematics

Annotation item

Candidates should read this notice carefully before answering the questions.

1. This volume is ***6 pages, with the full mark of 150 and the examination time of 120 minutes. After the exam, please return the test paper and the answer sheet together.

2. Before answering the question, please be sure to fill in your name and test certificate number in the designated position of the test paper and answer sheet with a signature pen with 0.5mm black handwriting.

3. The answers must be filled in and written on the answer sheet as required, and the answers on the test paper and draft paper are invalid.

1. Multiple-choice question: This big question is a small question of *** 10, with 3 points for each small question and 30 points for * * *. Of the four options given in each small question, exactly one meets the requirements of the topic. Please fill in the letter code before the correct option in the corresponding position on the answer sheet.

The reciprocal of 1 -4 Yes

a . 4 B- 4 c . d

The arithmetic square root of 2. 9 yes

A.3 B.-3 C.8 1 D.-8 1

3.0.00003 1 expressed by scientific notation, the result is

a . 3. 1× 10-4b . 3. 1× 10-5c . 0.3 1× 10-4d . 3 1× 10-6

4. If it is meaningful in the real number range, the value range of is

A.B. C. D。

5. As shown in the figure, if the diameter ⊙O is AB=4, the point C is on ⊙O, and ∠ ABC = 30, the length of AC is

A. 1 B。

C.D.2

6. A textile factory randomly selected 100 pieces of similar products for quality inspection, and found that

Five of them are unqualified, so it is estimated that the qualified products in the factory's 654.38+million products are about

95 thousand pieces

C.9500 pieces D.5000 pieces

7. If the solution of the equation about X is a positive real number, the value range of M is

A.m≥2 B.m≤2

Cm > 2cm < 2

8. As shown in the figure, in the rhombic ABCD, AB = 5, ∠ BCD = 120, so the diagonal.

The length of AC is

15

C. 10 D.5

9. As shown in the figure, it is known that the diagonal BD of □ABCD is 4 cm, and □ABCD surrounds a pair of them.

When the center of O rotates180, the path length of point D is

A.4π cm B.3π cm

C.2π cm D.π cm

10. In the plane rectangular coordinate system xOy, point P (2 2,2) is known and point Q is on the Y axis.

△PQO is an isosceles triangle, then the point Q*** that satisfies the condition is

A.5 B.4 C.3 D.2

Fill in the blanks: this big question is ***8 small questions, each with 3 points and ***24 points. There is no need to write the answer process, please fill in the answer directly in the corresponding position on the answer sheet.

1 1. If the image of the proportional function passes through the point (1, -2), then the value of k is equal to ▲.

12. If the similarity ratio of △ABC∽△DEF, △ABC and △DEF is 1: 2, then the perimeter ratio of △ABC and △DEF is ▲.

13. Decomposition factor: = ▲.

14. Six figures of 1, 2, 3, 4, 5 and 6 are engraved on the six faces of the cube dice with uniform texture. If you roll this dice once, the probability that the number on it is even is ▲.

15. In the plane rectangular coordinate system, the coordinates of the two endpoints of the known line segment MN are

M (-4,-1), N(0, 1), translate the line segment MN to get the line segment M'N'.

(points m and n are converted into positions of points M' and N' respectively), if the coordinates of point M' are

(-2,2), then the coordinate of point n' is ▲.

16. As shown in the figure, Zhang Xiao folded it with a rectangular piece of paper ABCD that was broken on both sides.

In the paper game, after he folded the paper along EF, the point D and the point C fell in the positions of D' and C' respectively.

If ∠ EFB = 65 is measured with a protractor, ∠AED' is equal to ▲ degrees.

17. As shown in the figure, the side length of the square ABCD is 4, the point M is on the side DC, and the points M and N are closed.

AC symmetry on the diagonal, if DM= 1, then tan ∠ adn = ▲.

18. Let x 1 and x2 be two roots of the unary quadratic equation X2+4x-3 = 0.

2x 1 (x22+5x2-3)+A = 2, then A = ▲.

3. Solution: This big question is * *10, and the score is ***96. Please answer in the designated area of the answer sheet, and write a written explanation, proof process or calculation steps when answering.

19. (Full score for this small question 10)

Calculation: (1);

(2) .

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

As shown in the figure, the diameter AB of ⊙O is perpendicular to the chord CD, and the vertical foot P is the midpoint of OB.

CD = 6 cm, find the length of diameter AB.

2 1. (Full score for this small question)

As shown in the figure, the straight line intersects the hyperbola at points A (2, 1) and B. 。

(1) Find the values of m and k;

(2) Write the coordinates of point B directly without understanding the equations of X and Y;

(3) Does the straight line pass through point B? Please explain the reason.

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

Randomly select a certain number of eighth-grade students in a certain area to take the mock exam of geography exam, and count the exam scores (X points). The specific statistical results are shown in the following table:

Statistical table of simulation test results of eighth grade geography exam in a certain area

Fractional segment 90 < x ≤100 80 < x ≤ 90 70 < x ≤ 80 60 < x ≤ 70 x ≤ 60.

No.12001461642 480 217

(1) Fill in the blanks:

(1) this sampling survey * * * tested the students;

(2) The median score of the students who participated in the simulation test of geography exam falls on the score section ▲;

(3) If the statistical result is represented by a fan-shaped statistical chart, the degree of the fan-shaped central angle corresponding to the number of people with a score of 90 < x ≤ 100 is ▲;

(2) those who have scored 60 points or above in the geography exam are qualified, and the required pass rate is not less than 97%. It is known that 1 17 students scored 60 points in this exam. Does the calculation show that the pass rate of the simulation exam of geography exam meets the requirements?

23. (The full score for this short question is 9)

The ninth grade (1) class of Guangming Middle School carries out mathematical practice activities. Xiao Li walked east along the east-west expressway at a speed of 50 meters per minute. At a, he measured that building C was 60 east-west. Twenty minutes later, he went to building B and measured that building C was 45 northwest. Find the distance from Building C to AB Expressway. (known)

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

(1) A batch of goods weighing 490 tons were distributed to two ships, A and B. Now, the two ships A and B have carried out their tasks respectively. Among the goods transported, A carries 30 tons more than B. What are the tasks to be distributed to A and B respectively?

(2) Write an application problem with the following requirements:

① It is the problem of distance application. All three data, 100, must be used without adding other data.

As long as you make up your own questions, don't answer them.

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

As shown in the figure, it is known that points B, F, C and E are on a straight line, FB=CE and AC = DF.

Can AB‖ED be proved by the above known conditions? If yes, please give proof; If not, please choose a suitable condition from the following three conditions, add it to the known conditions, make AB‖ED hold, and give the proof.

There are three conditions to choose from (please select one):

①AB = ED；

②BC = EF；

③∠ACB=∠DFE。

26. (Full score for this small question 10)

Xiao Shen is going to call Xiao Chen. Due to improper storage, the two numbers of Xiao Chen's mobile phone number in the phone book are blurred. If these two illegible numbers are represented by X and Y respectively, then Xiao Chen's mobile phone number is 139x370y580 (the mobile phone number consists of 1 1). Xiao Shen remembers this 65438.

(1) Find the value of x+y;

(2) Find the probability of dialing the mobile phone number twice.

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

As shown in the figure, in the right-angle ABCD, AB=m(m is a constant greater than 0), BC=8, and E is the moving point on the straight line BC (not coincident with B and C). Connect DE as EF⊥DE, where EF and ray BA intersect at point F, let CE=x and BF = Y. 。

(1) Find the functional relationship between y and x;

(2) If m=8, what is the value of x and the maximum value of y?

(3) If △DEF is to be an isosceles triangle, what should be the value of m?

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

It is known that the parabola Y = AX2+BX+C passes through two points A (-4,3) and B (2 2,0). When x=3 and X =-3, the vertical coordinates of the corresponding points on this parabola are equal. The straight line L passing through point C (0 0,2) is parallel to the X axis, and O is the coordinate origin.

(1) Find the analytical formula of straight line AB and this parabola;

(2) The circle with A as the center and AO as the radius is marked as ⊙A, so as to judge the positional relationship between the straight line L and ⊙A and explain the reasons;

(3) Let the abscissa of point D on straight line AB be-1 and P(m, n) be the moving point on parabola Y = AX2+BX+C, when

When the perimeter of △PDO is the smallest, find the area of quadrilateral CODP.