20 1 1 Baotou senior high school entrance examination mathematics

20 10 Baotou senior high school entrance examination paper

mathematics

Precautions:

1. This volume 1~8 pages, full mark 120, examination time 120 minutes.

Candidates must answer the questions directly with a blue-black pen or a ballpoint pen.

Be sure to fill in the items in the binding line clearly before answering the questions.

1. Multiple-choice question: This big question has 12 small questions, with 3 points for each small question, totaling 36 points. There is only one correct option for each small question. Please fill in the letter code of the correct option in the brackets after the question.

The cube root of 1.27 is ()

The third century BC.

2. In the following operations, the correct one is ().

A.B. C. D。

3. In the function, the value range of the independent variable is ()

A.B. C. D。

4. The National Stadium "Bird's Nest" has a building area of 258,000 square meters, which is expressed as () by scientific notation, rounded to two significant figures.

A. square meters

C. square meters

5. Known in, the value of is ().

A.B. C. D。

6. In the following figures, there are () in both axisymmetric figures and centrally symmetric figures.

A.4 B.3 C.2 D. 1

7. In order to know the physical condition of ninth grade students, a school randomly selected 30 students, tested the number of sit-ups at 1 min, and drew the histogram of frequency distribution as shown in the figure. Please calculate according to the figure, the number of sit-ups between 15 and 20 times is ().

a . 0. 1b

8. After the cube is unfolded along some edges, the plane figure you can get is ().

9. Simplify, and the result is ()

A.B. C. D。

10. Xiao Ming throws two cube dice with uniform texture and the same size at the same time. The six faces of the dice are engraved with 1 to 6 points respectively. The probability that the sum of points thrown face up is a multiple of 3 is ().

A.B. C. D。

1 1. The following propositions are known:

1 if, then;

2 If, then;

③ The point on the bisector of the angle is equal to the distance on both sides of the angle;

Diagonal bisection of parallelogram.

The number of propositions in which both the original proposition and the inverse proposition are true is ()

1。

12. The two real roots of a quadratic equation are, and the value of is ().

a . 1 b . 12 c . 13d . 25

Fill-in-the-blank question: This big question has 8 small questions, each with 3 points, totaling 24 points. Please fill in the answer on the horizontal line of the question.

13. The solution set of the inequality group is.

14. In the comprehensive practice class, the number of works (unit: pieces) of six students are: 5, 7, 3, 6 and 4 respectively; If the average value of this set of data is 5, then the median value of this set of data is 1.

15. The line segment is translated by the line segment, and the corresponding point of the point is, then the coordinate of the corresponding point of the point is.

16. As shown in the figure, if it is tangent to a point and intersects with two points in,, and, the area of the shaded part in the figure is (reserved).

17. Cut a 20 cm long iron wire into two sections and draw a square around the length of each section of iron wire, then the minimum value of the sum of the areas of these two squares is cm2. ..

18. As shown in the figure, it is known that the image of the linear function and the image of the inverse proportional function intersect at a point in the first quadrant and intersect with the axis at a point, and the area is 1, then the length is (keep the root sign).

19. As shown in the figure, sum is known to be two congruent right triangles. The length of hypotenuse is10cm, and the acute angle is 30. Put these two triangles into the shape as shown in figure (1), so that all points are on the same straight line and coincide. In the figure (1),

20. It is known that the image of quadratic function intersects the axis at a point, and the intersection point with the positive semi-axis of the axis is below. Draw the following conclusions: ①; ② ; ③ ; ④ The number of correct conclusions is 1 piece.

3. Solution: There are 6 small questions in this big question, with a total of 60 points. When answering, it is required to write the necessary text description, calculation process or reasoning process.

2 1. (Full score for this small question)

A school wants to recruit a math teacher. The school conducted three ability tests on three candidates, A, B and C, and the perfect score of each test was 100. According to the results, the best candidate was selected. The test scores of the three candidates are shown in the following table:

Test results of test items

Methyl ethylene propylene

Teaching ability 85 73 73

Scientific research ability 70 765 438+0 65

Organizational capacity 64-72 84

(1) Decide who to hire according to the average score of the three tests, and explain the reasons;

(2) According to the actual needs, the school determines everyone's score in the three ability tests of teaching, scientific research and organization according to the ratio of 5: 3: 2, and explains the reasons.

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

As shown in the figure, the line segments represent the heights of buildings A and B, respectively. The elevation of the point measured from the point is 60, and the elevation of the point measured from the point is 30. It is known that the height of building A is meters.

(1) Find the height of Building B;

(2) Find the distance between Building A and Building B (the result is accurate to 0.0 1 m).

(Reference data:)

23. (Full score for this small question 10)

A shopping mall tries to sell a kind of clothing, which costs one in 60 yuan. It is stipulated that the sales unit price shall not be lower than the cost unit price during the trial sale period, and the profit shall not be higher than 45%. After the trial sale, it is found that the sales volume (pieces) and the sales unit price (yuan) conform to a linear function, when; When.

(1) Find the expression of linear function;

(2) If the profit of the shopping mall is RMB, try to write the relationship between the profit and the sales unit price; When the sales unit price is set at several yuan, the shopping mall can get the maximum profit. What is the maximum profit?

(3) If the profit of the mall is not lower than that of 500 yuan, try to determine the interval of the sales unit price.

24. (Full score for this small question 10)

As shown in the figure, it is known that the diameter is IS, the point is above, and the straight line passing through the point intersects with the extension line of the point at the point,,.

(1) Verification: the tangent of Yes;

(2) Verification:

(3) A point is a midpoint and an intersection, and if so, it is a value.

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

As shown in the figure, it is known that cm, cm and point are the midpoint.

(1) If point P moves from point B to point C at a speed of 3cm/s on BC line and point Q moves from point C to point A on CA line.

(1) If the moving speed of point Q is equal to the moving speed of point P, is it the same after 1 s, please explain the reason;

② If the moving speed of point Q is not equal to that of point P, when the moving speed of point Q is what, can it be congruent?

(2) If point Q starts from point C at the speed of ②, and point P starts from point B at the same time at the original speed, and both move counterclockwise along three sides, how long will it take for point P to meet point Q for the first time?

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

It is known that the image of the quadratic function () passes through this point, and the straight line () intersects the axis at this point.

(1) Find the analytic formula of quadratic function;

(2) There is a point () on the straight line (this point is in the fourth quadrant), which makes the triangle with vertices similar to the triangle with vertices, and then finds the coordinates of this point (expressed by the included algebraic expression);

(3) If (2) holds, is there a point on the parabola that makes the quadrilateral a parallelogram? If yes, the requested value and the area of the quadrilateral; If it does not exist, please explain why.

(see the senior high school entrance examination network)