1. Fill in carefully: (This big question is 12 small questions, with 3 points for each small question and * * * 36 points).

1. If the square root is meaningful, the value range of x is.

2. If the simplest quadratic radical is the same quadratic radical, then a=.

3. As we all know, 2 is the root of a quadratic equation, so the value of k is.

Question 7

4. Let sum be two real roots of the equation, then =.

5. If the quadratic equation with one variable about x has no real root, the range of m is.

6. It is known that in △ABC, ∠ c = 90, AB= 10cm, sinA=, then the length of BC is cm.

7. As shown in the figure, the light P is above the crossbar AB, and the shadow of AB under the light is CD, AB‖CD, AB=2cm, CD=6cm, and the distance from P to CD is 3m, so the distance from P to AB is m. 。

8. It is known that D and E are points on the AB side and AC side of △ABC, respectively. To make △ABC similar to △ADE, just add one condition: Yes (just fill in one).

9. The probability of two consecutive coin flips, both heads up.

Yes

10. As shown in the figure, there is a lovely one in the square dotted box of 12×7.

Fox, in which the similar triangle is right.

1 1. If the symmetry axis of the parabola is the y axis,

Map number 10

Then m=

12. If the parabola passes through points A(0, -3), B(2, -3) and C(-2, 5), the coordinate of another point D on the parabola with ordinate 5 is.

Second, careful choice: (There are 4 small questions in this big question, 3 points for each small question, *** 12 points)

13. The following calculation is correct ()

A.B. C. D。

14. enlarge the length of each side of Rt△ABC by three times to get rt △ a ′ b ′ c ′, then the relationship between the cosine of acute angle a and a ′ is ().

The CBI is not sure.

1 5. Two opaque bags, A and B, are respectively filled with 1 red ball, 2 yellow balls, 2 red balls and 4 yellow balls, and are evenly mixed, and then1ball is extracted from the two bags A and B respectively. Give the following statements: ① The probability of taking out the red ball from A's bag is less than that of taking out the red ball from B's bag; (2) The probability of pulling out the red ball from the bag A is equal to the probability of pulling out the red ball from the bag B; (3) The probability of pulling the red ball out of bag A is the probability of pulling the red ball out of bag B, and the correct statement is ()

A.①② B. ② C. ②③ D. ①③

16. It is known that the image of the quadratic function is as shown in the figure, so the case of the root of the equation about x is ().

A. there is no real number root B. there are two real number roots with different symbols.

C. there are two equal real roots. D. there are two real roots with different signs.

Third, seriously answer: (This big question is 6 small questions, ***38 points)

17. Calculation (8 points for this small question):

⑴ ⑵

18. Solve the following equation (8 points for this small problem):

⑴ ⑵

19. (This small question is 5 points) As shown in the figure, there is a billboard MN on the roof of a building. Someone measured the elevation angles ∠NAE and ∠MCE of point B and point D, point N and point M respectively with a goniometer with a height of1.5m.. If BD=8m, DF = 6560.

20. (5 points for this short question) When trying a new shampoo, you need to choose two different additives from six additives with aromaticity of 0,/kloc-0, 2, 3, 4 and 5 respectively. According to the principle of experimental design, one of the three additives with aromaticity of 0, 1 2 is usually selected at random, and then one additive with aromaticity of 3 is selected. Test the aromaticity of the sum of their aromaticity. Please show all the possible results of aromaticity test of two different additives by tree diagram or list, and find out the probability that the sum of aromaticity is equal to 5.

2 1. (This small question has 6 points) As shown in the figure, it is known that E is a point in a square ABCD with a side length of 4, DE=3, and the ray DF⊥DE is in D. Is there such an m on DF, which makes the triangle with the vertices of C, D and M similar to △ADE? If yes, request the length of DM that meets the conditions; If it does not exist, please explain why.

22. (6 points in this small question) "Smoking is harmful to health!" In order to strengthen the macro-management of cigarette production and sales, the state implements an additional tax policy on cigarettes sold. Now we know that the market price of a certain brand of cigarettes is 70 yuan. Without tax, we sell 165438+ ten thousand cigarettes every year. If the state levies an additional tax, the tax rate will be X% (that is, for every 10x yuan sold, the annual sales will be reduced by 65,438 yuan).

23. If the rectangular ABCD can be divided into n small rectangles in some way, so that each small rectangle is similar to the original rectangular ABCD, then we say that the rectangular ABCD can be self-similar. It is known that AB= 1 and BC=x(x≥ 1).

(1) If the following diagram can be divided by self-similarity, please draw a sketch of the division in the diagram and find the value of x. 。

⑵ If the rectangular ABCD can be divided into three self-similar segments, please draw two different sketches and write the corresponding value of X directly.

①x =； ②x =。

24. (8 points in this small question) It is known that the vertex of the parabola is p (,), which intersects with the X axis at point A and point B, and intersects with the Y axis at point C, where the coordinate of point B is (1, 0).

(1) Find the functional relationship of this parabola;

⑵ If the parabola axis of symmetry intersects the X axis at point D, is there such a point Q on the line segment AC that △ADQ is an isosceles triangle? If yes, request the coordinates of the qualified point q; If it does not exist, please explain why.