I. Multiple-choice questions (the full score of this question is 24 points, and there are 8 small questions in total, with 3 points for each small question).
L, the following statement:
(1) is an irrational number.
(2) The zeroth power of any number is equal to 1.
(3)
(4) When is the correct one? ()
a， 1 b，2 c，3 d，4
2. If the semi-meridians of two circles are 4 and 6 respectively, and the center distance is 10, then the positional relationship between the two circles is ().
A, including b, circumscribed c, intersected d, circumscribed
3. As shown in the figure, if there are two points E and F on the diagonal AC in ABCD and AE=CF, the logarithm of congruent triangles in the figure is ().
A, 3 pairs of B, 4 pairs of C, 5 pairs of D, 6 pairs.
4. It is known: then the mirror image of the function must not pass ()
A, the first quadrant b, the second quadrant c, the third quadrant d and the fourth quadrant
5. The value range of the independent variable X of the function is ()
A, b, all real numbers c, d,
6. In the circle inscribed quadrilateral ABCD, it is known that ∠ A: ∠ B: ∠ C = 2: 1: 4, then ∠D is equal to ().
A, B, C, D,
7. The distance between the two cities along the river is kilometers, the speed of the ship in still water is kilometers/hour, and the speed of the water flow is kilometers/hour, so the time required for the ship to make a round trip is ().
A, B, C, D,
8. If the image of the quadratic function is as shown on the right, then the following inequality does not hold.
Yes ().
a、gt； 0 B、C、D、
2. Fill in the blanks (the full score of this question is 24 points, and there are 8 small questions in total, with 3 points for each small question)
9. If the ratio of the external angles corresponding to ∠A∠B∠C in △ABC is 3: 4: 5, the tangent of the minimum internal angle is _ _.
10, it is known that point p is in the second quadrant, and the distance to the axis is 2, and the distance to the y axis is 3, then the coordinate of point p is _ _.
1 1, if, acute angle = _ _ _ degrees.
12. If half of the difference between the two bottoms of an isosceles trapezoid is equal to its height, then the degree of the smaller bottom angle in this trapezoid is _ _ _ _ _.
13. The opposite sides of ∠A and ∠B in △ ABC are A and B respectively. It is known that when A > B, there must be ∠ a >; B, please use the word _ _ _ _ to describe the above proposition.
14, factorization in real number range: _ _ _ _ _ _.
15. If the equation has two unequal real roots, the maximum integer value of m is _.
16, as shown in the figure, PT is the tangent of Ω Ω, the tangent point is t, m is a point within Ω Ω o, PM passes through Ω Ω Ω Ω Ω Ω Ω Ω Ω Ω Ω Ω Ω Ω Ω Ω Ω Ω Ω Ω Ω 9
Third, the drawing question (this question is out of 4 points, only one small question)
Draw with compasses and rulers, but don't write, keep it as a trace.
17. To cut a semicircular iron sheet on a right triangle (as shown below), you need to draw a half picture on this iron sheet first, so that its center is on AC and tangent to AB and BC.
Fourth, answer the question (the full mark of this question is 68, and there is a small question of 10 in * *).
18, (full score for this small question)
The two roots of the quadratic equation of one variable are less than 1, so try to take the value range.
19, (full score for this small question)
There are 7 employees in a hotel * * *, and the salaries of all employees are shown in the following table:
Answer the following questions. (Fill in the horizontal line directly):
(1) The average salary of all employees in the restaurant is _ _ _ _ _ _ yuan.
(2) The median salary of all employees is _ _ _ _ yuan.
(3) Is it more appropriate to describe the general salary level of employees in this restaurant with average or median?
A: _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _.
(4) After the manager's salary is removed, the average salary of other employees is _ _ _ _ _ yuan. Can it also reflect the general level of employees' posture in this restaurant? A: _ _ _ _ _ _ _ _ _ _.
20. (This small question is full of 6 points);
As shown in the picture on the right, lighthouse C measured by seagoing ships in B is in the northeast. From B, sail due north at a speed of 15 nautical miles per hour. Two hours later, it arrived at A, and lighthouse C was in its northeast. Find the distance from b to lighthouse C.
2 1. Simplify the following categories (full marks for this small question)
( 1) (2)
22. (The full score for this short question is 6)
The distance between A and B is 150km. Two cars, A and B, leave from A and B at the same time, face to face and meet in two hours. After meeting, they continued to drive at the original speed. When car A arrived at place B, it immediately went back the same way, which was twice as fast as before. As a result, a car and b car arrive at a place at the same time, and find the original speed and the speed of b car.
23. It is known that △ABC is an equilateral triangle, D and F are points on BC and AB respectively, CD=BF, and AD is an equilateral triangle ADE. ..
(1) Verify △ ACD △ CBF;
(2) Where is the point D on 2)BC, the quadrilateral CDEF is a parallelogram, and ∠DEF=? Prove your conclusion.
24. (The full score for this short question is 6)
As shown in the figure, in quadrilateral ABCD, diagonal AC and BD intersect at point E. If AC bisects ∠DAB and AB=AE and AC=AD, there are four conclusions as follows:
( 1)ac⊥bd；
(2)BC = DE；
(3)DBC =∠DAB；
(4)△ Abe is a regular triangle.
Please write the serial number of the correct conclusion (fill in all the serial numbers you think are correct).
25. (The full score for this short question is 8)
Student A walks 3 kilometers per hour. 1.5 hours later, classmate b chased party a at a speed of 4.5 kilometers per hour, and party b walked for t hours.
(1) Write the relationship between the distance S traveled by students A and B and the time T;
(2) Make their images in the same coordinate system;
(3) Find the coordinates of the intersection of two straight lines and write its practical significance.
26. (The full score of this small question is 8) It is known that P is a point on the BC string of the equilateral △ABC circumscribed circle, and AP passes BC to E,
Proof: (1) (2)
27. (Full score for this small question 10)
As shown in the figure, in the known inscribed triangle ⊙, BC is the diameter, and the tangent passing through point A as ⊙O intersects with the extension line of CB at point P, and the chord BD makes ∠ABD=∠PAC.
(1) verification: AC=AD
(2) Verification:
(3) If the inequality group is a positive integer solution, BC is the solution of the equation, BP=, BD=, and the functional relationship between summation;
(4) Under the conclusion of (3), when BD=2BP, find the sine value of ∠ p. 。