First, multiple-choice questions (3 points for each small question, out of 24 points)
1. The root of the unary quadratic equation is ()
A.x 1= 1，x2=6 B.x 1=2，x2=3 C.x 1= 1，x2=-6 D.x 1=- 1，x2=6
2. Among the following four geometric figures, the geometric figure in which the front view, left view and top view are congruent figures is ().
A. sphere B. cylinder C. triangular prism D. cone
3. The point with equal distance to three sides of a triangle is a triangle ()
A. Intersection of three bisectors of angles B. Intersection of three heights
C. Intersection point of vertical lines on three sides D. Intersection point of three median lines
4. If the area of a rectangle is 6cm2, then the functional relationship between its length and width is represented by an image.
Roughly ()
A B C D
5. Among the following functions, the inverse proportional function is ().
A.B. C. D。
6. In Rt△ABC, ∠ C = 90, a=4 and b=3, then the value of cosA is ().
A.B. C. D。
7. As shown in figure (1), in △ABC, ∠ A = 30, ∠ C = 90 AB median vertical line (1).
If AC is at point D and AB is at point E, the following conclusion is wrong ().
a、AD=DB B、DE=DC C、BC=AE D、AD=BC
8. The quadrangle obtained by connecting the midpoints of the sides of the isosceles trapezoid in turn is ()
A, rectangle b, diamond c, square d, parallelogram
Fill in the blanks (3 points for each small question, out of 2 1 point)
9. calculate tan 45 =.
10. Suppose the function is an inverse proportional function and the value of m is.
1 1. Please write the analytical formula of the inverse proportional function so that it is in the second quadrant and the fourth quadrant.
12. In a right triangle, if two right-angled sides are 6 cm and 8 cm respectively, then the median line on the hypotenuse is long.
For cm.
13. As we all know, the circumference of a diamond is and the length of the diagonal is, so the area of this diamond is.
It's (cm) 2.
14. Given that the intersection of the proportional function and the inverse proportional function is (2,3), then the other one
The intersection point is (,).
15. As shown in the figure, AC=DB is known, and it is necessary to add △ ABC △ DCB.
On the condition that.
Third, answer the question (this big question ***9 small questions, out of 75 points)
16. (8 points in this small question) Solve the equation:
17. (This small question is 8 points.) As shown in the figure, in △ABD, c is a point on BD.
And AC⊥BD, AC = BC = CD. (1) proves that △ABD is an isosceles triangle.
(2) Find the degree of ∠ bad.
18. (This small question is 8 points) As shown in the figure, in extracurricular activities, Xiao Ming measured the elevation of the top of flagpole A with a goniometer. It is known that the height CD of the goniometer is meters, so find the height of flagpole AB. (accurate to the meter)
(Optional data:,,)
19. (8 points in this small question) The turnover of a store in April was 400,000 yuan, and the turnover in May was higher than that in April. In June, it increased by 5 percentage points, that is, by 5%, and the turnover reached 506,000 yuan. Find the percentage of growth in May.
20. (8 points in this small question) "If one party is in trouble, all parties will support it". On June 2nd this year 165438+ Ejina suffered a flood disaster, which touched the hearts of the people in the county. The hospital is going to send a doctor and a nurse from three doctors A, B and C and two nurses A and B to support the flood relief work in Ejina.
(1) If a doctor and a nurse are randomly selected, all possible results are represented by tree diagram (or list method).
(2) Find the probability of choosing doctor A and nurse A accurately.
2 1. (8 points in this small question) As shown in the figure, in △ABC, AC=BC, ∠ C = 90, AD is the bisector of △ABC, DE⊥AB, and the vertical foot is E. 。
(1) Given CD=4cm, find the length of AC.
(2) verification: AB = AC+CD.
22.(8 points) There is a δ ABC in the square paper of 12×24 as shown in the figure (the side length of each small square is 1 unit). Now, move Δ ABC to the right by 8 units and 3 units respectively to get Δ A1b1c1; Then turn δa 1b 1c 1 clockwise by 90? Get δ A2B2C2. Please make Δ a1b1c1and Δ a2b2c2 in the given grid paper.
23. (The full mark of this question is 9 points)
As shown in the figure, four equations are given: ① AE = AD; ②AB = AC； ③OB = OC； ④ ∠ B = ∠ C. Now we choose three of them, two as known conditions and one as conclusion.
(1) Please write a correct proposition and prove it;
Please write at least three such correct propositions.
24.( 10) As shown in the figure, it is known that the inverse proportional function and the linear function y=2x- 1, in which the image of the linear function passes through (a, b), (a+ 1, b+k).
(1) Find the analytical formula of inverse proportional function;
(2) As shown in Figure 4, point A is known to be in the first quadrant, and the coordinates of point A are found on the images of the above two functions;
(3) Using the result of (2), may I ask: Is there a point P on the X axis that makes △AOP an isosceles triangle? If it exists, find out all the coordinates of P points that meet the requirements; If it does not exist, please explain why.