1. Multiple choice questions: (* * 15 small questions, 3 points for each question, 45 points for * *).

1, in the following statement, the correct number is ().

① Any number has an arithmetic square root; ② Only positive numbers have arithmetic square roots;

③ Negative numbers must have no arithmetic square root; ④ The arithmetic square root must be a positive number.

1 (B)2 (C)3 (D)4。

2. If it is known that the image of the linear function and the image of the inverse proportional function intersect at point P(4, n), then the resolution function of the linear function is ().

(A) (B) (C) (D)

3, and the quadratic root is the same class is ()

(A) (B) (C) (D)

4, known, then the following proportional formula is ()

(A) (B) (C) (D)

5. In △ABC, AB=AC, ∠ A = 36, BD bisects ∠ABC at point D, and DE bisects ∠ BC at point E, so the number of triangles similar to △ABC in this triangle is ().

1 (B)2 (C)3 (D)0。

6. In △ABC, ∠ c = 90, and if so, the value is () (A) (B) (C) (D).

7, known, then the range of acute angle α is ()

(A) (B)

(C) (D)

Some students use the shadow of the water tower to measure the height of the tower. At a certain moment, they measured that the shadow length of a 1.8-meter-high bamboo pole was 0.6 meters. But when they immediately measured the height of the tower, because the water tower was close to a building, not all the shadows fell on the ground, but some fell on the wall. They measured the length of the shadow left on the ground as 12. 1 meter.

(a) 40.5m (b) 36.3m (c) 37.7m (d)13.5m.

9. As shown in the figure, in △ABC, AD⊥BC is in D, and the conditions are as follows:

①∠b+∠DAC = 90； ②∠B =∠DAC； ③ = ;

(4) ④AB =BD BC, where it can be judged that △ABC is a right triangle ().

1 (B)2 (C)3 (D)4。

10, if the point is on the inverse proportional function image, the following conclusion is correct ().

(A) (B) (C) (D)

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

(A) (B) (C) and (d)

12, as shown in the figure, in △ABC, p is a point above AB, in the following four cases:

①∠ACP =∠B； ②∠APC =∠ACB； ③∠CAP =∠BAC； ④ .

It can be determined that the similarity between △APC and △ACB is ()

(A)①②④ (B)①③④ (C)②③④ (D)①②③

13, a class of students to explore the relationship between spring length and external force, from the experimental records to get the corresponding data in the table below, then the function image about x and y is ().

Weight (x grams) 0 50/kloc-0 00/kloc-0 50 200 250 300 400 500

Pointer position (y cm) 2 3 4 5 6 7 7.5 7.5 7.5

(A) (B) (C) (D)

14. The unary quadratic equation about x has two unequal real roots, so the largest integer of x is ().

2 (B)- 1 (C)0 (D) 1

15, if it is the root of an unary quadratic equation and the root of an unary quadratic equation, then the value of is equal to ().

(A) 1 or 2 (B)0 or -3 (C)- 1 or -2 (D)0 or 3.

Fill in the blanks: (***5 small questions, 4 points for each small question, ***20 points)

16, when the value of the algebraic expression is 7, the value of the algebraic expression is.

17, simplified =.

18, if the two roots of the equation about x are, then the result of factorization with quadratic trinomial is.

19, as shown in the figure, in △ABC, ∠ABC=900, in △BCD, ∠BDC=900, AC= 13, AB=5. If the two right triangles in the figure are similar, BD=.

20. It is known that the point P is a point on the straight line y=2x-5, and the distance from the point P to the X axis is three times that to the Y axis, so the coordinate of the point P is _ _ _ _ _ _ _ _ _ _ _ _ _.

Three. Problem solving: (***55 points)

2 1. Solve the following unary quadratic equation in an appropriate way: (4 points for each small question, *** 16 points)

( 1) (2)

(3) (4)

22. (9 points in this question) The wing shape of an aircraft is shown in figure AB‖CD, and the lengths of AC, BD and CD are calculated according to the data in the figure. (Results Retain the root number)

23. (8 points for this question) Draw the image of the function and answer the following questions with the image:

(1) When, find the range of function value y 1, y2;

(2) When x takes what value, the value of function y 1 satisfies the conditional sum?

(3) What is the value of x?

24. (6 points in this question) It is known that the triangle area surrounded by the straight line Y = KX+3 and the two coordinate axes is 24, and the resolution function is found.

25. (8 points in this question) It is known that in △ABC, ∠ B = 35, AD is the height on the side of BC, and Ad2 = BD CD. Please draw a chart according to the known conditions.

(1) describes △ADC∽△BDA.

(2) Find the degree of ∠BCA.

26. (8 points in this question) One root of the known equation is-1, and it is evaluated; If the equation has other roots, then find them.

Reference answer

I. Multiple choice questions: (15×3=45)

The title is12345678 91012131415.

Answer A A C B B A A A C C C C C C A D D D D d