Chongqing in 2000
I. Fill in the blanks (4 points for each question, 32 points for * * *)
1. Calculation: = _ _ _ _ _ _ _.
2. The solution of the equation is _ _ _ _ _ _ _.
3. Decomposition factor: = _ _ _ _ _ _.
4. As shown in the figure, in the rectangular coordinate ABCD, AB=2, BC = 1, E is a point on DC, ∠DAE=∠BAC, then the length of EC is _ _ _ _ _ _ _.
5. The tax calculation method of deposit interest stipulated by the state is: interest tax = interest × 20%. The annual interest rate of one-year time deposit in the bank is 2.25%. Today, Xiao Wang took out the principal and interest due in one year and paid the interest tax, 4.5 yuan, so the money that Xiao Wang kept in the bank a year ago was _ _ _ _ _ _ _.
6. As shown in the figure, ⊙O 1 and ⊙O2 are circumscribed at point P, and the inner common tangent PC and the outer tangent AB(A and B are the tangent points on ⊙O 1 and ⊙O2 respectively) intersect at point C, and it is known that ⊙ o/kloc-0.
7. As shown in the figure, in △ABC, AD= 1, DC = 2, AB = 4, E is a point above AB, and the area of △DEC is equal to half the area of △ABC, so the length of EB is _ _ _ _ _ _ _.
8. There is a point on the image of the inverse proportional function, whose coordinates are two quadratic equations about t, and the distance from p to the origin is, then the analytical formula of the inverse proportional function is _ _ _ _ _ _ _ _.
Second, multiple-choice questions (5 points for each small question, ***40 points)
9. Calculation, the result is correct ()
(A) (B) (C) (D)
10. As shown in the figure, in the parallelogram ABCD, DB = DC, ∠ C = 700, AE⊥ BD is in E, then ∠DAE is equal to ().
200 (B)250 (C)300 (D)350
1 1. If the score is 0, the value of x is ().
(a) or (B) (C) (0)
12. As shown in the figure, in the rectangular ABCD, AB= 1, AD=, and the arc MPN with the center point E in BC is tangent to AD, then the area of the shaded part in the figure is ().
(A) (B) (C) (D)
13. A family of three (father, mother and daughter) will join a tour group. A travel agency told them that "parents buy full tickets and daughters are half price". B tour group told them that "family tours can be priced according to group tickets, that is, everyone charges at full price". If the original fares of the two travel agencies are the same, then the preferential condition is ().
(a) A is more favorable than B; (b) B is more advantageous than a; (c) A is the same as B; (d) related to the original fare.
14. As shown in the figure, in ⊙O, the chord AD‖BC, DA=DC, ∠AOC= 1600, then ∠BCO is equal to ().
200 (B)300 (C)400 (D)500
15. If the image of the known function is as shown in the figure, then the image of the function can only be ().
16. As shown in the figure, at △ABC, ∠ BAC = 900, D is the midpoint of BC, and AE⊥AD intersects the CB extension line at E, then the conclusion is correct ().
(A)△AED∽△ACB(B)△AEB∽△ACD(C)△BAE∽△ACE(D)△AEC∽△DAC
Third, answer questions (***2 small questions, with a total score of 32 points)
17.( 16) In order to strengthen the public's awareness of water conservation, a city has formulated the following water charge standards: when the monthly water consumption of each household does not exceed 7 cubic meters, it will be charged 1.0 yuan per cubic meter, plus the urban sewage treatment fee in 0.2 yuan; For the part exceeding 7 cubic meters, the charge per cubic meter is 1.5 yuan, and the urban sewage treatment fee of 0.4 yuan will be added. Assume that a household's monthly water consumption is X (cubic meters) and the water fee payable is Y (yuan).
(1) Write the functional relationship between Y and X when the water consumption is less than 7 cubic meters and more than 7 cubic meters respectively;
(2) If a unit * * * has 50 users, the monthly water fee for * * * is 54 1.6 yuan, and the water consumption of each household does not exceed 10 cubic meter, then how many users may consume less than 7 cubic meters of water this month?
18. As shown in the figure, the image of the quadratic function has only one common point p with the X axis, and the intersection point with the Y axis is Q. The straight line passing through point Q intersects with the X axis at point A and intersects with the image of the quadratic function at another point B. If so, find the analytic expression of the quadratic function.
Four, solve the problem (16 points)
19. It is known that AC and AB are chords of ⊙O, and AB > AC.
(1) As shown in figure 1, can you determine a point E on AB so that AC2=AE? AB, why?
(2) As shown in Figure 2, under the conclusion of condition (1), extend EC to P and connect PB. If PB=PE, try to judge the positional relationship between PB and ⊙O, and explain the reasons.
(3) Under the condition (2), if E is the midpoint of PD, is C the midpoint of PE? Why?