Seek the mathematics examination paper of Chongqing senior high school entrance examination in 2006.

In 2006, junior high school graduates in Chongqing entered higher schools and entered the senior high school entrance examination.

First, multiple-choice questions:

The reciprocal of 1.3 is ()

A.- the third century BC.

2. The result of calculation is ()

A.B. C. D。

3. The radius of ⊙O is 4, and the distance from the center of O to the straight line is 3, so the positional relationship between the straight line and ⊙ O is ().

A. Intersection B. Tangency C. Separation D. Uncertainty

4. The range that makes the score meaningful is ()

A.B. C. D。

5. The solution set of inequality group is ()

A.b.c.d has no solution.

6. As shown in the figure, if the diameter CD of ⊙O passes through the midpoint G of the chord EF and ∠ EOD = 40, then ∠DCF is equal to ().

A.80 B. 50 C. 40 D. 20

7. (Curriculum Reform) As shown in the figure, a geometric figure composed of several identical small cubes has three views, so the number of small cubes that make up this geometric figure is. ()

A.3 B.4 C. 5 D. 6

The solution of (non-curriculum reform) fractional equation is ()

A.B.

C.D.

8. Observe the statistics of the annual growth rate of per capita income of rural residents in Chongqing during the Tenth Five-Year Plan period issued by the Municipal Bureau of Statistics. The following statement is true ()

A the per capita income of rural residents in A.2003 was lower than that in 2002.

B the per capita income of rural residents has been lower than 9% of the previous year for two consecutive years.

C in C.2004, when the per capita income of rural residents was the highest.

D the growth rate of per capita income of rural residents is quite different from that of the previous year, but the per capita income of rural residents continues to increase.

9. Exemption from agricultural tax has greatly improved farmers' enthusiasm for production. The town government instructed farmers to process the produced local products into three different packages, A, B and C, and sell them in the market. The relevant information is as follows:

Quality (g/bag) Sales price (yuan/bag) Packaging cost (yuan/bag)

A 400 4.8 0.5

B 300 3.6 0.4

C 200 2.5 0.3

During the Spring Festival, these three kinds of packaged native products sold 1200 kg, so in this sale, the biggest profit of these three kinds of packaged native products is ().

Not sure.

10. (Curriculum reform) There are two unified cubes A and B (each side of the cube is marked with the numbers 1, 2, 3, 4, 5 and 6 respectively). If Xiaoli throws up the number of cube A and Xiaoming throws up the number of cube B to determine point P (), then the determined point P falls on the known parabola once each.

A.B. C. D。

(Non-curriculum reform) It is known that a quadratic equation with one variable has two unequal real roots and satisfies them, then the value is ().

A.3 or-1b.3c.1d. –3 or 1.

Second, fill in the blanks:

1 1. The highest temperature in Chongqing on a certain day is 17℃, and the lowest temperature is 5℃, so the maximum temperature difference on that day is℃.

12. Decomposition factor: =

13. As shown in the figure, given a straight line, ∠ 1 = 40, then ∠2= degrees.

14. If the circumference of the bottom surface of the cylinder is, and the height is 1, the area of the cylinder side development diagram is.

15. Waste batteries are very harmful to the environment. A button cell can pollute 600 cubic meters of water (equivalent to a person's lifetime drinking water). There are 50 students in a class. If every student throws away a button cell a year and none of it is recycled, then the water that can be polluted in the button cell discarded by the students in this class is expressed as cubic meters by scientific counting method.

16. (Curriculum reform area) As shown in the figure, if the image of the sum of functions is known to intersect at point P, it can be found according to the image, and the solution of the binary linear equations is

(Non-curriculum reform) Simplification: =

17. As shown in the figure, A and B are grid points in a 4×5 network, and the side length of each small square in the grid is 1. Please clearly mark the position of all lattice points C that make the triangle with vertices A, B and C an isosceles triangle in the diagram.

18. The number of a column arranged according to a certain rule is arranged in sequence. If the column is arranged according to this rule, the seventh number of this column is.

19. As shown in the figure, the two sides OC and OA of the right-angle AOCB are located on the axis and the axis respectively, and the coordinate of point B is b (), and d is a point on the side AB. Fold △ADO along the straight line OD, so that the point A just falls on the point E on the diagonal line OB. If the point e is on the image of the inverse proportional function, the analytical formula of the function is

20. As shown in the figure, △ABC is inscribed in ⊙O, and the degree of the arc subtended by ∠A is 120.

The bisectors of ∠ABC and ∠ACB intersect at point D and point E respectively, and CE and BD intersect at point F, and the following four conclusions are drawn: ①; ② ; ③ ; (4). The conclusion is definitely correct. The serial number is

Iii. Answer: (This big question is 6 small questions, ***60 points)

2 1. (5 points for each small question, *** 10)

(1) calculation:;

(2) Solve the equation:

22. As shown in the figure, A, D, F and B are on the same straight line, with AD = BF and AE = BC.

And AE∨BC

Verification: (1) △ AEF △ BCD; (2)EF∑CD。

23.( 10) During the social practice in the summer vacation, students in Xiaoming's group contacted a toy manufacturer to assemble toys for the factory, and the factory agreed to assemble 240 sets of toys. These toys are divided into three models: A, B and C, and their number ratio and the number of toys assembled by each person per hour are as follows:

If everyone can assemble the same type of toys at the same speed, complete the following blanks according to the above information:

(1) As can be seen from the above statistics, Class A toys have sets, Class B toys have sets, and Class C toys have sets.

(2) If it takes everyone the same time to assemble 16 sets of type A toys and 12 sets of type C toys, then this value means that everyone can assemble type C toy sets every hour.

24.( 10) The Institute of Agricultural Sciences recommended Yujiang 1 and Yujiang 2 to farmers. Under the same field management and soil quality conditions, the yield per unit area of No.2 rice is 20% lower than that of No.1 rice, but the quality of No.2 rice is good and the price is higher than that of No.1 rice. It is known that the purchase price of No.1 rice country is 1.6 yuan/kg.

(1) What is the national purchase price of No.2 rice? Are the benefits of planting No.1 rice and No.2 rice the same on two plots of Tian Li with the same field management, drawings and area?

(2) Last year, Xiao Wang planted without me and without me. II. Rice is managed in the same field in two fields with the same soil quality and area. After harvesting, Xiao Wang sold all the rice to the country. When it was sold to the country, the national purchase price of rice without II was set as 2.2 yuan/kg, and the purchase price was the same as my rice price in the whole country, so Xiao Wang earned 1040 yuan more than that without rice price. I grow rice, so Xiao Wang sold it to the country last year.

25. As shown in the figure, in the trapezoidal ABCD, AB∥CD, ∠ BCD = 90, AB= 1, BC=2, and tan∠ADC=2.

(1) Verification: DC = BC;

(2) E is the point inside the trapezoid, F is the point outside the trapezoid, and ∠EDC=∠FBC, DE=BF, try to judge the shape of △ECF and prove your conclusion;

(3) under the condition of (2), when be: ce = 1: 2 and ∠ BEC = 135, find the value of sin∠BFE.

26. Machining needs lubrication to reduce friction. An enterprise processes 90kg of lubricating oil for a large mechanical equipment, and the reuse rate of the oil is 60%. According to this calculation, the actual fuel consumption for processing a large mechanical equipment is 36kg. In order to build a conservation-oriented society and reduce fuel consumption, both workshop A and workshop B of the enterprise organize personnel to tackle key problems and reduce actual fuel consumption.

(1) After the technical transformation of workshop A, the consumption of lubricating oil for processing a large mechanical equipment was reduced to 70kg, and the oil reuse rate was still 60%. What is the actual fuel consumption of processing a large mechanical equipment after technical transformation in workshop A?

(2) After technical transformation, workshop B not only reduced the consumption of lubricating oil, but also improved the reuse rate of oil. It is found that on the basis of technological innovation, the reuse rate of oil will increase by 65,438 0.6% for every reduction of lubricating oil consumption by 65438±0kg. In this way, the actual fuel consumption of workshop B for processing a large mechanical equipment decreased to 12kg. After technical innovation, workshop b asked. What is the reuse rate of oil?

Fourth, solve big problems:

27. It is known that there are two real roots of the equation, and the image of parabola passes through point A () and point B ().

(1) Find the analytical expression of this parabola;

(2) Let the other intersection of the parabola and the axis in (1) be C and the vertex of the parabola be D, and find the coordinates of points C and D and the area of △BCD; (Note: the vertex coordinate of parabola is ()

(3) P is a point on the line segment OC, and the passing point P is the axis of PH⊥, which intersects with the parabola at point H. If the straight line BC divides the △PCH into two parts with an area ratio of 2: 3, the coordinates of point P are required.

28. as shown in figure 28- 1, a triangular piece of paper ABC, ∠ ACB = 90, AC = 8, BC = 6. Cut this paper into two triangles along the center line CD of the hypotenuse AB (as shown in Figure 28-2). Translate the paper along the straight line (AB) (the points are always on the same straight line).

(1) When panning to the position shown in Figure 28-3, guess the quantitative relationship between sum in the figure and prove your guess;

(2) If the translation distance is and the overlapping area is, please write the functional relationship between sum and the range of independent variables;

(3) Whether there is such a value for the conclusion in (2); If it does not exist, please explain why.

Answer: multiple-choice question:1-5caabc6-10dbdcb.

2. Fill in the blanks:11.12; 12.； 13.40; 14.； 15.； 16. (curriculum reform), (non-curriculum reform); 17. As shown in the figure,

18.； 19.； 20.①③

Iii. 2 1. ( 1); (2)

22.( 1) Because AE∨BC, ∠ A = ∠ B.

Because AD=BF, AF=AD+DF=BF+FD=BD.

Because AE=BC, so △ AEF △ BCD.

(2) Because △ AEF △ BCD, ∠EFA=∠CDB. So EF∨CD

23.( 1) 132,48,60,(2) 4,6,

24.( 1) Get (yuan) from the meaning of the question;

(2) According to the meaning of the question, the number of kilograms of No.1 rice sold to the country is obtained.

Solution (kg)

(kg)

Answer: (1) When the national purchase price of No.2 rice is 2 yuan, the benefits of planting No.1 rice and No.2 rice are the same;

(2) Last year, Xiao Wang sold to the state 1 1700 kg of rice.

25.( 1) when DC intersects DC at m, the vertical line AM passes through a,

Then AM=BC=2

And tan∠ADC=2, so. In other words, DC = BC.

(2) isosceles triangle.

Proof: Because.

So, △ DEC △ BFC

So ...

So,

That is, △ECF is an isosceles right triangle.

③ If, then, then.

Because, again, so.

therefore

So ...

26.( 1) From the meaning of the question, get (kg)

(2) The consumption of lubricating oil for processing a large mechanical equipment in Workshop B is kg.

From the meaning of the question, get

Pack up, take it

Solution: (Give up)

Answer: (1) After the technical transformation, the actual oil consumption of processing a large mechanical equipment in Workshop A is 28kg.

(2) After the technical transformation, the lubricating oil consumption for processing a large mechanical equipment in workshop B is 75 kg? The reuse rate of oil is 84%.

27.( 1) Solve the equation

By, have

So the coordinates of point A and point B are A (1, 0) and B (0, 5) respectively.

Substitute the coordinates of a (1, 0) and b (0, 5) respectively.

To solve this system of equations, you must

Therefore, the analytical formula of parabola is

By, make, get

To solve this equation, you must

So the coordinates of point C are (-5,0). From the formula of vertex coordinates, the point d (-2,9) is obtained.

The vertical line through d intersects m.

rule

So ...