I. Multiple-choice questions (Only one of the alternative answers to the following questions is correct. Please fill in the serial number of the correct answer in the table below under the corresponding question number. There are 8 small questions in this answer, with 3 points for each small question and 24 points for * * *).

1．（20 10? The opposite of Heyuan)-2 is ()

A．﹣2　　B．﹣　C．　D．2

2.20 1 1 March, 2008 11day, a 9.0 magnitude earthquake and tsunami occurred in Japan, which caused great losses to the Japanese people, and many people lost their homes. As of April1day, there were still about16 people taking refuge in various shelters.

A． 166× 103　　B． 16.6× 104　　C． 1.66× 105　　D．0. 166× 106

3．（2007? Taizhou) The expansion diagram of a geometry is as shown in the figure, then the vertex of the geometry has ().

A． 10/0 b.8 c.6 d.4.

4．（2006? Jinan) A fast food restaurant prepared a batch of box lunches with rice and different stir-fry dishes. There are 25 boxes of fried pork with shredded potatoes, 30 boxes of fried pork with celery, 10 box of fried eggs with peppers, and 15 box of fried pork with kidney beans. The size and shape of each box lunch are the same, so the probability of choosing one box without peppers is ().

A．　B．　C．　D．

5．（20 10? Fuzhou) It is known that the image of the inverse proportional function y= (k≠0) passes through the point (1, 3), then the image of the inverse proportional function is in ().

A. first and second quadrants B. first and third quadrants C. second and fourth quadrants D. third and fourth quadrants

6. Given that a point of intersection of the parabola y = x2-x-0/and the X axis is (m, 0), the value of the algebraic expression m2-m+2010 is ().

A．2008　　B．2009　　C．20 10　　D．20 1 1

7．（20 10? Lishui) As shown in the figure, after a square piece of paper with a side length of (m+3) is cut into a square with a side length of m, the rest is cut and spliced into a rectangle (without overlapping and seamless). If one side of the spliced rectangle is 3, the other side is ().

A．2m+3　　B．2m+6　　C．m+3　　D．m+6

8．（20 10? As shown in the figure of Tongnan County, quadrilateral ABCD is a square with a side length of 1, quadrilateral EFGH is a square with a side length of 2, point D coincides with point F, and points B, D(F) and H are on the same straight line. The translation in the H direction stops when the point B coincides with the point H. If the distance between the points D and F is X and the area of the overlapping part of the square ABCD and the square EFGH is Y, the image that can roughly reflect the functional relationship between Y and X is ().

A．　B．　C．　D．

Second, fill in the blanks (this big question ***8 small questions, 3 points for each small question, ***24 points)

9．（2005? Zhangzhou) calculation:-2× 3 = _ _ _ _ _ _ _.

10．（2009? Shaoyang) as shown in the figure, AB∥CD, straight line EF intersects AB and CD at two points, E and F respectively, EP bisects ∠AEF, and the crossing point F is FP⊥EP, and the vertical foot is P. If ∠ PEF = 30, then ∠ PFC = _ _ _ _ _.

11.It is known that the image of the linear function y=(a﹣ 1)x+b is as shown in the figure, so the value range of a is _ _ _ _ _ _ _ _.

12．（2004? Beibei District) In order to develop the agricultural economy and become rich and well-off, Wang Dabo, a professional chicken farmer, raised 2,000 chickens in 2004. Before going on the market, he randomly selected 10 chickens, and weighed them in the following table: It is estimated that the total weight of these chickens is _ _ _ _ _ _ _ _ kg.

Weight (unit: kg) 2 2.2 2.5 2.8 3

Quantity (unit: only)12421

13. As shown in the figure, in trapezoidal ABCD, AB∥DC, AB⊥BC, AB=2cm, CD = 4 cm. A circle centered on a point O on BC passes through two points A and D, and ∠ AOD = 90, then the distance from the center O to the chord AD is _ _.

14．（2009? Shenzhen) Xiaoming and Xiaobing participated in the physical and chemical experiment operation test organized by the school. The recent five test results are shown in the figure, so the relationship between the variance S 12 of Xiaoming's five grades and the variance S22 of Xiaobing's five grades is S12 _ _ _ _ _ _ _ S22.

(Fill in ">", "<" and "=")

15．（2009? Qingyang) As shown in the figure, square OEFG and square ABCD are similar shapes, the coordinates of point F are (1, 1), and the coordinates of point C are (4,2), so the coordinates of the similarity centers of these two squares are _ _ _ _ _ _ _ _.

16. There is a column number a 1, a2, a3, a4, a5, …, where a 1=5×2+ 1, a2=5×3+2, a3=5×4+3, A4 =.

Iii. Solving problems (this big problem consists of ***2 questions, each with 8 points, *** 16 points)

17．（2006? Neijiang) Simplify first and then evaluate:, where a = b =1.

18．（2008? Qingyang) In the grid paper as shown in the figure, each small square is a square with a side length of 1 unit, and the three vertices of △ABC are all on the grid. (The vertices of each small square are called grid points)

(1) Draw △ A1b1c1after △ABC is shifted down by 3 units;

(2) Draw △A2B2C2 after △ABC rotates 90 clockwise around point O, and find the route length that point A rotates to A2.

Fourth, solve the problem (this big problem ***2 questions, each question 10, ***20 points)

19．（2007? In order to investigate the students' participation in extracurricular sports activities in a middle school in Linfen, a sampling survey was conducted to investigate the interests and hobbies of several students from five aspects, such as basketball, volleyball, table tennis, football and others (each student can only choose one of them), and the survey results were drawn into the following two incomplete statistical figures. Please answer the following questions according to the information provided in the figures:

(1) How many students were investigated in this investigation?

(2) In the fan-shaped statistical chart, what is the central angle of the table tennis part?

(3) Complete the bar chart;

(4) If there are 1800 students in the whole school, how many students like basketball in this school?

20. As shown in the figure, a turntable is evenly divided into six equal parts, and each sector is marked with a corresponding number. Party A and Party B rotate the turntable respectively, so that the number in the area pointed by the pointer is X after Party A rotates the turntable, and the number in the area pointed by the pointer is Y after Party B rotates the turntable (when the pointer is on the boundary, rotate it again until it points to an area).

(1) Write directly the probability that the number in the indicated area is negative after A rotates the turntable;

(2) Find the probability that the point (x, y) falls in the second quadrant by tree diagram or list method.

V. Solving problems (there are ***2 problems in this big problem, each with 10 score and ***20 score).

21.The "oil pipeline project for every village" has accelerated the pace of building a new socialist countryside in Jinzhou. As shown in the figure, villagers in village C want to build a cement road to connect village C with county-level highways. At highway A, it is measured that village C is 60 east of north, advancing 600 meters, and at highway B, it is measured that village C is 45 east of north.

(1) In order to save resources, it is required to build the shortest road length, and try to find the qualified road length. (Accurate to the meter, reference data: = 1.4 14, = 1.732, =2, = 1)

(2) According to the budget, it will cost about RMB 300,000 yuan to build a cement road with a length of 1000 meters. According to the relevant national policies, the government will allocate RMB100,000 yuan for the construction of this cement road, and the rest will be raised by the villagers spontaneously. Try to find out how many yuan the villagers need to raise by themselves to build this cement road.

22. When a clothing store sells a certain T-shirt at the marked price, each piece can make a profit in 45 yuan; If you sell each item at a 10% discount, you can still make a profit, 25 yuan.

(1) How much is the purchase price and the list price of each piece of this T-shirt?

(2) If each T-shirt is purchased according to the purchase price calculated in (1) and sold at a marked price, the mall can sell this kind of T-shirt 100 every day. If each T-shirt is reduced by 1 yuan, four more T-shirts can be sold every day. How much is each T-shirt reduced for sale? Get the biggest profit every day? What is the maximum profit?

Six, answer questions (this big question ***2 questions, each question 10 points, ***20 points)

23. As shown in the figure, AB is the diameter of ⊙O, crossing point E on ⊙O is the tangent of ⊙O, intersecting AB extension line at point C, crossing point A is AD⊥CE at point D, and intersecting with ⊙O at point F, connecting AE and BF.

Whether (1)AE is the bisector of ∠CAD, and explain the reasons;

(2) If CB=2 and CE=4, find the radius of ⊙O and the length of BF.

24．（2007? Quanzhou) Li Ming takes a bus from Quanzhou along expressway to A. It is known that the average speed of the bus is 100 km/h, and the distance from Quanzhou after driving for t hours is s 1 km.

(1) Please express s1with an algebraic expression containing t;

(2) Suppose another wang hong takes a bus from A to Quanzhou along the same expressway at the same time. It is known that the functional relationship between the distance s2 (km) from Quanzhou and the driving time t (h) is s2=kt+b(k and t are constants, k≠0). If it takes Li Hong 9 hours to return to Quanzhou from A, and when t=2, S2 = 560.

② Before two cars meet, when the driving time t is within what range, the distance between the two cars is less than 288km?

Seven, answer the question (this question *** 12 points)

25. As shown in figure 1, in Rt△ABC, ∠ ACB = 90, ∠ A = 30, P is any point on the side of BC, and point Q is the moving point of AC, with CP and PQ as sides to make equilateral △PCF and equilateral △PQE, respectively, to connect EF.

(1) Try to explore the positional relationship between EF and AB and prove it;

(2) As shown in Figure 2, when point P is any point on the BC extension line, is the conclusion (1) valid? Please explain the reason.

(3) As shown in Figure 3, in Rt△ABC, ∠ ACB = 90, ∠ A = M, P is a point on the extension line of BC, and point Q is an AC boundary moving point. Make isosceles △PCF and isosceles △PQE around CP and PQ, respectively, so that PC=PF, PQ=PE, and connect EF. Why?

Eight, answer questions (this question *** 14 points)

26. As shown in the figure, it is known that a parabola passes through the origin O and another point A on the X axis, and its symmetry axis X =-2 intersects with the X axis at point C, and the straight line Y =-2x+1passes through a point B(2, m) on the parabola and intersects with the Y axis X =-2 at points D and D respectively.

(1) Find the value of m and the function relation corresponding to this parabola;

(2)① Judge the shape of △CBE and explain the reasons; ② Judge the position relationship between CD and BE;

(3) If P(x, y) is a moving point on the parabola, is there such a point P that PB=PE? If it exists, try to find the coordinates of all qualified points p; If it does not exist, please explain the reason.

20 1 1 year in Jinzhou City, Liaoning Province, a model of mathematics examination paper.

Reference answers and analysis of test questions

I. Multiple-choice questions (Only one of the alternative answers to the following questions is correct. Please fill in the serial number of the correct answer in the table below under the corresponding question number. There are 8 small questions in this answer, with 3 points for each small question and 24 points for * * *).

1．（20 10? The opposite of Heyuan)-2 is ()

A．﹣2　　B．﹣　C．　D．2

Test center: the opposite number.

Analysis: The inverse of a number is to add a ﹣ sign in front of it.

Answer: the inverse of the solution: 2 is 2. So choose D. 。

Comments: This question examines the meaning of the inverse number. The inverse number of a number is to add a "﹣" before this number. The inverse number of a positive number is negative, the inverse number of a negative number is positive, and the inverse number of 0 is 0.

2.20 1 1 March, 2008 11day, a 9.0 magnitude earthquake and tsunami occurred in Japan, which caused great losses to the Japanese people, and many people lost their homes. As of April1day, there were still about16 people taking refuge in various shelters.

A． 166× 103　　B． 16.6× 104　　C． 1.66× 105　　D．0. 166× 106

Test center: scientific notation-indicating a larger number.

Special topic: regular questions.

Analysis: The scientific notation is expressed in the form of a× 10n, where/kloc-0 /≤| a | <10, and n is an integer. When determining the value of n, it depends on how many decimal places are moved when the original number is changed into a, and the absolute value of n is the same as the number of decimal places moved. When the absolute value of the original number is greater than/kl. When the absolute value of the original number is <1,n is negative.

Solution: The universal scientific notation of166,000 is expressed as1.66×105.

So choose C.

Comments: This topic examines the representation of scientific notation. The representation of scientific notation is in the form of a× 10n, where1≤| a | <10, and n is an integer. The key to representation is to correctly determine the value of a and the value of n. 。

3．（2007? Taizhou) The expansion diagram of a geometry is as shown in the figure, then the vertex of the geometry has ().

A． 10/0 b.8 c.6 d.4.

Test center: the expanded drawing of geometry.

Analysis: The three-dimensional figure is determined to be a triangular prism by the folding of the plane figure and the characteristics of the surface expansion diagram of the three-dimensional figure, and the problem is solved according to the characteristics of the triangular prism.

Solution: According to the observation diagram, this is an expanded diagram of a triangular prism with three squares on its sides, so there are six vertices in the geometry.

So choose C.

Comments: The key to this problem is to determine the expansion diagram of triangular prism first, and then determine that the number of vertices is 2×3=6.

4．（2006? Jinan) A fast food restaurant prepared a batch of box lunches with rice and different stir-fry dishes. There are 25 boxes of fried pork with shredded potatoes, 30 boxes of fried pork with celery, 10 box of fried eggs with peppers, and 15 box of fried pork with kidney beans. The size and shape of each box lunch are the same, so the probability of choosing one box without peppers is ().

A．　B．　C．　D．

Test center: probability formula.

Analysis: dividing the number of boxes without pepper by the total number of boxes is the probability of choosing one box without pepper.

Solution: There are 25 boxes of fried pork with shredded potatoes, 30 boxes of fried pork with celery, 10 boxes of fried eggs with peppers, and 15 boxes of fried pork with kidney beans, all of which are 80 boxes, and 70 boxes without peppers, so the probability of choosing one box without peppers is =.

So choose a.

Comments: This question is relatively easy to examine the probability under possible conditions. The knowledge points used are: probability = the ratio of the number of cases requested to the total number of cases.

5．（20 10? Fuzhou) It is known that the image of the inverse proportional function y= (k≠0) passes through the point (1, 3), then the image of the inverse proportional function is in ().

A. first and second quadrants B. first and third quadrants C. second and fourth quadrants D. third and fourth quadrants

Test center: the nature of inverse proportional function.

Analysis: Using the properties of inverse proportional function, k = 3 > 0, the function is located in the first and third quadrants.

Solution: The image passing point (1, 3) of the inverse proportional function y= (k≠0),

∴ Substitute y= (k≠0), k=3, that is, k > 0,

According to the properties of inverse proportional function, the image of inverse proportional function is in the first and third quadrants.

So choose B.

Comments: This question examines the nature of inverse proportional function, focusing on the value of k in y=.

6. Given that a point of intersection of the parabola y = x2-x-0/and the X axis is (m, 0), the value of the algebraic expression m2-m+2010 is ().

A．2008　　B．2009　　C．20 10　　D．20 1 1

Test site: the intersection of parabola and x axis; Algebraic evaluation.

Analysis: According to the parabola y=x2﹣x﹣ 1 and the intersection with the X axis is (m, 0), it is obtained by substituting it into resolution function, and the value of m2﹣m is obtained, and the correct answer is obtained by substituting it into m2﹣m+20 10.

Solution: Solution: ∵ Parabola y=x2﹣x﹣ 1 An intersection with the X axis is (m, 0).

∴ Substitute the point (m, 0),

0=m2﹣m﹣ 1，

∴m2﹣m= 1，

The value of ∴ algebraic expression m2 ∴ m+2010 is,

m2﹣m+20 10= 1+20 10=20 1 1．

So choose D.

Comments: This question mainly examines the algebraic value of the whole method of substitution, which is the key question in the senior high school entrance examination in recent years. Students should use this method correctly.

7．（20 10? Lishui) As shown in the figure, after a square piece of paper with a side length of (m+3) is cut into a square with a side length of m, the rest is cut and spliced into a rectangle (without overlapping and seamless). If one side of the spliced rectangle is 3, the other side is ().

A．2m+3　　B．2m+6　　C．m+3　　D．m+6

Test center: algebraic expression's mixed operation.

Analysis: Since a square paper with a side length of (m+3) is cut into a square with a side length of m, the remaining part is cut into a rectangle (without overlapping and seamless), then the area of the remaining part can be obtained according to the area of the square, and the length of one side of the rectangle is 3, and the length of the other side can be obtained by using the area formula of the rectangle.

Solution: Solution: The rest according to the meaning of the question is

（m+3）2﹣m2=m2+6m+9﹣m2=6m+9，

And the length of one side of the spliced rectangle is 3,

The length of the other side is (6m+9) ÷ 3 = 2m+3.

So choose a.

Comments: This question mainly examines the division of polynomial by monomial, and the key to solving the problem is to be familiar with the division law.

8．（20 10? As shown in the figure of Tongnan County, quadrilateral ABCD is a square with a side length of 1, quadrilateral EFGH is a square with a side length of 2, point D coincides with point F, and points B, D(F) and H are on the same straight line. Put square ABCD along f? The translation in the H direction stops when the point B coincides with the point H. If the distance between the points D and F is X and the area of the overlapping part of the square ABCD and the square EFGH is Y, the image that can roughly reflect the functional relationship between Y and X is ().

A．　B．　C．　D．

Test center: function image of moving point problem.

Special topic: application problem.

Analysis: The overlapping part of square ABCD and square EFGH is mainly divided into three parts, which is a piecewise function. The correct answer can be obtained by solving the corresponding functions in three cases respectively.

Solution: solution: DF=x, and the overlapping area of square ABCD and square EFGH is y.

①y= DF2= x2（0≤x＜ ）；

②y= 1（ ≤x＜2 ）；

③∵BH=3 ﹣x

∴y= BH2= x2﹣3 x+9（2 ≤x＜3 ）．

To sum up, the image is

So choose B.

Figure: ①

②

③

Comments: When solving the problem of moving point, the key is to find the functional relationship between the given two variables according to the conditions, especially in geometric problems, we should pay more attention to the mastery and flexible application of the basic properties.

Second, fill in the blanks (this big question ***8 small questions, 3 points for each small question, ***24 points)

9．（2005? Zhangzhou) calculation:-2× 3 =-6.

Test center: multiplication of rational numbers.

Analysis: Calculated according to rational number multiplication rule.

Answer: Solution:-2× 3 =-(2× 3) =-6.

Comments: The law of multiplication of non-zero rational numbers: two numbers are multiplied, the same sign is positive, the different sign is negative, and the absolute value is multiplied.

10．（2009? Shaoyang) As shown in the figure, AB∥CD, straight line EF and AB, CD intersect at E and F respectively, EP bisects ∠AEF, the crossing point F is FP⊥EP, and the vertical foot is P. If ∠ PEF = 30, then ∠PFC= 60.

Test site: the nature of parallel lines; Definition of angular bisector; Vertical line

Special topic: calculation problems.

Analysis: Since PE is an angular bisector, it is known that ∠ AEF = 60, and AB∥CD, so ∠EFD can be found, and PF ∠ PE, so ∠ PF⊥PE can be found, so it is easy to find ∠ PFC. 。

Solution: Solution: ∵EP bisects ∠AEF, ∠ PEF = 30,

∴∠AEF=60°．

And ∵AB∥CD,

∴∠AEF=∠EFD=60°．

∵FP⊥EP，

∴∠PFE=90°﹣30°=60°，

∴∠PFC= 180°﹣∠PFE﹣∠EFD=60°．

Answer: 60.

Comments: The knowledge points used in this question are the definition of angle bisector, the definition of vertical line and the property that two straight lines are parallel and the internal dislocation angle is equal.

11.It is known that the image of the linear function y=(a﹣ 1)x+b is as shown in the figure, so the value range of a is a >1.

Test center: the image of a linear function.

Special topic: combination of numbers and shapes.

Analysis: The sign of a﹣ 1 is judged according to the quadrant that the image of the linear function y=(a﹣ 1)x+b passes through, and the value range of a is obtained.

Solution: According to the diagram, the image of linear function y = (a |1) x+b passes through the first, second and third quadrants.

∴ a ∴1> 0, that is, a >1;

So the answer is: a >1.

Comments: This question examines the image of a function. This kind of problem can be solved by the idea of combining numbers with shapes, which is also a common method for solving exercises quickly.

12．（2004? Beibei District) In order to develop the agricultural economy and become rich and well-off, Wang Dabo, a professional chicken farmer, raised 2000 chickens in 2004. Before going on the market, he randomly selected 10 chickens, and the weight statistics are as follows: It is estimated that the total weight of these chickens is 5000 kg．.

Weight (unit: kg) 2 2.2 2.5 2.8 3

Quantity (unit: only)12421

Test center: weighted average; Estimate the population with samples.

Special topic: calculation problems.

Analysis: First calculate the sample average, estimate the population with the sample, and then multiply it by the total of 2000.

Solution: Solution: × ×2000=5000kg．.

So the answer is 5000.

Comments: First calculate the sample average, and then further estimate the overall average, thus calculating the total weight.

13. As shown in the figure, in trapezoidal ABCD, AB∥DC, AB⊥BC, AB=2cm, CD = 4 cm. A circle centered on a point O on BC passes through two points A and D, and ∠ AOD = 90, then the distance from the center O to the chord AD is cm.

Test site: vertical diameter theorem; Determination of congruence of right triangle; The nature of isosceles triangle; Determination of isosceles triangle; Pythagorean theorem; Determination of rectangle; Right trapezoid.

Analysis: The comprehensive nature of this question is strong. According to congruent triangles's judgment and nature, isosceles right triangle's judgment and nature, Pythagorean theorem and right trapezoid's nature, we can know.

Solution: as shown in the figure, AE⊥CD, e for the vertical foot, OF⊥AD, f for the vertical foot,

The quadrilateral AECB is rectangular,

CE=AB=2cm，DE=CD﹣CE=4﹣2=2cm，

∵∠AOD=90°，AO=OD，

So △AOD is an isosceles right triangle,

AO=OD，∠OAD=∠ADO=45°，BO=CD，

∵AB∥CD，

∴∠BAD+∠ADC= 180°

∴∠ODC+∠OAB=90°，

∵∠ODC+∠DOC=90°，

∴∠DOC=∠BAO，

∵∠B=∠C=90°

∴△ABO≌△OCD，

∴OC=AB=2cm，OB=CD=4cm，BC=BO+OC=AE=6cm，

According to Pythagorean theorem, AD2=AE2+DE2,

Get AD=2 cm,

∴AO=OD=2 cm，

S△AOD= AO? DO= AD? OF，

∴OF= cm．

Comments: This question uses congruent triangles's judgment and properties, isosceles right triangle's judgment and properties, Pythagorean theorem and the properties of right trapezoid to solve.

14．（2009? Shenzhen) Xiaoming and Xiaobing participated in the physical and chemical experiment operation test organized by the school. The recent five test results are shown in the figure, so the relationship between the variance S 12 of Xiaoming's five grades and the variance S22 of Xiaobing's five grades is S12 < S22.

(Fill in ">", "<" and "=")

Test center: variance.

Analysis: First, read the test data of Xiao Ming and Xiao Bing from the picture, and compare the sizes after calculating the variance respectively. You can also see the small ∵BF∥CD from the picture.