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20 12, Benxi, Liaoning, model essay on mathematics examination paper.

20 1 1 year Jinzhou City, Liaoning Province, the mathematics examination paper is the same.

1. 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 under the corresponding question number in the table below. There are 8 small questions in this answer, with 3 points for each small question and * * * 24 points).

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

A.-2 B.-Area 2

2.20 1 1 March11day, an earthquake and tsunami of magnitude 9.0 occurred in Japan, which caused great losses to the Japanese people and many people lost their homes. As of April 1 day, there are still about166,000 people taking refuge in various shelters. These data can be represented by scientific symbols as follows.

a . 166× 103 b . 16.6× 104 c . 1.66× 105d . 0. 166× 106

3.(2007? Taizhou) The expanded diagram of a geometric figure is as shown in the figure, so the vertex of this geometric figure has ().

A. 10

4.(2006? Jinan) A fast food restaurant has prepared a batch of box lunches, which contain rice and different kinds of stir-fried dishes. 25 boxes of shredded pork with potato, 30 boxes of shredded pork with celery, 0/0 box of scrambled eggs with pepper and 0/5 box of shredded pork with kidney bean. Each box is the same size and shape, so the probability of choosing a box without pepper 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 the intersection of the parabola y = x2-x- 1 and the X axis is (m, 0), the value of the algebraic formula m2-m+20 10 is ().

2008b.2009 c.2010d.2011

7.(20 10? Lishui) As shown in the figure, after cutting a square paper with a side length of (m+3) into a square with a side length of m, the rest parts are cut and spliced into a rectangle (no overlap, no seam). If one side of the splicing rectangle is 3 and the other side is ().

2m+3m+6cm+3m+6cm.

8.(20 10? As shown in the map 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 point D and the point F is x, and the area of the overlapping part between 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。

2. Fill in the blanks (this big question is ***8 small questions, with 3 points for each small question and 24 points for * * *).

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

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

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

12.(2004? Beibei District) In order to develop the agricultural economy, get rich and run towards a well-off society, Wang, a professional chicken farmer, raised 2,000 chickens in 2004. Before listing, he randomly selected 10 chickens and weighed them according to 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) 1 242 1

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

14.(2009? Xiaoming and Xiao Bing took part in the physical and chemical experiment operation examination organized by the school. The results of the last five tests are shown in the figure, so the relationship between the variance of Xiaoming's five grades is S 12, and that of Xiao Bing's five grades is S12 _ _ _ _ _ _ _ S22.

(fill in ">", "

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 similar centers of these two squares are _ _ _ _ _ _ _ _.

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

Third, solve the problem (this big problem ***2 questions, 8 points for each question, *** 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 all three vertices of △ABC are on the grid point. (The vertices of each small square are called grid points)

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

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

Iv. Answer questions (there are 2 questions in this big question, each with 10 and ***20 points)

19.(2007? In order to investigate students' participation in extracurricular sports activities in a middle school in Linfen City, a sampling survey was used to investigate the interests of several students from five aspects: 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 statistics. Please answer the following questions according to the information provided in the picture:

(1) How many students were surveyed in this survey?

(2) What is the central angle of table tennis in the fan chart?

(3) completing the bar graph;

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

As shown in the figure, a turntable is divided into six equal parts, and each sector is marked with a corresponding number. Party A and Party B respectively rotate the dial so that the number in the area pointed by the pointer is X after Party A rotates the dial, and the number in the area pointed by the pointer is Y after Party B rotates the dial (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. Answer questions (there are 2 questions in this big question, each with 10 and ***20 points).

2 1. "oil pipeline project for every village" has accelerated the pace of building a new socialist countryside in Jinzhou. As the picture shows, villagers in village C want to build a cement road to connect village C with county-level highways. On Highway A, it is measured that Village C is 60 east of north and 600 meters ahead. 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, the cost of building a cement road with a length of 1 1,000m is about 300,000 yuan. According to the relevant national policies, the government allocated 654.38 million yuan for the construction of this cement road, and the rest was raised by the villagers spontaneously. Try to find out how much money the villagers need to raise to repair this cement road.

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

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

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

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

23. As shown in the figure, AB is the tangent line with a diameter of ⊙O and the intersection point E is ⊙O, which intersects with the AB extension line at point C, and the intersection point A is AD⊥CE at point D and intersects 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 length of radius ⊙O and BF.

24.(2007? Quanzhou) Li Ming takes a bus from Quanzhou to a place along the expressway. 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 9 hours for Li Hong to return to Quanzhou from A, when t=2, S2 = 566.

② Before the two cars meet, when the driving time t is in 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, Q is the moving point of AC, and CP and PQ are used 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 BC extension line, and Q is the 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 the question (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, its symmetry axis X =-2 intersects with the X-axis at point C, and the straight line Y =-2x+ 1 passes through the point B(2, m) on the parabola and intersects with the Y-axis and the straight line X =-2 at points D and E respectively.

(1) Find the functional relationship between the value of m and this parabola;

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

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

20 1 1 year Jinzhou City, Liaoning Province, the mathematics examination paper is the same.

Reference answers and analysis of test questions

1. 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 under the corresponding question number in the table below. There are 8 small questions in this answer, with 3 points for each small question and * * * 24 points).

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

A.-2 B.-Area 2

Test center: reverse sign.

Analysis: The inverse of a number is to put 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 reciprocal. The reciprocal of a number is to add a "-"in front of it. The reciprocal of a positive number is negative, the reciprocal of a negative number is positive, and the reciprocal of 0 is 0.

2.20 1 1 March11day, an earthquake and tsunami of magnitude 9.0 occurred in Japan, which caused great losses to the Japanese people and many people lost their homes. As of April 1 day, there are still about166,000 people taking refuge in various shelters. These data can be represented by scientific symbols as follows.

a . 166× 103 b . 16.6× 104 c . 1.66× 105d . 0. 166× 106

Test center: scientific notation-indicating larger numbers.

Topic: standard questions.

Analysis: scientific notation is expressed in the form of a× 10n, where 1 ≤| a | < 10, and n is an integer. When determining the value of n, it depends on how many digits the decimal point moves when the original number becomes a, and the absolute value of n is the same as the number of digits the decimal point moves. When the absolute value of the original number is greater than 1. When the absolute value of the original number is < 1, n is negative.

Solution: The general scientific notation of 166 is 1.66× 105.

So choose C.

Comments: This topic examines the expression of scientific notation. The expression of scientific notation is a× 10n, where 1 ≤| A | < 10, and n is an integer. The key to the expression is to correctly determine the value of a and the value of n.

3.(2007? Taizhou) The expanded diagram of a geometric figure is as shown in the figure, so the vertex of this geometric figure has ().

A. 10

Test site: geometric expansion diagram.

Analysis: According to the characteristics of the folding of the plane figure and the plane expansion diagram of the three-dimensional figure, the three-dimensional figure is determined to be a triangular prism, 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 side, so there are six vertices in geometry.

So choose C.

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

4.(2006? Jinan) A fast food restaurant has prepared a batch of box lunches, which contain rice and different kinds of stir-fried dishes. 25 boxes of shredded pork with potato, 30 boxes of shredded pork with celery, 0/0 box of scrambled eggs with pepper and 0/5 box of shredded pork with kidney bean. Each box is the same size and shape, so the probability of choosing a box without pepper is ().

A.B. C. D。

Test center: probability formula.

Analysis: The number of boxes without peppers divided by the total number of boxes is the probability of choosing a box without peppers.

Solution: There are 25 boxes of shredded pork with potato, 30 boxes of shredded pork with celery, 80 boxes of scrambled eggs with pepper 10 and 5 boxes of shredded pork with kidney beans 15, and 70 boxes without pepper, so the probability of choosing a box without pepper 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 requested cases 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 property of inverse proportional function, k = 3 > 0, the function is located in the first quadrant and the third quadrant.

Solution: Image passing point (1, 3) of inverse proportional function y= (k≠0).

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

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

So choose B.

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

6. Given that the intersection of the parabola y = x2-x- 1 and the X axis is (m, 0), the value of the algebraic formula m2-m+20 10 is ().

2008b.2009 c.2010d.2011

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

Analysis: according to the parabola y=x2﹣x﹣ 1 and an intersection point of the x axis is (m, 0), the value of m2﹣m is obtained by substituting it into m2﹣m+20 10. The correct answer is obtained.

Solution: solution: ∵ parabola y=x2﹣x﹣ 1 and an intersection of the x axis is (m, 0).

Substitution point (m, 0),

0=m2﹣m﹣ 1,

∴m2﹣m= 1,

The algebraic expression m2 ∴ m+20 10 has the value,

m2﹣m+20 10= 1+20 10=20 1 1.

So choose D.

Comments: This question mainly examines the algebraic value of divisible method of substitution, which is the key question type 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 cutting a square paper with a side length of (m+3) into a square with a side length of m, the rest parts are cut and spliced into a rectangle (no overlap, no seam). If one side of the splicing rectangle is 3 and the other side is ().

2m+3m+6cm+3m+6cm.

Test site: mixed operation of algebraic expressions.

Analysis: Because a square paper with a side length of (m+3) is cut into a square with a side length of m, and the rest is cut into a rectangle (without overlapping and seamless), the area of the rest 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 depends on the meaning of the problem

(m+3)2﹣m2=m2+6m+9﹣m2=6m+9,

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 investigates that polynomials are divisible by monomials, and the key to solving the problem is to be familiar with the law of divisibility.

8.(20 10? As shown in the map 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 point D and the point F is x, and the area of the overlapping part between 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 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 combining numbers with shapes, which is also a common method to solve exercises quickly.

12.(2004? Beibei District) In order to develop the agricultural economy, get rich and run towards a well-off society, Wang, 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 5000 Jin. ..

Weight (unit: kg) 2 2 2 2 5 2 8 3

Quantity (unit: only) 1 242 1

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

Special topic: calculation problems.

Analysis: first calculate the average value of samples, estimate the population with samples, and then multiply by the total number of 2000.

Solution: solution: × ×2000=5000kg. ..

So the answer is 5000.

Comments: Calculate the sample average first, and then further estimate the overall average, so as to calculate the total weight.

13. As shown in the figure, in trapezoidal abcd, ABCD, AB⊥BC, AB=2cm, CD = 4 cm. A circle centered on point O on BC passes through point A and point D, and ∠ AOD = 90, then the distance from point O to 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: This question is comprehensive. According to the judgment and properties of congruent triangles, isosceles right triangle, Pythagorean theorem and right trapezoid, we can know.

Solution: As shown in the figure, AE⊥CD, E is vertical foot, OF⊥AD, F is 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? Yes,

∴OF= cm.

Comments: This question is solved by congruent triangles's judgment and properties, isosceles right triangle's judgment and properties, Pythagorean theorem and right trapezoid's properties.

14.(2009? Xiaoming and Xiao Bing took part in the physical and chemical experiment operation examination organized by the school. The results of the last five tests are shown in the figure, so the variance relationship between Xiaoming's fifth grade S 12 and Xiao Bing's fifth grade S22 is S 12 < S22.

(fill in ">", "

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.