Description:
1. This paper is * * 6 pages, including multiple-choice questions (65438 questions +0 to 8, * * 8) and non-multiple-choice questions (9 to 28 questions, * * 20). The full mark of this volume is 150, and the examination time is 65438.
2. Before answering questions, candidates must fill in their names and admission ticket numbers in the corresponding positions on the answer sheet, and at the same time, they must fill in their names, admission ticket numbers and graduation schools in the binding line of the test paper, and fill in the seat number in the lower right corner of the first side of the test paper.
3. All questions must be answered on the special "answer sheet", multiple-choice questions should be answered with 2B pencil, and non-multiple-choice questions should be answered with 0.5mm black ink pen at the designated position. It is invalid to answer questions on the test paper or draft paper.
4. The drawing must be answered with 2B pencil, and please describe it clearly in black and bold.
A, multiple-choice questions (this topic * * * a total of 8 small questions, each small question 3 points, * * * 24 points. Only one of the four options given in each small question meets the requirements of the topic. Please mark the letter code before the correct option in the corresponding position on the answer sheet).
The reciprocal of 1 Yes ()
A.B. C. D。
2. The result of calculation is ()
A.B. C. D。
3. As shown in the figure, two points on the number axis correspond to real numbers respectively.
The following conclusion is correct ()
A.B.
C.D.
4. Among the following four kinds of geometric figures, the geometric figure whose left view is quadrilateral * * * has ().
1。
5. As shown in the figure, on the square paper, translate the triangle A in Figure ① to Figure ②.
The position shown in, together with triangle B, becomes a rectangle, and then the lower part is flattened.
Dynamic method, the correct is ()
A. First translate 3 squares downward, and then translate 1 square to the right.
B. First, move 2 squares downward, and then move 1 square to the right.
C. First, translate 2 squares downward, and then translate 2 squares to the right.
D. First, translate 3 squares downward, and then translate 2 squares to the right.
6. A new shirt was tried on in a shopping mall, and the sales situation within one week is shown in the following table:
Model (cm) 38 39 40 4 1 42 43
Quantity (Pieces) 25 30 36 50 28 8
The store manager wants to know which model is the best seller, and in the statistics of the above data, the most meaningful one for the store manager is ().
A. Mean B. Mode C. Median D. Variance
7. As shown in the figure, the following four groups of conditions are given:
① ;
② ;
③ ;
④ .
Among them, the enabling condition * * * has ()
A. 1 Group B.2 Group C.3 Group D.4
8. The following is a list of figures arranged according to certain rules:
No.1:;
Second place:;
Third place:;
……
Number:.
Then, among the numbers 10, 1 1, 12 and 13, the largest number is ().
A. number10 b. number11C. number12 d. number 13.
Two. Fill in the blanks (There are 10 small questions in this big question, with 3 points for each small question and * * 30 points. There is no need to write the answer process, please fill in the answer directly in the corresponding position on the answer sheet).
9. calculation.
10. The meaningful range is.
1 1. The area of Jiangsu Province is about 102 600km2. , which can be expressed as km2 by scientific notation.
12. The image of the inverse proportional function is in the fourth quadrant.
13.in 2008, the per capita annual income of farmers in a county was 7 800 yuan, and it is planned that by 20 10, the per capita annual income of farmers will reach 9 100 yuan. If the average growth rate of per capita annual income is 0, the equation can be formulated.
14. If, then.
15. As shown in the figure, a circular turntable is divided into five sector areas, which are marked with the numbers 1, 2, 3, 4 and 5 respectively. The position of the dial pointer is fixed, and it is allowed to stop freely after rotating the dial. When the turntable stops rotating once, the probability that the pointer points to the area marked with even number is (even number), and the probability that the pointer points to the area marked with odd number is recorded.
16. As shown, yes, the diameter chord. If, then.
17. Given that the side length of a regular hexagon is 1cm, draw an arc with its three non-adjacent vertices as the center and 1cm as the radius (as shown in the figure), then the sum of the lengths of the three arcs is cm (the result is reserved).
18. As shown in the figure, it is known that the center line is trapezoidal, and its area is, so the area is cm2. ..
Three. Solution (this big question * * *, there are 10 small questions, and the score is * * 96. Please answer in the designated area of the answer sheet, and write the necessary text description, proof process or calculus steps when answering).
19. (The full mark of this question is 8) Calculation:
( 1) ; (2) .
20. (The full mark of this question is 8) A city has tested the academic level of ninth grade students, and the results are divided into four grades: A, B, C and D. In order to understand the results of this math test, the relevant departments * * * selected 2,000 students from four groups in the city, including rural areas, counties, towns and cities, for statistical analysis, and the statistical chart of the corresponding data is as follows:
(1) Please fill in three missing data in the above table;
(2) If there are 60,000 ninth-grade students in this city, try to estimate the number of students with grades above (inclusive) in this city.
2 1. (The full mark of this question is 8) Three babies were born in a hospital. Assuming that the probability of having boys and girls is the same, what is the probability of 1 boy and 2 girls among the three babies?
22. (The full mark of this question is 8) Car A travels from A to B, the road ahead is an ordinary expressway, and the rest are expressways. It is known that the speed of the car is 60km/h on the ordinary highway and 65,438+000 km/h on the expressway, and the car travels from A to B for 2.2h hours.
According to the above information, please put forward a problem solved by binary linear equations and write out the solution process.
23. (The full mark of this question is 10) As shown in the figure, in a trapezoid, two points are on the side and the quadrilateral is a parallelogram.
What is the equivalent relationship between (1) and? Please explain the reasons;
(2) When, verification: it is a rectangle.
24. (The full mark of this question is 10) As shown in the figure, the vertex of the image of the known quadratic function is. The image and axis of quadratic function intersect at the origin and another point, and its vertex is on the symmetry axis of function image.
(1) Find the coordinates between points;
(2) When the quadrilateral is a diamond, find the relationship between functions.
25. (The full mark of this question is 10) As shown in Figure 5 minutes, there are observation points A and B on both sides of the route, the distance from point A to the route is 2km, and point B is located 60 northeast of point A, which is 0/0 km away from point A/kloc-0. At present, a ship is sailing from point C, which is located 76 southwest of point B, from west to east along the route, and will arrive at point A in 5 minutes.
(1) Find the distance from observation point B to the route;
(2) Find the sailing speed of the ship (the result is accurate to 0. 1 km/h).
, )
26. (The full mark of this question is 10)
(1) observation and discovery
Xiao Ming folds the triangular piece of paper along a straight line passing through point A, so that AC falls on the edge of AB, the crease is AD, and the piece of paper unfolds (as shown in Figure ①); Fold the triangle paper again, so that point A and point D coincide, and the crease is EF, which is obtained by flattening the paper (Figure ②). Xiao Ming thinks it is an isosceles triangle. Do you agree? Please explain the reason.
(2) Practice and application
Fold the rectangular piece of paper along a straight line passing through point B, so that point A falls on point F on the side of BC, and the crease is BE (as shown in Figure ③); Fold along the straight line passing through point E, so that point D falls on the point on BE, and the crease is EG (as shown in Figure ④); Flatten the paper again (Figure 5). Find the size in Figure ⑤.
27. (The full mark of this question is 12)
The image of the functional relationship between the sales profit (10,000 yuan) and the sales volume (10,000 liters) of an oil product sold by a gas station in May is shown by the dotted line in the figure. The sales profit of the gas station was 40,000 yuan when the price was adjusted in June 13, and 55,000 yuan when the oil was filled in June 15. (Sales profit = (price-cost price) × sales volume)
Please answer the following questions according to the information provided in the picture and all the sales records of this oil product at the gas station in May:
(1) When the sales volume is determined, the sales profit is 40,000 yuan;
(2) functional relationships corresponding to line segments AB and BC are obtained respectively;
(3) We call the profit from selling one liter of oil the profit rate. Then, among the sales information expressed by OA, AB and BC, which one has the largest profit rate? (Write the answer directly)
28. (The full mark of this question is 12) As shown in the figure, it is known that the ray DE intersects the axis at points and points respectively. The moving point starts from the point and moves at a speed of 1 unit length/second to the left in the axial direction, while the moving point p starts from the point d and also moves at a speed of 1 unit length/second in the direction of ray DE.
(1) Please use the included algebraic expressions to represent the coordinates of point C and point P respectively;
(2) With point C as the center and a unit length as the radius, the axis intersects with point A and point B (point A is on the left side of point B) to connect PA and Pb.
(1) When it has something in common with ray DE, the value range is;
② When it is an isosceles triangle, the value of.
Reference Answers and Scoring Suggestions of Mathematics Examination Paper for Senior High School Entrance Examination in Jiangsu Province in 2009
First, multiple-choice questions (there are 8 small questions in this big question, with 3 points for each small question and 24 points for * * *).
Title 1 2 3 4 5 6 7 8
Option A B C B D B C A
Fill in the blanks (there are 10 small questions in this big question, with 3 points for each small question and 30 points for * * *).
9.910.1.12.2, 4 13.
14. 1 15. 16.25 17. 18. 16
Three. Solution (this big question * *, 10 small question, * * 96 points. The solution must be written with the necessary text description, reasoning steps or proof process).
19. Solution: (1) Original formula. (4 points)
(2) the original formula. (8 points)
20. Solution: (1) 280,48, 180. (3 points)
(2) Among the selected students, the unqualified number is * * *.
Therefore, the number of people at or above the qualified level is,
It is estimated that the number of qualified and above students in this city is.
A: It is estimated that about 54,720 people in this city will pass the exam. (8 points)
2 1. solution: the tree diagram is analyzed as follows:
1 boys 2 girls.
Answer: 1 boy 2 The probability of a girl is. (8 points)
22. Solution: The answer to this question is not unique. The following solutions are for reference.
Solution 1 Question: How many kilometers are ordinary roads and expressways? (3 points)
Solution: Let the length of ordinary highway be km and the height highway be km.
According to the meaning of the problem, draw a solution (7 points)
Answer: The length of ordinary highway is 60km, and the length of expressway is 120 km. (8 points)
Option 2 Question: How many hours did the car drive on the ordinary highway and the highway respectively? (3 points)
Solution: suppose the car drives H on the ordinary highway and H on the highway.
According to the meaning of the problem, draw a solution (7 points)
Answer: The car traveled 1h on the ordinary highway and 1.2h on the expressway. (8 points)
23.( 1) Solution:. ( 1)
The reason for this is the following：
,
Quadrilateral and quadrilateral are parallelograms.
.
A quadrilateral is a parallelogram.
.
. (5 points)
(2) Prove that quadrilateral and quadrilateral are parallelograms,
.
.
A quadrilateral is a parallelogram and a quadrilateral is a rectangle. (10)
24. Solution: (1), so the coordinates of the vertices are. (3 points)
Because the image of the quadratic function passes through the origin, its vertex is on the symmetry axis of the image of the quadratic function, and the points are symmetrical about the straight line, so the coordinates of the points are. (6 points).
(2) Because the quadrilateral is a diamond, and the points are symmetrical about the straight line, the coordinates of the points are.
Because the image of quadratic function passes through points,,,, so
solve
So the relationship of quadratic function is. (10)
25. Solution: (1) sets intersect with points.
Yes,.
Here we go again.
Inches (kilometers).
The distance from the observation point to the route is 3 kilometers. (4 points)
(2) yes.
Yes,.
.
Yes,.
.
, (km/h).
A: The speed of the ship is about 40.6 km/h (10 minute).
26. Solution: (1) Agreed. As shown in the figure, set and intersect at points. From the folding point of view, it is equally divided, so.
Also known as folding,
So,
So ... So,
Which is an isosceles triangle. (5 points)
(2) According to the folding, the quadrilateral is a square, so. You can see from the folding, so.
Therefore. (10)
27. Solution 1: (1) According to the meaning of the question, when the sales profit is 40,000 yuan, the sales volume is (ten thousand liters).
A: When the sales volume is 40,000 liters, the sales profit is 40,000 yuan. (3 points)
(2) The coordinate of this point is 13 to 15, and the profit is (ten thousand yuan).
So the sales volume is (ten thousand liters), so the coordinates of the point are.
Let the functional relationship corresponding to the line segment be, then solve.
The functional relationship corresponding to the line segment is. (6 points)
From 15 to 3 1, the sales volume is 50,000 liters, and the profit is (ten thousand yuan).
The profit from selling this oil product this month is (ten thousand yuan), so the coordinates of the point are.
Let the functional relationship corresponding to the line segment be, then solve.
Therefore, the functional relationship corresponding to the line segment is. (9 points)
(3) line segments. (12)
Solution 2: (1) According to the meaning of the question, the functional relationship corresponding to the line segment is.
When.
A: When the sales volume is 40,000 liters, the sales profit is 40,000 yuan. (3 points)
(2) According to the meaning of the question, the functional relationship corresponding to the line segment is,
Namely. (6 points)
Substitution, so the coordinates of the point are.
As of June 5438+05, the inventory at the time of oil supply was (ten thousand liters).
When the sales volume is more than 50,000 liters, that is, in the sales relationship corresponding to this line segment,
Cost price per liter of oil (yuan).
Therefore, the functional relationship corresponding to this line segment is
. (9 points)
(3) line segments. (12)
28. Solution: (1). (2 points)
(2) (1) When the center of the circle moves from one point to the left, make a point to one point and keep moving to the left.
Yes, it is.
When the point is on the left side of the point, the passing point is taken as ray, and the vertical foot is taken as,
If you get it, then you can get it.
Shit, that's shit
When there is a common point with the ray, the value range of is. (5 points)
(2) when, more than the axis, vertical ruler for, have.
.
, that is.
Solution. (7 points)
When, when,
Solution. (9 points)
When? Yes.
.
, that is.
Solution (irrelevant, give up). ( 1 1)
When it is an isosceles triangle, or, or, or. (12)