(Time for closed-book examination: 120, full mark 120)
First, multiple-choice questions (this topic is entitled *** 12 small questions, with 3 points for each small question, out of 36 points).
The reciprocal of 1 Yes ()
A.B. C. D。
2. In real numbers, irrational numbers have ().
1。
3. As shown in the figure,, and intersect at the point,,,
It is equal to ()
A.B. C. D。
4. The figure below is both an axisymmetric figure and a centrally symmetric figure ().
A.B. C. D。
5. If the inequality group has a real number solution, the value range of the real number is ()
A.B. C. D。
6. In the inverse proportional function, when it decreases with the increase of, the image of the quadratic function is roughly as shown in the following figure ().
7. The top view of the geometry shown on the left side of the figure below is ()
8. As shown in the figure, the side length of each small square is 1, so the triangle (shaded part) in the figure below is similar to that in the figure on the left ().
9. If the average value of a set of data 2, 4, 6 and 8 is 6, the variance of this set of data is ().
A. 8th century BC to 40th century BC
10. If, the size relationship of is ()
The CBI is not sure.
1 1. It is known that a quadratic equation with one variable has two real roots, so the value of the equation is ().
A.B. C. D。
12. As shown in the figure, in an isosceles triangle, the point is the bottom.
The moving point on the side is the midpoint, if
The minimum value of is 2, then the perimeter of is ()
A.B. C. D。
II. Fill in the blanks (6 small questions in this big question, 3 points for each small question, full mark 18)
1 0 2
three
five
13. Decomposition factor:.
14. As a linear function of, the right table lists some corresponding values.
Then.
15. As shown in the figure, in the middle, points,, and are the midpoint. If the point is rotated counterclockwise, the distance traveled by the point during the rotation is. (result retention)
16. As shown, yes, the diameter is divided into,, and then.
17. The following figure is a statistical chart based on the donation of a junior high school to the earthquake-stricken area. It is understood that there are 2000 students in this school. Please calculate the donation of this school according to the statistical chart.
18. If the real number is satisfied, the minimum value of is.
Third, answer the question (this big question ***9 small questions, out of 66 points)
19. (Full score for this small question)
Do the math.
20. (The perfect score for this short question is 6)
As shown in the figure, it is the last point, and the point,,.
Verification:
2 1. (The full score of this small question is 6) Simplify first and then evaluate.
, among which,
22. (The full score for this short question is 7)
As shown in the figure, ship A is in the northwest of the port, far away from the sea surface of the port, and sails for the port at the speed of 12 knots. Ship B left the port at a constant speed in the northeast, and now both ships are leaving at the same time. Two hours later, Ship B is in the direction of Owner A, and find the sailing speed of Ship B (accurate to 0. 1 knot, refer to the data.
23. (The full score for this short question is 7)
A workshop needs to produce 220 products. After completing 100 pieces, improve the operation method and handle 10 pieces every day. Finally, it takes four days to complete the task. How many products are produced every day after improving the operation method?
24. (The full score for this short question is 7)
There is a small ball in the pocket, two of which are white balls and the others are red balls. These balls are exactly the same in shape, size and texture. If you can't see the ball, take a ball out of your pocket. The probability that it is a red ball is.
( 1);
(2) Take two balls as 1 and the rest as 2, 3, ..., and randomly take out a small ball without putting it back, and then randomly take out a small ball to find the probability that the number of the second ball is greater than the number of the first ball.
25. (The full score for this short question is 8)
Company A has 40 model products and 60 model products, which are distributed to its subordinate stores A and B, of which 70 are in store A and 30 are in store B, all of which have been sold out. The profit (yuan) of each of these two products sold by these two stores is as follows:
Profit type
Profit type
Jia Branch 200 170
Store B 160 150
(1) Assuming that the products are distributed to Store A, the total profit of the company selling this 100 product is (yuan), and the value range of the sum of the function relations is found;
(2) If the company requires the total profit to be no less than 65,438+07, 560 yuan, explain how many different distribution schemes there are and design them;
(3) In order to promote sales, the company decided to sell only the products of Store A, and the profit of each product was RMB, but after the profit, the profit of each product was still higher than that of Store A, Store A and Store B, and the profit of each product remained unchanged. How does the company design the distribution scheme to maximize the total profit?
26. (The full score for this short question is 9)
As shown in the figure, it is a right angle, the point is the midpoint of the line segment, the point is the moving point on the ray (not coincident with the point), and the connection, operation, vertical foot are, connection, intersection operation and intersection.
(1) Verification:;
(2) In what range, quadrilateral is trapezoid, and explain the reasons;
(3) In what range, there are points on the line segment that meet the conditions, and explain the reasons.
27. (Full score for this small question 10)
As shown in the figure, it is known that a parabola intersects an axis at a point and intersects an axis at a point.
(1) Find the analytical formula of parabola and the coordinates of its vertices;
(2) Let a straight line intersect with a point. Is there a point on the perpendicular of the line segment that makes the distance from the point to the line equal to the distance from the point to the origin? If it exists, find the coordinates of the point; If it does not exist, please explain the reason;
(3) When the point is perpendicular to the axis, the intersection line is at this point, and the parabola translates along its symmetry axis, so there is always a common point between the parabola and the line segment. Try to explore: how many unit lengths can a parabola translate upward at most? How many unit lengths can you translate downward at most?
In 2008, Huangshi City, Hubei Province took the senior high school entrance examination in mathematics.
Answers and scoring criteria
First, multiple-choice questions (3 points for each small question, out of 36 points)
The title is123455678911112.
Answer C B C B A A D B B A D D
Fill in the blanks (3 points for each small question, full mark 18)
13. 14. 1 15.
16. 17.25 180 18.2
Third, answer the question (this big question ***9 small questions, out of 66 points)
19. solution: original formula (4 points)
(5 points)
. (6 points)
20. proof: (2 points)
Say it again,
. (5 points)
. (6 points)
2 1. solution: original formula
(2 points)
. (4 points)
When, when,
Original formula. (6 points)
22. According to the meaning of the question, suppose that the speed of ship B is nautical miles per hour, and after two hours, ship A is at the point and ship B is at the point, then it is nautical miles, nautical miles.
In,,
. (2 points)
In,,
. (4 points)
,
.
.
A: The sailing speed of the B ship is about 19.7 knots. (7 points)
23. If one product is produced every day after the improved operation method, one product is produced every day before the improvement.
According to the meaning of the question. (3 points)
Tidy up.
The solution is still. (5 points)
Give up when.
.
A: After improving the operation method, 60 products are produced every day. (7 points)
24.( 1) According to the meaning of the question. (3 points)
(2) At that time, the two labels of these five balls were 1, and the other labels were 2, 3 and 4 respectively.
All possible results of a small ball label that takes the ball twice are as follows:
From the above table, the probability is. (7 points)
25. according to the meaning of the question, shop a has two products, shop b has two products and shop b has two products.
( 1)
.
From the solution. (2 points)
(2) by,
.
, ,39,40.
There are three different distribution schemes.
① At that time, there were 38 types A, 32 types B, 2 types B and 28 types B. 。
② At that time, there were 39 pieces of type A, 3 1 piece of type B, 0/piece of type B and 29 pieces of type B. 。
③ At that time, there were 40 types A, 30 types B, 0 types B and 30 types B. 。
(3) According to the meaning of the question:
.
① At the right time, that is, 40 pieces of Type A, 30 pieces of Type B, 0 pieces of Type B and 30 pieces of Type B, the total profit can be maximized.
(2) At an appropriate time, all kinds of schemes that meet the meaning of the question make the total profit the same.
(3) If it is timely, that is, type A 10, type B 60, type B 30 and type B 0, the total profit can be maximized. (8 points)
26.( 1) in,,,.
,
, .
, ,
.
.
. (3 points)
(2) Multiply (1), and,
, that is.
If, then,
, .
When or, the quadrilateral is a trapezoid. (6 points)
(3) do, vertical foot for, then.
, .
It's also the midpoint, yes, the midpoint.
Yes, the middle vertical line.
.
Point to H.
,
.
.
.
Say it again,
.
When there is a point in the world, the conditions are met. (9 points)
27.( 1) Let the analytical formula of parabola be substituted.
,
Vertex (two points)
(2) Assuming that the point that meets the conditions exists, it is set according to the meaning of the question.
The analytical formula of the straight line is,
The angle between it and the axis is that the vertical line is set to cross, then.
So, the distance from point to point is.
Here we go again. (4 points)
.
Square and arrange:
.
There are points that meet the conditions, and the coordinates are. (6 points)
(3) Obtained from above.
① If the parabola moves upward, the analytical formula can be set as.
When.
When.
Or ...
. (8 points)
② If the parabola moves down, the analytical formula can be set as.
By,
Yes
, .
It can translate up to 72 unit lengths and at least 1/4 unit lengths. (10 minutes)