The first part of the multiple-choice questions (***30 points)
First, multiple-choice questions (this big question * *10 small questions, 3 points for each small question, out of 30 points)
1. In the following figures, the one that is both axisymmetric and centrally symmetric is ().
A.B. C. D。
2. In the function, the value range of the independent variable is ()
ABC and D.
3. In the following figures of 1, ∠ 1 is greater than ∠2 ().
4. On the number axis, the solution set of inequality group is correct ().
5. The solution of the unary quadratic equation is ()
A.x 1=0，x2= B.x=2 C.x 1=0，x2=2 D.x=
6. If the product of two roots of the equation is 2, then ()
A.B. C. D。
7. Six students in a class participated in the physical fitness test, and the results were as follows: 80, 90, 75, 75, 80, 80. The following statement is incorrect ()
A. mode 80 b, median 75 c, average 80 d, interval 15.
8. In a square grid, if placed as shown in the left figure, the value of tan∠AOB is ().
A.B. C. D。
9. Given that the generatrix length of the cone is 5cm, the side area is 15πcm2, and the radius of the circle at the bottom of the cone is ().
A.1.5cm B.3cm C.4cm D.6cm
10. If, the functional relationship between the information in the table and is ().
A.B.
C.D.
The second part is not a multiple-choice question (* *120)
II. Fill in the blanks (6 small questions in this big question, 3 points for each small question, full mark 18)
1 1. The result of formula-+is.
12. As shown in the figure, it is known that point E is a point on circle O, and b and c are bisectors of the lower arc, so the degree is degrees.
13. If the image of the function passes through this point, the value of is.
14. If the upper base of the trapezoid is 3cm long and the middle line is 5㎝, the lower base of the trapezoid is ㎝.
15 the image of the known linear function y=kx+b is shown in the figure. When x < 0, the value range of y is.
16. As shown in the figure, the area of square ABCD is 1, and m is the midpoint of AB, so the area of the shaded part in the figure is.
Three. Solution: (This big question is ***9 small questions, and the score is *** 102. The solution should be written in words, proof process or calculation steps. )
17. (The full score of this small question is 9) Simplify first and then evaluate.
18. (The full score of this small question is 9) As shown in the figure, the umbrella cover of an umbrella can be seen as 12 pieces of the same isosceles triangle cloth. Measure the edge OA = OB = 56 cm of a triangle OAB.
(1) Find the degree of ∠AOB;
(2) Find the area of △OAB (excluding the area of overlapping parts during sewing).
19. (The full score of this small question is 10. ) The 2008 Olympic Games was held in Beijing. In order to know how all students like to watch the Olympic Games, a student union of a school randomly surveyed 200 students and made a frequency distribution table according to the survey results:
Frequency of favorite items (number of people) frequency
soccer
Basketball 56
volleyball
Badminton 34
table tennis
swim
Diving 18
Track and field 8
The total is 200
(1) complete frequency distribution table;
(2) In this sample survey, which Olympic events do students like to watch best? Which game do you like least?
(3) According to the above survey, try to estimate the number of students in our school 1800 who like watching badminton matches best.
20. (The full score of this small question is 10) After the earthquake in Sichuan Province, the materials transported from Chengdu to Wenchuan disaster area must be transported from the west or south line. The western route is about 800 kilometers, and the southern route is about 80 kilometers. The motorcade on the southbound left immediately after 18 hours, and as a result, both motorcades arrived at the same time. It is known that two motorcades are traveling at the same speed, so find out the time it takes for the motorcade to walk on the west line.
2 1. (The full score of this small question is 12) Xiao Wang and Xiao Ming play the game with purple with the same turntable as shown in the figure. The rules of the game are as follows: Turn the turntable twice continuously. If the colors turned out twice are the same or matched with purple (if one turntable turns out blue and the other turntable turns out red, it is matched with purple), Xiao Wang gets 1.
(1) Please find out the winning probability of Xiao Wang and Xiao Ming by the list method.
(2) Do you think this game is fair to both sides? Please explain the reasons; If it is unfair, please modify the rules to make the game fair to both sides.
22. (The full mark of this small question is 12) When solving a quadratic equation with images, one method we adopt is to draw a parabola and a straight line in a plane rectangular coordinate system, and the abscissa of the intersection of the two images is the solution of the equation.
(1) Fill-in-the-blank problem: Solving a quadratic equation with an image can also be solved in this way: draw a parabola and a straight line in a plane rectangular coordinate system, and the abscissa of their intersection point is the solution of the equation. (4 points)
(2) Given the image of the function (as shown in the figure), use the image to find the approximate solution of the equation (the result retains two significant figures).
23. (The full score of this small question is 12) As shown in the figure, AB is the diameter ⊙O, BC is the tangent ⊙O, and the tangent point is B. OC is parallel to the chord AD, and OA=2.
(1) Verification: DC is the tangent of ⊙O;
(2) the value;
(3) If, find the length of the CD.
24. (The full score of this small question is 14) as shown in figure 1. It is known that the coordinates of the three vertices in the quadrilateral OABC are O (0 0,0), A (0 0,n) and C (m m,0). The moving point P starts from the point O and moves to the point C along the line segments OA, AB and BC in turn, with the moving distance of z,
The image of the area s of △OPC changing with z is shown in Figure 2. M, n are constants, m > 1, n > 0.
(1) Please determine the value of n and the coordinates of point B;
(2) When the moving point P is the vertex of the parabola Y = AX+BX+C passing through points O and C, and it is on the hyperbola Y =, find the area of the quadrilateral OABC at this time.
25. (The full score of this small question is 14) As shown in the figure, in the middle, there is an isosceles trapezoid (), whose base is coincident with that, and its two waists fall on it respectively, which is the midpoint.
(1) Find the area of the isosceles trapezoid;
(2) Operation: Fixed, move the isosceles trapezoid to the right at a speed of units per second until the points coincide. Let the exercise time be seconds and the isosceles trapezoid after exercise be (as shown in figure 15).
Explore 1: Can a quadrilateral be a diamond in the process of movement? If yes, request the value at this time; If not, please explain why.
Inquiry 2: Let the area of the overlapping part with the isosceles trapezoid during the movement be the function of summation.
(alternative questions) 24. (The full mark of this small question is 14) As shown in the figure, two right-angled sides OA and OB are on the positive half axis of X axis and the negative half axis of Y axis respectively, C is a point above OA, OC=OB, and the parabola (where M and P are constants, and) passes through two points A and C.
(1) proves that: (p, 0) is on a parabola;
(2) M and P are used to represent the length of OA and OC respectively;
(3) When M and P satisfy what relation, the area of is the largest.
answer
First, multiple-choice questions:
B，D，D，C，A，D，B，A，B，A
Fill in the blanks (this topic is entitled ***6 small questions, 3 points for each small question, *** 18 points)
Title:111213
answer
69 -2
Title 14 15 16
Answer 7 y
17. Original formula =
When,
18. Solution: (1)≈AOB = 360÷ 12 = 30 (degrees). (3 points)
(2) For high BD, ∠ AOB = 30 in Rt△BDO,
OB = 56cm cm
∴ Bo = 2bd, BD = 28, (6 points)
(or write db = bosin30 = 28)
∴△OAB area =× OA× BD = 784. (cm2) (9 points) (No points will be deducted for lack of units)
Frequency of favorite items (number of people) frequency
Football 32
Basketball 56
volleyball
Badminton 34
table tennis
Swimming 126%
Diving 18
Track and field 8
Total 200 100%
19.( 1) 4 o'clock
(2) Most students like watching basketball.
Students who least like watching track and field events (6 points)
(3) (10)
20. Solution: How many hours will it take for the motorcade to take the westbound route? It depends on the question: (1)
, (5 points)
To solve this equation, you must
. (8 points)
After testing, it is the solution of the original equation. (9 points)
A: It takes 20 hours for the motorcade to take the western route. (10)
2 1. solution: (1)
Red, yellow, blue and green
Red (red) (red yellow) (red blue) (red green)
Yellow (yellow red) (yellow yellow) (yellow blue) (yellow green)
Blue (blue red) (blue yellow) (blue blue) (blue green)
Green (green red) (green yellow) (green blue) (green green)
(4 points)
As can be seen from the table: (Little Wang Ying) (Xiao Ming wins)
(2) Unfair competition (7 points)
Xiao Wang scored and Xiao Ming scored.
There are:
Unfair game (10 score)
Modify the rules of the game: if the color is the same or matched with purple twice, Xiao Wang will get 5 points; Otherwise Xiao Ming gets 3 points.
(Note: the answer is not unique, all reasonable rules are scored) (12 points)
22.( 1) (4 points)
(2) Draw a straight line image. (8 points) 2 points.
The approximate solution of the equation obtained from the image is:
.6 points (12 points)
23.( 1) Connection outside diameter
∵BC is the tangent of⊙ O, ∴∠b = 90°.
∫AD∨OC
∴∠ 1=∠3,
∠2=∠4
OA = OD
∴∠2=∠3,
∴∠ 1=∠4
OB = OD，OC=OC
∴△OCD≌△OCB
∴∠ODC=90
∴DC is the tangent of⊙ O; (4 points)
(2) It is easy to prove △ ADB ∽△ODC.
= (8 points)
(3)∵ =
∴
∴ (12 points)
24. solution: (1) as can be seen from the figure, when p moves from o to a, the area of △POC is S = Mz, z gradually increases from 0 to 2, and then s gradually increases from 0 to m, so OA = 2 and n = 2. (1 min).
Similarly, AB = 1, then the coordinate of point B is (1, 2). (3 points)
(2)∵ parabola y = ax+bx+c passes through points o (0 0,0), c (m m,0),
(4 points)
As shown in figure 1, let the parabola passing through points o, c and p be l.
(I) when p moves on OA, both o and p are on the y axis,
At this time, p, o and c cannot be on the same parabola.
At this time, the parabola L does not exist, so the value of m does not exist. (5 points)
(ii) When P moves on AB, that is, when 0
The vertex of parabola L is p (,2).
Y = on the hyperbola, you can get m =, ∫> 2,
If it is inconsistent with X = ≤ 1, it will be discarded. (7 points) (6 points)
It is easy to find the analytical formula of straight line BC:, (8 points)
(iii) When P moves on BC, let the coordinate of P be (x, y), and when P is the vertex, X =,
So y = =, the vertex p is (,),
∵ 1 & lt； x = & ltm,∴m>； 2, and ∵P is on the hyperbola, y =,
So x =, after simplification, is 5m-22m+22 = 0.
Solution,, (10 integral)
And the meaning of question 2 < x =<m is not appropriate, so it will be abolished. ( 1 1)
Only one value meets the criteria:. (12)
At this time, the area of the quadrilateral OABC = =. (14)
24.( 1) Omit (2 points)
(2) Let y=0
∴ x2-p2-(m + 2)x +(m + 2)p = 0，
(x-p)(x + p)-(m + 2)(x-p)= 0，
That is, (x-p) (x+p-m-2) = 0,
∴ x 1 = p, x2 = m+2-p. (6 points)
∵
m+2-p & gt； p
∴ (7 points)
(3)∵OC=OB The area of a right triangle is =
= = (12 points)
∴ When and m >-2, the area of the right triangle formed by x 1 and two right-angled sides of x2 is the largest, and the largest area is or. (14)
25. Solution: As shown in figure 1, (1) passes through this point.
,,, is the midpoint.
GM = 2。 1.
The midpoint of.
2 points
The area of the isosceles trapezoid is 12.3 minutes.
(2) It can be a diamond with four points.
As shown in fig. 2,
A quadrilateral is a parallelogram with six points.
When the quadrangle is a diamond,
At this time, you can get it.
Seconds, the quadrilateral is a diamond. Eight minutes.
(3) There are two situations:
(1) When,
Method 1:,
The area of the overlapping part is:
When, the functional relationship with is 1 1 point.
2 when,
Set and intersect at this point, and then
,
That's because ...
The area of the overlapping part is:
14 point