(Full score 150, test time 120 minutes)
A, fill in carefully, this big question * *12 small question, each small question is 3 points ***36 points. Fill in the answer directly on the line in the question.
The reciprocal of 1 It's _ _ _ _ _ _ _.
2. In the function, the value range of the independent variable x is _ _ _ _ _ _ _ _ _.
3. The forest called "the lung of the earth" is disappearing from the earth at the rate of 65,438+0,500,000 hectares per year, and the annual loss of the forest is expressed as _ _ _ _ _ _ _ _ _ _ _ _ _ _ _.
4. If the average value of data 2, 3, x and 4 is 3, the mode of this set of data is _ _ _ _ _ _ _ _ _ _ _ _.
5. Observe the following equations in order:
-
Please guess that the 10 th equation should be _ _ _ _ _ _ _ _ _ _ _ _ _ _ _.
6. The image of the function is in each quadrant, and the value of y increases with the increase of x and _ _ _ _ _ _ _.
7. Move point A( 1, -3) to point A1(3,0) by translation, and move the point in the same way.
P (2 2,3) moves to P 1, so the coordinate of point P 1 is (_ _ _ _ _ _ _).
8. The root of the equation is _ _ _ _ _ _ _ _.
9. Regular triangle, regular quadrangle, regular pentagon and regular hexagon.
Can't separate dense shop is _ _ _ _ _ _ _.
10. As shown in the figure, the large square grid consists of 16 small squares with a side length of 1.
Composition, the area of the shaded part in the figure is _ _ _ _ _ _ _ _.
1 1. Put a conical paper tube with a bottom radius of 3cm and a height of 4cm along a line.
When the bus is truncated, the area of the side expansion diagram is _ _ _ _ _ _ _ _.
(The result is represented by the included formula)
12. As shown in the figure, quadrilateral ABCD is a rectangular piece of paper with AD = 2AB.
If the angle A is folded along the crease DE passing through the point D, the point A will fall on it.
A 1 on BC, then ∠ ea1b = _ _ _ _ _ _ _ _ _ _.
Second, choose the topic (4 points for each topic, ***4 small questions, * *16 points, and write the code of the correct option in brackets).
13. The following operation is correct ()
A.B.
C.D.
14. As shown in the figure, the front view of the teacup is ().
15 Given that the radii of two circles are 3cm and 5cm respectively, and the distance between the centers is 8cm, then the positional relationship between the two circles ().
A. phase separation B. circumscribed C. intersected D. inscribed
16. As shown in the picture, a boat and a speedboat came from.
The image of the driving process from port a to port b changes with time,
According to the image, the following conclusion is wrong ()
A.the speed of this ship is 20 kilometers per hour.
The speed of the speedboat is 40 kilometers per hour.
C. The ship left Hong Kong two hours earlier than the speedboat.
D. the speedboat can't catch up with the boat
Third, be patient: this big question * * has 10, ***98 points, solution.
Promise to write the necessary written instructions to prove the process or calculation steps.
17.(8 points)
18.(8 points) Simplify before evaluating.
19.(8 points) Solve inequality groups:
20.(8 points) As shown in the figure, A, B, C and D are four points on ⊙O, AB=DC, △ABC and.
Is△ △DCB congruent? Why?
2 1.(8 points) A class will hold a graduation party. In order to encourage everyone to participate, it is stipulated that each student needs to turn the following two turntables A and B respectively (each turntable is equally divided). If the sum of the numbers after the turntable stops is 7, the students will perform a singing program; If the sum of the numbers is 9, the students will perform a story-telling program; If the sum of numbers is other numbers, they correspond to performances and other programs respectively. Please use list method (or tree diagram) to find out the probability of this classmate performing singing program and story-telling program respectively.
22.(8 points) If a city wants to build a quadrangle garden on the vacant land of a parallelogram ABCD, it is required that the area occupied by the garden is half that of the ABCD, with the four vertices of the quadrangle garden as the population, and it is required to be located at the four sides of the ABCD respectively. Please design two schemes:
Scheme (1): As shown in figure (1), two entrances and exits, E and F, have been identified. Please draw a quadrangular garden that meets the requirements on the drawing (1) and briefly explain the drawing method;
Scheme (2): As shown in Figure (2), an entrance m has been determined. Please draw a trapezoidal garden that meets the requirements on Figure (2) and briefly explain the drawing method.
23.( 12) Loquat is one of the famous fruits in Putian, and there are 100 loquat trees in an orchard. The average yield of each tree is 40 kilograms. Now, all kinds of loquat trees are ready to increase their yield. But if a variety of trees are planted, the distance between trees and the sunlight received by each tree will be reduced. According to practical experience, the average yield of all loquat trees in the orchard decreased by 0.25 kg after production. Q: How many loquat trees need to be planted to maximize the total output of loquat trees in the orchard after production? What is the maximum output?
Note: The vertex coordinates of parabola are
24.( 12) In May and June this year, various cities in our province were hit by heavy rain, and the water level soared. A city flood rescue team received a report at B: someone was trapped at A, a flooded building, and the situation was critical! The rescue team measured that A was 600 northeast of B (pictured). The team decided to divide into two groups: the first group immediately swam to A to save people, the second group ran 120 meters from land to C, and then swam from C to A to save people. It is known that A is 300 northeast of C, and rescuers swim at a speed of 65438 in the water. The speed of running on land is 4 meters per second. Which rescue team will arrive first? Please explain the reason (reference data = 1.732).
25.( 12 point) Given the rectangular ABCD and point P, when point P is at any position in BC (as shown in Figure (1)), it is easy to draw a conclusion: Please explore: What is the quantitative relationship when point P is at the position in Figure (2) and Figure (3) respectively? Please write your conclusions about the above two situations and prove your conclusions with Figure (2).
A: The conclusion of the inquiry on Figure (2) is _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
The exploration conclusion in Figure (3) is _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _.
Proof: As shown in Figure (2)
26.( 14) As shown in the figure, the parabola passes through three points: A (-3,0), B (0 0,4) and C (4 4,0).
(1) Find the analytical formula of parabola.
(2) It is known that AD = AB(D is on the line segment AC), and a moving point P moves from point A along the line segment AC at a speed of/kloc-0 per second; At the same time, another moving point Q moves from point B along BC line at a certain speed. After moving for t seconds, divide the line PQ vertically by BD to find the value of t;
(3) In the case of (2), is there a point m on the parabola axis of symmetry that minimizes the value of MQ+MC? If it exists, request the coordinates of point m; If it does not exist, please explain why.
(Note: Parabolic symmetry axis is)
Reference answer
1. Fill in the blanks for big questions *** 12 small questions, with 3 points for each small question and 36 points for * * *.
1.3, 2., 3., 4.3, 5., 6. Improve.
7. (4,6), 8.9. Regular Pentagon, 10. 10, 1 1. , 12.60
Second, multiple-choice questions ***4 small questions, 4 points for each small question, *** 16 points.
13.D 14。 A 15。 B 16。 D
III. Solutions and drawings
17.
2 1, solution 1: express the sum of all the obtained numbers by tabular method.
As can be seen from the above table, there are nine situations for the sum of two numbers.
therefore
A: The probability of this student performing a singing program is, and the probability of performing a story-telling program is.
22. Solution: Scheme (1)
Painting 1: Painting 2: Painting 3:
(1) F For FH∨AD cross (1) F For FH∨AB cross (1), take a point on AD.
AD is at point h, and AD is at point h, so DH = cf
(2) Take a little G (2) on DC E as EG∑AD(2) and take it on CD.
Connect EF, FG, GH and DC to point g.
He, quadrilateral EFGH connects EF, FG, GH, connects EF, FG, GH,
Is a quadrilateral to be drawn; He, then quadrilateral EFGH him, then quadrilateral EFGH.
It's a quadrangle to be drawn. It's a quadrangle to be drawn.
(4 points for correct drawing, 1 point for briefly describing drawing)
Scheme (2) Drawing method: (1) The intersection m is MP∑AB, and the intersection AD is at point P,
(2) Take a little Q from AB and connect PQ.
(3) cross m into MN∑PQ, and cross DC at point n,
Connect QM, PN, MN
Quadrilateral QMNP is the quadrangle to be drawn.
(2 points for correct drawings, 1 point for brief description of drawings)
The answer to this question is not unique, as long as it meets the requirements. )
23. solution: if x trees are planted, the total output of the orchard will be y kilograms.
According to the meaning of the question: y = (100+x) (40–0.25x)
= 4000–25x+40x–0.25 x2 =-0.25 x2+ 15x+4000
Because a =-0.25 < 0, y has the maximum value at this time.
Answer; (omitted)
24 solution: As the intersection of AD⊥BC and BC, the extension line of A is at point D, A is 600 northeast of B, ∠ABD=300, and A is 300 northeast of C, so ∠ACD=600.
Because ∠ABC=300 and ∠BAC=300, ∠ABD= ∠BAC, so AC=BC.
AC= 120 because BC= 120.
In Rt△ACD, ∠ACD=600 and AC= 120, so CD=60 and AD =
In Rt△ABD, because ∠ABD=300, AB=
The first set of time: the second set of time:
Because 207.84 > 150, the second group arrived first.
25: All conclusions are PA2+PC2=PB2+PD2 (Figure 2 2 points, Figure 3 1 minute).
It is proved that, as shown in Figure 2, the intersection point P is MN⊥AD at point M and BC at point N,
Because in ∨ BC, MN⊥AD of MN⊥BC.
At Rt△AMP, PA2=PM2+MA2.
In Rt△BNP, PB2=PN2+BN2.
At Rt△DMP, PD2=DM2+PM2.
In Rt△CNP, PC2=PN2+NC2.
So PA2+PC2=PM2+MA2+PN2+NC2.
PB2+PD2=PM2+DM2+BN2+PN2
Because the quadrilateral MNCD of MN⊥AD, MN⊥NC and DC⊥BC is a rectangle.
So MD=NC, AM = BN,
So PM2+MA2+PN2+NC2 = PM2+DM2+BN2+PN2.
That is, PA2+PC2=PB2+PD2.
26( 1) Solution 1: Let the analytical formula of parabola be y = a (x +3 )(x-4).
Because B (0 0,4) is on a parabola, 4 = a (0+3) (0-4) is solved to get a=-1/3.
So the parabolic analytical formula is
Solution 2: Let the analytical formula of parabola be,
According to the meaning of the question: c=4 and solve it.
So the analytical formula of parabola is
(2) connect DQ, in rt delta AOB,
So AD=AB= 5, AC=AD+CD=3+4 = 7, CD = AC-AD = 7-5 = 2.
Because BD vertically divides PQ, PD=QD, PQ⊥BD, so ∠PDB=∠QDB.
Because AD=AB, ∠ABD=∠ADB, ∠ABD=∠QDB, DQ∨AB.
So ∠CQD=∠CBA. ∠CDQ =∠ cab, so △CDQ∽△ cab.
that is
So AP = ad-DP = ad-dq = 5 -=–=,
So the value of t is
(3) There is a point m on the symmetry axis that minimizes the value of MQ+MC.
Reason: Because the symmetry axis of parabola is
Therefore, A (-3,0) and C (4 4,0) are symmetrical about a straight line.
If the intersection line connecting AQ is at point M, the value of MQ+MC is the smallest.
Q is QE⊥x axis, at point E, so ∠QED=∠BOA=900.
DQ∨AB，∠ BAO=∠QDE，△DQE ∽△ABO
that is
So QE=, Germany =, so OE = OD+ Germany =2+ =, so Q (,).
Let the analytical formula of straight line AQ be
Then the next step is
Therefore, the analytical formula of straight line AQ is simultaneous.
Therefore, m
Then: there is a point m on the axis of symmetry that minimizes the value of MQ+MC.