(Examination time: 100 minutes? Full score: 120)
I. Multiple-choice questions (the full score of this big question is 42 points, and each small question is 3 points)
Of the four alternative answers to the following questions, only one is correct. Please use 2B pencil to black out the letter code of the answer you think is correct on the answer sheet as required.
The reciprocal of 1.5 is (? )
a . 5 B- 5？ c？ d？
2. The solution of equation x+2 = 1 is (? )
A.3？ B.-3 C. 1 D.- 1
3. It is reported that the west ring high-speed railway in our province is expected to be completed and opened to traffic by the end of 20 15, with a planned total investment of 27. 1 100 million yuan. The data of 2,765,438+000,000,000 is expressed as (? )
a . 27 1× 108 b . 2.7 1× 109？ C.2.7 1× 10 10？ d . 2.7 1× 10 1 1
Figure 1
A b? C D
4. A set of data: -2 1, 1, 2 1. So the pattern of this set of data is (? )A.-2？ B.0 C. 1 D.2
5. As shown in figure 1, the top view of the geometric figure is (? )
6. In a right triangle, one acute angle is equal to 60, then the degree of the other acute angle is (? )
A. 120？ B.90？ C.60？ Cao30
7. As shown in Figure 2, it is known that the included angle between AB∨CD and ∠ 1 )
A.∠2b∠3c∠4d∠5
8. As shown in Figure 3, △ABC and △DEF are symmetrical about y axis. Given a (-4,6), b (-6,2) and E (2, 1), the coordinates of point d are (? )A.(-4，6) B.(4，6) C.(-2， 1)？ Article 6, paragraph 2
Figure 2
Figure 3
?
9. The following formula factorizes from left to right, which is (? )
a . a2+4a-2 1 = a(a+4)-2 1 b . a2+4a-2 1 =(a-3)(a+7)？
C.(a-3)(a+7)=a2+4a-2 1？ a2+4a-2 1=(a+2)2-25
10. After two price reductions, the retail price of a drug per bottle dropped from 100 yuan to 8 1 yuan. It is known that the percentage of two price reductions is x,
Then the equation that X satisfies is (? )
a . 100( 1+x)2 = 8 1 b . 100( 1-x)2 = 8 1 c . 100( 1-x %)2 = 8 1？ D. 100x2=8 1
1 1. The lateral expansion of the cone is a sector with a radius of 8cm and a central angle of120, so the radius of the circle at the bottom of the cone is (? )? A.cm B.cm？ C.cm？ D.cm
12. There are three balls marked with the numbers 3, 1 and -2 in an opaque bag. These balls are all the same except those marked with numbers. If two balls are randomly drawn from the bag, the probability that the sum of the two numbers on the two balls is negative is (? )A. B. C？ D.
13. Translate parabola y=x2 to get parabola y=(x+2)2, then the translation process is correct (? )
A. translate two units to the left. B. translate two units to the right?
C. move up two units. Move down two units.
14. If K 1 > 0 > K2 is known, then the functions y=k 1x and y= the image in the same plane rectangular coordinate system is roughly ().
Answer? b？ c？ D
?
Fill in the blanks (full score for this big question 16, 4 points for each small question)
15.3 notebooks with a unit price of RMB and 5 pencils with a unit price of RMB. Do you need to pay? Yuan.
Figure 4
16. In the function, the value range of the independent variable x is. 17. As shown in Figure 4, AD is the height of △ABC, and AE is the diameter of the circumscribed circle of △ABC ⊙ O.
And AB=, AC=5, AD=4, then the diameter AE of ⊙O =.
18. As shown in Figure 5, △COD is the graph obtained after △AOB rotates 40 clockwise around point O,
If point C happens to fall on AB, and the degree of ∠AOD is 90, what is the degree of ∠B? .
Figure 5
Third, answer the question (the full score of this big question is 62 points) 19. (Full score 10) Calculation: (1)?
(2) Solve the inequality and find its positive integer solution.
20. (Full score: 8) Hainan is rich in tourism products. Students in Class 9 (1) of a school randomly surveyed tourists' love for some tourism products, and asked tourists to choose their favorite products among the listed tourism products, only one of which can be selected. The following is an incomplete statistical chart compiled by the students:
Complete the following questions according to the above information:
(1) Please complete the bar chart;
(2) 400 tourists were randomly investigated; In the pie chart, the central angle occupied by part A is 72? Degree;
(3) According to the survey results, please estimate that there are about 1500 tourists like Li Jin.
2 1. (Full score: 8) Hainan melons and fruits are fragrant in May. The unit price of seedless litchi and egg mango sold in a supermarket is ***30 kg in 26 yuan and 22 yuan respectively. Uncle Li spent 708 yuan on these two fruits. How many kilograms did Uncle Li buy?
Figure 6
22. (Full score: 9) As shown in Figure 6, a nuclear submarine measured a depression angle of 30 at point A 600 meters below the sea surface DF, and there was a black box at point C right in front of the seabed. Continue to sail straight at the same depth1464m to reach point B, and measure the depression angle of 45 at point C right in front of the seabed. Find the depth DF from point C to the sea surface (the result is accurate to one place, reference data: ≈ 65438).
23. (Full score 13) As shown in Figure 7, the diagonal of the square ABCD intersects at point O, the bisector of ∠CAB intersects with BD and BC at points E and F respectively, intersects with BH⊥AF at point H, and intersects with AC and CD at points G and P respectively, connecting GE and GF.
(1) Verification: △ OAE △ OBG.
(2) Question: Is the quadrilateral BFGE a diamond? If yes, please prove it; If not, please explain why.
Figure 7
A
D
B
C
F
G
O
H
P
E
(3) Try to find the value of: (Results keep the root number).
24. (Full mark: 14) As shown in Figure 8, a parabola with a straight line x=2 passes through two points A (- 1 0) and C (0 0,5), and the other intersection with the X axis is B. It is known that M (0, 1) and E (a a,0).
(1) Find the analytical expression of this parabola.
(2) When a= 1, find the maximum area of the quadrilateral MEFP and the coordinates of point P at this time.
Figure 8
O
A
E
F
B
M
C
P
x
y
(3) If △PCM is an isosceles triangle with point P as its vertex, what is the value of a and the perimeter of the quadrilateral PMEF is the smallest? Please explain the reason.
Standby chart
A
O
M
C
E
F
x
B
y
P
?
Hainan province 20 14 junior high school graduates' academic level examination
Reference answers of mathematics subject test questions
I. Multiple-choice questions (the full score of this big question is 42 points, and each small question is 3 points)
Title number
1
2
three
four
five
six
seven
eight
nine
10
1 1
12
13
14
answer
B
D
C
C
C
D
D
B
B
B
A
B
A
C
Fill in the blanks (full score for this big question 16, 4 points for each small question)
15.(3a+5b) 16。 And 17. 18.60 ?
Third, answer questions:
80
1 12
Seventy two
60
76
19.( 1) Solution: Original formula
? (2) Solution:
The positive integer solution of inequality is:
20. Solution: (1) 60 ÷15%-80-72-60-76 =112 (person), as shown in the figure,
(2) 6015% = 400 (person), 80/400× 360 = 72,
(3)1500× (112 ÷ 400) = 420 (person),
2 1. solution: let uncle Li buy x kilograms of seedless litchi and y kilograms of egg mango.
Judging from the meaning of the question,
Solution:.
Answer: Uncle Li bought seedless litchi 12 Jin and egg mango 18 Jin.
22.？ Solution: make CE⊥AB in E,
According to the meaning, AB= 1464, ∠ EAC = 30, ∠ CBE = 45,
Let CE=x, then BE=x,
In Rt△ACE, tan30 === =,
Get 3x= 1464+x,
Solution: x=732(+ 1)≈2000 meters,
AD+CE=2000+600=2600
That is, the black box c is about 2600 meters away from the sea.
23. Solution: (1) Proof:
∵ quadrilateral ABCD is a square
∴OA=OB,∠AOE=∠BOG=90
A
D
B
C
F
G
O
H
P
E
∵BH⊥AF∴∠AHG=90
∴∠GAH+∠AGH=90 =∠OBG+∠AGH
∴∠GAH=∠OBG
∴△OAE≌△OBG.
(2) The quadrilateral BFGE is a diamond for the following reasons:
∠∠GAH =∠BAH，AH=AH，∠AHG=∠AHB
∴△AHG≌△AHB
∴GH=BH
∴AF is the perpendicular bisector of line BG.
∴EG=EB,FG=FB
∠∠BEF =∠BAE+∠ABE =，∠BFE=90 -∠BAF=67.5
∴∠BEF=∠BFE
∴EB=FB
∴EG=EB=FB=FG
∴ The quadrilateral BFGE is a diamond.
(3) Let OA=OB=OC=a, and the side length of the rhombic GEBF is B. 。
∫ The quadrilateral BFGE is a diamond,
∴GF∥OB，∴∠CGF=∠COB=90，
∴∠GFC=∠GCF=45，
∴CG=GF=b
(OG = OE = A-B, OC-CG = A-B from △ OAE △ OBG, CG=b)
∴OG=OE=a-b, in Rt△GOE, we can get: from Pythagorean theorem.
∴AC=,AG=AC-CG=
∫PC∨ab，∴△CGP∽△AGB，
∴,
AE = GB from( 1)△OAE?△OBG
∴
G
24. Solution: (1) Let the parabola be a quadratic function, like passing through points A (- 1, 0) and C (0 0,5).
∴
Solution:
∴ The functional relationship of quadratic function is
That is, y =-x2+4x+5.
(2) When a= 1, E( 1, 0), F(2, 0),
Let the coordinate of p be (x, -x2+4x+5).
The intersection point p is perpendicular to the y axis, and the vertical foot is g,
MEFP area of quadrilateral
=
=
=
=
Therefore, the maximum area of the quadrilateral MEFP at that time was,
At this point, the p coordinate is.
(3)EF= 1, move the point m to the right by 1 unit to get the point M 1, and then make the point M 1 a symmetrical point M2 about the x axis. In quadrilateral FMEF, since the side lengths PM and EF are fixed values, in order to minimize the perimeter of quadrilateral FMEF, ME+PF is the minimum value, because Me = M66. So point F should be the intersection of straight line M2P and X axis. From OM= 1, OC=5, the ordinate of point P is 3, and from Y =-x2+4x+5, point P () can be obtained.
The coordinates of the point M2 are (1,-1).
Therefore, the analytical formula of the straight line M2P is: