1. Multiple choice questions: (There are 6 questions in this big question, 4 points for each question, out of 24 points).
1 . c 2。 B 3。 D 4。 A 5。 B 6。 D
Two. Fill in the blanks: (This topic is entitled *** 12, with 4 points for each question, out of 48 points)
7.。 8.9.。 10.(-3, 2). 1 1.(- 1, 2).
12 .. 13. and so on. 14 .. 15.-2.
16 ..17.2.18.60 or 70
Iii. (There are 6 questions in this big topic, 19-22, with 8 points for each question; Questions 23 and 24, each 10. Out of 52 points)
19. solution: the original formula = ……………………………………………………………… (1min).
=
=
=.....................(3 points)
∵ = ....................(2 points)
Original formula =......................(2 points)
20. Solution: ..................... (1)
...................... (1 min)
..................... (2 points)
Sketch ..................... (4 points)
2 1. Proof: (1)∫‖
∴ ..................... (1min)
∵
∴ ..................... (1min)
∴‖......................(2 points)
(2)∵
..................... (2 points)
∴ ..................... (1min)
The area of ∵ is 18.
∴ ..................... (1min)
22.( 1) by the known ........................................................................................................ (1).
According to the image, when; When,; When,;
So, the solution,; ................... (3 points)
So the resolution function is; ................ (1 min)
(2) Timely, timely, timely,
Solution,; ................ (1 min)
When, in a known order;
Another time,; So,;
Get from; ............. (1 min)
;
That is, the drug content is not less than 20 mg for more than 25 minutes, so disinfection is effective. ...( 1)
23. Solution: (1) Figure (omitted)
‖ , ,
, ,
,
............... (4 points)
(2) Point C is regarded as point H,
Cross Mn at point f (1point)
∵
∴ ch = ahfh = AE = 200...( 1)
Let AH=CH=X,
Then,
Ⅶ in Rt△CFE
∴ ...(2 points)
The answer is x = 400 ........................ (1min).
Zemi ... (1)
24. Solution: (1)√.
∴AD= 1 SAR =2
∵
.................. (2 points)
∠∠A is a positive angle.
∴ ..............( 1 min)
(2) Figure ................. (2 points)
Solution 1: Intersection A is a vertical foot and point H.
In,,,
∴, ...( 1 min)
In,,,
∴ ...( 1 min)
If it is an acute angle (or point H is on the side of BC)
Then ... (1 min)
∵
The solution is ... (1)
If it is obtuse (or point H is on the extension line of CB side)
rule
∵
The solution is ... (1)
∴ The length of BD is or
Solution 2: Point B is BH⊥AC, and the vertical foot is H.
∵
∴ ,
∵ ....................... (1min)
In Rt△ABH,
∴
Solution or ....................... (2 points)
∴ In due course, ................. (1 min)
When, ........................ (1 min)
Iv. (For this big question, ***2 questions, 25 questions 12 points, 26 questions 14 points, out of 26 points)
25. (This title is ***2 small questions, 5 points +7 points, full score 12 points)
(1)∫ Intersections A (4 4,0) and C (0 0,2)
....................... (2 points)
∴ ....................... (1min)
When x= -2, y=0.
∴ Point is on the image of quadratic function; ..................... (2 points)
(3) The symmetry axis of quadratic function is the straight line x= 1.
∴ d ( 1，0)...................( 1)
Point e is on the axis of symmetry, which is parallel to the y axis.
∴
Again,,,,
Easy to obtain
∴ ,
So ........................ (2 points)
If a triangle with vertices c, d and e is similar to △ABC,
There are two situations:
I) when,
In other words, the solution is:
The coordinate of point E is .......................... (2 points).
Ii) In a timely manner,
In other words, the solution is:
The coordinate of point E is .......................... (2 points).
To sum up, the coordinates of point E are or.
26. (This title is ***3 small questions, 4 points +5 points +5 points, full score 14 points)
Solution: (1) According to the meaning of the question, we can get: A (4 4,0), B (0 0,3), AB=5.
I) when ∠ baq = 90, ..................... (1)
∴
Solution ............... (1 min)
Ii) When ∠ BQA = 90, BQ=OA=4.
.................. (1 min)
∴Q or ............. (1 min)
(2) Make the point P fall at the point E on the line segment AB after folding.
Then ∠EAQ =∠PAQ∠EQA =∠PQA, .......... (1 min).
What are you doing?
∴∠PAQ=∠BQA
∴∠EAQ=∠BQA
That is ab = QB = 5 ...................... (1).
∴ ,
∴, that is, point E is the midpoint of AB.
Passing point e is EF⊥BQ, vertical foot is point e, passing point q is QH⊥OP, vertical foot is point h,
Then, ⅷ
Say it again,
∴ ,
Therefore, ∴......................(2 points)
∴ ....................... (1min)
(3) When point C is on line PQ, the extension lines of BQ and AC extend to point F,
* ac⊥ab
∴
namely
∴ ..................( 1 min)
∫DQ‖AC, DQ=AC, and d is the midpoint of BC.
∴ FC = 2dq = 2ac ................. (1min)
∴
In Rt△BAC, = 4................( 1).
When point c is on the extension line of PQ, the intersection of BQ and AC is f, and the intersection of AD and BQ is g,
∫CQ‖ AD, CQ = AD, and D is the midpoint of BC.
∴ AD=CQ=2DG
∴ CQ=2AG=2PQ
∴ fc = 2af ................. (1min)
∴
In Rt△BAC, …………………………………………… (1).