Test site: vertical diameter theorem; Congruent triangles's judgment and nature.
Analysis: According to the vertical diameter theorem, find AD, prove △ ADO △ OFE, and deduce OF=AD, and you can get the answer.
Answer: Solution: ∫OD? AC，AC=2，
? AD=CD= 1，
∵OD？ AC，EF？ AB，
ADO=？ OFE=90？ ,
∫OE∑AC，
DOE=？ ADO=90？ ,
Dao+? DOA=90？ ,? DOA+？ EF=90？ ,
Tao =? EOF，
In addo and OFE,
,
? △ addo△ ?△OFE(AAS),
? OF=AD= 1，
So choose C.
Comments: This topic examines the nature and judgment of congruent triangles and the application of the vertical diameter theorem. The key to solve this problem is to find out the length of △ ado △ ofe and AD. Note: The diameter perpendicular to the chord bisects the chord.
8. As shown in the figure, in the rectangular ABCD, AB
A. line segment ef b. line segment de c. line segment ce d. line segment BE
Test center: function image of moving point problem.
Analysis: Do BN? AC, vertical foot is n, FM? AC, feet are m, DG AC, the vertical foot is g, find out the time when the minimum values of line segments EF, CE and BE appear respectively, and then draw a conclusion.
Answer: Solution: Be a BN? AC, vertical foot is n, FM? AC, feet are m, DG AC, the vertical foot is g.
According to the shortest vertical line segment, when point E coincides with point M, AE
According to the shortest vertical line segment, when point E coincides with point G, that is, AED >: when, DE has the minimum value, so B is correct;
∵ CE = AC-AE, CE decreases with the increase of AE, so C is wrong;
According to the shortest vertical line segment, when point E coincides with point N, AE
Therefore, choose: B.
Comments: This question mainly examines the function image of the moving point problem, and determining the time when the minimum value of the function appears according to the shortest vertical line segment is the key to solving the problem.
Fill in the blanks (***4 small questions, 4 points for each small question, full score 16)
9. As shown in the figure, it is known that the sector radius is 3cm and the central angle is 120? The area of the sector is 3? Square centimeters. (the result was retained? )
Test center: calculate the sector area.
Topic: the finale.
Analysis: Know the sector radius and central angle, and use the sector area formula to get it.
Answer: from S= known.
S=？ 32=3? Square centimeters.
Comments: This question mainly examines the calculation of sector area, and knows the calculation formula of sector area S=.
10. At a certain moment, it is measured that the shadow length of a bamboo pole with a height of 2m is 1m and the shadow length of a building is 12m, so the height of the building is 24 m.
Similar triangles's application.
Analysis: According to the proportional formula of the height of the object and the length of the shadow at the same time and place, the solution can be obtained.
Solution: Solution: Let the height of this building be xm.
Judging from the meaning of the question, =,
The solution is x=24,
That is, the height of this building is 24 m.
So the answer is: 24.
Comments: This question examines the application of similar triangles, remembering that the height of objects in the same place is directly proportional to the shadow growth is the key to solving the problem.
1 1. As shown in the figure, the coordinates of two intersections of parabola y=ax2 and straight line y=bx+c are A (﹣ 2,4) and B (﹣ 1, 1) respectively, so the equation about X is AX2 ﹣.
Test site: the nature of quadratic function.
Special topic: combination of numbers and shapes.
Analysis: According to the intersection of quadratic function image and linear function image, the solution of the equations is 0, so it is easy to get the solution of the equation AX2-Bx-c = 0 about X. 。
Solution: Solution: The coordinates of the two intersections of parabola y=ax2 and straight line y=bx+c are A (-2,4) and B (1, 1) respectively.
? The solution of the equation is,
That is, the solution of the equation AX2-bx-c = 0 about X is X 1 =-2, and x2= 1.
So the answer is X 1 =-2, x2= 1.
Comments: This question examines the nature of quadratic function: quadratic function y=ax2+bx+c(a? The vertex coordinate of 0) is (﹣,) and the symmetrical straight line is x=﹣. The intersection of quadratic function image and linear function image is also studied.
12. for a positive integer n, define F(n)=, where F(n) represents the sum of squares of the first and last bits of n, for example, F(6)=62=36, f (123) = f (123) = 650. Fk+ 1(n)=F(Fk(n))。 For example: f1(123) = f (123) =10, F2( 123)= 1
( 1): F2(4)= 37，f 20 15(4)= 26；
(2) If F3m(4)=89, the minimum value of positive integer m is 6.
Test center: regular type: types of numbers.
Special topic: new definition.
Analysis: By observing the first 8 data, we can get the rule. These numbers are seven cycles, and we can calculate them according to these laws.
Solution: solution: (1) F2 (4) = f (f1(4)) = f (16) =12+62 = 37;
F 1(4)=F(4)= 16，F2(4)=37，F3(4)=58，
F4(4)=89，F5(4)= 145，F6(4)=26，F7(4)=40，F8(4)= 16，
It is observed that these numbers are 7 cycles, and 20 15 is 287 times of 7, so f 2015 (4) = 26;
(2) According to (1), these numbers are 7 cycles, F4(4)=89=F 18(4), so 3m= 18, so m=6.
So the answer is: (1) 37,26; (2)6.
Comments: This question belongs to the law of digital change. By observing the first few data, we can get the law, and finding out the changing law skillfully is the key to solve the problem.
Iii. Answer questions (*** 13 small questions, out of 72 points)
13. Calculation: (-1) 20 15+SIN 30? ﹣(? ﹣3. 14)0+( )﹣ 1.
Test center: the operation of real numbers; Zero exponential power; Negative integer exponential power; Trigonometric function value of special angle.
Special topic: calculation problems.
Analysis: The first term of the original formula is calculated according to the meaning of power, the second term is calculated according to the trigonometric function value of special angle, the third term is calculated according to the law of zero exponential power, and the last term is calculated according to the law of negative exponential power.
Solution: The original formula =- 1+- 1+2 =.
Comments: This question examines the operation of real numbers, and mastering the algorithm is the key to solve this problem.
14. As shown in the figure, in △ABC, AB=AC, D is the midpoint of BC, BE? AC in e, verification: △ACD∽△BCE.
Testing Center: similar triangles's Judgment.
Special topic: proving the problem.
Analysis: according to the properties of isosceles triangle, from AB=AC, D is the midpoint of BC, and AD? BC, easy to get? ADC=？ BEC=90？ , plus the common angle, so we can draw a conclusion according to the similarity of two triangles with equal angles.