Entry Examination PaperCandidate Name: ________Score:___________(总分100+20)1、Multiple Choice(18’)1)If there are no dancers that aren't slim and no singers that aren't dancers, then which statements are alwaystrue?( ).A.There is not one slim person that isn't a dancerB.All singers are slimC.Anybody slim is also a singerD.None of the above2)In the equation (x-5)2+(y-2)2=16, the center of the circle is answer choices( ).A.(5,2)B.(-5, -2)C.(-5, -3)D.(5, 3)3)In the following diagram,which of the following is not an example of an inscribed angle of circle O( ).A.NST ∠B.MNS ∠C.SNT ∠D.NSM ∠Q3 Q4 Q54)What can you NOT conclude from the diagram at the right? ( ).A. c=dB. a=bC. c 2 + e 2=b 2D. e=d5)If m ∠KLM=20° and measure of arc MP=30 ° ,what is m ∠KNP?( ).A.25°B.50°C.35°D.70°6)What is the negation of the statement ''The coat is blue''? ( ).A. the coat is greenB. the coat is sometimes blueC. the coat is not blueD. it is not true that the coat is not blue7)Which of the following is equal to cos35°( ).A. Sin35°B. Cos55°C. Sin55°D. cos145°8)Look at this series: 80, 10, 70, 15, 60, … What number should come next?( ).A. 20B. 25C. 30D. 509)What is the contrapositive of the proposition ''If a polygon has three sides then it is a triangle''?( ).A.''If a polygon is a triangle, then it has less than three sides.''B.''If a polygon is not a triangle, then it does not have three sides.''C.''If a polygon is not a triangle, then it has more than three sides.''D.''If a polygon is a triangle, then it does not have three sides.''2、Fill in the blank with sometimes, always, or never. (14’)1)Two tangents to the same circle from the same point are_______ congruent to each other.2)If two inscribed angles are congruent, then their intercepted arcs are________ congruent.3)If a line bisects an arc, then it_______bisects the chord of the arc.4)The measure of a central angle is______equal to the measure of its intercepted arc.5)If a radius bisects a chord of a circle, then it____bisects the minor arc of the chord.6)If two arcs are congruent, an inscribed angle of one arc is______congruent to an inscribed angle of the otherarc.7)If two chords of a circle are not congruent then the shorter chord is_______ closer to the center of the circle.3、Find the value of x in each figure below.(8’)4、The circle C has equation(10’)0195242022=+--+y x y xThe centre of C is at the point M1)Find the coordinate of the point M and the radius of the circle C.2)N is the point with coordinate (25,32), find the length of the line MN.5、Use the reference angle method above to solve the following:(12’)()⎪⎭⎫ ⎝⎛-43sin 1π ()⎪⎭⎫ ⎝⎛629cos 2π ()()︒420tan 3()⎪⎭⎫ ⎝⎛49sec 4π— ()()︒510csc 5 ()⎪⎭⎫ ⎝⎛319cot 6π6、For each the following statement ，do each of the following(8’)：“All Park View students will graduate.”Conditional: _______________________;Symbol________________;Converse: ________________________;Symbol________________;Inverse: __________________________;Symbol________________;Contrapositive: ____________________;Symbol________________.7、In circle O, diameter AB and ED intersect at center O;chord BD and tangent CB , Secant CDA,if the measure ofarc EA equals 80°,the measure of arc AD equals 100°,find (5’)：1)m ∠EOB=_____________; 2)m ∠BAD=_____________; 3)m ∠C=_____________;4)m ∠CBD=_____________; 5)m ∠EDB=_____________.8、Find the m ∠DGF to the nearest whole degree.(4’)：Extra Questions:(20’)1、Square ABCD has side length s, a circle centered at E has radius r,and r and s are both rational. The circlepasses through D, and D lies on BE. Point F lies on the circle, on the same side of BE as A. Segment AF is tangent to the circle, and 259+=AF . What issr ?2、All of the triangles in the diagram below are similar to isosceles triangle ABC, in which AB=AC. Each of the 7smallest triangles has area 1, and triangle ABC has area 40. What is the area of trapezoid DBCE?1、Multiple Choice:1) B ; 2) A ; 3) A ; 4) D ; 5) C ; 6)C ; 7) C ; 8) A ;9) B .2、Fill in the blank with sometimes, always, or never.1. Always ;2. Always ;3.Sometimes ;4.Always ;5. Always ; f. Always ; g. Never.3、Find the value of x in each figure below.(1) 86° (2)74°4、The circle C has equation.(1) 49 (2)255、Use the reference angle method above to solve the following: (1)22- (2) 23- (3)3(4)2 (5) 2 (6)336、For each the following statement ，do each of the following ：Conditional: _If students are All Park View ’s,then they will graduate__; Symbol____q p →____;Converse: __If students will graduate ,then students are All Park View ’s___;Symbol____p q →______;Inverse: __If students are not All Park View ’s,then they will not graduate_____;Symbol____qp ⌝→⌝__________;Contrapositive: _If students will not graduate ,then students are not All Park View ’s____;Symbol____pq ⌝→⌝___.7、1)m ∠EOB=100°; 2)m ∠BAD=40°; 3)m ∠C=50°; 4)m ∠CBD=40° 5)m ∠EDB=50°.8、132°Extra questions ： 1)952)24。