Transcription
The Oakwood AcademyCircle Theorems StandardQuestions (G10)Page 1
The Oakwood AcademyQ1.(a)A, B and C are points on the circumference of a circle with centre O.Not drawnaccuratelyWork out the size of angle x.Answer . degrees(1)Page 2
The Oakwood Academy(b)P, Q and R are points on the circumference of a circle with centre O.Not drawnaccuratelyWork out the size of angle y.Give a reason for your answer.Answer . degreesReason .(2)(Total 3 marks)Page 3
The Oakwood AcademyQ2.AB is a tangent to the circle.Not drawn accuratelyWrite down the value of x.Give a reason for your answer.Answer . degreesReason .(Total 2 marks)Page 4
The Oakwood AcademyQ3.(a)AB is a chord of the circle.TA and TB are tangents to the circle.Not drawn accuratelyWork out the size of angle x.Answer . degrees(2)Page 5
The Oakwood Academy(b)The diagram shows a circle, centre O.C and D are points on the circumference.COE is a straight line.DE is a tangent.Not drawn accuratelyWork out the size of angle y.You must show your working, which may be on the diagram.Answer . degrees(3)(Total 5 marks)Page 6
The Oakwood AcademyQ4.The diagram shows a circle, centre O.Not drawnaccurately(a)Work out the size of angle x.Answer . degrees(1)(b)Work out the size of angle y.Answer . degrees(3)(Total 4 marks)Page 7
The Oakwood AcademyQ5.Points A, B, C and D are on the circumference of the circle.CDE is a straight line.Not drawn accurately(a)Work out the size of angle BCD.Give a reason for your answer.Answer . degreesReason .(2)(b)Work out the size of angle ABC.Answer . degrees(1)(Total 3 marks)Page 8
The Oakwood AcademyQ6.PAQ and PB are tangents to the circle.AC BCNot drawn accuratelyWork out the size of angle x.You must show your working which may be on the diagram.Answer . degrees(Total 4 marks)Page 9
The Oakwood AcademyQ7.(a)P, Q, R and S are points on the circumference of the circle.Not drawn accuratelyWork out the size of angle x.Answer . degrees(1)(b)The diagram shows a circle and a tangent at T.Not drawn accuratelyWrite down the size of angle w.Give a reason for your answer.Answer . degreesReason .(2)Page 10
The Oakwood Academy(c)A, C and D are points on the circle, centre O.BA and BC are tangents to the circle.Not drawn accuratelyWork out the size of the angle y.Answer . degrees(3)(Total 6 marks)Page 11
The Oakwood AcademyQ8.(a)O is the centre of the circle.Write down the size of angle a.Not drawn accuratelyAnswer . degrees(1)(b)Write down the size of angle b.Give a reason for your answer.Not drawn accuratelyAnswer . degreesReason .(2)Page 12
The Oakwood Academy(c)A, B, C and D are points on a circle, centre O.Not drawn accuratelyx y z 290 Work out the values of x, y and z.x . degreesy . degreesz . degrees(3)(Total 6 marks)Page 13
The Oakwood AcademyQ9.(a)The diagram shows a circle, centre O.Not drawn accuratelyWork out the value of x.Answer . degrees(1)(b)The diagram shows a cyclic quadrilateral.Not drawn accuratelyWork out the value of y.Answer . degrees(2)(Total 3 marks)Page 14
The Oakwood AcademyQ10.A, B, C, D and E are points on a circle.AC is parallel to ED.Not drawn accurately(a)Write down the size of angle x.Answer . degrees(1)(b)Work out the size of angle y.Answer . degrees(3)(Total 4 marks)Page 15
The Oakwood AcademyQ11.P, Q and R are points on a circle.Triangle PQR is isosceles.XY is a tangent to the circle at P.Not drawn accuratelyWork out the size of angle RPY.Answer . degrees(Total 2 marks)Page 16
The Oakwood AcademyQ12.A, B, C and D are points on the circumference of a circle centre O.AC is a diameter.Angle DAC 42 Not drawn accurately(a)Write down the value of x.Answer . degrees(1)(b)Work out the value of y.Answer . degrees(1)(Total 2 marks)Page 17
The Oakwood AcademyM1.(a)35B1(b)100B1Angle at centre twice angle on circumferenceMust use words ‘centre’ and ‘circumference’ (or ‘perimeter’)Allow poor spelling even though both words givenoe (strand) (i)Q1[3]M2.43B1Alternate segment (theorem)Strand (i) Do not accept AlternateDependent on B1Q1[2]M3.(a)(180 38) 2M171May be on diagram if no contradictionA1(b)ODE 90 seen or impliedor CDO 25or COD 130Page 18
The Oakwood AcademyMay be on diagramB1DOE 50or CDE 115or 140 seenMay be on diagramM140A1Additional Guidance40 with no working seenB1M1A1115 is B1M1 unless from clearly incorrect workinge.g. 115 leading to an answer of 65 is M1 only[5]M4.(a)150B1(b)360 150 or 210or 360 their 150oeOCA 18 seen or impliedor 180 18 75 or 87M1360 18 75 210or 360 18 75 their 210oeOCB 75 18 or 57 seen or implied180 93 30 or 87 30M1dep57A1[4]Page 19
The Oakwood AcademyM5.(a)108B1Opposite angle of a cyclic quadrilateralStrand (i)(add up to 180)Must have 108Q1Additional GuidanceMust see “opposite” and “cyclic” (oe e.g. quadrilateral in a circle)(b)125B1[3]M6.ABC 52May be on diagramM1BAC 52or BAQ 104or ACB 76May be on diagramM1depPAB 76or PBA 76May be on diagramM1dep28Clear evidence that 28 is for angle xA1Page 20
The Oakwood AcademyAdditional GuidanceAngles may be on diagramACB 52 and ABC 52M1 only[4]M7.(a)56B1(b)70B1Alternate segment (theorem)Strand (i)Dependent on B1Q1dep(c)2 47 or 94or Angle BOA 47or Angle BOC 47or Angle BAC 47or Angle BCA 47May be on diagram (obtuse angle)M190 or right angle symbol seen at A orCor 180 90 47or (180 2 47) 2oeM1Page 21
The Oakwood Academy43A1[6]M8.(a)35B1(b)40B1Opposite angles of cyclic quad (add up to) 180 oeStrand (i) No need to mention 180 if angle given as 40Accept ‘supplementary’ to mean adds to 180.Q1(c)x 55y 110z 125If answer line blank mark diagram or script.B2 any two correctB2 y 110 and x z 180B2 z 125 and y 2xB1 any one correctB1 values less than 180 such that y 2x or x z 180B3[6]M9.(a)70B1(b)4y y 180 or 5y 180 oeor 180 5Page 22
The Oakwood AcademyM136A1[3]M10.(a)70B1(b)ADE 34or AED 180 70 or 110or ADC 180 70 34 or 76Angles seen on diagram must be in correct placeM1ADE 34and AED 180 70 or 110M1dep36A1[4]M11.180 (2 35)RQP 110 marked on diagramB1110B1[2]Page 23
The Oakwood AcademyM12.(a)42B1(b)48B1[2]Page 24
Circle Theorems Standard Questions (G10) The Oakwood Academy Page 2 Q1.(a) A, B and C are points on the circumference of a circle with centre O. Not drawn . (oe e.g. quadrilateral in a circle) (b) 125 B1 [3] M6. ABC 52 May be on diagram M1 BAC 52 or BAQ 104 or ACB 76 May be on diagram M1dep PAB 76 or PBA 76 May be on diagram
