Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2014 | Oct-Nov | (P1-9709/13) | Q#2

Question In the diagram, OADC is a sector of a circle with centre O and radius 3 cm. AB and CB are tangents  to the circle and angle  radians. Find, giving your answer in terms of  and ,       i.       the perimeter of the shaded region,    ii.       the area of the shaded region. Solution     i.   It is evident […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2014 | Oct-Nov | (P1-9709/12) | Q#2

Question The diagram shows a triangle AOB in which OA is 12 cm, OB is 5 cm and angle AOB is a right  angle. Point P lies on AB and OP is an arc of a circle with centre A. Point Q lies on AB and OQ is an arc of a circle with centre B. […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2014 | Oct-Nov | (P1-9709/11) | Q#8

Question In the diagram, AB is an arc of a circle with centre O and radius 4 cm. Angle AOB is  radians. The  point D on OB is such that AD is perpendicular to OB. The arc DC, with centre O, meets OA at C.      i.       Find an expression in terms of  for the perimeter of the shaded region […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2014 | May-Jun | (P1-9709/13) | Q#3

Question The diagram shows part of a circle with centre O and radius 6 cm. The chord AB is such that angle  AOB = 2.2 radians. Calculate     i.       the perimeter of the shaded region,    ii.       the ratio of the area of the shaded region to the area of the triangle AOB, giving your answer in  the form k : 1. Solution […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2014 | May-Jun | (P1-9709/12) | Q#4

Question The diagram shows a sector of a circle with radius  cm and centre . The chord AB  divides the sector into a triangle AOB and a segment AXB. Angle AOB is  radians.      i.       In the case where the areas of the triangle AOB and the segment AXB are  equal, find the value of the constant  for which .    ii.  […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2014 | May-Jun | (P1-9709/11) | Q#6

Question The diagram shows triangle ABC in which AB is perpendicular to BC. The length of AB is 4 cm and angle CAB is  radians. The arc DE with centre A and radius 2 cm meets AC at D and AB at E. Find, in terms of,      i.       the area of the shaded region,    ii.       the perimeter […]