# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2013 | Oct-Nov | (P1-9709/13) | Q#6

Question The diagram shows sector OAB with centre O and radius 11 cm. Angle  radians. Points C and D lie on OA and OB respectively. Arc CD has centre O and  radius 5 cm. i.       The area of the shaded region ABDC is equal to k times the area of the unshaded  region OCD. Find k.    ii.    […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2013 | Oct-Nov | (P1-9709/12) | Q#2

Question Fig. 1 shows a hollow cone with no base, made of paper. The radius of the cone is 6  cm and the height is 8 cm. The paper is cut from A to O and opened out to form the  sector shown in Fig. 2. The circular bottom edge of the cone in Fig. 1 becomes the  […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2013 | Oct-Nov | (P1-9709/11) | Q#8

Question The inside lane of a school running track consists of two straight sections each of  length x metres, and two semicircular sections each of radius r metres, as shown in  the diagram. The straight sections are perpendicular to the diameters of the  semicircular sections. The perimeter of the inside lane is 400 metres. i.       Show that the area, Am2, […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2013 | Oct-Nov | (P1-9709/11) | Q#6

Question The diagram shows a metal plate made by fixing together two pieces, OABCD  (shaded) and OAED (unshaded). The piece OABCD is a minor sector of a circle with  centre O and radius . The piece OAED is a major sector of a circle with centre O and radius . Angle AOD is  radians. Simplifying your answers […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2013 | May-Jun | (P1-9709/13) | Q#2

Question The diagram shows a circle C with centre O and radius 3 cm. The radii OP and OQ  are extended to S and R respectively so that ORS is a sector of a circle with centre  O. Given that PS = 6 cm and that the area of the shaded region is equal to the area  […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2013 | May-Jun | (P1-9709/12) | Q#4

Question The diagram shows a square ABCD of side 10 cm. The mid-point of AD is O and BXC is an arc of a circle with centre O.      i.       Show that angle BOC is 0.9273 radians, correct to 4 decimal places.    ii.       Find the perimeter of the shaded region.   iii.       Find the area of the shaded region. Solution […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2013 | May-Jun | (P1-9709/11) | Q#3

Question In the diagram, OAB is a sector of a circle with centre O and radius 8 cm. Angle BOA  is  radians. OAC is a semicircle with diameter OA. The area of the semicircle  OAC is twice the area of the sector OAB.      i.       Find  in terms of .    ii.       Find the perimeter of the complete figure in terms […]