# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | Oct-Nov | (P1-9709/13) | Q#5

Question The diagram shows a major arc AB of a circle with centre O and radius 6 cm. Points C and D on OA  and OB respectively are such that the line AB is a tangent at E to the arc CED of a smaller  circle also with centre O. Angle COD = 1.8 radians. i.       Show that […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | Oct-Nov | (P1-9709/12) | Q#6

Question The diagram shows a metal plate ABCD made from two parts. The part BCD is a semicircle. The part DAB is a segment of a circle with centre O and radius 10 cm. Angle BOD is 1.2 radians.     i.       Show that the radius of the semicircle is 5.646 cm, correct to 3 decimal places.    ii.       Find the perimeter of the […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | Oct-Nov | (P1-9709/11) | Q#3

Question In the diagram OCA and ODB are radii of a circle with centre O and radius  cm. Angle  adians. CD and AB are arcs of circles with centre O and radii  cm and  cm respectively. The  perimeter of the shaded region ABDC is 4.4r cm.      i.       Find the value of .    ii.       It is given that the area of […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | May-Jun | (P1-9709/13) | Q#6

Question The diagram shows triangle ABC where AB=5cm, AC=4cm and BC=3cm. Three circles with centres  at A, B and C have radii 3 cm, 2 cm and 1 cm respectively. The circles touch each other at  points E, F and G, lying on AB, AC and BC respectively. Find the area of the shaded region EFG. Solution It is […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | May-Jun | (P1-9709/12) | Q#6

Question The diagram shows a circle with radius r cm and centre O. The line PT is the tangent to the circle at  P and angle  radians. The line OT meets the circle at Q.      i.       Express the perimeter of the shaded region PQT in terms of r and .   ii.       In the case where  and , find the area of […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | May-Jun | (P1-9709/11) | Q#7

Question In the diagram, AOB is a quarter circle with centre O and radius r. The point C lies on the arc AB  and the point D lies on OB. The line CD is parallel to AO and angle  radians.      i.       Express the perimeter of the shaded region in terms of r,  and .    ii.       For the case […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | Feb-Mar | (P1-9709/12) | Q#9

Question a.     Figure 1 In Fig. 1, OAB is a sector of a circle with centre O and radius r. AX is the tangent at A to the arc AB and angle .      i.       Show that angle .    ii.       Find the area of the shaded segment in terms of r and .   b.     Figure 2 […]