# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | Oct-Nov | (P1-9709/13) | Q#7

Question The diagram shows a rectangle ABCD in which AB = 5 units and BC = 3 units. Point P lies on DC  and AP is an arc of a circle with centre B. Point Q lies on DC and AQ is an arc of a circle with centre  D.      i.       Show that angle ABP = 0.6435 radians, correct […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | Oct-Nov | (P1-9709/12) | Q#4

Question The diagram shows a semicircle with centre O and radius 6 cm. The radius OC is perpendicular to  the diameter AB. The point D lies on AB, and DC is an arc of a circle with centre B.      i.       Calculate the length of the arc DC.    ii.       Find the value of giving your answer correct to 3 […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | Oct-Nov | (P1-9709/11) | Q#5

Question The diagram shows an isosceles triangle ABC in which AC = 16 cm and AB = BC = 10 cm. The circular arcs BE and BD have centres at A and C respectively, where D and E lie on AC.      i.       Show that angle BAC = 0.6435 radians, correct to 4 decimal places.    ii.       Find the […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | May-Jun | (P1-9709/13) | Q#7

Question The diagram shows two circles with centres A and B having radii 8 cm and 10 cm respectively. The  two circles intersect at C and D where CAD is a straight line and AB is perpendicular to CD. (i)          Find angle ABC in radians. (ii)        Find the area of the shaded region. Solution (i)   It is evident from the diagram […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | May-Jun | (P1-9709/12) | Q#4

Question The diagram shows a circle with radius r cm and centre O. Points A and B lie on the circle and  ABCD is a rectangle. Angle AOB = 2 radians and  cm.     i.       Express the perimeter of the shaded region in terms of r and .    ii.       In the case where  and , find the area of the shaded region. […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | Feb-Mar | (P1-9709/12) | Q#4

Question In the diagram, AB=AC=8 cm and angle  radians. The circular arc BC has centre A, the  circular arc CD has centre B and ABD is a straight line.                     i.       Show that angle  radians.                   ii.       Find the perimeter of the shaded region. Solution      i.   It is evident from the diagram that; Therefore; We are given that ABD is a straight line. […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | May-Jun | (P1-9709/11) | Q#8

Question In the diagram, OAXB is a sector of a circle with centre O and radius 10 cm. The length of the chord  AB is 12 cm. The line OX passes through M, the mid-point of AB, and OX is perpendicular to  AB. The shaded region is bounded by the chord AB and by the arc of […]