Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2011 | Oct-Nov | (P1-9709/11) | Q#5

  Question The diagram represents a metal plate , consisting of a sector  of a circle with centre  and radius , together with a triangle  which is right-angled at C. Angle  radians and  is perpendicular to . i.       Find an expression in terms of  and  for the perimeter of the plate. ii.    For the case where  and  , find […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2011 | Oct-Nov | (P1-9709/13) | Q#4

Question In the diagram, ABCD is a parallelogram with AB=BD=DC=10cm and angle ABD= 0.8 radians. APD and BQC are arcs of circles with centres B and D respectively.     i.       Find the area of the parallelogram ABCD.    ii.       Find the area of the complete figure ABQCDP.   iii.       Find the perimeter of the complete figure ABQCDP. Solution i.   Expression for the area […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2011 | Oct-Nov | (P1-9709/12) | Q#6

Question The diagram shows a circle  touching a circle  at a point . Circle  has centre A and radius 6cm, and circle  has centre B and radius 10 cm. Points D and E lie on  and  respectively and DE is parallel to AB. Angle  radians and angle  radians.     i.       By considering the perpendicular distances of D and E […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2011 | May-Jun | (P1-9709/13) | Q#7

Question In the diagram, AB is an arc of a circle, centre O and radius 6 cm, and angle  radians. The line AX is a tangent to the circle at A, and OBX is a straight line.     i.       Show that the exact length of AX is  cm.  Find, in terms of  and ,    ii.       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 2011 | May-Jun | (P1-9709/11) | Q#9

Question In the diagram, OAB is an isosceles triangle with  and angle  radians. Arc PST has centre O and radius , and the line ASB is a tangent to the arc PST at S.     i.       Find the total area of the shaded regions in terms of  and .    ii.       In the case where  and , find the total perimeter […]