# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2015 | Oct-Nov | (P2-9709/22) | Q#7

Question      i.       Show that the exact value of    ii.   The diagram shows the curve  for . The shaded region is bounded by the  curve and the lines ,  and . Find the exact volume of the solid obtained when  the shaded region is rotated completely about the x-axis. Solution      i.   We […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2015 | Oct-Nov | (P2-9709/21) | Q#5

Question      i.       Find    ii.       Find the exact value of Solution      i.   We are required find; We know that;  Therefore; Hence; Rule for integration of  is: Rule for integration of  is: Rule for integration of  is: Rule for integration of  is:        ii.   We are required to find […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2015 | May-Jun | (P2-9709/23) | Q#6

Question The diagram shows part of the curve and its point of intersection P with the x-axis.      i.       Find the exact x-coordinate of P.    ii.       Show that the equation of the curve can be written and use integration to find the exact area of the shaded region enclosed by the curve and the […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2015 | May-Jun | (P2-9709/22) | Q#6

Question The diagram shows part of the curve and its point of intersection P with the x-axis.      i.       Find the exact x-coordinate of P.    ii.       Show that the equation of the curve can be written and use integration to find the exact area of the shaded region enclosed by the curve and the […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2015 | May-Jun | (P2-9709/21) | Q#6

Question     i.       Prove that  .    ii.       Hence A.  Solve the equation  for . B.  Find the exact value of Solution      i.  We are given that;   provided that   provided that    ii.  a.  We are required to solve the equation; As demonstrated in (i); Hence;   provided that Now we have […]