Hits: 42

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2015 | Oct-Nov | (P2-9709/23) | Q#5

Hits: 42 Question It is given that     i.       Show that    ii.       Use an iterative formula based on the equation in part (i) to find the value of a correct to 3  decimal places. Give the result of each iteration to 5 decimal places. Solution      i.   We are given that; Rule for […]

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

Hits: 26   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. […]

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

Hits: 13   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 […]

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

Hits: 40 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 […]

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#4

Hits: 51 Question The diagram shows the curve  and its minimum point M.      i.       Show that the x-coordinate of M is .    ii.       The region shaded in the diagram is enclosed by the curve and the lines ,   and  . Use integration to show that the area of the shaded region is . […]

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

Hits: 29 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 […]

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#4

Hits: 41     Question The diagram shows the curve  and its minimum point M.      i.       Show that the x-coordinate of M is .    ii.       The region shaded in the diagram is enclosed by the curve and the lines ,   and  . Use integration to show that the area of the shaded region […]

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

Hits: 36 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 […]

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#5

Hits: 26 Question i.       Given that show that the positive constant a satisfies the equation    ii.       Use an iterative formula, , with  to find the value of correct to 3 decimal places. Give the result of each iteration to 5 decimal places. Solution      i.  We are given that; Rule for integration of  is: […]