Hits: 36

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2013 | Oct-Nov | (P2-9709/23) | Q#6

Hits: 36     Question A.  Find i.        ii.          B.  Use the trapezium rule with 2 intervals to estimate the value of giving your answer correct to 2 decimal places. Solution A.    i.   We are required to find; Rule for integration of  is: Rule for integration of  is: Rule for […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2013 | Oct-Nov | (P2-9709/22) | Q#6

Hits: 42   Question A.         Find B.   i.       Use the trapezium rule with 2 intervals to estimate the value of giving your answer correct to 3 decimal places. ii.       Using a sketch of the graph of  for , explain whether the trapezium rule  gives an under-estimate or an over-estimate of the true value of […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2013 | Oct-Nov | (P2-9709/22) | Q#1

Hits: 8 Question i.       Find ii.       Hence find , expressing your answer in the form ln a, where a is an integer. Solution i.   We are required to find; Rule for integration of  is: This integral is valid only when . ii.   We are required to find; Rule for integration of  is: This […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2013 | Oct-Nov | (P2-9709/21) | Q#6

Hits: 38     Question A.  Find i.        ii.        B.  Use the trapezium rule with 2 intervals to estimate the value of giving your answer correct to 2 decimal places. Solution A.    i.   We are required to find; Rule for integration of  is: Rule for integration of  is: Rule for integration […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2013 | May-Jun | (P2-9709/22) | Q#7

Hits: 61     Question A.  Find the exact area of the region bounded by the curve , the x-axis and the lines   and . The diagram shows the curve , for and its minimum point M. Find the exact x- coordinate of M. Solution A.    We are required to find area under the […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2013 | May-Jun | (P2-9709/22) | Q#1

Hits: 30 Question A curve is such that . The point (3, 2) lies on the curve. Find the equation of the curve.  Solution We can find equation of the curve from its derivative through integration; For the given case; Therefore; Rule for integration of  is: This integral is valid only when . If a […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2013 | May-Jun | (P2-9709/23) | Q#3

Hits: 190   Question i.       Show that  .  ii.       Hence show that Solution      i.   We are given that; From this we can write; From this we can write; It can be formulated as; Hence;    ii.   We are required to show that; We have found in (i) that; Therefore; Rule for integration […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2013 | May-Jun | (P2-9709/21) | Q#3

Hits: 80 Question i.       Show that  . ii.       Hence show that Solution      i.   We are given that; From this we can write; From this we can write; It can be formulated as; Hence;      ii.   We are required to show that; We have found in (i) that; Therefore; Rule for integration […]