Hits: 79

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2014 | Oct-Nov | (P2-9709/22) | Q#5

Hits: 79     Question The diagram shows part of the curve and its maximum point M. The shaded region is bounded by the curve, the axes and the line  through M parallel to the y-axis.      i.       Find the exact value of the x-coordinate of M.    ii.       Find the exact value of the […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2014 | Oct-Nov | (P2-9709/22) | Q#2

Hits: 70 Question i.       Find where a is a positive constant.    ii.       Deduce the value of Solution      i.  We are given that; Rule for integration of  is: Rule for integration of , or ;      ii.   We are required to deduce the value of. From (i) we have demonstrated; Therefore replacing […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2014 | Oct-Nov | (P2-9709/23) | Q#3

Hits: 66   Question A.         Find B.         Find the exact value of Solution A.   We are required to find; We know that; It can be written for  as; It can be rearranged as; Hence, integral can be written as; Rule for integration of  is: Rule for integration of  is: Rule for integration of  is: […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2014 | Oct-Nov | (P2-9709/21) | Q#3

Hits: 56   Question A.         Find B.         Find the exact value of Solution A.   We are required to find; We know that; It can be written for  as; It can be rearranged as; Hence, integral can be written as; Rule for integration of  is: Rule for integration of  is: Rule for integration of  is: […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2014 | May-Jun | (P2-9709/23) | Q#7

Hits: 76   Question It is given that i.       Show that    ii.       Show by calculation that the value of a lies between 1.0 and 1.5.   iii.       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 […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2014 | May-Jun | (P2-9709/23) | Q#3

Hits: 92 Question A.         Find B.   i.       Use the trapezium rule with three intervals to find an approximation to giving your answer correct to 3 significant figures. Solution A.   We are required to find; Rule for integration of  is: B.   i.   We are required to apply Trapezium Rule to evaluate; The […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2014 | May-Jun | (P2-9709/22) | Q#7

Hits: 78 Question It is given that     i.       Show that    ii.       Show by calculation that the value of a lies between 1.0 and 1.5.   iii.       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 […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2014 | May-Jun | (P2-9709/22) | Q#3

Hits: 88   Question A.         Find B.   i.       Use the trapezium rule with three intervals to find an approximation to giving your answer correct to 3 significant figures. Solution A.   We are required to find; Rule for integration of  is:   B.   i.   We are required to apply Trapezium Rule to […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2014 | May-Jun | (P2-9709/21) | Q#6

Hits: 103   Question i.       Show that ii.       Use the trapezium rule with four intervals to find an approximation to giving your answer correct to 3 significant figures. Solution i.   We are required to show that; Rule for integration of  is: This integral is valid only when . Division Rule; Power Rule; ii.   […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2014 | May-Jun | (P2-9709/21) | Q#5

Hits: 141   Question i.       Prove that  .    ii.       Hence a.  Find the exact value of b.  Evaluate Solution      i.   We are given that; except where  or undefined   provided that We have the trigonometric identity; Therefore; Hence;      ii.   a.   We are required to find the exact value […]