Hits: 69

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2019 | May-Jun | (P2-9709/23) | Q#4

Hits: 69 Question a.   Find the exact value of Show all necessary working. b.  Use the trapezium rule with two intervals to find an approximation to Solution a.     We are required to show; We know that , therefore; Rule for integration of  is: Rule for integration of  is: Rule for integration of  is: Rule […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2019 | May-Jun | (P2-9709/22) | Q#4

Hits: 43 Question a.   Find the exact value of Show all necessary working. b.  Use the trapezium rule with two intervals to find an approximation to Solution a.     We are required to show; We know that , therefore; Rule for integration of  is: Rule for integration of  is: Rule for integration of  is: Rule […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2018 | Oct-Nov | (P2-9709/23) | Q#6

Hits: 47 Question The diagram shows the curve  for . The region R is  bounded by the curve, the axes and the line .      i.       Use the trapezium rule with two intervals to find an approximation to the area of  R, giving your answer correct to 3 significant figures.    ii.       The […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2018 | Oct-Nov | (P2-9709/21) | Q#6

Hits: 26 Question The diagram shows the curve  for . The region R is  bounded by the curve, the axes and the line .      i.       Use the trapezium rule with two intervals to find an approximation to the area of  R, giving your answer correct to 3 significant figures.    ii.       The region R […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2018 | Feb-Mar | (P2-9709/22) | Q#3

Hits: 37 Question      i.       Use the trapezium rule with four intervals to find an approximation to giving your answer correct to 3 significant figures.    ii.       Hence find an approximation to Solution i.   We are required to apply Trapezium Rule to evaluate; The trapezium rule with  intervals states that; We are given that […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2017 | May-Jun | (P2-9709/21) | Q#6

Hits: 36 Question The diagram shows the curve  for . The shaded region is bounded by the  curve and the lines , and y = 0.      i.       Use the trapezium rule with two intervals to find an approximation to the area of the shaded  region, giving your answer correct to 3 significant figures.     […]

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#1

Hits: 14   Question Use the trapezium rule with four intervals to find an approximation to Solution We are required to apply Trapezium Rule to evaluate; The trapezium rule with  intervals states that; We are given that there are four intervals, . We are also given that and . Hence; 1 2 3 4 5 […]

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#1

Hits: 22 Question Use the trapezium rule with four intervals to find an approximation to Solution We are required to apply Trapezium Rule to evaluate; The trapezium rule with  intervals states that; We are given that there are three intervals, . We are also given that and . Hence; 1 2 3 4 5 Therefore;

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: 49 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#3

Hits: 46   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: 39   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 2013 | Oct-Nov | (P2-9709/23) | Q#6

Hits: 23     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: 31   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 | (P2-9709/21) | Q#6

Hits: 31     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 2012 | Oct-Nov | (P2-9709/22) | Q#4

Hits: 85     Question The diagram shows the part of the curve  for .      i.       Use the trapezium rule with 2 intervals to estimate the value of giving your answer correct to 2 decimal places.    ii.       The line y=x intersects the curve at point P. Use the iterative formula to determine the […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2012 | Oct-Nov | (P2-9709/23) | Q#6

Hits: 85     Question      i.       Use the trapezium rule with 2 intervals to estimate the value of Giving your answer correct to 2 decimal places.    ii.       Find Solution      i.   We are required to apply Trapezium Rule to evaluate; The trapezium rule with  intervals states that; We are given that there […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2012 | Oct-Nov | (P2-9709/21) | Q#6

Hits: 55     Question      i.       Use the trapezium rule with 2 intervals to estimate the value of Giving your answer correct to 2 decimal places.    ii.       Find Solution      i.   We are required to apply Trapezium Rule to evaluate; The trapezium rule with  intervals states that; We are given that there […]