Hits: 110

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2019 | Oct-Nov | (P2-9709/22) | Q#6

Hits: 110 Question a.   Show that b.   Find the exact value of Show all necessary working. Solution a.     We are required to show; Rule for integration of  is: Division Rule; Power Rule; b.     We are required to find; Since , we can rearrange to write; 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 2019 | May-Jun | (P2-9709/21) | Q#4

Hits: 101 Question a.   Find b.   Find the exact value of Show all necessary working. Solution a.   We are given that; Rule for integration of  is: Rule for integration of  is: Rule for integration of  is: b.   We are required to find the exact value of; 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 2019 | Oct-Nov | (P2-9709/23) | Q#5

Hits: 76 Question It is given that Where  is a constant.     i.       Show that    ii.       Using the equation in part (i), show by calculation that 0.5 < a < 0.75.   iii.       Use an iterative formula, based on the equation in part (i), to find the value of a  correct to 3 significant […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2019 | Oct-Nov | (P2-9709/21) | Q#5

Hits: 75 Question It is given that Where  is a constant.     i.       Show that    ii.       Using the equation in part (i), show by calculation that 0.5 < a < 0.75.   iii.       Use an iterative formula, based on the equation in part (i), to find the value of a  correct to 3 significant […]

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: 124 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: 72 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 | Feb-Mar | (P2-9709/22) | Q#6

Hits: 72 Question a.   Show that b.   Find Solution a.     We are required to show; Rule for integration of  is: Rule for integration of  is: Division Rule; Power Rule; Multiplication Rule; b.     We are required to find;   provided that   provided that 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 2018 | Oct-Nov | (P2-9709/23) | Q#6

Hits: 66 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: 44 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 | May-Jun | (P2-9709/23) | Q#7

Hits: 51   Question      i.       Show that    ii.       Solve the equation  for , giving your answers  correct to 3 significant figures.   iii.        Find Solution      i.   We are given;   provided that   provided that      ii.   We are required to solve the equation for . […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2018 | May-Jun | (P2-9709/22) | Q#7

Hits: 69   Question      i.       Show that    ii.       Solve the equation  for , giving your answers  correct to 3 significant figures.   iii.       Find Solution      i.   We are given;   provided that   provided that      ii.   We are required to solve the equation for . As demonstrated in […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2018 | May-Jun | (P2-9709/21) | Q#7

Hits: 56 Question i.       Express  in the form , where  and . Give the value  of  correct to 4 decimal places.    ii.       Using your answer from part (i), solve the equation for . Solution      i.   We are given the expression; We are required to write it in the form; If  and are […]

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#6

Hits: 56   Question      i.       Show that    ii.       Hence find the exact value of .   iii.       Find Solution      i.   We are given;   provided that   provided that   provided that      ii.     provided that Therefore; Hence; Therefore; Hence;   iii.   We are required to find; […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2017 | Feb-Mar | (P2-9709/22) | Q#7

Hits: 67   Question The diagram shows part of the curve The shaded region is bounded by the curve and the two axes.        i. Show that  can be expressed in the form where the values of the constants  and are to be determined.    ii.Find the exact area of the shaded region. Solution […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2016 | Feb-Mar | (P2-9709/22) | Q#8

Hits: 45 Question      i.       Show that .    ii.       Using the identity in part (i),                a.   find the least possible value of as x varies.                             b.  find the exact value of Solution      […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2017 | Oct-Nov | (P2-9709/23) | Q#4

Hits: 43 Question      i.       Find    ii.       Given that find the value of the positive constant a. Solution      i.   We are required to find; We have the trigonometric identity; It can be rearranged as; Therefore;   provided that It can be rearranged as; Therefore; 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 2017 | Oct-Nov | (P2-9709/22) | Q#6

Hits: 44 Question      i.       Find the exact value of    ii.       Given that Find the value of positive constant a. Solution      i.   We are required to find; Rule for integration of  is: Rule for integration of  is: Rule for integration of  is: Rule for integration of  is:      ii.   We […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2017 | Oct-Nov | (P2-9709/21) | Q#4

Hits: 37 Question      i.       Find    ii.       Given that find the value of the positive constant a. Solution      i.   We are required to find; We have the trigonometric identity; It can be rearranged as; Therefore;   provided that It can be rearranged as; Therefore; 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 2017 | May-Jun | (P2-9709/23) | Q#7

Hits: 26 Question a)   Find b)    i.    Find ii.    Hence find giving your answer in the form . Solution a)     We are required to find; Rule for integration of  is: First we integrate . From  we can obtain; 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 2017 | May-Jun | (P2-9709/22) | Q#7

Hits: 79 Question a)   Find b)    i.    Find ii.    Hence find giving your answer in the form . Solution a)     We are required to find; Rule for integration of  is: First we integrate . From  we can obtain; Rule for integration of  is: Rule for integration of  is: Rule for integration of  is: […]