Hits: 188

# 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: 188 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#2

Hits: 54 Question Find the exact value of Solution We are given that; Rule for integration of  is: Rule for integration of , or ; Rule for integration of  is:

# 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#2

Hits: 45 Question Find the exact value of Solution We are given that; Rule for integration of  is: Rule for integration of , or ; Rule for integration of  is:

# 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: 103 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#2

Hits: 31 Question Show that Solution We are required to show; Rule for integration of  is: Division Rule; Power Rule;

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

Hits: 97 Question Show that Solution We are required to show; Rule for integration of  is: Division Rule; Power Rule;

# 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#6

Hits: 48 Question It is given that where a is a positive constant. i.       Show that    ii.       Use the equation in part (i) to show by calculation that 1.5 < a < 1.6.   iii.       Use an iterative formula based on the equation in part (i) to find the value of a correct to […]

# 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#6

Hits: 141 Question It is given that where a is a positive constant.     i.       Show that    ii.       Use the equation in part (i) to show by calculation that 1.5 < a < 1.6.   iii.       Use an iterative formula based on the equation in part (i) to find the value of a correct […]

# 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#3

Hits: 92 Question Without using a calculator, find the exact value of Solution      i.   We are given that; Rule for integration of  is: Rule for integration of , or ; 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 | Feb-Mar | (P2-9709/22) | Q#5

Hits: 109 Question It is given that a is a positive constant such that i.       Show that    ii.       Use the equation in part (i) to show by calculation that 1.0 < a < 1.5.   iii.       Use an iterative formula based on the equation in part (i) to find the value of […]

# 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: 108 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 | Feb-Mar | (P2-9709/22) | Q#5

Hits: 43 Question It is given that a is a positive constant such that i.       Show that    ii.       Use an iterative formula based on the equation in part (i) to find the value of a correct to 4  significant figures. Give the result of each iteration to 6 significant figures. Solution      i.   […]

# 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#5

Hits: 39 Question Given that find the value of the constant a correct to 3 decimal places. Solution      i.   We are given that; Rule for integration of , or ; Taking logarithm of both sides;  for any

# 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#3

Hits: 79 Question Given that find the value of the constant a correct to 3 significant figures. Solution     We are given that; Rule for integration of , or ; Taking logarithm of both sides;  for any

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2016 | Oct-Nov | (P2-9709/23) | Q#5

Hits: 74 Question The diagram shows the curve for 0 ≤ x ≤ 6. The region bounded by the curve and the lines x = 0, x = 6 and y = 0 is denoted by R.        i.       Use the trapezium rule with 2 strips to find an estimate of the area of R, […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2016 | Oct-Nov | (P2-9709/22) | Q#3

Hits: 56 Question The definite integral  is defined by    i.   Show that  .    ii.   Sketch the curve  for .   iii.   State whether an estimate of obtained by using the trapezium rule will be more than or less than 8e −2. Justify your answer. Solution      i.   We are given that; Rule […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2016 | Oct-Nov | (P2-9709/21) | Q#4

Hits: 57 Question     i.       It is given that the positive constant a is such that    ii.       Show that   iii.       Use an iterative formula , to find 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 2016 | May-Jun | (P2-9709/23) | Q#6

Hits: 71   Question a)   Find b)  Without using a calculator, find the exact value of giving your answer in the form . c)     The diagram shows the curve for 0 ≤ x ≤ 6. The region bounded by the curve and  the lines x = 0, x = 6 and y = 0 […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2016 | May-Jun | (P2-9709/22) | Q#6

Hits: 104 Question a)   Find b)  Without using a calculator, find the exact value of giving your answer in the form . c)     The diagram shows the curve for 0 ≤ x ≤ 6. The region bounded by the curve and  the lines x = 0, x = 6 and y = 0 is […]

# 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: 108 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 […]