Hits: 177

# 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: 177 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: 145 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: 89 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 | (P2-9709/23) | Q#2

Hits: 47 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#5

Hits: 82 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#2

Hits: 32 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 | May-Jun | (P2-9709/23) | Q#5

Hits: 57 Question i.       Find the quotient and remainder when is divided by .    ii.       Hence find the exact value of giving the answer in the form where k and a are constants. Solution      i.   Hence quotient is and remainder is .    ii.   We are required to solve; When a […]

# 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: 194 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#5

Hits: 103 Question i.       Find the quotient and remainder when is divided by .    ii.       Hence find the exact value of giving the answer in the form where k and a are constants. Solution      i.   Hence quotient is and remainder is .    ii.   We are required to solve; When a […]

# 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: 148 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: 91 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: 111 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 | (P2-9709/23) | Q#2

Hits: 27 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#6

Hits: 63 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 | Oct-Nov | (P2-9709/21) | Q#2

Hits: 84 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#7

Hits: 60   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 | (P2-9709/23) | Q#6

Hits: 45 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#7

Hits: 108   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 | (P2-9709/22) | Q#6

Hits: 110 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#7

Hits: 71 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 […]