Hits: 101

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#8

Hits: 101 Question     i.       Express  in the form , where and  , giving the value of  correct to 2 decimal places.    ii.       Hence solve the equation  for . Solution      i.   We are given the expression; We are required to write it in the form; If  and are positive, then; can be written […]

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#7

Hits: 80 Question A curve is defined by the parametric equations for .       i.       Find the exact gradient of the curve at the point for which .    ii.       Find the value of at the point where the gradient of the curve is 2, giving the value correct to 3 significant figures. Solution […]

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: 66 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#7

Hits: 50   Question      i.       Show that    ii.       Hence, show that   iii.       Solve the equation For . Show all the necessary working. Solution i.   First we are required to show that;   provided that   provided that   provided that ii.   We are required to show that; As shown in […]

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: 39 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#6

Hits: 53   Question a.   Showing all necessary working, solve the equation for . b.   Showing all necessary working, solve the equation for . Solution a.     We are given;   provided that   provided that Let , then; We are given that ; interval for  can be found as follows. Multiplying entire inequality with […]

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: 47 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#6

Hits: 39   Question a.   Showing all necessary working, solve the equation for . b.   Showing all necessary working, solve the equation for . Solution a.     We are given;   provided that   provided that Let , then; We are given that ; interval for  can be found as follows. Multiplying entire inequality with […]

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: 44 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#7

Hits: 42 Question a.                                 i.       Express  in the form , where and  .                           ii.       Hence find the smallest positive value of  satisfying the equation b. Solve the equation for , showing all necessary working and giving the answers correct to 2  decimal places. Solution      i.   We are given the expression; We […]

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: 59 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#7

Hits: 30 Question a.                                 i.       Express  in the form , where and  .                           ii.       Hence find the smallest positive value of satisfying the equation  b.  Solve the equation for , showing all necessary working and giving the answers correct to 2  decimal places. Solution      i.   We are given the expression; We […]

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 2019 | Feb-Mar | (P2-9709/22) | Q#7

Hits: 69 Question The parametric equations of a curve are for . At the point P on the curve, the gradient of the curve is 2.      i.       Show that the value of the parameter at P satisfies the equation .    ii.       By first expressing in the form , where R > 0 and  […]

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: 51 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 2019 | Feb-Mar | (P2-9709/22) | Q#1

Hits: 60 Question     i.       Show the equation For . Show all necessary working. Solution We are given that; Let , then; Now we have two options. Since ; Using calculator Now we find all solutions in the interval . Properties of Domain Range Periodicity Odd/Even Translation/ Symmetry We utilize the periodicity/symmetry property of   […]

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

Hits: 48 Question     i.       Use the factor theorem to show that (2x+3) is a factor of    ii.       Show that the equation  can be expressed as   iii.       Solve the equation For . Solution      i.   We are given that; We are also given that is a factor of . When a polynomial, […]

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

Hits: 50   Question The diagram shows the curve with equation for values of x such that . Find the x-coordinate of the stationary point M, giving your answer correct to 3  significant figures. Solution We are required to find the x-coordinate of stationary point M. A stationary point on the curve is the point […]

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 […]