Hits: 114

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | Feb-Mar | (P1-9709/12) | Q#1

Hits: 114 Question A curve passes through the point (4, −6) and has an equation for which . Find the equation of the curve. Solution We are required to find the equation of the curve from the given derivative. We can find equation of the curve from its derivative through integration; We are given; Therefore; […]

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: 121 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: 95 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: 86 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 | Oct-Nov | (P2-9709/22) | Q#5

Hits: 68   Question Find the exact coordinates of the stationary point of the curve with equation Solution We are required to find the exact coordinates of the stationary point of the curve. A stationary point on the curve is the point where gradient of the curve is  equal to zero; Therefore, we find the […]

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#4

Hits: 48 Question The sequence of values converges to the value .      i.       Use the iterative formula to find the value of correct to 4 significant figures.  Give the result of each iteration to 6 significant figures.    ii.       State an equation satisfied by and hence determine the exact value of . 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#3

Hits: 43 Question The variables x and y satisfy the equation y = Kxa, where K and a are constants. The  graph of ln y against ln x is a straight line passing through the points (0.22,  3.96) and (1.32, 2.43), as shown in the diagram. Find the values of K and a, correct to […]

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#2

Hits: 63 Question                     i.       Solve the equation                   ii.       Hence, using logarithms, solve the equation giving the answer correct to 3 significant figures. Solution SOLVING EQUALITION: PIECEWISE      i.   Let, . We have to consider both moduli separately and it leads to following cases;  OR We have the equation; We have to consider […]

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: 76   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#6

Hits: 70   Question The diagram shows the curve with equation The maximum point is denoted by M.      i.       Find an expression for  and determine the gradient of the curve at the point  where the   curve crosses the x-axis.    ii.       Show that the x-coordinate of the point M satisfies the equation   iii. […]

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#5

Hits: 53 Question The polynomial  is defined by where  and  are constants. It is given that  is a factor of and that  remainder is 27 when  is divided by .     i.       Find the values of a and b.    ii.       Hence factorise   completely.   iii.       State the number of roots of the equation p(2y) […]

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: 68 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 | May-Jun | (P2-9709/21) | Q#3

Hits: 48 Question Find the equation of the normal to the curve at the point (3, 1). Solution  We are given equation of the curve as; We are required to find the equation of normal to the curve at the point (3, 1). To find the equation of the line either we need coordinates of […]

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#2

Hits: 52   Question      i.       Solve the inequality .    ii.       Hence find the greatest integer satisfying the inequality  Solution SOLVING INEQUALITY: PIECEWISE      i.   Let, . We can write it as; We have to consider both moduli separately and it leads to following cases; When If then above four intervals translate to […]

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#7

Hits: 65   Question The equation of a curve is      i.       Find an expression for  and show that the gradient of the curve at the point  (−1, 2)  is .   ii.       Show that the curve has no stationary points.   iii.       Find the x-coordinate of each of the points on the curve at […]

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: 60   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: 53 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#4

Hits: 35 Question The polynomial  is defined by where  is a constant. It is given that  is a factor of     i.       Find the value of a .    ii.       Using this value of a, factorise completely.    iii.       Hence solve the equation , giving the answer correct to 2 significant figures. Solution      i.   […]