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

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 (i); Therefore; […]

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

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 3  […]

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#5

Question A curve has equation Find the equation of the tangent to the curve at the point where it crosses the y-axis. Solution We are given that curve with equation  and we are required to find the equation of  the tangent to the curve at point where it crosses the y-axis i.e.  . 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#4

Question     i.       Solve the equation  .    ii.       Hence solve the equation giving the value of u correct to 4 significant figures. Solution      i.   We are given the equation; Power Rule; Division Rule;  and are inverse functions. The composite function is an identity function, with  domain the positive real numbers. Therefore; Taking […]

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#3

Question i.       Find the quotient when   is divided by  ,  and show that the remainder is 1.    ii.       Show that the equation  has no real root. Solution      i.   Hence quotient is and remainder is .      ii.   We are required to show that following equation has no real roots; When […]

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#2

Question A curve has equation      i.       Find the x-coordinate of the stationary point.    ii.       Determine whether the stationary point is a maximum or minimum point. Solution i.   First we are required to find the x-coordinate of the stationary point of the curve. A stationary point on the curve is the point where […]

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#1

Question     Solve the inequality . Solution SOLVING INEQUALITY: PIECEWISE 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 following with their corresponding inequality; When When When If then above four intervals translate to following […]