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

  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 where gradient […]

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#7

  Question The diagram shows the curve with equation  for . At  the points P and Q on the curve, the gradient of the curve is 3.      i.    Find an expression for .    ii.     By first expressing  in the form , where R > 0 and ,  find the x-coordinates of […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2018 | Oct-Nov | (P2-9709/21) | Q#7

  Question The diagram shows the curve with equation  for . At  the points P and Q on the curve, the gradient of the curve is 3.      i.     Find an expression for .    ii.     By first expressing  in the form , where R > 0 and ,  find the x-coordinates of […]

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#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 find […]

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 | (P2-9709/21) | Q#5

Question The parametric equations of a curve are for .     i.       Find the gradient of the curve at the point for which  radian.    ii.       Find the value of at the point on the curve where the tangent is parallel to the y-axis. Solution      i.   We are required to find gradient 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#2

  Question A curve has equation . Find the equation of the tangent to the curve at the point for which . Solution      i.   We are given that curve with equation  and we are required to find the equation of the  tangent to the curve at origin . To find the equation of […]