Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2011 | May-Jun | (P2-9709/23) | Q#8

  Question i.       Prove that    ii.       Hence a.   Solve for  the equation b.   find the exact value of . Solution      i.   We are given that; We utilize following relations;   provided that   provided that Therefore; We utilize following relation; Therefore;    ii.   We are required to solve; As demonstrated in […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2011 | May-Jun | (P2-9709/23) | Q#6

    Question The curve y = 4×2 ln x has one stationary point.      i.       Find the coordinates of this stationary point, giving your answers correct to 3 decimal places.    ii.       Determine whether this point is a maximum or a minimum point. Solution      i.   We are required to find the coordinates […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2011 | May-Jun | (P2-9709/23) | Q#5

    Question A curve has equation x2+2y2+5x+6y =10. Find the equation of the tangent to the curve at the point (2,-1). Give your answer in the form ax+by+c=0, wher a,b and c are integers. Solution We are required to find equation of tangent to the curve at the point (2,-1). To find the equation […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2011 | May-Jun | (P2-9709/23) | Q#3

  Question The sequence defined by , Converges to the value .      i.       Find the value of correct to 3 decimal places. Show your working, giving each calculated  value of the sequence to 5 decimal places.    ii.       Find, in the form , an equation of which is a root. Solution      i.   […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2011 | May-Jun | (P2-9709/23) | Q#7

  Question The cubic polynomial  is defined by where  and  are constants. It is given that  is a factor of  and that, when is divided by , the remainder is 24.      i.       Find the values of  and .    ii.       When  and  have these values, factorise p(x) completely. Solution      i.  We […]