# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2004 | Oct-Nov | (P2-9709/02) | Q#8

Question i.       Express  in the form , where  and , giving the exact values of R and .    ii.       Hence show that   iii.       By differentiating , show that if  then .   iv.       Using the results of parts (ii) and (iii), show that Solution      i.   We […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2004 | Oct-Nov | (P2-9709/02) | Q#7

Question The diagram shows the curve y = 2ex + 3e-2x. The curve cuts the y-axis at A.      i.       Write down the coordinates of A.    ii.       Find the equation of the tangent to the curve at A, and state the coordinates of the point where  this tangent meets the x-axis.   […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2004 | May-Jun | (P2-9709/02) | Q#7

Question      i.By expanding , show that    ii.Hence, or otherwise, show that Solution      i.   We have; We apply following addition formula. Therefore; We apply following two formulae. We have the trigonometric identity; Therefore, we can replace; Hence;    ii.   We are required to show that; As we have demonstrated in […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2004 | Oct-Nov | (P1-9709/01) | Q#10

Question A curve has equation  .      i.       Write down expressions for  and    ii.      Find the coordinates of the stationary point on the curve and determine its nature.   iii.       Find the volume of the solid formed when the region enclosed by the curve, the x-axis and the lines x = 1 and x = 2 is rotated […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2004 | Oct-Nov | (P1-9709/01) | Q#7

Question A curve is such that  and  is a point on the curve.      i.       Find the equation of the normal to the curve at P, giving your answer in the form .    ii.       Find the equation of the curve. Solution i.   To find the equation of the normal to the curve at P; To find the equation […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2004 | May-Jun | (P1-9709/01) | Q#7

Question The diagram shows part of the graph of   and the normal to the curve at . This normal meets the -axis at R. The point Q on the -axis and the point S on the curve are such that PQ and SR are parallel to the -axis.      i.       Find the equation of the normal at P […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2004 | May-Jun | (P1-9709/01) | Q#2

Question Evaluate   Solution Writing the given expression in standard form; Rule for integration of  is: In the given case;