# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2007 | Oct-Nov | (P2-9709/02) | Q#8

Question The diagram shows the curve and its maximum point M.      i.       Find the x-coordinate of M.    ii.       Show that the tangent to the curve at the point where x = 1 passes through the origin.   iii.       Use the trapezium rule with two intervals to estimate the value […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2007 | Oct-Nov | (P2-9709/02) | Q#7

Question      i.       Prove the identity    ii.       Using the identity, or otherwise, find the exact value of Solution      i.   We are given that; We have algebraic formula; Since we know that ; We have the trigonometric identity; From this we can write ; Since we know that ; […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2007 | Oct-Nov | (P2-9709/02) | Q#1

Question Show that Solution We are required to show that; Rule for integration of  is: This integral is valid only when . Division Rule;

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2007 | May-Jun | (P2-9709/02) | Q#6

Question      i.       Express cos2 x in terms of cos 2x.    ii.       Hence show that   iii.       By using an appropriate trigonometrical identity, deduce the exact value of Solution      i.   We are required to show   in terms of . From this we can write; Therefore;    ii.   […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2007 | Oct-Nov | (P1-9709/01) | Q#2

Question Find the area of the region enclosed by the curve , the x-axis and the lines x = 1 and x = 4. Solution To find the area of region under the curve , we need to integrate the curve from point  to  along x-axis. For the given case; Rule for integration of  is:

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2007 | May-Jun | (P1-9709/01) | Q#10

Question The equation of a curve is  . i.       Obtain expressions for  and .    ii.       Find the coordinates of the stationary point on the curve and determine the nature of the stationary point.   iii.       Show that the normal to the curve at the point (−2, −2) intersects the x-axis at the point (−10, 0).   iv.       Find the area of the region enclosed […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2007 | May-Jun | (P1-9709/01) | Q#2

Question The diagram shows the curve .  The shaded region is bounded by the curve, the x-axis and the lines  and . Find the volume of the solid obtained when this shaded region is rotated completely about the x-axis, giving your answer in terms of . Solution Expression for the volume of the solid formed when the shaded […]