# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2008 | Oct-Nov | (P2-9709/02) | Q#8

Question      i.                     a.   Prove the identity                  b.   Hence prove that    ii.       By differentiating , show that if  then .     iii.       Using the results of parts (i) and (ii), find the […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2008 | Oct-Nov | (P2-9709/02) | Q#6

Question Find the exact coordinates of the point on the curve   at which . Solution We are given that; We are required to find; Second derivative is the derivative of the derivative. If we have derivative of the curve   as , then  expression for the second derivative of the curve  is; Therefore […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2008 | May-Jun | (P2-9709/02) | Q#7

Question The equation of the curve is .     i.       Show that    ii.       Find the coordinates of each of the points on the curve where the tangent is parallel to the x- axis. Solution      i.   We are given; We are required to find . To find from an implicit […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2008 | May-Jun | (P2-9709/02) | Q#6

Question It is given that the curve has one stationary point.      i.       Find the x-coordinates of this point.    ii.       Determine whether this point is a maximum or a minimum point. Solution      i.   We are required to find the coordinates of stationary point of the curve; A stationary […]