# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2005 | Oct-Nov | (P2-9709/02) | Q#7

Question The diagram shows the part of the curve y = sin2 x for  .      i.       Show that    ii.       Hence find the x-coordinates of the points on the curve at which the gradient of the curve is  0.5.   iii.       By expressing sin2 x in terms of cos […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2005 | Oct-Nov | (P2-9709/02) | Q#6

Question A curve is such that . The point (0, 1) lies on the curve.      i. Find the equation of the curve.    ii. The curve has one stationary point. Find the x-coordinate of this point and determine whether it  is a maximum or a minimum point. Solution      i.   We […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2005 | Oct-Nov | (P2-9709/02) | Q#4

Question The equation of the curve is .     i.       Show that    ii.       Find the equation of the tangent to the curve at the point (2, 4), giving your answer in the form ax+by=c. Solution      i.   We are given that; Therefore; Rule for differentiation of  is: If  and  are functions […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2005 | May-Jun | (P2-9709/02) | Q#5

Question i.By differentiating , show that if then . ii. The parametric equations of a curve are x = 1 + tanθ , y = secθ , for . Show that .   iii.Find the coordinates of the point on the curve at which the gradient of the curve is . Solution      i.   […]