# 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#6

Question The parametric equations of a curve are Where t takes all positive values.      i.       Show that    ii.       Find the equation of the tangent to the curve at the point where .   iii.       The curve has one stationary point. Find the y-coordinate of this point, and determine whether  […]

# 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#1

Question Solve the inequality . Solution SOLVING INEQUALITY: PIECEWISE Let, . We can write it as; We have to consider both moduli separately and it leads to following cases; When If then above four intervals translate to following with their corresponding inequality; When When When If then above four intervals translate to following […]

# 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 | Oct-Nov | (P1-9709/01) | Q#5

Question The equation of a curve is  and the equation of a line is . The curve and the line intersect at the points A and B.      i.       The mid-point of AB is M. Show that the coordinates of M are .    ii.       Find the coordinates of the point Q on the curve at which the tangent is parallel […]

# 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#6

Question The curve   and the line  intersect at two points. Find i.       the coordinates of the two points,    ii.       the equation of the perpendicular bisector of the line joining the two points. Solution      i.   To find the coordinates of intersection points; If two lines (or a line and a curve) intersect each other at a point then […]