Hits: 183

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2009 | Oct-Nov | (P1-9709/12) | Q#1

Hits: 183 Question The equation of a curve is such that  . Given that the curve passes through the point (4, 6), find the equation of the curve. Solution We can find equation of the curve from its derivative through integration; For the given case; Therefore; Rule for integration of  is: Rule for integration of  is: Rule for […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2009 | Oct-Nov | (P1-9709/11) | Q#6

Hits: 244 Question A curve is such that , where k is a constant.     i.       Given that the tangents to the curve at the points where  and  are perpendicular, find the value of .    ii.       Given also that the curve passes through the point (4, 9), find the equation of the curve. Solution      i.   If two lines […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2009 | Oct-Nov | (P1-9709/11) | Q#4

Hits: 222 Question The equation of a curve is .     i.       Find the coordinates of the stationary point on the curve and determine its nature.    ii.       Find the area of the region enclosed by the curve, the x-axis and the lines    and . Solution      i.   Coordinates of stationary point on the curve  can be found from the derivative […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2009 | May-Jun | (P1-9709/01) | Q#11

Hits: 1550 Question The diagram shows the curve  for . The curve has a maximum point at A and a minimum point on the x-axis at B. The normal to the curve at C (2, 2) meets the normal to the curve at B at the point D. i.       Find the coordinates of A and B.    ii.       Find the equation of […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2009 | May-Jun | (P1-9709/01) | Q#9

Hits: 1001 Question The diagram shows part of the curve . i.       Find the gradient of the curve at the point where .    ii.       Find the volume obtained when the shaded region is rotated through 360o about the x-axis, giving your answer in terms of . Solution      i.   Gradient (slope) of the curve at the particular point is […]