# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2003 | May-Jun | (P1-9709/01) | Q#6

Question      i. Sketch the graph of the curve , for . The straight line , where  is a constant, passes through the maximum point of this curve for .    ii. Find the value of k in terms of .   iii. State the coordinates of the other point, apart from the origin, where the line and the curve intersect. Solution i. […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2003 | Oct-Nov | (P1-9709/01) | Q#9

Question The diagram shows points  and  on the curve . The tangent to the curve at B crosses the x-axis at C. The point D has coordinates (2, 0). i.       Find the equation of the tangent to the curve at B and hence show that the area of triangle BDC is    ii.       Show that the volume of the solid formed when […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2003 | Oct-Nov | (P1-9709/01) | Q#5

Question The diagram shows a trapezium ABCD in which BC is parallel to AD and angle . The coordinates of A, B and D are (2, 0), (4, 6) and (12, 5) respectively.      i.       Find the equations of BC and CD.    ii.       Calculate the coordinates of C. Solution i.   First we find the equation of . To […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2003 | Oct-Nov | (P1-9709/01) | Q#4

Question A curve is such that  . The curve passes through the point (1, 5).      i.       Find the equation of the curve.     ii.       Find the set of values of  for which the gradient of the curve is positive. Solution i.   To find the equation of the curve; We can find equation of the curve from its […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2003 | Oct-Nov | (P1-9709/01) | Q#1

Question Find the coordinates of the points of intersection of the line  and the curve . Solution If two lines (or a line and a curve) intersect each other at a point then that point lies on both lines i.e. coordinates of that point have same values on both lines (or on the line and the curve). Therefore, […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2003 | May-Jun | (P1-9709/01) | Q#7

Question The line  has equation . The line  passes through the point  and is perpendicular to . i.       Find the equation of .    ii.       Given that the lines  and  intersect at the point B, find the length of AB. Solution      i.   To find the equation of the line either we need coordinates of the two points on […]