# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2007 | Oct-Nov | (P1-9709/01) | Q#9

Question A curve is such that  and the point P(2, 9) lies on the curve. The normal to the curve at P meets the curve again at Q. Find i.       the equation of the curve,    ii.       the equation of the normal to the curve at P   iii.       the coordinates of Q. Solution      i.   We are given the equation; We can […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2007 | Oct-Nov | (P1-9709/01) | Q#6

Question The three points A (3, 8), B (6, 2) and C (10, 2) are shown in the diagram. The point D is such that the line DA is perpendicular to AB and DC is parallel to AB. Calculate the coordinates of D. Solution It is evident that point D is the intersection of lines AD & DC. Therefore to […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2007 | Oct-Nov | (P1-9709/01) | Q#1

Question Determine the set of values of the constant k for which the line  does not intersect the curve . Solution First we find the conditions when line and the curve intersect. This we can do by equating equations of line and the curve. If line and the curve do not intersect then above equation has no real […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2007 | May-Jun | (P1-9709/01) | Q#6

Question The diagram shows a rectangle ABCD. The point A is (2, 14), B is (−2, 8) and C lies on the x-axis. Find     i.       the equation of BC    ii.       the coordinates of C and D. Solution      i.   To find the equation of the line either we need coordinates of the two points on the line (Two-Point form […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2007 | May-Jun | (P1-9709/01) | Q#1

Question Find the value of the constant  for which the line  is a tangent to the curve . Solution Since line is tangent to the curve i.e. both intersect each other at a single point. To find that point; If two lines (or a line and a curve) intersect each other at a point then that point lies on […]