Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2006 | Oct-Nov | (P1-9709/01) | Q#7

  Question The diagram shows the curve y = x(x − 1)(x − 2), which crosses the x-axis at the points O(0, 0), A(1, 0) and B(2, 0).     i.       The tangents to the curve at the points A and B meet at the point C. Find the x-coordinate of C.    ii.       Show by integration that the area of the shaded region […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2006 | Oct-Nov | (P1-9709/01) | Q#5

Question The three points A(1, 3), B(13, 11) and C(6, 15) are shown in the diagram. The perpendicular from C to AB meets AB at the point D. Find i.       the equation of CD,    ii.       the coordinates of D. Solution      i.   To find the equation of the line either we need coordinates of the two points on the line […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2006 | May-Jun | (P1-9709/01) | Q#9

Question A curve is such that  and P (1, 8) is a point on the curve. i.       The normal to the curve at the point P meets the coordinate axes at Q and at R. Find the coordinates of the mid-point of QR.    ii.   Find the equation of the curve. Solution      i.   To find the mid-point […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2006 | May-Jun | (P1-9709/01) | Q#5

Question The curve  intersects the line  at two points. Find the distance between the two points. Solution Expression to find distance between two given points  and is: So first we need to find the coordinates of points of intersection of the curve and the line. If two lines (or a line and a curve) intersect each other […]