# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2005 | Oct-Nov | (P1-9709/01) | Q#3

Question In the diagram, ABED is a trapezium with right angles at E and D, and CED is a straight line. The lengths of AB and BC are  and  respectively, and angles BAD and CBE are and  respectively. i.       Find the length of CD in terms of .    ii.       Show that angle CAD = Solution From the given information we can […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2005 | Oct-Nov | (P1-9709/01) | Q#10

Question A curve is such that  and (1, 4) is a point on the curve. i.       Find the equation of the curve.    ii.        A line with gradient  is a normal to the curve. Find the equation of this normal, giving your answer in the form .   iii.       Find the area of the region enclosed by the curve, the […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2005 | Oct-Nov | (P1-9709/01) | Q#9

Question The equation of a curve is  and the equation of a line  is , where  is a constant. i.       In the case where , find the coordinates of the points of intersection of  and the curve.    ii.       Find the set of values of  for which  does not intersect the curve.   iii.       In the case where , one of the […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2005 | Oct-Nov | (P1-9709/01) | Q#7

Question Three points have coordinates A (2, 6), B (8, 10) and C (6, 0). The perpendicular bisector of AB meets the line BC at D. Find     i.       the equation of the perpendicular bisector of AB in the form ax + by = c,    ii.       the coordinates of D. Solution i.   To write the equation of the perpendicular bisector of […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2005 | Oct-Nov | (P1-9709/01) | Q#5

Question The diagram shows the cross-section of a hollow cone and a circular cylinder. The cone has radius 6 cm and height 12 cm, and the cylinder has radius  cm and height cm. The cylinder just fits inside the cone with all of its upper edge touching the surface of the cone. i.       Express h in terms of r and […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2005 | May-Jun | (P1-9709/01) | Q#10

Question The equation of a curve is . i.       Show that the whole of the curve lies above the x-axis.    ii.       Find the set of values of x for which  is a decreasing function of x. The equation of a line is , where k is a constant.   iii.       In the case where k = 6, find the coordinates of the […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2005 | May-Jun | (P1-9709/01) | Q#9

Question A curve has equation  . i.       The normal to the curve at the point (4, 2) meets the x-axis at P and the y-axis at Q. Find the length of PQ, correct to 3 significant figures.    ii.       Find the area of the region enclosed by the curve, the x-axis and the lines x = 1 and […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2005 | May-Jun | (P1-9709/01) | Q#5

Question The diagram shows a rhombus ABCD. The points B and D have coordinates (2, 10) and (6, 2) respectively, and A lies on the x-axis. The mid-point of BD is M. Find, by calculation, the coordinates of each of M, A and C. Solution M is the mid-point of BD. To find the mid-point of a line we […]