Hits: 872

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2013 | Oct-Nov | (P1-9709/13) | Q#4

Hits: 872   Question The diagram shows a pyramid OABC in which the edge OC is vertical. The horizontal base OAB is a triangle, right-angled at O, and D is the mid-point of AB. The edges OA, OB and OC have lengths of 8 units, 6 units and 10 units respectively. Unit vectors ,  and  are parallel to , […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2013 | Oct-Nov | (P1-9709/12) | Q#4

Hits: 350   Question Relative to an origin , the position vectors of three points A and B are given by and      i.       In the case where , find the unit vector in the direction of .    ii.       Find the values of  for which angle . Solution      i.   We are given that; In the case where , A […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2013 | Oct-Nov | (P1-9709/11) | Q#3

Hits: 460   Question The diagram shows a pyramid OABCD in which the vertical edge OD is 3 units in length. The point E is the centre of the horizontal rectangular base OABC. The sides OA and AB have lengths of 6 units and 4 units respectively. Unit vectors ,  and  are parallel to ,  and  respectively.     i.       Express […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2013 | May-Jun | (P1-9709/13) | Q#8

Hits: 463   Question The diagram shows a parallelogram OABC in which relative to an origin , the position vectors of three points A, B and C are given by and i.       Use a scalar product to find angle BOC. ii.       Find a vector which has magnitude 35 and is parallel to the vector . Solution      i.   We recognize that […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2013 | May-Jun | (P1-9709/12) | Q#6

Hits: 361 Question Relative to an origin , the position vectors of three points A and B are given by , and where  and  are constants.      i.       State the values of p and q for which  is parallel to .    ii.       In the case where , find the value of  for which angle BOA is .   iii.       In the case where […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2013 | May-Jun | (P1-9709/11) | Q#6

Hits: 331   Question Relative to an origin , the position vectors of three points A, B and C are given by ,         and         where  and  are constants.      i.       Show that  is perpendicular to  for all non-zero values of  and .    ii.       Find the magnitude of  in terms of  and .   […]