Hits: 228

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2010 | Oct-Nov | (P1-9709/13) | Q#10

Hits: 228 Question The diagram shows triangle , in which the position vectors of  and  with respect to  are given by &  is a point on  such that , where  is a constant.     i.       Find angle .    ii.     Find  in terms of  and vectors ,  and .   iii.   Find the value of  given that  is perpendicular to […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2010 | Oct-Nov | (P1-9709/12) | Q#9

Hits: 797 Question The diagram shows a pyramid OABCP in which the horizontal base OABC is a square of side 10 cm and the vertex P is 10 cm vertically above O. The points D, E, F, G lie on OP, AP, BP, CP respectively and DEFG is a horizontal square of side 6 cm. The height of […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2010 | Oct-Nov | (P1-9709/11) | Q#5

Hits: 512 Question The diagram shows a pyramid OABC with a horizontal base OAB where OA = 6 cm, OB = 8 cm and angle . The point C is vertically above O and OC = 10 cm. Unit vectors ,  and  are parallel to ,  and  as shown. Use a scalar product to find angle ACB. Solution i. […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2010 | May-Jun | (P1-9709/13) | Q#6

Hits: 236 Question Relative to an origin , the position vectors of the points ,  and   are given by i.       Use a scalar product to find angle ABC.    ii.       Find the perimeter of triangle ABC, giving your answer correct to 2 decimal places. Solution i.   We recognize that angle ABC is between vectors  and  Therefore, first we find vectors  and […]

PPast Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2010 | May-Jun | (P1-9709/12) | Q#5

Hits: 284 Question Relative to an origin , the position vectors of the points  and  are given by and i.       Find the value of the  for which  is perpendicular to .    ii.       Find the value of the  for which magnitude of   is 7. Solution i.   If  and  & , then  and  are perpendicular. Therefore we need to find the […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2010 | May-Jun | (P1-9709/11) | Q#10

Hits: 645 Question The diagram shows the parallelogram OABC. Given that  and , find i.       the unit vector in the direction of .    ii.       the acute angle between the diagonals of the parallelogram,   iii.       the perimeter of the parallelogram, correct to 1 decimal place. Solution i.   A unit vector in the direction of  is; Therefore, for the given case; […]