Hits: 450

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2011 | Oct-Nov | (P1-9709/13) | Q#6

Hits: 450 Question Relative to an origin , the position vectors of points A and B are  and , respectively.      i.       Use a scalar product to calculate angle BOA. The point C is the mid-point of AB. The point D is such that .    ii.       Find . Solution      i.   We recognize that angle BOA is between  and . […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2011 | Oct-Nov | (P1-9709/12) | Q#3

Hits: 395 Question Relative to an origin , the position vectors of points A and B are given by and where  is a constant.      i.       Find the value of  for which angle AOB =.    ii.       In the case where , find the vector which has magnitude 28 and is in the same direction as . Solution      i.   […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2011 | Oct-Nov | (P1-9709/11) | Q#8

Hits: 343 Question Relative to an origin , the point A has position vector  and the point B has position vector  , where  is a constant.      i.       Find .    ii.       Hence show that there are no real values of  for which  and  are perpendicular to each other.   iii.       Find the values of  for which angle AOB =. Solution      i.   A […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2011 | May-Jun | (P1-9709/13) | Q#5

Hits: 669 Question In the diagram, OABCDEFG is a rectangular block in which  cm and  cm. Unit vectors ,  and  are parallel to ,  and  respectively. The point P is the mid-point of DG, Q is the centre of the square face CBFG and R lies on AB such that AR = 4 cm.     i.       Express each of the […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2011 | May-Jun | (P1-9709/12) | Q#8

Hits: 819 Question Relative to an origin , the position vectors of the points ,  and  are given by and i.       Find angle ABC. The point D is such that ABCD is a parallelogram.    ii.       Find the position vector of D. Solution      i.   We recognize that angle ABC is between  and . Therefore, we need the scalar/dot product of […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2011 | May-Jun | (P1-9709/11) | Q#4

Hits: 1062 Question The diagram shows a prism ABCDPQRS with a horizontal square base APSD with sides of length 6 cm. The cross-section ABCD is a trapezium and is such that the vertical edges AB and DC are of lengths 5 cm and 2 cm respectively. Unit vectors ,  and  are parallel to AD, AP and AB respectively. […]