Hits: 569

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | Oct-Nov | (P1-9709/13) | Q#7

Hits: 569   Question The diagram shows a triangular pyramid ABCD. It is given that i.       Verify, showing all necessary working, that each of the angles DAB, DAC and CAB is 90o.    ii.       Find the exact value of the area of the triangle ABC, and hence find the exact value of the volume of the pyramid.  [The volume V of a […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | Oct-Nov | (P1-9709/12) | Q#9

Hits: 882 Question Relative to an origin O, the position vectors of points A, B and C are given by and i.       Use a scalar product to find angle AOB. ii.       Find the vector which is in the same direction as  and of magnitude 15 units.  iii.       Find the value of the constant p for which  perpendicular to . Solution      i.   It […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | Oct-Nov | (P1-9709/11) | Q#9

Hits: 2598 Question The diagram shows a cuboid OABCDEFG with a horizontal base OABC in which OA = 4 cm and  AB = 15 cm. The height OD of the cuboid is 2 cm. The point X on AB is such that AX = 5 cm and  the point P on DG is such that DP = p […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | May-Jun | (P1-9709/13) | Q#9

Hits: 536 Question The position vectors of points A, B and C relative to an origin O are given by and where p is a constant. i.       Find the value of p for which the lengths of AB and CB are equal. ii.       For the case where p=1, use a scalar product to find angle ABC. Solution      i.   […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | May-Jun | (P1-9709/12) | Q#3

Hits: 670 Question Relative to an origin , the position vectors of points A and B are given by and The point C is such that . Find the unit vector in the direction of . Solution A unit vector in the direction of  is; Therefore for the given case; Therefore, we need to find . We are given that; A […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | May-Jun | (P1-9709/11) | Q#10

Hits: 1081   Question Relative to an origin O, the position vectors of points A, B and C are given by and respectively, where k is a constant. i.       Find the value of k in the case where angle AOB=90o. ii.       Find the possible values of k for which the lengths of AB and OC are equal. The point D is such […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | Feb-Mar | (P1-9709/12) | Q#7

Hits: 1328 Question The diagram shows a pyramid OABC with a horizontal triangular base OAB and vertical height OC.  Angles AOB, BOC and AOC are each right angles. Unit vectors ,  and  are parallel to OA, OB  and OC respectively, with OA = 4 units, OB = 2.4 units and OC = 3 units. The point P on CA […]