Hits: 51

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | Oct-Nov | (P1-9709/13) | Q#10

Hits: 51 Question Relative to an origin O, the position vectors of points A, B and X are given by and i.Find and show that AXB is a straight line. The position vector of point C is given by . ii.Show that CX is perpendicular to AX. iii.Find the area of triangle ABC. Solution i. […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | Oct-Nov | (P1-9709/12) | Q#7

Hits: 40 Question The diagram shows a three-dimensional shape OABCDEFG. The base OABC and the upper  surface DEFG are identical horizontal rectangles. The parallelograms OAED and CBFG both lie in  vertical planes. Points P and Q are the mid-points of OD and GF respectively. Unit vectors  and  are parallel to  and  respectively and the unit […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | Oct-Nov | (P1-9709/11) | Q#10

Hits: 44 Question Relative to an origin O, the position vectors of points A, B, C and D, shown in the diagram, are given  by are given by and i.       Show that AB is perpendicular to BC. ii.       Show that ABCD is a trapezium. iii.       Find the area of ABCD, giving your answer correct to […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | May-Jun | (P1-9709/13) | Q#6

Hits: 29 Question The diagram shows a solid figure ABCDEF in which the horizontal base ABC is a triangle right- angled at A. The lengths of AB and AC are 8 units and 4 units respectively and M is the mid-point of  AB. The point D is 7 units vertically above A. Triangle DEF lies […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | May-Jun | (P1-9709/12) | Q#8

Hits: 146 Question The position vectors of points A and B, relative to an origin O, are given by and Where  is a constant. i.Find the value of  for which the angle AOB=90o. ii.Find the values of  for which the lengths of OA and OB are equal. The point C is such that . iii.In […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | May-Jun | (P1-9709/11) | Q#7

Hits: 164 Question The diagram shows a three-dimensional shape in which the base OABC and the upper surface  DEFG are identical horizontal squares. The parallelograms OAED and CBFG both lie in vertical  planes. The point M is the mid-point of AF. Unit vectors  and  are parallel to OA and OC respectively and the unit vector […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | Feb-Mar | (P1-9709/12) | Q#5

Hits: 231 Question Two vectors,  and , are such that and Where is a constant.     i.      Find the values of for which is perpendicular to .   ii.     Find the angle between  and when q = 0. Solution i.   We are given that; If  and & , then  and  are perpendicular. Therefore, if […]