Hits: 353

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2005 | Oct-Nov | (P2-9709/02) | Q#7

Hits: 353     Question The diagram shows the part of the curve y = sin2 x for  .      i.       Show that    ii.       Hence find the x-coordinates of the points on the curve at which the gradient of the curve is  0.5.   iii.       By expressing sin2 x in terms […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2005 | Oct-Nov | (P2-9709/02) | Q#3

Hits: 211   Question i. Express  in the form , where  and , giving exact  value of R and the value of  correct to 2 decimal places.    ii. Hence solve the equation Giving all solutions in the interval . Solution      i.   We are given that; We are required to write it in […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2005 | May-Jun | (P2-9709/02) | Q#7

Hits: 228   Question      i. By expanding , and using double-angle formulae, show that    ii. Hence, or otherwise, show that Solution      i.   We have; We apply following addition formula. Therefore; We apply following two formulae. We have the trigonometric identity; Therefore, we can replace; Hence;    ii.   We are required […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2005 | May-Jun | (P1-9709/01) | Q#7

Hits: 785   Question The function  is defined for the domain .      i.       Find the range of .    ii.       Sketch the graph of . A function g is defined by , for , where A is a constant.   iii.     State the largest value of  for which  has an inverse.   iv.       When  has this value, obtain an expression, in terms […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2005 | Oct-Nov | (P1-9709/01) | Q#1

Hits: 314 Question Solve the equation , for . Solution We have; We need to express the equation in terms of single trigonometric ratio; We have the trigonometric identity; We can write it as; Hence the equation becomes; To solve this equation for , we can substitute . Hence, Now we have two options; Since; Using calculator we can find the values of […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2005 | May-Jun | (P1-9709/01) | Q#3

Hits: 627 Question      i.       Show that the equation  can be expressed as .    ii.       Hence solve the equation , for . Solution i.   First we need to manipulate the given equation to write it in a single trigonometric ratio i.e. ; Dividing the entire equation by ; Using the relation ; ii.   To solve this equation for , Using calculator we […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2005 | Oct-Nov | (P1-9709/01) | Q#3

Hits: 823 Question In the diagram, ABED is a trapezium with right angles at E and D, and CED is a straight line. The lengths of AB and BC are  and  respectively, and angles BAD and CBE are and  respectively. i.       Find the length of CD in terms of .    ii.       Show that angle CAD = Solution From the given information […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2005 | Oct-Nov | (P1-9709/01) | Q#9

Hits: 471 Question The equation of a curve is  and the equation of a line  is , where  is a constant. i.       In the case where , find the coordinates of the points of intersection of  and the curve.    ii.       Find the set of values of  for which  does not intersect the curve.   iii.       In the case where , one […]