# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2003 | May-Jun | (P1-9709/01) | Q#6

Question      i. Sketch the graph of the curve , for . The straight line , where  is a constant, passes through the maximum point of this curve for .    ii. Find the value of k in terms of .   iii. State the coordinates of the other point, apart from the origin, where the line and the curve intersect. Solution i. […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2003 | Oct-Nov | (P1-9709/01) | Q#2

Question   i.  Show that the equation  may be written in the form  where  .    ii.       Hence solve the equation , for . Solution i.   We have; We need to express the equation in terms of  only because we are given that . We have the trigonometric identity; We can write it as; Hence the equation becomes; We can also write it as; Let; […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2003 | May-Jun | (P1-9709/01) | Q#2

Question Find all the values of  in the interval  which satisfy the equation; Solution First we need to manipulate the given equation to write it in a single trigonometric ratio; Dividing the entire equation by ; Using the relation  we can rewrite the equation as, To solve this equation for , we can substitute . Hence, Since given interval is  , for  interval can […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2003 | May-Jun | (P1-9709/01) | Q#9

Question The diagram shows a semicircle ABC with centre O and radius 8 cm. Angle  radians. i.       In the case where , calculate the area of the sector BOC.    ii.       Find the value of  for which the perimeter of sector AOB is one half of the perimeter of sector BOC.   iii.       In the case where , show that the exact length […]