# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2004 | May-Jun | (P1-9709/01) | Q#10

Question Functions  and  are defined by    ,    ,      i.       Find the set of values of  for which .    ii.       Find the range of  and state, with a reason, whether  has an inverse.   iii.       Show that the equation  has no real solutions.   iv.       Sketch, on a single diagram, the graphs of  and , making clear the relationship between the graphs. Solution […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2004 | Oct-Nov | (P1-9709/01) | Q#9

Question The function , where  is a constant, is defined for all real .      i.       In the case where , solve the equation . The function  is defined for all real .    ii.       Find the value of  for which the equation  has exactly one real solution. The function  is defined for the domain.   iii.       Express  in the form , where  and  are constants.   […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2004 | Oct-Nov | (P1-9709/01) | Q#6

Question The function  is defined for the domain .      i. Express  in the form , stating the values of  and .    ii. Hence find the values of  for which .   iii. State the range of . Solution i.   We have the function; We have the trigonometric identity; We can rewrite the identity as; Substituting the expression in the […]