# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2006 | Oct-Nov | (P1-9709/01) | Q#10

Question The function  is defined by  for .      i.       Find the set of values of  for which .    ii.       Express  in the form , stating the values of  and .   iii.       Write down the range of .    iv.       State, with a reason, whether  has an inverse. The function  is defined by   for .    v.       Solve the equation . Solution i. […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2006 | May-Jun | (P1-9709/01) | Q#11

Question Functions and  are defined by   for   where  is constant   for   ,      i. Find the values of  for which the equation  has two equal roots and solve the equation  in these cases.    ii. Solve the equation  when .   iii. Express  in terms of . Solution i.   We have the functions; We can write these functions as; We can equate both functions; Standard form […]