Functions (CIE-2007) Archives — O/A Level Solutions

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2007 | May-Jun | (P1-9709/01) | Q#11

  Question The diagram shows the graph of , where  for .      i.       Find an expression, in terms of , for  and explain how your answer shows that  is a decreasing function.    ii.       Find an expression, in terms of , for  and find the domain of .   iii.       Copy the diagram and, on your copy, sketch the graph of , making clear the relationship between […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2007 | May-Jun | (P1-9709/01) | Q#8

  Question The function f is defined by  for . It is given that  and  .      i.       Find the values of  and .    ii.       Find the x-coordinates of the points where the curve  intersects the x-axis.   iii.       Sketch the graph of . Solution i.   We have the function; We are given that; Adding both equations gives us; Substituting  in anyone of […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2007 | Oct-Nov | (P1-9709/01) | Q#11

Question The function  is defined by  for .      i.       Express  in the form , where ,  and  are constants.    ii.       State the range of .   iii.       Explain why  does not have an inverse. The function g is defined by   for , where  is a constant.   iv.       State the largest value of  for which  has an inverse.    v.       When  has this value, obtain an expression, in […]