Hits: 309

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2009 | Oct-Nov | (P1-9709/12) | Q#4

Hits: 309   Question Functions  and  are defined by  for .      i.       Find the range of .    ii.       Sketch the graph of .   iii.       State, with a reason, whether  has an inverse. Solution i.   We have the function; We can write it as; We know that; Hereby; We can find the range of   by substituting extreme possible values of ; Therefore; […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2009 | Oct-Nov | (P1-9709/11) | Q#10

Hits: 310   Question Functions  and  are defined by  , , , ,      i.       Solve the equation .    ii.       Express  and  in terms of .   iii.       Show that the equation   has no solutions.   iv.       Sketch in a single diagram the graphs of  and , making clear the relationship between the graphs. Solution i.   We have the functions; We can write […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2009 | Oct-Nov | (P1-9709/12) | Q#8

Hits: 206 Question The function  is such that  for ,      i.       Obtain an expression for  and explain why  is a decreasing function.    ii.       Obtain an expression for .   iii.       A curve has the equation . Find the volume obtained when the region bounded by the curve, the coordinate axes and the line is rotated through  about the x-axis. Solution i.   We […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2009 | May-Jun | (P1-9709/01) | Q#10

Hits: 987 Question The function  is defined by  for , where  is a constant.      i.       Express  in the form , where ,  and  are constants.    ii.       State the value of  for which the graph of  has a line of symmetry.   iii.        When  has this value, find the range of . The function g is defined by  for .   iv.       Explain […]