Hits: 599

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2008 | Oct-Nov | (P1-9709/01) | Q#10

Hits: 599   Question The function f is defined by    ,      i.       Sketch, in a single diagram, the graphs of  and , making clear the relationship between the two graphs. The function g is defined by    ,    ii.       Express  in terms of , and hence show that the maximum value of  is 9. The function h is defined by  […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2008 | Oct-Nov | (P1-9709/01) | Q#5

Hits: 521   Question The function f is such that  for , where  and  are positive constants. The maximum value of  is 10 and the minimum value is −2.      i.       Find the values of  and .    ii.       Solve the equation .   iii.       Sketch the graph of . Solution i.   We have the function; We know that; For ; […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2008 | May-Jun | (P1-9709/01) | Q#8

Hits: 431 Question Functions  and  are defined by    , , where  is a constant    ,      i.       Find the values of  for which the equation  has two equal roots.    ii.       Determine the roots of the equation  for the values of  found in part (i). Solution i.   We have the functions; First we find ; We are given that; Hence; Standard form of quadratic equation is; […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2008 | May-Jun | (P1-9709/01) | Q#6

Hits: 388 Question The function f is such that  for .      i.    Obtain an expression for  and hence explain why  is an increasing function.    ii.        Obtain an expression for for  and state the domain of . Solution i.   We have the function; The expression for  represents derivative of . Rule for differentiation of  is: Rule for differentiation […]