Hits: 272

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2013 | Oct-Nov | (P1-9709/13) | Q#1

Hits: 272 Question Solve the inequality . Solution We have; We solve the following equation to find critical values of ; Now we have two options; Hence the critical points on the curve for the given condition are  & 2. Standard form of quadratic equation is; The graph of quadratic equation is a parabola. If  (‘a’ is positive) then parabola  […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2013 | Oct-Nov | (P1-9709/12) | Q#10

Hits: 560 Question A curve has equation .      i.       Find the set of values of x for which y > 9.    ii.      Express  in the form , where a, b and c are constants, and  state the coordinates of the vertex of the curve. The functions f and g are defined for all real values of x by  and  , […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2013 | Oct-Nov | (P1-9709/12) | Q#8

Hits: 549   Question The function  is defined by  for .      i.       Solve the equation .    ii.       Find the range of .   iii.       Sketch the graph of . The function  is defined by  for .   iv.       State the maximum value of for which  has an inverse.    v.       Obtain an expression for . Solution i.   We have the function; We can write it as; […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2013 | Oct-Nov | (P1-9709/13) | Q#10

Hits: 531 Question The function  is defined by  for , where  is a constant. It is given that f is a one-one function.      i.       State the range of  in terms of  and find the smallest possible value of . The function  is defined by  for , where  and  are positive constants. It is given that, when ,  and .    ii.       Write down two equations […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2013 | Oct-Nov | (P1-9709/11) | Q#5

Hits: 481 Question The function  is defined by , for ,      i.       Define in a similar way the inverse function .    ii.       Solve the equation . Solution i.   We have the function; We can write it as; We write it as; To find the inverse of a given function  we need to write it in terms of  rather than in terms of […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2013 | May-Jun | (P1-9709/13) | Q#10

Hits: 360 Question A function  is defined by , for , where  is a constant.      i.       In the case where , solve the equation . The function  is defined by ,  .    ii.        Find the set of values of  for which the equation   has no real solutions. The function h is defined by ,  .   iii.       Find an expression for . Solution i. […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2013 | May-Jun | (P1-9709/12) | Q#9

Hits: 566 Question A function f is defined by , for .      i.       Find an expression for .    ii.       Determine, with a reason, whether  is an increasing function, a decreasing function or neither.   iii.       Find an expression for  and state the domain and range of . Solution i.   We have the function; The expression for  represents derivative of . We can rewrite […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2013 | May-Jun | (P1-9709/11) | Q#8

Hits: 557 Question      i.     Express  in the form , where ,  and  are constants.    ii.       The function  is defined by  for , where  is a constant. It is given that f is a one-one function. State the smallest possible value of . The value of  is now given to be 7.   iii.       Find the range of .   iv.       Find an expression for […]