Hits: 1171

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | Oct-Nov | (P1-9709/13) | Q#6

Hits: 1171 Question The functions f and g are defined by   for   for      i.       Find an expression for .    ii.       Solve the equation . Solution i.   We are given the function; 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 . As […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | Oct-Nov | (P1-9709/12) | Q#6

Hits: 1748   Question a.   The function f, defined by   for , is such that  and .                             i.       Find the values of the constants a and b.                           ii.       Evaluate . b.   The function g is defined by  for for . The range of g is given by  . Find the values of the constants c and d. Solution a.   i.   We […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | Oct-Nov | (P1-9709/12) | Q#2

Hits: 1165   Question A function f is defined by  for .      i.       Find an expression for  and find the point of intersection of the graphs of  and  .    ii.       Sketch, on the same diagram, the graphs of  and , making clear the  relationship between the graphs. Solution i.   We have; We write it as; To find the inverse of […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | Oct-Nov | (P1-9709/11) | Q#9

Hits: 1093   Question Functions f and g are defined for x > 3 by;      i.       Find and simplify an expression for gg(x).    ii.       Find an expression for  and state the domain of .   iii.       Solve the equation .  Solution      i.   We are given that; It can be written as; Therefore for ;    ii. […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | Oct-Nov | (P1-9709/11) | Q#2

Hits: 1166   Question A function f is defined by  for . It is given that f is an increasing  function. Find the largest possible value of the constant a. Solution We are given that function f is increasing function. To test whether a function  is increasing or decreasing at a particular point , we  take derivative of a function […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | May-Jun | (P1-9709/12) | Q#10

Hits: 1874   Question The function f is defined by , for .     i.       Solve the equation , giving your answer correct to 1 decimal place.    ii.       Find an expression for  and find the domain of .   iii.       Sketch, on the same diagram, the graphs of y=f(x) and . Solution      i.   We are given the function as; We […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | Feb-Mar | (P1-9709/12) | Q#8

Hits: 1135   Question The functions f and g are defined for  by i.       Show that  and obtain an unsimplified expression for . ii.       Find an expression for  and determine the domain of . iii.       Solve the equation . Solution      i.   We are given the functions; We can rewrite these as; First we find . Next we find .    […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | May-Jun | (P1-9709/11) | Q#9

Hits: 1111   Question The function f is defined by  for , .      i.        Find an expression for . The function g is defined by  for , where a is a constant.    ii.       Find the value of a for which .   iii.       Find the possible values of a given that the equation  has two equal roots. Solution      i. […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | May-Jun | (P1-9709/11) | Q#5

Hits: 1695   Question The equation of a curve is .      i.       Sketch the graph of  for , stating the coordinates of the point of  intersection with the y-axis. Points P and Q lie on the curve and have x-coordinates of  and  respectively.    ii.       Find the length of PQ correct to 1 decimal place. The line through […]