Hits: 53

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | Oct-Nov | (P1-9709/13) | Q#2

Hits: 53 Question The function g is defined by  for . By first completing the square, find an  expression for and state the domain of . Solution We are given that; We use method of “completing square” to obtain the desired form. We complete the square for the  terms which involve . We have the […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | Oct-Nov | (P1-9709/12) | Q#9

Hits: 74 Question Functions f and g are defined by;  for   for Where  is a constant.     i.      Find the value of for which the line is a tangent to the curve .   ii.     In the case where , find the set of values of for which .  iii.     In the case […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | Oct-Nov | (P1-9709/12) | Q#6

Hits: 79 Question a)   Given that x > 0, find the two smallest values of x, in radians, for which . Show  all necessary working. b)  The function is defined for . i.     Express f(x) in the form , where a and b are constants. ii.      Find the range of f. Solution a)   […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | Oct-Nov | (P1-9709/11) | Q#7

Hits: 92 Question The functions f and g are defined by  for  for . i.       Find the range of f and the range of g.    ii.       Find an expression for fg(x), giving your answer in the form  , where a, b and c are  integers.  iii.      Find an expression for , giving your answer […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | May-Jun | (P1-9709/13) | Q#4

Hits: 69 Question The function f is defined by  for . The function g is defined by for   where  and are constants.     i.       Find the greatest value of and the least value of which will permit the formation of the composite function gf. It is now given that the conditions for the formation of gf […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | May-Jun | (P1-9709/12) | Q#7

Hits: 309 Question The functions f and g are defined by , , i.Obtain expressions for and , stating the value of x for which is not defined. ii.Solve the equation Solution i. We are given;  for  for We have; We write them as; To find the inverse of a given function we need to […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | May-Jun | (P1-9709/11) | Q#9

Hits: 283 Question The functions f is defined by  for  ,     i.      State the range of .   ii.     Sketch the graph of . The functions g is defined by for , where is a constant.  iii.     State the largest value of for which g has an inverse.  iv.     For this value of , […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | May-Jun | (P1-9709/11) | Q#5

Hits: 447 Question The function f is defined by  for .     i.      Express in the form of where and are constants.   ii.     State the greatest value of .    The function g is defined by  for .  iii.     Find the value of for which . Solution i.   We have the expression;   […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | Feb-Mar | (P1-9709/12) | Q#8

Hits: 284 Question     i.      Express in the form of . The function f is defined by  for , where is constant.   ii.     State the largest value of for which is a decreasing function. The value of is now given to be 1.  iii.     Find an expression for and state the domain of . […]