Hits: 179

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | Oct-Nov | (P1-9709/13) | Q#11

Hits: 179 Question     i.      Express in the form of where a, b and c are constants. The function f is defined by  for .    ii.       State the largest value of the constant k for which f is a one-one function.  iii.     For this value of k find an expression for and state the […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | Oct-Nov | (P1-9709/13) | Q#9

Hits: 65 Question A curve has equation  and a line has equation , where  is a constant. i.Show that, for all values of k, the curve and the line meet. ii.State the value of k for which the line is a tangent to the curve and find the coordinates of the  point where the line […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | Oct-Nov | (P1-9709/13) | Q#2

Hits: 31 Question The function f is defined by  for . Determine, showing all necessary working, whether f is an increasing function, a decreasing  function or neither. Solution We are given function;   We are required to find whether is an increasing function, decreasing function or neither. To test whether a function is increasing or […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | Oct-Nov | (P1-9709/12) | Q#9

Hits: 153 Question The function f is defined by  for .     i.      Express in the form of where a and b are constants.   ii.     State the range of .  The function g is defined by  for .  iii.       State the largest value of k for which g has an inverse.   iv.     Given that […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | Oct-Nov | (P1-9709/11) | Q#11

Hits: 420 Question The one-one function f is defined by  for , where  is a constant. a.                    i.     State the greatest possible value of .              ii.     It is given that takes this greatest possible value. State the range of f and find an expression for .   b.    The function g is […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | Feb-Mar | (P1-9709/12) | Q#10

Hits: 263 Question The functions f and g are defined by  for  for . i.   a.   State the range of the function f. b.   State the range of the function g. c.   State the range of the function fg.    ii.       Explain why the function gf cannot be formed.   iii.       Find the set […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | Feb-Mar | (P1-9709/12) | Q#9

Hits: 247 Question A curve has equation  and a line has equation , where  is a constant. i.Find the set of values of  for which the curve and the line meet. ii.The line is a tangent to the curve for two particular values of . For each of these values find  the x-coordinate of the […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | May-Jun | (P1-9709/13) | Q#10

Hits: 559 Question The one-one function f is defined by  for , where c is a  constant.   i.       State the smallest possible value of c. In parts (ii) and (iii) the value of c is 4.    ii.       Find an expression for  and state the domain of .   iii.       Solve the equation , […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | May-Jun | (P1-9709/13) | Q#1

Hits: 105 Question Express 3×2 − 12x + 7 in the form a(x + b)2 + c, where a, b and c are constants.  Solution We have the expression; We use method of “completing square” to obtain the desired form. Next we complete the square for the terms which involve . We have the algebraic […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | May-Jun | (P1-9709/12) | Q#7

Hits: 849 Question The function is defined by  for .      i.       Express   in the form , where a and b are constants.    ii.       State the coordinates of the stationary point on the curve y = f(x). The function is defined by  for .   iii.       State the smallest value of k for […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | Feb-Mar | (P1-9709/11) | Q#2

Hits: 557 Question The equation of a curve is  , where  is a constant.     i.       Find the set of values of  for which the whole of the curve lies above the x-axis.    ii.       Find the value of  for which the line y + 2x = 7 is a tangent to the curve. Solution […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | May-Jun | (P1-9709/11) | Q#10

Hits: 764 Question The curve with equation  passes through the origin.     i.       Show that the curve has no stationary points.    ii.       Denoting the gradient of the curve by m, find the stationary value of m and  determine its nature. Solution i.   We are required to show that curve has no stationary points. […]