# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2003 | May-Jun | (P1-9709/01) | Q#6

Question      i. Sketch the graph of the curve , for . The straight line , where  is a constant, passes through the maximum point of this curve for .    ii. Find the value of k in terms of .   iii. State the coordinates of the other point, apart from the origin, where the line and the curve intersect. Solution i. […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2003 | Oct-Nov | (P1-9709/01) | Q#10

Question Functions  and  are defined by    ,    ,      i.       Find the value of  for which .    ii.       Express each of  and  in terms of .   iii.     Show that the equation  has no real roots.   iv.     Sketch, on a single diagram, the graphs of  and , making clear the relationship between these two graphs. Solution […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2003 | May-Jun | (P1-9709/01) | Q#11

Question The equation of a curve is .      i. Express  in the form , stating the numerical values of  and .    ii. Hence, or otherwise, find the coordinates of the stationary point of the curve.   iii. Find the set of values of  for which . The function g is defined by  for .   iv. State the domain and range […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2003 | May-Jun | (P1-9709/01) | Q#5

Question The function  is defined by , for  , where a and b are constants. It is given that  and .      i. Find the values of a and b.    ii. Solve the equation . Solution i.   We are given that; We utilize the given data. Subtracting both equations; We can substitute  in any of the above two equations to find the value […]