Hits: 770

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2007 | May-Jun | (P1-9709/01) | Q#11

Hits: 770   Question The diagram shows the graph of , where  for .      i.       Find an expression, in terms of , for  and explain how your answer shows that  is a decreasing function.    ii.       Find an expression, in terms of , for  and find the domain of .   iii.       Copy the diagram and, on your copy, sketch the graph of , making clear the […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2007 | Oct-Nov | (P1-9709/01) | Q#9

Hits: 504 Question A curve is such that  and the point P(2, 9) lies on the curve. The normal to the curve at P meets the curve again at Q. Find i.       the equation of the curve,    ii.       the equation of the normal to the curve at P   iii.       the coordinates of Q. Solution      i.   We are given the equation; […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2007 | Oct-Nov | (P1-9709/01) | Q#8

Hits: 281 Question The equation of a curve is .     i.       Express  and  in terms of .    ii.       Find the  coordinates of the two stationary points and determine the nature of each stationary point. Solution      i.   We are given the equation; For the given case; Rule for differentiation of  is: Rule for differentiation of  is: Rule for differentiation […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2007 | May-Jun | (P1-9709/01) | Q#10

Hits: 540 Question The equation of a curve is  . i.       Obtain expressions for  and .    ii.       Find the coordinates of the stationary point on the curve and determine the nature of the stationary point.   iii.       Show that the normal to the curve at the point (−2, −2) intersects the x-axis at the point (−10, 0).   iv.       Find the area of the […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2007 | May-Jun | (P1-9709/01) | Q#1

Hits: 478 Question Find the value of the constant  for which the line  is a tangent to the curve . Solution Since line is tangent to the curve i.e. both intersect each other at a single point. To find that point; If two lines (or a line and a curve) intersect each other at a point then that point […]