Hits: 484

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2011 | May-Jun | (P1-9709/11) | Q#3

Hits: 484   Question i.       Sketch the curve ii.      The region enclosed by the curve, the x-axis and the y-axis is rotated through 360◦ about the x-axis. Find the volume obtained, giving your answer in terms of . Solution      i.   Standard form of quadratic equation is; The graph of quadratic equation is a parabola. If […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2011 | Oct-Nov | (P1-9709/13) | Q#10

Hits: 447 Question The diagram shows the line  and the curve , meeting at  and .     i.       Find the area of the shaded region.    ii.       Find the volume obtained when the shaded region is rotated through 360◦ about the y-axis. Solution     i.   It is evident from the diagram that; To find the area of region under the curve […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2011 | Oct-Nov | (P1-9709/13) | Q#8

Hits: 369 Question A curve  has a stationary point at . It is given that, where k is a constant. i.       Show that  and hence find the x-coordinate of the other stationary point, Q.    ii.       Find  and determine the nature of each of the stationary points P and Q.   iii.       Find . Solution i.   A stationary point […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2011 | Oct-Nov | (P1-9709/12) | Q#8

Hits: 460 Question The equation of a curve is . Find     i.       an expression for  and the coordinates of the stationary point on the curve,    ii.       the volume obtained when the region bounded by the curve and the x-axis is rotated through  about the x-axis. Solution i.   Gradient (slope) of the curve is the derivative of equation of […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2011 | Oct-Nov | (P1-9709/12) | Q#7

Hits: 461 Question A curve is such that   . The line  is the normal to the curve at the point  on the curve. Given that the x-coordinate of  is positive, find     i.       the coordinates of P,    ii.       the equation of the curve. Solution i.   We are given that equation of the line is; We can rearrange the equation of the […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2011 | Oct-Nov | (P1-9709/11) | Q#10

Hits: 607 Question The diagram shows the curvemeeting the x-axis at A and the y-axis at B. The y-coordinate of the point C on the curve is 3.     i.       Find the coordinates of B and C.    ii.       Find the equation of the normal to the curve at C.   iii.       Find the volume obtained when the shaded region is rotated through  about […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2011 | May-Jun | (P1-9709/13) | Q#4

Hits: 340 Question a)   Differentiate  with respect to . b)   Find   and hence find the value of a . Solution a)   We are given that; Rule for differentiation of  is: Rule for differentiation of  is: b)     We are given that; Rule for integration of  is: Now we find the value of;

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2011 | May-Jun | (P1-9709/12) | Q#11

Hits: 1381 Question The diagram shows part of the curve . The curve has a maximum point at M and meets the x-axis at O and A.     i.       Find the coordinates of A and M.    ii.       Find the volume obtained when the shaded region is rotated through 360o about the x-axis, giving your answer in terms of . […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2011 | May-Jun | (P1-9709/12) | Q#1

Hits: 560 Question Find . Solution Rule for integration of  is: Rule for integration of  is:

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2011 | May-Jun | (P1-9709/11) | Q#7

Hits: 520 Question A curve is such that  and the point  lies on the curve. i.       Find the equation of the curve.    ii.       Find the set of values of x for which the gradient of the curve is less than . Solution     i.   We can find equation of the curve from its derivative through integration; For the given case; […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2011 | Oct-Nov | (P1-9709/11) | Q#4

Hits: 316 Question A function  is defined for  and is such that . The range of the function is given by .      i.       State the value of  for which  has a stationary value.    ii.       Find an expression for  in terms of . Solution i.   We have; The expression for  represents derivative of . A stationary point  on the curve  is the point where gradient of […]