# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2010 | May-Jun | (P1-9709/12) | Q#11

Question The function  is defined for the domain .      i.       Solve the equation .    ii.       Sketch the graph of .   iii.       Find the set of values of  for which the equation  has no solution. The function  is defined for the domain .   iv.       State the largest value of  for which g has an inverse.    v.        For […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2010 | May-Jun | (P1-9709/12) | Q#10

Question The equation of a curve is .     i.        Find .    ii.      Find the equation of the tangent to the curve at the point where the curve intersects the y-axis.   iii.       Find the set of values of  for which  is an increasing function of . Solution     i.   Rule for differentiation of  is: Rule […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2010 | May-Jun | (P1-9709/12) | Q#9

Question The diagram shows the curve  and the line , which intersect at points A and B. Find the area of the shaded region. Solution It is evident from the diagram that; However, we need the limits to integrate the equations of line & curve.  It is evident that these limits are from point A to point B. Therefore we […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2010 | May-Jun | (P1-9709/12) | Q#8

Question A solid rectangular block has a square base of side  cm. The height of the block is  cm and the total surface area of the block is 96 cm2. i.       Express  in terms of  and show that the volume,  cm3, of the block is given by Given that  can vary,    ii.       find the stationary value of , […]

# PPast Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2010 | May-Jun | (P1-9709/12) | Q#5

Question Relative to an origin , the position vectors of the points  and  are given by and i.       Find the value of the  for which  is perpendicular to .    ii.       Find the value of the  for which magnitude of   is 7. Solution i.   If  and  & , then  and  are perpendicular. Therefore we need to find the scalar/dot product […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2010 | May-Jun | (P1-9709/12) | Q#4

Question In the diagram,  is the point  and  is the point . The line  passes through  and is parallel to . The line  passes through  and is perpendicular to . The lines  and  meet at . Find the coordinates of . Solution It is evident from the diagram that point C is the intersection of lines AC […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2010 | May-Jun | (P1-9709/12) | Q#2

Question The diagram shows part of the curve  , where a is a positive constant. Given that the volume obtained when the shaded region is rotated through  about the x-axis is , find the value of . Solution Expression for the volume of the solid formed when the shaded region under the curve  is rotated completely about the x-axis […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2010 | May-Jun | (P1-9709/12) | Q#

Question      i.       Show that the equation  can be written in the form    ii.       Solve the equation , for . Solution i.   We have the equation; We have the relation , therefore, ii.   To solve the equation , for , as demonstrated in (i), we can write the given equation as; To solve this equation for , Using calculator […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2010 | May-Jun | (P1-9709/12) | Q#3

Question The functions  and  are defined for  by      i.       Find the range of .    ii.       Find the value of the constant  for which the equation  has equal roots. Solution i.   Standard form of quadratic equation is; The graph of quadratic equation is a parabola. If  (‘a’ is positive) then parabola opens upwards and its vertex is the minimum […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2010 | May-Jun | (P1-9709/12) | Q#6

Question      i.     Find the first 3 terms in the expansion of  in ascending powers of .    ii.       Given that there is no term in  in the expansion of , find the value of the constant .   iii.       For this value of , find the coefficient of  in the expansion of . Solution i.   Expression for […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2010 | May-Jun | (P1-9709/12) | Q#7

Question a)   Find the sum of all the multiples of 5 between 100 and 300 inclusive. b)   A geometric progression has a common ratio of  and the sum of the first 3 terms is 35. Find  i.       the first term of the progression, ii.       the sum to infinity. Solution a)   It is evident that each next multiple of […]