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# 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#5

Hits: 90  Question i.    Sketch, on the same diagram, the graphs of  and  for . ii.       Verify that  is a root of the equation , and state the other root of this equation for which .  iii.       Hence state the set of values of , for , for which Solution i.   We are required to sketch  and  for . First we sketch  for […]

# 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#9

Hits: 58 Question The diagram shows a quadrilateral ABCD in which the point A is , the point B is  and the point C is . The diagonals AC and BD intersect at M. Angle   and . Calculate     i.        the coordinates of M and D,    ii.       the ratio . Solution     i.   First we find […]

# 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: 72 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: 61 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 | (P1-9709/12) | Q#6

Hits: 189 Question The diagram shows a circle  touching a circle  at a point . Circle  has centre A and radius 6cm, and circle  has centre B and radius 10 cm. Points D and E lie on  and  respectively and DE is parallel to AB. Angle  radians and angle  radians.     i.       By considering the perpendicular distances of D […]

# 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#4

Hits: 66 Question The equation of a curve is  and the equation of a line is , where  is a constant.     i.       In the case where , find the coordinates of the points of intersection of the line and the curve.    ii.       Find the value of  for which the line is a tangent to the curve. Solution     i.   […]

# 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#3

Hits: 76 Question Relative to an origin , the position vectors of points A and B are given by and where  is a constant.      i.       Find the value of  for which angle AOB =.    ii.       In the case where , find the vector which has magnitude 28 and is in the same direction as . Solution      i.   […]

# 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#2

Hits: 53 Question The functions  and  are defined for  by where  and  are constants. Given that  and , find      i.       the values of  and ,    ii.       an expression for . Solution i.   We are given that; We need to find  and . First we find ; We have; For ; Now we evaluate ; We are given that; Therefore; Now […]

# 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#1

Hits: 96 Question      i.       Find the first 3 terms in the expansion of , in ascending powers of .    ii.       Use the result in part (i) to find the coefficient of  in the expansion of  . Solution i.   First rewrite the given expression in standard form. Expression for the Binomial expansion of  is: In the given case: Hence; ii. […]

# 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#10

Hits: 118 Question a)   An arithmetic progression contains 25 terms and the first term is −15. The sum of all the terms in  the progression is 525. Calculate            i.       the common difference of the progression         ii.       the last term in the progression       iii.       the sum of all the positive terms in the progression.  […]