# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2014 | Oct-Nov | (P2-9709/22) | Q#7

Question i.       Express  in the form , where  and , giving the  value of  correct to 2 decimal places.    ii.       Hence solve the equation for .   iii.       Find the greatest possible value of as  varies, and determine the smallest positive value of  for which this greatest value occurs. Solution      i.   We […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2014 | Oct-Nov | (P2-9709/22) | Q#6

Question The polynomial is defined by The diagram shows the curve which crosses the x-axis at  and .      i.       Divide by a suitable linear factor and hence show that is a root of the equation    ii.       Use the iterative formula to find correct to 2 decimal places. Give the   result of each iteration […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2014 | Oct-Nov | (P2-9709/22) | Q#5

Question The diagram shows part of the curve and its maximum point M. The shaded region is bounded by the curve, the axes and the line  through M parallel to the y-axis.      i.       Find the exact value of the x-coordinate of M.    ii.       Find the exact value of the area of […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2014 | Oct-Nov | (P2-9709/22) | Q#3

Question A curve has equation Find the equation of the normal to the curve at the point (1, 2). Give your answer in the form ax + by  + c = 0, where a, b and c are integers. Solution We are given equation of the curve as; We are required to find the equation […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2014 | Oct-Nov | (P2-9709/22) | Q#2

Question i.       Find where a is a positive constant.    ii.       Deduce the value of Solution      i.  We are given that; Rule for integration of  is: Rule for integration of , or ;      ii.   We are required to deduce the value of. From (i) we have demonstrated; Therefore replacing  with;

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2014 | Oct-Nov | (P2-9709/22) | Q#4

Question a.   Find the value of x satisfying the equation 2 ln (x – 4) − ln x = ln 2. b.   Use logarithms to find the smallest integer satisfying the inequality 1.4y > 1010 Solution a.   We are given; Power Rule; Division Rule; Taking anti-logarithm of both sides;  for any We have […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2014 | Oct-Nov | (P2-9709/22) | Q#1

Question Solve the equation. Solution SOLVING EQUATION: PIECEWISE Let, . We have to consider both moduli separately and it leads to following cases;  OR We have the equation; We have to consider both moduli separately and it leads to following cases; Hence, the only solution for the given equation is; SOLVING EQUATION: ALGEBRAICALLY […]