Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2016 | Oct-Nov | (P2-9709/23) | Q#7

Question      i.       Express in the form , where a and b are integers.    ii.       Hence express in the form where R > 0 and  .   iii.       Using the result of part (ii), solve the equation  for . Solution      i.   We are given the expression;   provided that   provided that […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2016 | Oct-Nov | (P2-9709/23) | Q#6

Question A curve has parametric equations      i.       Find an expression for in terms of t.    ii.       Find the exact value of at the stationary point.   iii.       Find the gradient of the curve at the point where it crosses the x-axis. Solution      i.   We are required to find  for the parametric […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2016 | Oct-Nov | (P2-9709/23) | Q#5

Question The diagram shows the curve for 0 ≤ x ≤ 6. The region bounded by the curve and the lines x = 0, x = 6 and y = 0 is denoted by R.        i.       Use the trapezium rule with 2 strips to find an estimate of the area of R, giving your […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2016 | Oct-Nov | (P2-9709/23) | Q#4

Question The polynomial is defined by  where  is a constant. It is given that  is a factor of     i.       Use the factor theorem to find the value of .    ii.       Factorise p(x) and hence show that the equation p(x) = 0 has only one real root.   iii.       Use logarithms to […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2016 | Oct-Nov | (P2-9709/23) | Q#3

Question      i.       Find    ii.       Without using a calculator, find the exact value of Solution      i.   We are required to find; We know that ; Therefore; Hence; Rule for integration of  is: Rule for integration of  is: Rule for integration of  is:    ii.   We are required to find the exact […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2016 | Oct-Nov | (P2-9709/23) | Q#2

Question The variables x and y satisfy the equation y = Kxp, where K and p are constants. The graph of ln y  against ln x is a straight line passing through the points (1.28, 3.69) and (2.11, 4.81), as shown in  the diagram. Find the values of K and p correct to 2 decimal […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2016 | Oct-Nov | (P2-9709/23) | Q#1

Question The sequence of values given by the iterative formula With initial value , converges to .      i.       Determine the value of correct to 3 decimal places, giving the result of each iteration to 5  decimal places.    ii.       State an equation satisfied by and hence find the exact value of . Solution      […]