Year 2012 October November (P2-9709/21) Archives — O/A Level Solutions

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2012 | Oct-Nov | (P2-9709/23) | Q#3

    Question Solve the equation , for . Solution We are required to solve; Therefore; We have the trigonometric identity; Let , then; Since , therefore; Using calculator we can find that; Properties of Domain Range Periodicity Odd/Even Translation/ Symmetry We utilize the periodicity/symmetry property of   to find other solutions (roots):  But it […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2012 | Oct-Nov | (P2-9709/21) | Q#8

    Question i.       By differentiating , show that if  θ then .    ii.       Hence show that Giving the values of a and b.   iii.       Find the exact value of Solution      i.   We are given that; We are required to show that; Since   provided that ; Therefore; If  and  are […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2012 | Oct-Nov | (P2-9709/21) | Q#7

  Question The polynomial , where a and b are constants, is denoted by . It is given that  when  is divided by  the remainder is 4, and that when  is divided by the remainder is 12.     i.       Find the values of  and .    ii.       When a and b have these values, find […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2012 | Oct-Nov | (P2-9709/21) | Q#6

    Question      i.       Use the trapezium rule with 2 intervals to estimate the value of Giving your answer correct to 2 decimal places.    ii.       Find Solution      i.   We are required to apply Trapezium Rule to evaluate; The trapezium rule with  intervals states that; We are given that there are two […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2012 | Oct-Nov | (P2-9709/21) | Q#4

  Question The parametric equations of a curve are for t < 0.      i.       Show that in terms of t.    ii.       Find the exact coordinates of the only point on the curve at which the gradient is 3. Solution      i.   We are required to find  for the parametric equations given below; […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2012 | Oct-Nov | (P2-9709/21) | Q#3

    Question Solve the equation , for . Solution We are required to solve; Therefore; We have the trigonometric identity; Let , then; Since , therefore; Using calculator we can find that; Properties of Domain Range Periodicity Odd/Even Translation/ Symmetry We utilize the periodicity/symmetry property of   to find other solutions (roots):  But it […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2012 | Oct-Nov | (P2-9709/21) | Q#1

  Question Solve the inequality . Solution SOLVING INEQUALITY: PIECEWISE Let, . We can write it as; We have to consider both moduli separately and it leads to following cases; When If then above four intervals translate to following with their corresponding inequality; When When When If then above four intervals translate to following with […]