Hits: 86

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2014 | May-Jun | (P2-9709/23) | Q#8

Hits: 86 Question The diagram shows the curve , for and its maximum point M.     i.       Show that    ii.       Hence find the x-coordinate of M, giving your answer correct to 2 decimal places.. Solution      i.   We are given that; Therefore; We apply product rule to find the derivative. If  and  are […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2014 | May-Jun | (P2-9709/23) | Q#1

Hits: 70 Question Solve the inequality . Solution SOLVING INEQUALITY: 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; It cannot be solved for x.   Hence, the only solution […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2014 | May-Jun | (P2-9709/22) | Q#8

Hits: 116 Question The diagram shows the curve , for and its maximum point M. i.       Show that      ii.       Hence find the x-coordinate of M, giving your answer correct to 2 decimal places.. Solution      i.   We are given that; Therefore; We apply product rule to find the derivative. If  and  are […]

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

Hits: 77     Question Solve the inequality . Solution SOLVING INEQUALITY: 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; It cannot be solved for x. Hence, the only […]

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

Hits: 76     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 […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2014 | May-Jun | (P2-9709/21) | Q#1

Hits: 180     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 […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2014 | June | Q#8

Hits: 15   Question Solve each of the following inequalities: a.   b.   . Solution a.   b.     We solve the following equation to find critical values of ; Now we have two options; Hence the critical points on the curve for the given condition are  & . Standard form of quadratic equation is; The graph of quadratic […]

Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2014 | June | Q#4

Hits: 43   Question a.                                i.       Express  in the form  where p and q are integers.                          ii.       Hence write down the maximum value of . b.                                i.       Factorise  .                            ii.       Sketch the curve with equation  , stating the values of x where the curve  crosses the x-axis and the […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2014 | May-Jun | (P1-9709/11) | Q#2

Hits: 734   Question      i.       Express  in the form  .    ii.       Hence, or otherwise, find the set of values of  satisfying . Solution i.   We have the expression; We use method of “completing square” to obtain the desired form. We complete the square for the terms which involve . We have the algebraic formula; For the given case we can compare […]