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Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2003 | Oct-Nov | (P2-9709/02) | Q#6

Hits: 168   Question The diagram shows the curve y=(4−x)ex and its maximum point M. The curve cuts the x-axis at A  and the y-axis at B.     i.       Write down the coordinates of A and B.    ii.       Find the x-coordinate of M.   iii.       The point P on the curve has x-coordinate p. The tangent to the curve at P passes […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2003 | Oct-Nov | (P2-9709/02) | Q#5

Hits: 174   Question      i.       By sketching a suitable pair of graphs, for x < 0, show that exactly one root of the equation    is negative.    ii.       Verify by calculation that this root lies between -1.0 and -0.5.   iii.       Use the iterative formula to determine the root correct to 2 decimal places, showing the result of each iteration. […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2003 | Oct-Nov | (P2-9709/02) | Q#2

Hits: 108     Question Two variable quantities x and y are related by the equation where a and k are constants. Four pairs of values of x and y are measured experimentally. The result of plotting ln y against x is  shown in the diagram. Use the diagram to estimate the values of a and k. […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2003 | Oct-Nov | (P2-9709/02) | Q#1

Hits: 106     Question Solve the inequality . Solution SOLVING INEQUALITY: PIECEWISE Let, . It can be written as; We have to deal with two separate cases; When ; When Therefore; Therefore; Hence, Hence, We have the inequality; It can be written in standard form as; We have to consider two separate cases; When […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2003 | May-Jun | (P2-9709/02) | Q#7

Hits: 183 Question The parametric equations of a curve are      i. Show that    ii. Find the equation of the tangent to the curve at the point where .   iii. For the part of the curve where , find the coordinates of the points where the tangent  is parallel to the x-axis. Solution      i.   We are required to […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2003 | May-Jun | (P2-9709/02) | Q#5

Hits: 155     Question      i.       By sketching a suitable pair of graphs, show that the equation Has exactly one root.    ii.       Verify by calculation that this root lies between 1.0 and 1.4.   iii.       Use the iterative formula  to determine the root correct to 2 decimal places, showing the […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2003 | May-Jun | (P2-9709/02) | Q#1

Hits: 142     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 […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2002 | Oct-Nov | (P2-9709/02) | Q#4

Hits: 185   Question      i.       By sketching a suitable pair of graphs, show that there is only one value of x in  the interval    that is a root of the equation    ii.       Verify by calculation that this root lies between 1 and 1.5.   iii.       Show that this value of x is also a root of the equation   iv.       Use […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2002 | Oct-Nov | (P2-9709/02) | Q#1

Hits: 314     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 […]