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Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2009 | Oct-Nov | (P2-9709/22) | Q#7

Hits: 51   Question The diagram shows the curve y = x2 cos x, for , and its maximum point M.     i.       Show by differentiation that the x-coordinate of M satisfies the equation    ii.       Verify by calculation that this equation has a root (in radians) between 1 and 1.2.   iii. […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2009 | May-Jun | (P2-9709/02) | Q#7

Hits: 53     Question The diagram shows the curve and its minimum point M.      i.       Find the exact coordinates of M.    ii.       Show that the curve intersects the line y = 20 at the point whose x-coordinate is the root of  the equation   iii.       Use the iterative formula […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2008 | Oct-Nov | (P2-9709/02) | Q#7

Hits: 61   Question      i.       By sketching a suitable pair of graphs, show that the equation Where x is in radians, has only one root in the interval .    ii.       Verify by calculation that this root lies between 0.5 and 1.   iii.       Show that, if a sequence of values […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2008 | May-Jun | (P2-9709/02) | Q#8

Hits: 53   Question The constant , where , is such that     i.       Find an equation satisfied by , and show that it can be written in the form ii.       Verify, by calculation, that the equation  ) has a root between 3 and 3.5.    iii.       Use the iterative […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2007 | Oct-Nov | (P2-9709/02) | Q#2

Hits: 51   Question The sequence of values given by the iterative formula With initial value , converges to .      i.       Use this iterative formula to find correct to 2 decimal places, showing the result of each  iteration to 4 decimal places.    ii.       State an equation that is satisfied by  , […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2007 | May-Jun | (P2-9709/02) | Q#5

Hits: 50   Question      i. By sketching a suitable pair of graphs, show that the equation Where x is in radians, has only one root in the interval .    ii. Verify by calculation that this root lies between 1.0 and 1.2.   iii. Show that this root also satisfies the equation   iv. […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2006 | Oct-Nov | (P2-9709/02) | Q#5

Hits: 31   Question The diagram shows a chord joining two points, A and B, on the circumference of a circle with centre  O and radius r. The angle AOB is radians, where . The area of the shaded  segment is one sixth of the area of the circle.     i.       Show that  satisfies […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2006 | May-Jun | (P2-9709/02) | Q#6

Hits: 44     Question      i. By sketching a suitable pair of graphs, show that there is only one value of x that is a root of the  equation    ii. Verify, by calculation, that this root lies between 1 and 2.   iii. Show that, if a sequence of values given by the […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2005 | Oct-Nov | (P2-9709/02) | Q#5

Hits: 99     Question      i.       By sketching a suitable pair of graphs, show that there is only one value of x that is a root of  the equation    ii. Verify by calculation that this root lies between 1 and 2.   iii. Show that this root also satisfies the equation   […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2005 | May-Jun | (P2-9709/02) | Q#3

Hits: 68   Question The sequence of values given by the iterative formula With initial value , converges to .      i.       Use this iterative formula to find correct to 2 decimal places, showing the result of each  iteration.    ii.       State an equation satisfied by , and hence find the exact value […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2004 | Oct-Nov | (P2-9709/02) | Q#6

Hits: 69     Question      i.       By sketching a suitable pair ofgraphs, 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 0.8 and 0.9 radians.   iii.       Show that this value […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2004 | May-Jun | (P2-9709/02) | Q#2

Hits: 81   Question The sequence of values given by the iterative formula With initial value , converges to .      i. Use this iterative formula to find correct to 3 decimal places, showing the result of each  iteration.    ii.  State an equation satisfied by , and hence show that the exact value of […]

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: 110   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 | May-Jun | (P2-9709/02) | Q#5

Hits: 75     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 2002 | Oct-Nov | (P2-9709/02) | Q#4

Hits: 109   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 […]