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# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2010 | Oct-Nov | (P2-9709/23) | Q#2

Hits: 2   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, giving 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 2010 | Oct-Nov | (P2-9709/22) | Q#6

Hits: 8     Question The curve with equation intersects the line y = x + 1 at the point P.      i.       Verify by calculation that the x-coordinate of P lies between 1.4 and 1.6.    ii.       Show that the x-coordinate of P satisfies the equation   iii.       Use the iterative […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2010 | Oct-Nov | (P2-9709/21) | Q#6

Hits: 9     Question The curve with equation intersects the line y = x + 1 at the point P.      i.       Verify by calculation that the x-coordinate of P lies between 1.4 and 1.6.    ii.       Show that the x-coordinate of P satisfies the equation   iii.       Use the iterative […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2010 | May-Jun | (P2-9709/23) | Q#6

Hits: 6   Question      i.       By sketching a suitable pair of graphs, show that the equation has only one root.    ii.       Verify by calculation that this root lies between 1.3 and 1.4.   iii.       Show that, if a sequence of values given by the iterative formula converges, then it converges […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2010 | May-Jun | (P2-9709/22) | Q#6

Hits: 1     Question      i.       By sketching a suitable pair of graphs, show that the equation has only one root.    ii.       Verify by calculation that this root lies between 1.3 and 1.4.   iii.       Show that, if a sequence of values given by the iterative formula converges, then it […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2010 | May-Jun | (P2-9709/21) | Q#7

Hits: 8     Question      i.       By sketching a suitable pair of graphs, show that the equation  has only one root.    ii.       Verify, by calculation that this root lies between x=0 and x=0.5.   iii.       Show that, if a sequence of values given by the iterative formula converges, then it […]

# 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: 14   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 | Oct-Nov | (P2-9709/21) | Q#7

Hits: 3   Question The diagram shows the curve y = e– x. The shaded region R is bounded by the curve and the lines y = 1 and x = p, where p is a constant.      i. Find the area of R in terms of p.    ii. Show that if the area […]

# 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: 8     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: 20   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: 11   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: 11   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: 5   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: 5   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: 12     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: 65     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: 28   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: 33     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: 36   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: 69   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. […]