# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2011 | Oct-Nov | (P2-9709/23) | Q#7

Question The diagram shows the curve . The curve has a gradient of 3 at the point P.      i.       Show that the x-coordinate of P satisfies the equation    ii.       Verify that the equation in part (i) has a root between x = 3.1 and x = 3.3.   iii.       Use the […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2011 | Oct-Nov | (P2-9709/22) | Q#5

Question      i.       By sketching a suitable pair of graphs, show that the equation Where x is in radians, has only one root for .      ii.       Verify by calculation that this root lies between x=1.1 and x=1.2.   iii.       Use the iterative formula to determine this root correct to 2 significant […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2011 | Oct-Nov | (P2-9709/21) | Q#6

Question      i.       Verify by calculation that the cubic equation has a root that lies between x=0.7 and x=0.8.    ii.       Show that this root also satisfies an equation of the form where the values of a and b are to be found.   iii.       With these values of a and b, use the […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2011 | May-Jun | (P2-9709/23) | Q#3

Question The sequence defined by , Converges to the value .      i.       Find the value of correct to 3 decimal places. Show your working, giving each calculated  value of the sequence to 5 decimal places.    ii.       Find, in the form , an equation of which is a root. Solution      i.   […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2011 | May-Jun | (P2-9709/22) | Q#3

Question The sequence defined by , Converges to the value .      i.       Find the value of correct to 3 decimal places. Show your working, giving each calculated  value of the sequence to 5 decimal places.    ii.       Find, in the form , an equation of which is a root. Solution      i.   […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2011 | May-Jun | (P2-9709/21) | Q#7

Question      i.       By sketching a suitable pair of graphs, show that the equation has exactly two real roots.    ii.       Show by calculation that this root lies between 1.2 and 1.3.   iii.       Show that this root also satisfies the equation   iv.       Use an iteration process based on the equation in […]