# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2015 | Oct-Nov | (P2-9709/22) | Q#7

Question      i.       Show that the exact value of    ii.   The diagram shows the curve  for . The shaded region is bounded by the  curve and the lines ,  and . Find the exact volume of the solid obtained when  the shaded region is rotated completely about the x-axis. Solution      i.   We […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2015 | Oct-Nov | (P2-9709/22) | Q#6

Question The diagram shows the curve with parametric equations for .     i.       Show that .    ii.       Find the equation of the tangent to the curve at the point where the curve crosses the positive y-axis. Give the answer in the form y = mx +c. 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 2015 | Oct-Nov | (P2-9709/22) | Q#5

Question Find the x-coordinates of the stationary points of the following curves:      i.      ii.   Solution      i.   First we are required to find the x-coordinate of the stationary points of the following curve. A stationary point on the curve is the point where gradient of the curve is equal to […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2015 | Oct-Nov | (P2-9709/22) | Q#4

Question The polynomial  is defined by where  is a constant. It is given that  is a factor of     i.       Use the factor theorem to show that .    ii.       When ;           a.  Factorise p(x) completely,           b.  Solve the equation  for . Solution      i. […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2015 | Oct-Nov | (P2-9709/22) | Q#3

Question The variables x and y satisfy the equation y = Kxm, where K and m are constants. The graph of ln y  against ln x is a straight line passing through the points (0.22, 3.96) and (1.32, 2.43), as shown in  the diagram. Find the values of K and m, correct to 2 significant […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2015 | Oct-Nov | (P2-9709/22) | Q#2

Question The sequence of values given by the iterative formula With initial value , converges to .        i.       Determine the value of correct to 3 decimal places, giving the result of each iteration to 5  decimal places.    ii.       State an equation satisfied by and hence find the exact value of . Solution […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2015 | Oct-Nov | (P2-9709/22) | Q#1

Question      i.       Solve the equation .    ii.       Hence, using logarithms, solve the equation , giving the answer correct to 3  significant figures. Solution     SOLVING EQUATION: ALGEBRAICALLY i.   Let, . We can write it as; We have to consider two separate cases; When When We have the equation; It […]