# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2018 | May-Jun | (P2-9709/21) | Q#7

Question i.       Express  in the form , where  and . Give the value  of  correct to 4 decimal places.    ii.       Using your answer from part (i), solve the equation for . Solution      i.   We are given the expression; We are required to write it in the form; If  and are positive, then; […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2018 | May-Jun | (P2-9709/21) | Q#6

Question The cubic polynomial  is defined by where  is a constant. It is given that  is a factor of     i.       Use the factor theorem to find the value of  and hence factorise f(x) completely.    ii.       Hence, without using a calculator, solve the equation f(2x) = 3f(x). Solution      i.   We are given […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2018 | May-Jun | (P2-9709/21) | Q#5

Question The parametric equations of a curve are for .     i.       Find the gradient of the curve at the point for which  radian.    ii.       Find the value of at the point on the curve where the tangent is parallel to the y-axis. Solution      i.   We are required to find gradient of […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2018 | May-Jun | (P2-9709/21) | Q#4

Question The diagram shows the curve . The curve crosses the x-axis at the point P and has a maximum point M.      i.       Find the gradient of the curve at the point P.    ii.       Show that the x-coordinate of the point M satisfies the equation   iii.       Use an iterative formula based on […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2018 | May-Jun | (P2-9709/21) | Q#3

Question Without using a calculator, find the exact value of Solution      i.   We are given that; Rule for integration of  is: Rule for integration of , or ; Rule for integration of  is:

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2018 | May-Jun | (P2-9709/21) | Q#2

Question The variables x and y satisfy the equation , where A and B are constants. The graph of  ln y against x is a straight line passing through the points (2.2, 4.908) and (5.9, 11.008), as shown in  the diagram. Find the values of A and B, correct to 2 significant figures. Solution We […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2018 | May-Jun | (P2-9709/21) | Q#1

Question Solve the equation 3e2x−82ex +27 = 0, giving your answers in the form k ln 3. Solution We are given; Let ; Now we have two options. Since ; Taking natural logarithm of both sides;  for any Power Rule; Hence;