# 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#6

Question The equation of a curve is        i.       Show, by differentiation, that the gradient of the curve is always negative.    ii.       Use the trapezium rule with 2 intervals to estimate the value of giving your answer correct to 2 significant figures.     iii.   The diagram shows a […]

# 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#7

Question The parametric equations of a curve are      i. Show that    ii. Find the equation of the tangent to the curve at the point where .   iii. For the part of the curve where , find the coordinates of the points where the tangent  is parallel to the x-axis. Solution      i.   We are required to show that […]

# 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

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 value of […]

# 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#4

Question i. Show that the equation Can be written in the form ii. Hence solve the equation to For . Solution i. We are given; We apply following two addition formulae on both sides of given equation. Therefore; Since; ii. We are required to solve following equation doe . We have found in (i) that […]

# 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#3

Question The diagram shows the curve . The shaded region R is bounded by the curve and by the  lines x = 0, y = 0 and x = p.             i.       Find, in terms of p, the area of R.           ii.       Hence calculate the value of p for which the area of R is equal to 5. Give your answer […]

# 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#2

Question The polynomial  is denoted by .     i.       Find the value of the constant  for which    ii.       Hence solve the equation , giving your answers in an exact form. Solution     i.   We are given that; We are also given that; We equate the two equations. We can expand the R.H.S. Comparing terms on both sides of the […]

# 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#1

Question Solve the inequality . Solution SOLVING INEQUALITY: PIECEWISE Let, . We can write it as; We have to consider both moduli separately and it leads to following cases; When If then above four intervals translate to following with their corresponding inequality; When When When If then above four intervals translate to following with […]