# 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#8

Question      i.                     a.   Prove the identity                  b.   Hence prove that    ii.       By differentiating , show that if  then .     iii.       Using the results of parts (i) and (ii), find the […]

# 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

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 given by […]

# 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#6

Question Find the exact coordinates of the point on the curve   at which . Solution We are given that; We are required to find; Second derivative is the derivative of the derivative. If we have derivative of the curve   as , then  expression for the second derivative of the curve  is; Therefore […]

# 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#5

Question Show that Solution We are required to show that; Rule for integration of  is: For ; Rule for integration of  is: This integral is valid only when . Division Rule; Power Rule; Division Rule;

# 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#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;    ii.   We are required to solve following equation […]

# 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#2

Question The polynomial , where a is a constant, is denoted by . It is given that is a factor of . i.       Find the value of  .    ii.       When  has this value, factorise  completely. Solution      i.  We are given that;    We are also given that is a factor […]

# 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#3

Question The variables x and y satisfy the equation y = A(b-x), where A and b are constants. The graph of ln y  against ln x is a straight line passing through the points (0, 1.3) and (1.6, 0.9), as shown in the  diagram. Find the values of A and b, correct to 2 […]

# 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#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 […]