Hits: 64

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2013 | May-Jun | (P2-9709/22) | Q#8

Hits: 64   Question      i.       Prove the identity    ii.       Hence solve the equation For . Solution      i.   We are required to prove the identity; We know that; Therefore;    provided that    ii.   We are required to solve the equation; From (i) we know that; Therefore; Since , therefore Let […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2013 | May-Jun | (P2-9709/22) | Q#7

Hits: 56     Question A.  Find the exact area of the region bounded by the curve , the x-axis and the lines   and . The diagram shows the curve , for and its minimum point M. Find the exact x- coordinate of M. Solution A.    We are required to find area under the […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2013 | May-Jun | (P2-9709/22) | Q#6

Hits: 56     Question      i.       By sketching a suitable pair of graphs, show that the equation   has only one root.    ii.       Verify by calculation that this root lies between x = 0.7 and x = 0.8.   iii.       Show that this root also satisfies the equation   iv.       Use the iterative […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2013 | May-Jun | (P2-9709/22) | Q#1

Hits: 27 Question A curve is such that . The point (3, 2) lies on the curve. Find the equation of the curve.  Solution We can find equation of the curve from its derivative through integration; For the given case; Therefore; Rule for integration of  is: This integral is valid only when . If a […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2013 | May-Jun | (P2-9709/22) | Q#4

Hits: 79   Question The variables x and y satisfy the relation .      i.       By taking logarithms, show that the graph of y against x is a straight line.    ii.       Find the exact value of the gradient of this line and state the coordinates of the point at which  the line […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2013 | May-Jun | (P2-9709/22) | Q#3

Hits: 152   Question    i.       The polynomial , where  is a constant, is denoted by . It is given that   is a factor of . Find the value of .    ii.       When  has this value, find the remainder when  is divided by . Solution      i.  We are given that; We […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2013 | May-Jun | (P2-9709/22) | Q#2

Hits: 74     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 […]