Hits: 142

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2010 | May-Jun | (P2-9709/22) | Q#8

Hits: 142 Question i.       Prove the identity    ii.       Hence solve the equation For . Solution      i.   We are given that; We utilize following two addition formulae;    ii.   We are required to solve; As demonstrated in (i); Therefore; Since   provided that ; Since ; Therefore, we solve  for […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2010 | May-Jun | (P2-9709/22) | Q#6

Hits: 147     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 1.3 and 1.4.   iii.       Show that, if a sequence of values given by the iterative formula converges, then it […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2010 | May-Jun | (P2-9709/22) | Q#5

Hits: 177     Question The equation of a curve y=x3e-x.      i.       Show that the curve has a stationary point where x = 3.    ii.       Find the equation of the tangent to the curve at the point where x = 1. 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 2010 | May-Jun | (P2-9709/22) | Q#4

Hits: 130     Question a.   Show that b.   By using an appropriate trigonometrical identity, find the exact value of Solution a.     We are required to show that; Rule for integration of  is:   b.     We are required to find exact value of; We know that , therefore; Hence; Rule for integration of […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2010 | May-Jun | (P2-9709/22) | Q#2

Hits: 151   Question The diagram shows the part of the curve y = xe-x. The shaded region R is bounded by the curve and by the lines x = 2, x = 3 and y = 0.      i.       Use the trapezium rule with two intervals to estimate the area of R, giving […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2010 | May-Jun | (P2-9709/22) | Q#7

Hits: 111   Question The polynomial , where a and b are constants, is denoted by . It is given that when  is divided by  the remainder is 30, and that when  is divided by  the remainder is 18. i.       Find the values of  and .    ii.       When a and b have […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2010 | May-Jun | (P2-9709/22) | Q#3

Hits: 134   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 […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2010 | May-Jun | (P2-9709/22) | Q#1

Hits: 188   Question Given that 13x = (2.8)y, use logarithms to show that y = kx and find the value of k correct to 3  significant figures. Solution We are given; Taking natural logarithm of both sides; Power Rule;