# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2009 | May-Jun | (P2-9709/02) | Q#8

Question a)   Find the equation of the tangent to the curve at the point where . b)                  i.       Find the value of the constant A such that           ii.       Hence show that Solution a.     We are given that curve with equation  and […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2009 | May-Jun | (P2-9709/02) | Q#7

Question The diagram shows the curve and its minimum point M.      i.       Find the exact coordinates of M.    ii.       Show that the curve intersects the line y = 20 at the point whose x-coordinate is the root of  the equation   iii.       Use the iterative formula with initial […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2009 | May-Jun | (P2-9709/02) | Q#5

Question Solve the equation sec x=4 – 2 tan2 x, giving all solutions in the interval . Solution We are required to solve the equation; Since , therefore, we can write . It is evident that it is a quadratic equation in . Let , then we can write; Now we have two options. […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2009 | May-Jun | (P2-9709/02) | Q#4

Question The parametric equations of a curve are x = 4 sin θ , y = 3 – 2 cos 2θ , where . Express  in terms of θ, simplifying your answer as far as possible. Solution We are required to express that   in terms of θ for the parametric equations given below; […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2009 | May-Jun | (P2-9709/02) | Q#3

Question The diagram shows the curve for values of x from 0 to 2.      i.       Use the trapezium rule with two intervals to estimate the value of giving your answer correct to 2 decimal places.    ii.       State, with a reason, whether the trapezium rule gives an under-estimate or an […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2009 | May-Jun | (P2-9709/02) | Q#6

Question The polynomial , where a and b are constants, is denoted by . It is given that   is a factor of , and that when  is divided by    the remainder is 4. i.       Find the values of  and . ii.       When  and  have these values, find the other two […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2009 | May-Jun | (P2-9709/02) | Q#2

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 […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2009 | May-Jun | (P2-9709/02) | Q#1

Question Given that , use logarithms to find the value of  correct to 3 significant figures. Solution We are given; Taking natural logarithm of both sides; Power Rule;