# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2007 | Oct-Nov | (P2-9709/02) | Q#8

Question The diagram shows the curve and its maximum point M.      i.       Find the x-coordinate of M.    ii.       Show that the tangent to the curve at the point where x = 1 passes through the origin.   iii.       Use the trapezium rule with two intervals to estimate the value […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2007 | Oct-Nov | (P2-9709/02) | Q#7

Question      i.       Prove the identity    ii.       Using the identity, or otherwise, find the exact value of Solution      i.   We are given that; We have algebraic formula; Since we know that ; We have the trigonometric identity; From this we can write ; Since we know that ; […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2007 | Oct-Nov | (P2-9709/02) | Q#6

Question i.       Express  in the form , where  and , giving the  exact value of R and the value of  correct to 2 decimal places.    ii.       Hence solve the equation Giving all solutions in the interval . Solution      i.   We are given the expression; We are required to write […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2007 | Oct-Nov | (P2-9709/02) | Q#4

Question The equation of a curve is y = 2x − tan x, where x is in radians. Find the coordinates of the stationary points of the curve for which Solution We are required to find the coordinates of stationary points of the curve with equation; A stationary point on the curve is […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2007 | Oct-Nov | (P2-9709/02) | Q#2

Question The sequence of values given by the iterative formula With initial value , converges to .      i.       Use this iterative formula to find correct to 2 decimal places, showing the result of each  iteration to 4 decimal places.    ii.       State an equation that is satisfied by  , and hence […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2007 | Oct-Nov | (P2-9709/02) | Q#1

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

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2007 | Oct-Nov | (P2-9709/02) | Q#5

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, solve the equation . Solution      i.  We are given that;    We are also given that […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2007 | Oct-Nov | (P2-9709/02) | Q#3

Question Solve the inequality . Solution SOLVING INEQUALITY: PIECEWISE Let  and , then; We consider two separate cases. When When We have the inequality; We have to consider two separate cases; When When Therefore the inequality will hold for ; Hence; SOLVING INEQUALITY: ALGEBRAICALLY Let, . Since given equation/inequality is of the […]