# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2004 | Oct-Nov | (P2-9709/02) | Q#8

Question i.       Express  in the form , where  and , giving the exact values of R and .    ii.       Hence show that   iii.       By differentiating , show that if  then .   iv.       Using the results of parts (ii) and (iii), show that Solution      i.   We […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2004 | Oct-Nov | (P2-9709/02) | Q#7

Question The diagram shows the curve y = 2ex + 3e-2x. The curve cuts the y-axis at A.      i.       Write down the coordinates of A.    ii.       Find the equation of the tangent to the curve at A, and state the coordinates of the point where  this tangent meets the x-axis.   […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2004 | Oct-Nov | (P2-9709/02) | Q#6

Question      i.       By sketching a suitable pair ofgraphs, show that there is only one value of x in  the interval  that is a root of the equation    ii.       Verify by calculation that this root lies between 0.8 and 0.9 radians.   iii.       Show that this value of x […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2004 | Oct-Nov | (P2-9709/02) | Q#5

Question The curve with equation y = x2 ln x, where x > 0, has one stationary point.      i.       Find the x-coordinate of this point, giving your answer in terms of e.    ii.       Determine whether this point is a maximum or a minimum point. Solution      i.   We […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2004 | Oct-Nov | (P2-9709/02) | Q#3

Question Find the values of x satisfying the equation 3 sin 2x = cos x, for 0◦ ≤ x ≤ 90◦. Solution We are given; We apply following formula; Using calculator we can find that; Properties of Domain Range Odd/Even Periodicity Translation/ Symmetry It is evident from periodicity and symmetry properties of that […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2004 | Oct-Nov | (P2-9709/02) | Q#2

Question Solve the equation , where x ≠ 0. Solution We are given; Taking natural logarithm of both sides; Multiplication Rule; Power Rule; Taking anti-logarithm of both sides;  for any Therefore;

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2004 | 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 […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2004 | Oct-Nov | (P2-9709/02) | Q#4

Question The cubic polynomial  is denoted by . It is given that  is a factor of , and that when  is divided by  the remainder is -6. Find the values of  and . Solution We are given that;   We are also given that is a factor of . When a polynomial, , is divided […]