# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2002 | Oct-Nov | (P2-9709/02) | Q#7

Question The equation of a curve is      i.       Show that    ii.       Find the coordinates of the points on the curve where the tangent is parallel to the x-axis. Solution      i.   We are given; We are required to find . To find  from an implicit equation, differentiate each term with respect to , using the […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2002 | Oct-Nov | (P2-9709/02) | Q#6

Question a)   Find the value of b)    The diagram shows part of the curve  . The shaded region R is bounded by the curve and by  the lines x =1, y = 0 and x = p. i.       Find, in terms of p, the area of R. ii.       Hence find, correct to 1 decimal place, the value of p […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2002 | Oct-Nov | (P2-9709/02) | Q#5

Question The angle x, measured in degrees, satisfies the equation      i.       By expanding each side, show that the equation may be simplified to    ii.       Find the two possible values of x lying between  and .   iii.       Find the exact value of , giving your answer as a fraction. Solution      i.   We are given; We apply […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2002 | Oct-Nov | (P2-9709/02) | Q#4

Question      i.       By sketching a suitable pair of graphs, 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 1 and 1.5.   iii.       Show that this value of x is also a root of 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 2002 | Oct-Nov | (P2-9709/02) | Q#3

Question      i.       Express  in terms of y, where    ii.       Hence solve the equation expressing your answers for x in terms of logarithms where appropriate. Solution      i.   We are given that , therefore; Hence,  where .    ii.   We are required to solve the equation; Let’s substitute ; As demonstrated in (i),  when , therefore; It is evident […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2002 | Oct-Nov | (P2-9709/02) | Q#2

Question The polynomial  is denoted by . It is given that  is a factor of , and that  when  is divided by  the remainder is -5. Find the values of  and . Solution We are given that; We are also given that  is a factor of . When a polynomial, , is divided by , and […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2002 | 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 […]