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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

Hits: 174   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 , […]

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

Hits: 163   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 […]

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

Hits: 153   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; […]

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

Hits: 184   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 […]

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

Hits: 174   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 […]

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

Hits: 165   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 […]

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

Hits: 310     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 […]