Hits: 171

# 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

Hits: 171   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. […]

# 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

Hits: 313     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 […]

# 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

Hits: 184     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 […]

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

Hits: 188   Question      i.By expanding , show that    ii.Hence, or otherwise, show that Solution      i.   We have; We apply following addition formula. Therefore; We apply following two formulae. We have the trigonometric identity; Therefore, we can replace; Hence;    ii.   We are required to show that; As we have […]

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

Hits: 219   Question i.       Express  in the form , where  and , giving the value of  correct to 2 decimal places.    ii.       Hence solve the equation Giving all solutions in the interval  correct to 1 decimal place.   iii.       Write down the least value of  as  varies. Solution      i. […]