# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2012 | May-Jun | (P1-9709/11) | Q#2

Question Find the coefficient of  in the expansion of  .   Solution First rewrite the given expression in standard form. Expression for the Binomial expansion of  is: In the given case: Hence;     Hence the coefficient of   is .

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2012 | Oct-Nov | (P1-9709/13) | Q#1

Question Find the coefficient of  in the expansion of . Solution First rewrite the given expression in standard form. Expression for the general term in the Binomial expansion of  is: In the given case: Hence; Since we are looking for the term of   : we can  equate  Subsequently substituting  in: Since we are interested in the coefficient of ;

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2012 | Oct-Nov | (P1-9709/12) | Q#1

Question In the expansion of , the coefficient of  is -280. Find the value of the constant . Solution First rewrite the given expression in standard form. Expression for the general term in the Binomial expansion of  is: In the given case: Hence; Since we are looking for the term of   : we can  equate Subsequently substituting  in: Since the coefficient […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2012 | Oct-Nov | (P1-9709/11) | Q#4

Question      i.       Find the first 3 terms in the expansion of , in ascending powers of .    ii.       Hence find the coefficient of  in the expansion of . Solution i.   First rewrite the given expression in standard form. Expression for the Binomial expansion of  is: In the given case: Hence; ii.   First we know from (i) that Therefore: […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2012 | May-Jun | (P1-9709/13) | Q#3

Question The first three terms in th expansion of  , in the ascending powers of  , are  . Find the values of the constants   and . Solution Expression for the Binomial expansion of  is: In the given case: Hence; Now We know that first three terms in th expansion of  are ; Comparing the given and derived expansions. First […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2012 | May-Jun | (P1-9709/12) | Q#3

Question The coefficient of  in the expansion of  is 90. , Find the value of positive constant . Solution Expression for the Binomial expansion of  is: We need to expand both terms one-by-one. First we expand In the given case: Hence; Similarly we also need to expand First rewrite the given expression in standard form. In the given case: Hence; Now […]