# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2011 | Oct-Nov | (P1-9709/13) | Q#1

Question The coefficient of  in the expansion of , is 30. Find the value of . Solution Expression for the Binomial expansion of  is: In the given case: Hence; Since the coefficient of  in the expansion of , is 30:

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2011 | Oct-Nov | (P1-9709/12) | Q#1

Question      i.       Find the first 3 terms in the expansion of , in ascending powers of .    ii.       Use the result in part (i) to 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.   We can […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2011 | Oct-Nov | (P1-9709/11) | Q#1

Question Find the term independent of  in the expansion of  . Solution Expression for the Binomial expansion of  is: In the given case: Hence; The term independent of  in the expansion of is .

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2011 | May-Jun | (P1-9709/13) | Q#1

Question The coefficient of  in the expansion of  , where is positive, is 90. Find the value of . 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; […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2011 | May-Jun | (P1-9709/12) | Q#2

Question      i.       Find the terms in  and  in the expansion of .    ii.       Given that there is no term in  in the expansion of , find the value of the constant . Solution i.   First rewrite the given expression in standard form. Expression for the Binomial expansion of  is: In the given case: Hence; Hence the required terms in […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2011 | May-Jun | (P1-9709/11) | Q#1

Question Find the coefficient of  in the expansion of  . Solution Expression for the Binomial expansion of  is: In the given case: Hence; The coefficient of   is .