Binomial Theorem/Expansion (CIE-P1-2014) Archives — O/A Level Solutions

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2014 | Oct-Nov | (P1-9709/13) | Q#1

Question In the expansion of , the coefficient of  is equal to the coefficient of . Find the value of the non-zero constant . Solution Expression for the general term in the Binomial expansion of  is: In the given case: Hence; Since we are looking for the terms with  : we can  equate Now we can find the term with; Substituting ; Substituting ; […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2014 | Oct-Nov | (P1-9709/12) | Q#3

Question      i.       Find the first 3 terms, in ascending powers of , in the expansion of . The coefficient of  in the expansion of  is 95.    ii.       Use the answer to part (i) to find the value of the positive constant . Solution i.   Expression for the Binomial expansion of  is: In the given case: Hence; ii.   To evaluate […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2014 | Oct-Nov | (P1-9709/11) | Q#1

Question In the expansion of , the coefficient of  is equal to the coefficient of . Find the value of the non-zero constant . Solution Expression for the general term in the Binomial expansion of  is: In the given case: Hence; Since we are looking for the terms with  :  we can  equate Now we can find the term with; Substituting ; […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2014 | May-Jun | (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 terms with  i.e. : we can  equate Now we can find the term with; Substituting ; Hence the coefficient of the term containing […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2014 | May-Jun | (P1-9709/12) | Q#2

Question Find the coefficient of  in the expansion of . Solution It is evident that to get the terms containing  in the product of we need; This will result; Hence we need first to find the terms with  and  i.e.  in the expansion of . First rewrite the given expression in standard form. Expression for the general term in the Binomial expansion of  is: In the […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2014 | May-Jun | (P1-9709/11) | Q#3

Question Find the term independent of  in the expansion of . . Solution Expression for the general term in the Binomial expansion of  is: In the given case: Hence; Since we are looking for the coefficient of the term independent of  i.e. , so we can  equate Hence, substituting ; Becomes; Hence coefficient of the term independent of  i.e.  is 7.