Binomial Theorem/Expansion (CIE-2015) Archives — O/A Level Solutions

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2015 | Oct-Nov | (P1-9709/13) | Q#2

Question Find the coefficient of x in the expansion of . Solution We are given expression as; 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  is 7.

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2015 | Oct-Nov | (P1-9709/12) | Q#2

Question In the expansion of , where k is a non-zero constant, the coefficients of  and  are equal. Find the value of k. Solution Expression for the general term in the Binomial expansion of  is: We are given the expression for expansion as; First we rewrite the expression in the standard form; In the given case: Hence; Since we […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2015 | Oct-Nov | (P1-9709/11) | Q#1

Question In the expansion of , where a is a non-zero constant, show that the coefficient of  is zero. Solution Expression for the Binomial expansion of  is: We are given; In the given case: Hence; It is evident that to get the terms containing  in the product of  we need; This will result in terms containing ; Hence coefficient of in the expansion […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2015 | May-Jun | (P1-9709/13) | Q#3

Question      i.      Write down the first 4 terms, in ascending powers of , of the expansion of .    ii.       The coefficient of  in the expansion of  is −200. Find the possible values of the constant . Solution i.   Expression for the Binomial expansion of  is: First we rewrite the expression in the standard form; In the given case: […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2015 | May-Jun | (P1-9709/12) | Q#3

Question      i.       Find the coefficients of  in the expansion of .    ii.       Find the coefficient of  in the expansion of . Solution i.   Expression for the general term in the Binomial expansion of  is: First we rewrite the expression in the standard form; In the given case: Hence; Since we are looking for the terms with : we can  equate […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2015 | May-Jun | (P1-9709/11) | Q#3

Question      i.       Find the first three terms, in ascending powers of , in the expansion of  a.   b.      ii.       Hence find the coefficient of  in the expansion of . Solution i.   a)   Expression for the Binomial expansion of  is: First we rewrite the given equation in the standard form; In the given case: Hence; b)   Expression for the […]