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Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | Oct-Nov | (P1-9709/13) | Q#3

Hits: 125 Question      i.       Find the term independent of x in the expansion of .    ii.       Find the value of a for which there is no term independent of x in the expansion of Solution i.   Expression for the general term in the Binomial expansion of  is: For the given case: Hence; Since we are looking for […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | Oct-Nov | (P1-9709/12) | Q#1

Hits: 74   Question Find the term independent of x in the expansion of . Solution Expression for the general term in the Binomial expansion of  is: For 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 […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | May-Jun | (P1-9709/13) | Q#1

Hits: 55   Question The coefficients of  and  in the expansion of  are equal. Find the value of the non-zero  constant a. Solution We need to equate the coefficients of  and  in the expansion of given expression.  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 […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | May-Jun | (P1-9709/12) | Q#1

Hits: 89   Question      i.       Find the coefficient of x in the expansion of .    ii.       Hence find the coefficient of x in the expansion of . Solution      i.   We are required to find the coefficient  of  in the expansion of given expression. We are given expression as; Expression for the general term in the Binomial expansion of […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | Feb-Mar | (P1-9709/12) | Q#2

Hits: 75   Question In the expansion of , the coefficient of x is 5. Find the value of the constant a. 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 […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | May-Jun | (P1-9709/11) | Q#1

Hits: 107   Question The coefficients of  and  in the expansion of  are  and  respectively. Find the value  of . . Solution We can find the coefficients of  and  in the expansion of given expression.  Let us first find the coefficient of  in the expansion of . We are given expression as;  Expression for the general term in the Binomial expansion of  is: […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | Oct-Nov | (P1-9709/13) | Q#2

Hits: 70   Question The coefficient of  in the expansion of  is 100. Find the value of the constant  a. Solution We can find the coefficient of  in the expansion of given expression by finding coefficients of  in  the expansion of individual terms of expression and then adding them. Let us first find the coefficient of  in the expansion of . […]

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

Hits: 95   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 . Please follow and like us: 0

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | Oct-Nov | (P1-9709/12) | Q#4

Hits: 257 Question In the expansion of , the coefficient of x is 7. Find the value of the constant n and hence find the coefficient of . Solution Binomial Theorem states that if  is a natural number; First we expand  . In the given case: Hence;   We will have the given product as; We consider only the terms containing […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | May-Jun | (P1-9709/13) | Q#1

Hits: 81 Question Find the coefficient of  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 […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | May-Jun | (P1-9709/12) | Q#4

Hits: 170 Question Find the term independent of  in the expansion of      i.             ii.        Solution i.   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 […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | May-Jun | (P1-9709/11) | Q#1

Hits: 191 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 . Please […]

Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | Feb-Mar | (P1-9709/12) | Q#1

Hits: 131   Question      i.       Find the coefficients of  and  in the expansion of .    ii.       It is given that, when  is expanded, there is no term in . Find the value of the constant . Solution i.   Expression for the general term in the Binomial expansion of  is: First we rewrite the expression in the standard […]

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

Hits: 77 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 […]

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

Hits: 90 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: […]

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

Hits: 118 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 […]

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

Hits: 119 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 […]

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

Hits: 152 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 : […]

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

Hits: 169 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 […]