Hits: 37

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | Oct-Nov | (P1-9709/13) | Q#1

Hits: 37 Question (i)          Expand  in ascending powers of y as far as the term in y2. (ii)       In the expansion of  the coefficient of x2 is 48. Find the value of the positive  constant . Solution i.   We are required to expand . Expression for the Binomial expansion of  is: In […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | Oct-Nov | (P1-9709/12) | Q#1

Hits: 40 Question The coefficient of  in the expansion of  is 3. Find the value of the constant a. Solution i.   First, we expand . Expression for the Binomial expansion of  is: In the given case: Hence;       Now can we find the coefficient of in the expansion of . We write […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | Oct-Nov | (P1-9709/11) | Q#1

Hits: 38 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 […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | May-Jun | (P1-9709/11) | Q#1

Hits: 657 Question The term independent of x in the expansion of , where k is a constant, is 540. (i)               Find the value of k. (ii)             For this value of k, find the coefficient of x2 in the expansion. Solution (i)   Expression for the general term in the Binomial expansion of  is: In […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | Feb-Mar | (P1-9709/12) | Q#1

Hits: 282 Question The coefficient of  in the expansion of  is -2160. Find the value of the constant . Solution We are given expression as; Expression for the general term in the Binomial expansion of  is: First rewrite the given expression in standard form. In the given case: Hence; Since we are looking for the […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | Oct-Nov | (P1-9709/13) | Q#1

Hits: 207 Question Find the coefficient of  in the expansion of . Solution We are required to expand; We can write it 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 coefficient of the term : we can equate; […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | Oct-Nov | (P1-9709/12) | Q#1

Hits: 328 Question Find the coefficient of in the expansion of . Solution We are required to expand; 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 : we can equate; Finally substituting  in: Therefore, the coefficient of […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | Feb-Mar | (P1-9709/12) | Q#2

Hits: 729 Question      i.       Find the coefficients of  and  in the expansion of .    ii.       Hence 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; […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | May-Jun | (P1-9709/13) | Q#2

Hits: 423 Question Find the coefficient of   in the expansion of . Solution We are required to find the coefficient of in the expansion of . We are given expression as; Expression for the general term in the Binomial expansion of  is: First rewrite the given expression in 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 2018 | May-Jun | (P1-9709/12) | Q#1

Hits: 767 Question The coefficient of  in the expansion of is 330. 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 […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | May-Jun | (P1-9709/11) | Q#1

Hits: 745 Question                     i.       Find the first three terms in the expansion, in ascending powers of , of .                   ii.       Given that the coefficient of  in the expansion of is 12, find the value of the constant a. Solution i.   Expression for the Binomial expansion of  is: First rewrite the given expression […]

# 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: 4954 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: 1364   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: 1098   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: 4045   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: 1068   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: 1340   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: 686   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: 605   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 2016 | Oct-Nov | (P1-9709/12) | Q#4

Hits: 1794 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 […]