Binomial Expansion (AQA AS Maths: Pure): Exam Questions

In the binomial expansion of

the coefficient of  is 12 976 128.

Find the value of .

Find the first 3 terms, in ascending powers of , of the binomial expansion of

giving each term in simplest form.

Find the first 3 terms, in ascending powers of , of the binomial expansion of

giving each term in simplest form.

 Use your answer to part (a) to estimate the value of .

Expand

giving your answer in descending powers of .

In the binomial expansion of

where is a non-zero constant, the coefficient of  is twice the coefficient of . 

Find the value of , giving your answer as a simplified fraction.

In the binomial expansion of

the coefficient of is 96.

Given that , find the value of .

Find the first 3 terms, in ascending powers of , of the binomial expansion of

giving each term in simplest form.

Use your answer to part (a) to estimate .

In the binomial expansion of

the coefficient of is equal to the coefficient of . 

Find the non-zero value of .

In the binomial expansion of

the coefficient of is four times the coefficient of .

Find the possible non-zero values of .

In the binomial expansion of

where and the coefficients of  and the coefficient of are equal.

Find an expression for  in terms of .

Find the coefficient of in the binomial expansion of 

Find the first 3 terms, in ascending powers of , of the binomial expansion of

giving each term in simplest form.

Given that  is small, so that and higher powers of can be ignored, it can be shown that

where and are integers.

Find and .

In the binomial expansion of

the coefficient of is 19 440.

Given that  is a positive integer, find the value of .

Expand

giving your answer in ascending powers of .

Expand

giving your answer in ascending powers of .

Find the coefficient of  in the expansion of

In the binomial expansion of

the coefficient of is .

Find the possible values of .

In the binomial expansion of

the coefficient of is equal to the coefficient of . 

Find the non-zero value of .

In the binomial expansion of

where and the coefficient of  is equal to the coefficient of .

Find the two possible expressions for  in terms of .

In the binomial expansion of

the coefficient of is equal to the coefficient of .

Given that and are non-zero, find the value of

Given that and  are integers, and that , find the possible values of  and .

Use the formula

to prove that

for all positive integer values of .

In the binomial expansion of 

the coefficient of  is equal to the coefficient of .  

Find the non-zero values of , giving your answers in the form where  and  are integers to be found.

In the binomial expansion of  the coefficient of is 216.

In the binomial expansion of  the coefficient of is 4860.

Find the possible values of  and .

Use the first 3 terms, in ascending powers of , of the expansion of 

to find an approximation for .

Find the percentage error in the approximation from part (a) to the exact value of

Solutions relying on calculator technology are not acceptable.

Given that

use algebra to show that satisfies the cubic equation

and hence write down the value of .

In the binomial expansion of

where is a positive integer greater than 3, the coefficient of  is 84.

Use algebra to show that satisfies

where and are integers to be found.

Hence, find all possible values of .

Given that  is a very small value, so that  (and higher powers of ) can be ignored, show that

where , and are integers to be found.

In the binomial expansion of

the coefficient of is -3240.

Use algebra to find the value of .

In the binomial expansion of  the coefficient of is -870 912.

In the binomial expansion of  the coefficient of is -1 557 135 360.

Find the possible values of  and .