Binomial Theorem (DP IB Analysis & Approaches (AA): HL): Exam Questions

Find the coefficient of the  term in the expansion

Consider the expansion of

Write down the number of terms in this expansion.

Find the first three terms, in descending powers of , of the expansion.

Consider the expansion of 

Find an expression, in terms of , for the coefficient of the  term.

The coefficient of the  term is 90.

Find the value of .

Consider the quadratic expression .

Write down the quadratic expression in the form

Find the coefficient of the  term in the expansion of . Give your answer in the form where  .

The coefficient of  in the expansion of is   

Find the possible values of 

The sum of the coefficients of the expansion is 

Determine which value of found in part (a) is correct.

Consider the expansion

The coefficient of the term is 36. Find the possible values of .

Consider the expansion of  The constant term is  

Find the value of .

Find the coefficient of the  term.

In the expansion of  the coefficient of the  term is , where

Find .

Consider the expansion of

Find the term in in the expansion.

Hence find the term in  in the expansion of

Consider the expansion of

Find the term in  in the expansion.

Hence find the term in  in the expansion of 

Consider the binomial expansion of  .​

Find the first four terms, in ascending powers of , of the expansion.

State the interval of convergence for the complete expansion.

By substituting an appropriate value into the expression found in part (a), find an approximation for the value of ​.

Consider the binomial expansion of  ​​.

Write down the first three terms, in ascending powers of , of the expansion.

State the interval of convergence for the complete expansion.

Using the expansion found in part (a), find an approximation for the value of ​ ,  giving your answer as an exact value in as simple a form as possible.

Consider the binomial expansion of  

Given that the coefficient of the term in is  ,  find

i) the value of

ii) the coefficient of the term in

iii) the first three terms of the expansion, in ascending powers of .

Consider the binomial expansion of  ​ ,  where .

For the case where the coefficient in is ,  show that .

For the value of found in part (a), find the coefficient of . 

Consider the binomial expansion of 

Show that    can be written in the form , and find the values of and .

Hence, or otherwise, find the first three terms of the expansion, in ascending powers of .

Given that

Find the value of .

Given that 

Find the value of .

Consider the expansion .

Write down and simplify the expansion in descending powers of.

Hence, find the exact value of .

Consider the expansion .

Write down and simplify the expansion in descending powers of .

Hence find the exact value of .

Given that 

Determine the value of .

Find the possible values of y and z.

Given that 

Determine the value of .

Find the possible values of and .

In the expansion of , the coefficient of the term in  is 210. 

Find the value of .

Consider the expansion of . The coefficient of the term is five times the coefficient of the  term. 

Find , giving your answer to 3 significant figures.

Consider the expansion of , where . The coefficient of the term in is equal to the coefficient of the term in  . 

Find .

The coefficient of the  term in the expansion of  is 

Find the value of 

Consider the binomial expansion of .

Find the first four terms, in ascending powers of , of the expansion.

Find the coefficient of the term in in the expansion of 

Consider the identity  ​ ,  where and  are constants to be determined.

Find the values of and .

Hence, or otherwise, find the binomial expansion of  ,  in ascending powers of , up to and including the term in .

State the interval of convergence for the expansion found in part (b).

Consider the binomial expansion of , where .

Given that the coefficient in  is ​  , show that 

Given also that the constant term is ​  , find

i) the value of

ii) the first three terms of the expansion , in ascending powers of .