 # Exam-Style Questions on Binomial Theorem

## Problems on Binomial Theorem adapted from questions set in previous Mathematics exams.

### 1.

IB Standard

If $$(x+5)^{10}$$ is expanded

(a) how many terms would there be?

(b) what is the coefficient of the term containing $$x^4$$?

### 2.

IB Standard

If $$(2x+7)^{6}$$ is expanded

(a) how many terms would there be?

(b) what is the coefficient of the term containing $$x^4$$?

### 3.

IB Standard

If you expanded $$(2x-3)^{15}$$, the term containing $$x^6$$ can be written as $$\binom{15}{a}\times(2x)^b\times(-3)^c$$

(a) Write down the values of $$a$$, of $$b$$ and $$c$$.

(b) Find the coefficient of the term containing $$x^6$$.

### 4.

IB Standard

The constant term in the expansion of $$x^4(2x^2+\frac{m}{x})^7$$ is 896

Find $$m$$.

### 5.

IB Standard

Consider the expansion of $$(3x+ \frac{c}{x})^8$$ where $$c \gt 0$$.

The coefficient of the term in $$x^4$$ is equal to the coefficient of the term in $$x^6$$.

Find c.

### 6.

A-Level

(a) Find the binomial expansion of $$(1-6x)^{\frac34}$$ up to and including the term in $$x^2$$.

(b) Find the binomial expansion of $$(16-6x)^{\frac34}$$ up to and including the term in $$x^2$$.

(c) Use your expansion from part (b) to find an estimate for $$19^{\frac34}$$ giving your answer in the form $$a + \frac{b}{c}$$ where a, b and c are positive integers with $$b \lt c$$.

The exam-style questions appearing on this site are based on those set in previous examinations (or sample assessment papers for future examinations) by the major examination boards. The wording, diagrams and figures used in these questions have been changed from the originals so that students can have fresh, relevant problem solving practice even if they have previously worked through the related exam paper.

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