## 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 Analysis and Approaches |

In the expansion of \( (x+j)^{9}\) where \(j \in \mathbb{R}\), the coefficient of the term in \(x^7\) is 144.

Find the possible values of \(j\).

## 5. | IB Standard |

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

Find \(m\).

## 6. | 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.

## 7. | 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 \( b \lt c \).

## 8. | IB Analysis and Approaches |

Consider the expansion of \( (7-x^2)^{n-1}\) where \(n \in \mathbb{Z}^+\).

Given that the coefficient of \(x^6\) is -9882516, find the value of \(n\).

If you would like space on the right of the question to write out the solution try this Thinning Feature. It will collapse the text into the left half of your screen but large diagrams will remain unchanged.

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.

The solutions to the questions on this website are only available to those who have a Transum Subscription.

Exam-Style Questions Main Page

To search the **entire Transum website** use the search box in the grey area below.

Do you have any comments about these exam-style questions? It is always useful to receive feedback and helps make this free resource even more useful for those learning Mathematics anywhere in the world. Click here to enter your comments.