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Exam-Style Questions.

Problems adapted from questions set for 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 Analysis and Approaches

Consider the expansion of:

$$ (3x^4+\frac{1}{5x})^n $$

where \( n \in \mathbb{Z}^+\)

Determine all possible values of \(n\) for which the expansion has a non-zero constant term.


4.

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 \(x^6\).


5.

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 \(j\).


6.

IB Analysis and Approaches

The expansion of \((x + g)^7\), where \(g \in \mathbb{Q}^+\), can be written as:

$$x^7 + ax^6 + bx^5 + cx^4 + dx^3 + ex^2 + fx + g^7$$

where \(a, b, c, d, e, f \in \mathbb{R}\).

Given that the coefficients, \( a, c \text{ and } d\), are the first three terms of a geometric sequence, find the value of \(g\).

Sierpinski's Triangle

7.

IB Standard

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

Find \(m\).


8.

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.


9.

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 \( b \lt c \).


10.

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 \(n\).


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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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