Senior Secondary (HKDSE) · Mathematics M1 (Calculus and Statistics)

Binomial expansion: Practice Questions

5 multiple-choice questions marked as you go, and 5 written questions with worked solutions. All on Binomial expansion.

10 questions23 marksFree, no account

Question 1

1 mark

Find the coefficient of \(x^2\) in the expansion of \((3+x)^4\).

Question 2

1 mark

Find the sum of the coefficients in the expansion of \( (2x-1)^5 \).

Question 3

1 mark

Find the coefficient of \(x^3\) in the expansion of \( (1+2x)(1+x)^5 \).

Question 4

1 mark

Find the coefficient of \(x^5\) in the binomial expansion of \( (1 + 4x)^7 \).

Question 5

1 mark

Given that the coefficient of \(x\) in the expansion of \((1-ax)(1+x)^5\) is \(10\), find the value of the constant \(a\).

Question 6

2 marks

Determine the number of terms in the expansion of \((a+b)^{2024}\).

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Question 7

3 marks

If the sum of all binomial coefficients in the expansion of $$(1+x)^n$$ is $$256$$, find the coefficient of $$x^3$$.

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Question 8

5 marks

Given that the coefficient of $$x^2$$ in the expansion of $$(1+3x)^n$$ is $$324$$, where $$n$$ is a positive integer. Find the coefficient of $$x^3$$ in the expansion of $$(1-2x)(1+3x)^n$$.

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Question 9

3 marks

Find the coefficient of \(x\) in the expansion of \((3x - \frac{2}{x})^5\).

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Question 10

5 marks

Consider the binomial expansion of \((x^2 + \frac{k}{x})^6\), where \(k\) is a positive constant.
(a) Find the general term in the expansion.
(b) If the term independent of \(x\) in the expansion is 240, find the value of \(k\).
(c) Using the value of \(k\) found in (b), find the coefficient of \(x^3\) in the expansion.

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