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Binomial Theorem · Paper 1 — Free Maths AA HL Practice Questions

1FoundationSAQ-SBinomial expansion and coefficientss4 marksPaper 1~6 min

In the expansion of

(2x + 3)^5

(a)

Write down the general term of the expansion in terms of

r

. [1 mark]

(b)

Find the coefficient of

x^3

. [3 marks]

Solutions

2MasterySAQ-SBinomial expansion and coefficientss5 marksPaper 1~8 min

Consider the binomial expansion of

\left(2x^3 - \dfrac{1}{x}\right)^n

, where

n \in \mathbb{Z}^+

(a)

Show that the coefficient of the term independent of

x

\dbinom{n}{\frac{n}{4}} 2^{\frac{n}{4}} (-1)^{\frac{3n}{4}}

, and state the condition

n

for this term to exist. [3 marks]

(b)

Hence, given that

n = 8

, find the value of the constant term. [2 marks]

Solutions

3ChallengeSAQ-LBinomial expansion and coefficientss8 marksPaper 1~12 min

Consider the binomial expansion of

(1 + kx)^n

, where

n \in \mathbb{Z}^+

and

k

is a positive constant. The coefficient of

x^2

112

and the coefficient of

x^3

448

(a)

Show that

(n-2)k = 12

. [2 marks]

(b)

Hence determine the value of

n

and the value of

k

. [3 marks]

(c)

Determine the coefficient of

x^4

in the expansion. [3 marks]

Solutions

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