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

1FoundationSAQ-SBinomial expansion and coefficientss5 marksPaper 1~8 min

Consider the binomial expansion of

(2 + x)^5

(a)

Write down the general term of the expansion in the form

\binom{5}{r} 2^{5-r} x^r

, and state the values of

r

that give valid terms. [1 mark]

(b)

Find the term in

x^3

in the expansion. [2 marks]

(c)

Given that the coefficient of

x^3

in the expansion of

(k + x)^5

270

, find the value of

k

. [2 marks]

Solutions

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

Consider the expansion of

(1 + 2x)^5

(a)

Write down the six numbers in Row 5 of Pascal's triangle. [2 marks]

(b)

Using your answer to part (a), expand

(1 + 2x)^5

, giving each coefficient in simplified form. [3 marks]

Solutions

3MasterySAQ-SBinomial expansion and coefficientss5 marksPaper 1~8 min

Consider the binomial expansion of

\left(2x^2 - \dfrac{3}{x}\right)^6

(a)

Show that the coefficient of

x^3

in the expansion is

-4320

. [3 marks]

(b)

Hence, find the coefficient of

x^3

in the expansion of

\left(2x^2 - \dfrac{3}{x}\right)^6(x + 2)

. [2 marks]

Solutions

4ChallengeSAQ-LBinomial expansion and coefficientss9 marksPaper 1~14 min

The expansion of

(1 + ax)^n

, where

n \in \mathbb{Z}^+

and

a \in \mathbb{R}

, has coefficients of

x^2

and

x^3

equal to

112

and

448

respectively.

(a)

Determine the values of

a

and

n

. [5 marks]

(b)

Find the sum of all coefficients in the expansion of

(1 + ax)^n

for the values found in part (a). [1 mark]

(c)

The expansion of

(1 + ax)^n

is multiplied by

(1 + x)

. Determine the coefficient of

x^5

in the resulting expansion, and hence deduce whether this coefficient is greater than, equal to, or less than the coefficient of

x^5

in the expansion of

(1 + ax)^n

alone. [3 marks]

Solutions

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