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evidence of binomial expansion (M1)

eg $\left( \begin{array}{c}n\\r\end{array} \right)$ ${a^{n - r}}{b^r}$ , attempt to expand

evidence of choosing correct term (A1)

eg ${8^{{\text{th}}}}{\text{ term, }}r = 7$ , $\left( \begin{array}{c}10\\7\end{array} \right)$ , ${(x)^3}{(3)^7}$

correct working (A1)

eg $\left( \begin{array}{c}10\\7\end{array} \right)$ ${(x)^3}{(3)^7}$ , $\left( \begin{array}{c}10\\3\end{array} \right)$ ${(x)^3}{(3)^7}$ ,

$262440{x^3}{\text{ (accept }}262000{x^3})$ A1 N3

[4 marks]

Topic 1 - Algebra » 1.3 » The binomial theorem: expansion of

{(a + b)}^{n}

${\left( {a + b} \right)^n}$ ,

$n \in \mathbb{N}$ .

Show 31 related questions

12N.2.sl.TZ0.4: The third term in the expansion of ${(2x + p)^6}$ is $60{x^4}$ . Find the possible values...
12M.1.sl.TZ2.7: Given that ${\left( {1 + \frac{2}{3}x} \right)^n}{(3 + nx)^2} = 9 + 84x + \ldots$ , find...
08N.2.sl.TZ0.2a: Expand ${(x - 2)^4}$ and simplify your result.
08M.2.sl.TZ2.2: Find the term ${x^3}$ in the expansion of ${\left( {\frac{2}{3}x - 3} \right)^8}$ .
12M.2.sl.TZ1.6a: Find b.
12M.2.sl.TZ1.6b: Find k.
10M.1.sl.TZ1.3a: Expand ${(2 + x)^4}$ and simplify your result.
10M.1.sl.TZ1.3b: Hence, find the term in ${x^2}$ in ${(2 + x)^4}\left( {1 + \frac{1}{{{x^2}}}} \right)$ .
09M.2.sl.TZ1.10a: Expand ${(x + h)^3}$ .
09M.1.sl.TZ2.3a: Write down the value of $n$ .
09M.1.sl.TZ2.3b: Write down a and b, in terms of p and/or q.
09M.1.sl.TZ2.3c: Write down an expression for the sixth term in the expansion.
10M.2.sl.TZ2.4: Find the term in ${x^4}$ in the expansion of ${\left( {3{x^2} - \frac{2}{x}} \right)^5}$ .
11N.2.sl.TZ0.5a: Write down the number of terms in the expansion.
11N.2.sl.TZ0.5b: Find the term in ${x^4}$ .
13M.2.sl.TZ2.6: The constant term in the expansion...
14M.2.sl.TZ1.2b: Find the term containing ${x^3}$ .
14M.2.sl.TZ2.7: Consider the expansion of ${x^2}{\left( {3{x^2} + \frac{k}{x}} \right)^8}$ . The constant...
13M.2.sl.TZ1.3a: Write down the value of $p$ , of $q$ and of $r$ .
13M.2.sl.TZ1.3b: Find the coefficient of the term in ${x^5}$ .
15M.2.sl.TZ2.4: The third term in the expansion of ${(x + k)^8}$ is $63{x^6}$ . Find the possible values...
15M.2.sl.TZ1.2a: Write down the number of terms in this expansion.
14N.2.sl.TZ0.6: Consider the expansion of ${\left( {\frac{{{x^3}}}{2} + \frac{p}{x}} \right)^8}$ . The...
15N.1.sl.TZ0.6: In the expansion of ${(3x + 1)^n}$ , the coefficient of the term in ${x^2}$ is $135n$ ,...
16N.1.sl.TZ0.3b: Hence or otherwise, find the term in ${x^3}$ in the expansion of ${(2x + 3)^5}$ .
16N.1.sl.TZ0.3a: Write down the values in the fifth row of Pascal’s triangle.
16M.2.sl.TZ2.5b: Find the coefficient of ${x^8}$ .
16M.2.sl.TZ1.4b: Hence, find the term in ${x^7}$ in the expansion of $5x{(x + 2)^9}$ .
16M.2.sl.TZ1.4a: Find the term in ${x^6}$ in the expansion of ${(x + 2)^9}$ .
16M.2.sl.TZ2.5a: Write down the number of terms of this expansion.
17N.2.sl.TZ0.6: In the expansion of $a{x^3}{(2 + ax)^{11}}$ , the coefficient of the term in ${x^5}$ is...

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Date	May 2014	Marks available	1	Reference code	14M.2.sl.TZ1.2
Level	SL only	Paper	2	Time zone	TZ1
Command term	Write down	Question number	2	Adapted from	N/A

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