Single binomial expansion - Binomial Theorem (positive integer n)

CAIE P1 2014 June Q3

3 Find the term independent of $x$ in the expansion of $\left( 4 x ^ { 3 } + \frac { 1 } { 2 x } \right) ^ { 8 }$.

CAIE P1 2016 June Q1

1 Find the term independent of $x$ in the expansion of $\left( x - \frac { 3 } { 2 x } \right) ^ { 6 }$.

CAIE P1 2002 November Q1

1 Find the value of the term which is independent of $x$ in the expansion of $\left( x + \frac { 3 } { x } \right) ^ { 4 }$.

CAIE P1 2010 November Q1

1 Find the term independent of $x$ in the expansion of $\left( x - \frac { 1 } { x ^ { 2 } } \right) ^ { 9 }$.

CAIE P1 2011 November Q1

1 Find the term independent of $x$ in the expansion of $\left( 2 x + \frac { 1 } { x ^ { 2 } } \right) ^ { 6 }$.

CAIE P1 2016 November Q2

2 Find the term independent of $x$ in the expansion of $\left( 2 x + \frac { 1 } { 2 x ^ { 3 } } \right) ^ { 8 }$.

CAIE P1 2017 November Q1

1 Find the term independent of $x$ in the expansion of $\left( 2 x - \frac { 1 } { 4 x ^ { 2 } } \right) ^ { 9 }$.

CAIE P1 2019 November Q1

1 Find the term independent of $x$ in the expansion of $\left( 2 x + \frac { 1 } { 4 x ^ { 2 } } \right) ^ { 6 }$.

OCR MEI C1 Q3

3 Find the term independent of $x$ in the expansion of $\left( x - \frac { 2 } { x } \right) ^ { 4 }$.

OCR MEI C1 Q4

4 The binomial expansion of $\left( 2 x + \frac { 5 } { x } \right) ^ { 6 }$ has a term which is a constant. Find this term.

OCR MEI C1 2013 January Q6

6 The binomial expansion of $\left( 2 x + \frac { 5 } { x } \right) ^ { 6 }$ has a term which is a constant. Find this term.

OCR MEI Paper 3 2018 June Q6

6 Find the constant term in the expansion of $\left( x ^ { 2 } + \frac { 1 } { x } \right) ^ { 15 }$.

Edexcel C2 Q2

find the first 4 terms, simplifying each term.
Find, in its simplest form, the term independent of $x$ in this expansion.
[0pt] [P2 June 2004 Question 3] \item The curve $C$ has equation $y = \cos \left( x + \frac { \pi } { 4 } \right) , 0 \leq x \leq 2 \pi$.
Sketch $C$.
Write down the exact coordinates of the points at which $C$ meets the coordinate axes.
Solve, for $x$ in the interval $0 \leq x \leq 2 \pi , \cos \left( x + \frac { \pi } { 4 } \right) = 0.5$, giving your answers in terms of $\pi$. \item Given that $\log _ { 2 } x = a$, find, in terms of $a$, the simplest form of
$\log _ { 2 } ( 16 x )$,
$\log _ { 2 } \left( \frac { x ^ { 4 } } { 2 } \right)$.
Hence, or otherwise, solve $\log _ { 2 } ( 16 x ) - \log _ { 2 } \left( \frac { x ^ { 4 } } { 2 } \right) = \frac { 1 } { 2 }$, giving your answer in its simplest surd form. \item (a) Given that $3 \sin x = 8 \cos x$, find the value of $\tan x$.
Find, to 1 decimal place, all the solutions of $3 \sin x - 8 \cos x = 0$ in the interval $0 \leq x < 360 ^ { \circ }$.
Find, to 1 decimal place, all the solutions of $3 \sin ^ { 2 } y - 8 \cos y = 0$ in the interval $0 \leq y < 360 ^ { \circ }$. \item \end{enumerate} $$f ( x ) = \frac { \left( x ^ { 2 } - 3 \right) ^ { 2 } } { x ^ { 3 } } , x \neq 0$$
Show that $\mathrm { f } ( x ) \equiv x - 6 x ^ { - 1 } + 9 x ^ { - 3 }$.
Hence, or otherwise, differentiate $\mathrm { f } ( x )$ with respect to $x$.
Verify that the graph of $y = \mathrm { f } ( x )$ has stationary points at $x = \pm \sqrt { } 3$.
Determine whether the stationary value at $x = \sqrt { } 3$ is a maximum or a minimum.

SPS SPS FM 2025 October Q5

5. In this question you must show detailed reasoning. Consider the expansion of $\left( \frac { x ^ { 2 } } { 2 } + \frac { a } { x } \right) ^ { 6 }$. The constant term is 960 .
Find the possible values of $a$.
[0pt] [BLANK PAGE]

AQA Paper 3 2021 June Q4

4

Show that the first three terms, in descending powers of $x$, of the expansion of $$( 2 x - 3 ) ^ { 10 }$$ are given by $$1024 x ^ { 10 } + p x ^ { 9 } + q x ^ { 8 }$$ where $p$ and $q$ are integers to be found.
4
Find the constant term in the expansion of $$\left( 2 x - \frac { 3 } { x } \right) ^ { 10 }$$