Binomial Expansion (Cambridge (CIE) AS Maths: Pure 1): Exam Questions

Expand $(2+x{)}^4.$

Find the coefficient of the term in $x^3$ in the expansion of $(2-x{)}^8$.

Find the first three terms, in ascending powers of $x$, in the expansion of $(3+x{)}^4$.

Use your answer to part (a) to estimate $(3.1{)}^4$.

In the expansion of $(a-x{)}^4$, the coefficient of the $x^2$ term is 96. Given that $a>0$, find the value of $a$.

Find the first three terms in the expansion of $(9-2x{)}^5$.

Use your answer to part (a) to estimate $(8.9{)}^5$.

In the expansion of $(a-2x{)}^5$, the coefficient of the $x^2$ term is equal to the coefficient of the $x^3$ term.  Find the value of $a$.

In the expansion of $(3+px{)}^6$, the coefficient of the $x^4$ term is four times the coefficient of the $x^2$ term.  Find the possible values of $p$.

Find the first three terms in the expansion of $(3+2x{)}^8$.

Given that $x$ is small such that $x^3$and higher powers of $x$ can be ignored show that

         $(1+x)(3+2x{)}^8\approx 6561+41553x+116640x^2$                   

In the expansion of $(p+qx{)}^5$, the coefficients of the $x^2$ term and the $x^3$ term are equal.

Find $p$ in terms of $q$.

In the expansion of $(a+bx{)}^4$, the coefficient of the $x^2$ term is equal to the coefficient of the $x^3$ term.

Show that $\frac{a}{b}=\frac{2}{3}$.

Given that $a$ and $b$ are integers, and that $10<b<15$, find the values of $a$ and $b$.

Fully expand $(4-x{)}^4$.

Fully expand  $(2-\frac{1}{3}x{)}^4$.

Find the coefficient of the term in $x^4$ in the expansion of $(3+2x{)}^9.$

Find the first three terms, in ascending powers of $x$, in the expansion of $(5-2x{)}^4.$

Use your answer to part (a) to estimate $(4.5{)}^4$.

In the expansion of $(4-px{)}^6$, the coefficient of the $x^4$ term is 19 440.
Given that $p$ is a positive integer find the value of $p$.

In the expansion of $(3a-2x{)}^6,$ the coefficient of the $x^3$ term is equal to the coefficient of the $x^4$ term.  Find the value of $a$.

Find the first three terms in the expansion of $(2-3x{)}^7$.

Given that $x$ is small such that $x^3$ and higher powers of $x$ can be ignored show that

         $(1-2x)(2-3x{)}^7\approx 128-1600x+8736x^2$                   

In the expansion of ${(p+qx)}^8$, the coefficients of the $x^2$ term and the $x^6$ term are equal.

Find $p$ in terms of $q$.

In the expansion of $(1+x{)}^n,$ the coefficient of the $x^3$ term is 84.

Find the value of $n$.

In the expansion of $(a+bx{)}^4,$ the coefficient of the $x^3$ term is 216.

In the expansion of $(a+bx{)}^6,$ the coefficient of the $x^4$ term is 4860.

Find the possible values of $a$ and $b$.

Expand .$(3-2x{)}^5$

Find the coefficient of the term in $x^4$ in the expansion of $(4-3x{)}^7.$

Given that ${}^{n}C_3=35$ find the value of $n$.

Use the first three terms, in ascending powers of $x$, in the expansion of $(3-5x{)}^4$ to find an approximation for $(2.6{)}^4$.

Using your calculator, find the percentage error in the approximation from part (a) to the exact value of $(2.6{)}^4$.

In the expansion of $(m-\frac{1}{4}x{)}^5$, the coefficient of the $x^3$ term is -10. Find the possible values of $m$.

In the expansion of  $(3a+\frac{1}{2}x{)}^6$, the coefficient of the $x^3$ term is equal to the coefficient of the $x^5$ term.  Find the values of $a$, giving your answers in the form $\frac{\sqrt{m}}{n}$, where $m$ and $n$ are integers to be found.

Find the first three terms in the expansion of $(4-3x{)}^9$.

Given that $x$ is small such that $x^3$ and higher powers of $x$ can be ignored show that

            $(3-2x^2)(4-3x{)}^9\approx 786432-5308416x+15400960x^2$                  

In the expansion of ${(p+qx)}^9$, the coefficient of the $x^3$ term is double that of the $x^5$ term. 
Find $p$ in terms of $q$.

In the expansion of $(1-3x{)}^n,$ the coefficient of the $x^3$ term is -3240.

Find the value of $n$.

In the expansion of $(a+bx{)}^8,$ the coefficient of the $x^5$ term is -870 912.

In the expansion of $(a+bx{)}^{12},$ the coefficient of the $x^3$ term is -1 557 135 360.

Find the possible values of $a$ and $b$.