DP Mathematics SL Questionbank

• Syllabus

1.3

Sub sections and their related questions

The binomial theorem: expansion of ${\left( {a + b} \right)^n}$, $n \in \mathbb{N}$ .

• 12N.2.sl.TZ0.4: The third term in the expansion of ${(2x + p)^6}$ is $60{x^4}$ . Find the possible values of p .
• 12M.1.sl.TZ2.7: Given that ${\left( {1 + \frac{2}{3}x} \right)^n}{(3 + nx)^2} = 9 + 84x + \ldots$ , find the...
• 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 of ${\left( {\frac{x}{a} + \frac{{{a^2}}}{x}} \right)^6}$...
• 14M.2.sl.TZ1.2a: Write down the number of terms in this 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 term...
• 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 ${x^5}$ .
• 14N.2.sl.TZ0.6: Consider the expansion of ${\left( {\frac{{{x^3}}}{2} + \frac{p}{x}} \right)^8}$. The constant...
• 15M.2.sl.TZ1.2a: Write down the number of terms in this expansion.
• 15M.2.sl.TZ2.4: The third term in the expansion of ${(x + k)^8}$ is $63{x^6}$. Find the possible values of...
• 15N.1.sl.TZ0.6: In the expansion of ${(3x + 1)^n}$, the coefficient of the term in ${x^2}$ is $135n$, where...
• 16M.2.sl.TZ1.4a: Find the term in ${x^6}$ in the expansion of ${(x + 2)^9}$.
• 16M.2.sl.TZ1.4b: Hence, find the term in ${x^7}$ in the expansion of $5x{(x + 2)^9}$.
• 16M.2.sl.TZ2.5a: Write down the number of terms of this expansion.
• 16M.2.sl.TZ2.5b: Find the coefficient of ${x^8}$.
• 16N.1.sl.TZ0.3a: Write down the values in the fifth row of Pascal’s triangle.
• 16N.1.sl.TZ0.3b: Hence or otherwise, find the term in ${x^3}$ in the expansion of ${(2x + 3)^5}$.
• 17N.2.sl.TZ0.6: In the expansion of $a{x^3}{(2 + ax)^{11}}$, the coefficient of the term in ${x^5}$ is 11880....
• 18M.2.sl.TZ2.5: Consider the expansion of ${\left( {2x + \frac{k}{x}} \right)^9}$, where k > 0 . The...

Calculation of binomial coefficients using Pascal’s triangle and $\left( {\begin{array}{*{20}{c}} n \\ r \end{array}} \right)$.

• 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.TZ1.2b: Find the term in ${x^3}$.
• 15M.2.sl.TZ2.4: The third term in the expansion of ${(x + k)^8}$ is $63{x^6}$. Find the possible values of...
• 15N.1.sl.TZ0.6: In the expansion of ${(3x + 1)^n}$, the coefficient of the term in ${x^2}$ is $135n$, where...
• 16N.1.sl.TZ0.3a: Write down the values in the fifth row of Pascal’s triangle.
• 16N.1.sl.TZ0.3b: Hence or otherwise, find the term in ${x^3}$ in the expansion of ${(2x + 3)^5}$.