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 \({(2x + 3)^5}\).