IB Mathematics AA SL  Questionbank
Binomial Theorem
Binomial Expansion & Theorem, Pascal’s Triangle & The Binomial Coefficient nCr…
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Question 1
[Maximum mark: 4]
Expand $(2x + 1)^4$ in descending powers of $x$ and simplify your answer.
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Question 2
[Maximum mark: 4]
Expand $(2x  3)^4$ in descending powers of $x$ and simplify your answer.
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Question 3
[Maximum mark: 6]
Consider the expansion of $(2x1)^9$.

Write down the number of terms in this expansion. [1]

Find the coefficient of the term in $x^2$. [5]
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Question 4
[Maximum mark: 5]
Consider the expansion of $(x3)^8$.

Write down the number of terms in this expansion. [1]

Find the coefficient of the term in $x^6$. [4]
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Question 5
[Maximum mark: 6]

Show that $(2n1)^3 + (2n+1)^3 = 16n^3+12n$ for $n \in \mathbb{Z}$. [3]

Hence, or otherwise, prove that the sum of the cubes of any two consecutive odd integers is divisible by four. [3]
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Question 6
[Maximum mark: 5]
The third term in the expansion of $(x+p)^8$ is $252x^6$. Find the possible values of $p$.
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Question 7
[Maximum mark: 5]
Consider the expansion of $\left(\dfrac{x^2}{2} + \dfrac{a}{x}\right)^6$. The constant term is $960$.
Find the possible values of $a$.
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Question 8
[Maximum mark: 6]
Consider the expansion of $\dfrac{(x+a)^7}{bx}$, where $a > 0$. The coefficient of the term in $x^5$ is $2$, and the coefficient of the term in $x^3$ is $1690$.
Find the value of $a$ and the value of $b$.
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Question 9
[Maximum mark: 6]
Consider the expansion of $\bigg(x^3+\dfrac{2}{x}\bigg)^8$.

Write down the number of terms in this expansion. [1]

Find the coefficient of the term in $x^4$. [5]
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Question 10
[Maximum mark: 6]
In the expansion of $px^2(5 + px)^8$, the coefficient of the term in $x^6$ is $3402$. Find the value of $p$.
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Question 11
[Maximum mark: 6]
Consider the expansion of $\bigg(3x + \dfrac{p}{x}\bigg)^8$, where $p > 0$. The coefficient of the term
in $x^4$ is equal to the coefficient of the term in $x^6$. Find $p$.
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Question 12
[Maximum mark: 7]
Let $f(x) = (x^2 + a)^5$.
In the expansion of the derivative, $f'(x)$, the coefficient of the term in $x^5$ is $960$. Find the possible values of $a$.
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Question 13
[Maximum mark: 7]
Consider the expansion of $\bigg(2x^6+\dfrac{x^2}{q}\bigg)^{10}$, $q \neq 0$. The coefficient of the term
in $x^{40}$ is twelve times the coefficient of the term in $x^{36}$. Find $q$.
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Question 14
[Maximum mark: 5]
In the expansion of $x(2x + 1)^n$, the coefficient of the term in $x^3$ is $20n$, where $n \in \mathbb{Z}^+$. Find $n$.
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Question 15
[Maximum mark: 5]
In the expansion of $(2x + 1)^n$, the coefficient of the term in $x^2$ is $40n$, where $n \in \mathbb{Z}^+$. Find $n$.
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Question 16
[Maximum mark: 6]

Write down and simplify the expansion of $(3x)^5$ in descending order of powers of $x$. [3]

Hence find the exact value of $(2.9)^5$. [3]
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Question 17
[Maximum mark: 7]
Given that $(5+nx)^2\bigg(1+\dfrac{3}{5}x\bigg)^n\hspace{0.25em}=\hspace{0.05em}25+100x+\cdots$, find the value of $n$.
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Question 18
[Maximum mark: 7]
Given that $(1 + x)^3(1 + px)^4 = 1 + qx + 93x^2 + \dots + p^4x^7$, find the possible values of $p$ and $q$.
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Question 19
[Maximum mark: 7]

Write down the quadratic expression $3x^2 + 5x  2$ in the form $(axb)(x+c)$.[2]

Hence, or otherwise, find the coefficient of the term in $x^9$ in the expansion
of $(3x^2+5x2)^5$. [5]
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What is the IB Math AA SL Questionbank?
The IB Math Analysis and Approaches (AA) SL Questionbank is a comprehensive set of IB Mathematics exam style questions, categorised into syllabus topic and concept, and sorted by difficulty of question. The bank of exam style questions are accompanied by high quality stepbystep markschemes and video tutorials, taught by experienced IB Mathematics teachers. The IB Mathematics AA SL Question bank is the perfect exam revision resource for IB students looking to practice IB Math exam style questions in a particular topic or concept in their AA Standard Level course.
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The AA SL Questionbank is designed to help IB students practice AA SL exam style questions in a specific topic or concept. Therefore, a good place to start is by identifying a concept that you would like to practice and improve in and go to that area of the AA SL Question bank. For example, if you want to practice AA SL exam style questions that have Exponents & Logarithms in them, you can go to AA SL Topic 1 (Number & Algebra) and go to the Exponents & Logarithms area of the question bank. On this page there is a carefully designed set of IB Math AA SL exam style questions, progressing in order of difficulty from easiest to hardest. If you’re just getting started with your revision, you could start at the top of the page with Question 1, or if you already have some confidence, you could start at the medium difficulty questions and progress down.
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