IB Math AA SL  Questionbank
Binomial Theorem
Binomial Expansion & Theorem, Pascal’s Triangle & The Binomial Coefficient nCr…
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Question 1
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easy
[Maximum mark: 4]
Expand $(2x + 1)^4$ in descending powers of $x$ and simplify your answer.
easy
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Question 2
calculator
easy
[Maximum mark: 4]
Expand $(2x  3)^4$ in descending powers of $x$ and simplify your answer.
easy
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Question 3
no calculator
easy
[Maximum mark: 5]
Consider the expansion of $(x+2)^5$.

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

Find the term in $x^3$. [4]
easy
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Question 4
calculator
easy
[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]
easy
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Question 5
calculator
easy
[Maximum mark: 6]
Consider the expansion of $x(3x+2)^7$.

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

Find the coefficient of the term in $x^3$. [5]
easy
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Question 6
calculator
easy
[Maximum mark: 5]
The third term in the expansion of $(x+p)^8$ is $252x^6$. Find the possible values of $p$.
easy
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Question 7
no calculator
easy
[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]
easy
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Question 8
no calculator
easy
[Maximum mark: 6]
Consider $\displaystyle \binom{6}{a} = \dfrac{6!}{a!\hspace{0.06em}\cdot\hspace{0.03em}4!}$ where $a \in \mathbb{Z}^+\hspace{0.1em}$.

Find the value of $a$. [2]

Determine the sum of the first three terms of $(13x)^6$ in ascending
powers of $x$, giving each term in its simplest form. [4]
easy
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Question 9
calculator
easy
[Maximum mark: 6]
Consider $\displaystyle \binom{7}{b} = \dfrac{7!}{b!\hspace{0.06em}\cdot\hspace{0.03em}4!}$ where $b \in \mathbb{Z}^+\hspace{0.1em}$.

Find the value of $b$. [2]

Determine the sum of the first four terms of $(1+2x)^7$ in ascending
powers of $x$, giving each term in its simplest form. [4]
easy
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Question 10
no calculator
easy
[Maximum mark: 5]
In the expansion of $(xk)^5$, where $k \in \mathbb{R}$, the coefficient of the term in $x^2$ is $270$.
Find the value of $k$.
easy
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Question 11
calculator
medium
[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 $a$.
medium
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Question 12
calculator
medium
[Maximum mark: 5]
Consider the expansion of $x\hspace{0.2em}\left(2x^2 + \dfrac{a}{x}\right)^7$. The constant term is $20\hspace{0.15em}412$. Find $a$.
medium
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Question 13
calculator
medium
[Maximum mark: 5]
Find the term independent of $x$ in the expansion of $\dfrac{1}{x} \left(\dfrac{1}{2x}  \dfrac{x^3}{3} \right)^7$.
medium
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Question 14
calculator
medium
[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]
medium
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Question 15
calculator
medium
[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 $p$.
medium
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Question 16
calculator
hard
[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 $a$.
hard
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Question 17
calculator
hard
[Maximum mark: 7]

Find the term in $x^2$ in the expansion of $(2x + 1)^5$. [3]

Hence find the term in $x^3$ in the expansion of $(x+3)(2x+1)^5$. [4]
hard
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Question 18
calculator
hard
[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 $p$.
hard
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Question 19
no calculator
hard
[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 $n$.
hard
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Question 20
no calculator
hard
[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 $n$.
hard
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Question 21
calculator
hard
[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 $q$.
hard
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Question 22
calculator
hard
[Maximum mark: 6]
Consider the expansion of $\left(2+x^3\right)^{n+2}$, where $n \in \mathbb{Z}^{+}$.
Given that the coefficient of $x^9$ is $1792$, find the value of $n$.
hard
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Question 23
no calculator
hard
[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]
hard
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Question 24
calculator
hard
[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 $n$.
hard
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Question 25
calculator
hard
[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]
hard
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Question 26
no calculator
hard
[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 $q$.
hard
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Frequently Asked Questions
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.
Where should I start in the AA SL Questionbank?
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.
How should I use the AA SL Questionbank?
The AA SL Questionbank is perfect for revising a particular topic or concept, indepth. For example, if you wanted to improve your knowledge of The Binomial Theorem, there are over 20 full length IB Math AA SL exam style questions focused specifically on this concept. Alternatively, Revision Village also has an extensive library of AA SL Practice Exams, where students can simulate the length and difficulty of an IB exam with the Mock Exam sets, as well as AA SL Key Concepts, where students can learn and revise the underlying theory, if missed or misunderstood in class.
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With an extensive and growing library of full length IB Math Analysis and Approaches (AA) SL exam style questions in the AA SL Question bank, finishing all of the questions would be a fantastic effort, and you will be in a great position for your final exams. If you were able to complete all the questions in the AA SL Question bank, then a popular option would be to go to the AA SL Practice Exams section on Revision Village and test yourself with the Mock Exam Papers, to simulate the length and difficulty of an actual IB Mathematics AA SL exam.
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Key Concepts
Helpful refreshers summarizing exactly what you need to know about the most important concepts covered in the course.
Past Papers
Full worked solutions to all past paper questions, taught by experienced IB instructors.