Subjects

IB Mathematics AA SL - Questionbank

Binomial Theorem

Binomial Expansion & Theorem, Pascal’s Triangle & The Binomial Coefficient nCr…

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Paper 2

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Question 1

no calculator

easy

[Maximum mark: 4]

Expand (2x+1)4(2x + 1)^4 in descending powers of xx and simplify your answer.

easy

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Question 2

calculator

easy

[Maximum mark: 4]

Expand (2x3)4(2x - 3)^4 in descending powers of xx and simplify your answer.

easy

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Question 3

calculator

easy

[Maximum mark: 6]

Consider the expansion of (2x1)9(2x-1)^9.

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

  2. Find the coefficient of the term in x2x^2. [5]

easy

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Question 4

calculator

easy

[Maximum mark: 5]

Consider the expansion of (x3)8(x-3)^8.

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

  2. Find the coefficient of the term in x6x^6. [4]

easy

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Question 5

no calculator

easy

[Maximum mark: 6]

  1. Show that (2n1)3+(2n+1)3=16n3+12n(2n-1)^3 + (2n+1)^3 = 16n^3+12n for nZn \in \mathbb{Z}. [3]

  2. 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 6

calculator

easy

[Maximum mark: 5]

The third term, in descending powers of xx, in the expansion of (x+p)8(x+p)^8 is 252x6252x^6. Find the possible values of pp.

easy

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Question 7

calculator

medium

[Maximum mark: 5]

Consider the expansion of (x22+ax)6\left(\dfrac{x^2}{2} + \dfrac{a}{x}\right)^6. The constant term is 960960.

Find the possible values of aa.

medium

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Question 8

calculator

medium

[Maximum mark: 6]

Consider the expansion of (x+a)7bx\dfrac{(x+a)^7}{bx}, where a>0a > 0. The coefficient of the term in x5x^5 is 22, and the coefficient of the term in x3x^3 is 16901690.

Find the value of aa and the value of bb.

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Question 9

calculator

medium

[Maximum mark: 6]

Consider the expansion of (x3+2x)8\bigg(x^3+\dfrac{2}{x}\bigg)^8.

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

  2. Find the coefficient of the term in x4x^4. [5]

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Question 10

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medium

[Maximum mark: 6]

In the expansion of px2(5+px)8px^2(5 + px)^8, the coefficient of the term in x6x^6 is 34023402. Find the value of pp.

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Question 11

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hard

[Maximum mark: 6]

Consider the expansion of (3x+px)8\bigg(3x + \dfrac{p}{x}\bigg)^8, where p>0p > 0. The coefficient of the term

in x4x^4 is equal to the coefficient of the term in x6x^6. Find pp.

hard

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Question 12

calculator

hard

[Maximum mark: 7]

Let f(x)=(x2+a)5f(x) = (x^2 + a)^5.

In the expansion of the derivative, f(x)f'(x), the coefficient of the term in x5x^5 is 960960. Find the possible values of aa.

hard

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Question 13

calculator

hard

[Maximum mark: 7]

Consider the expansion of (2x6+x2q)10\bigg(2x^6+\dfrac{x^2}{q}\bigg)^{10},  q0q \neq 0. The coefficient of the term

in x40x^{40} is twelve times the coefficient of the term in x36x^{36}. Find qq.

hard

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Question 14

no calculator

hard

[Maximum mark: 5]

In the expansion of x(2x+1)nx(2x + 1)^n, the coefficient of the term in x3x^3 is 20n20n, where nZ+n \in \mathbb{Z}^+. Find nn.

hard

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Question 15

no calculator

hard

[Maximum mark: 5]

In the expansion of (2x+1)n(2x + 1)^n, the coefficient of the term in x2x^2 is 40n40n, where nZ+n \in \mathbb{Z}^+. Find nn.

hard

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Question 16

no calculator

hard

[Maximum mark: 6]

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

  2. Hence find the exact value of (2.9)5(2.9)^5. [3]

hard

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Question 17

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hard

[Maximum mark: 7]

Given that (5+nx)2(1+35x)n=25+100x+(5+nx)^2\bigg(1+\dfrac{3}{5}x\bigg)^n\hspace{-0.25em}=\hspace{0.05em}25+100x+\cdots, find the value of nn.

hard

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Question 18

no calculator

hard

[Maximum mark: 7]

Given that (1+x)3(1+px)4=1+qx+93x2++p4x7(1 + x)^3(1 + px)^4 = 1 + qx + 93x^2 + \dots + p^4x^7, find the possible values of pp and qq.

hard

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Question 19

calculator

hard

[Maximum mark: 7]

  1. Write down the quadratic expression 3x2+5x23x^2 + 5x - 2 in the form (axb)(x+c)(ax-b)(x+c).[2]

  2. Hence, or otherwise, find the coefficient of the term in x9x^9 in the expansion
    of (3x2+5x2)5(3x^2+5x-2)^5. [5]

hard

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Frequently Asked Questions

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 step-by-step 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.

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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