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IB Mathematics AA HL - Popular Quizzes

The Binomial Theorem

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Question 1

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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 2

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easy

[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.

easy

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Question 3

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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.

medium

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Question 4

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medium

[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.

medium

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Question 5

no calculator

medium

[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.

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Question 6

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medium

[Maximum mark: 8]

Use the extension of the binomial theorem for nQn \in \mathbb{Q} to show that 1+x1x1+x+x22\sqrt{\dfrac{1+x}{1-x}} \approx 1 + x + \dfrac{x^2}{2}, x<1|x| < 1.

medium

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Question 7

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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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