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1.7.1 Binomial expansion

1.7.1 Binomial expansion

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Question 7
a.

Use binomial expansions to show that

1+5x1−x≈1+3x−32x2\displaystyle \sqrt{\frac{1 + 5x}{1 - x}} \approx 1 + 3x - \frac{3}{2}x^21−x1+5x​​≈1+3x−23​x2

for small values of xxx.

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b.

A student substitutes x=12\displaystyle x = \frac{1}{2}x=21​ into the expansion to find an estimate for 7\sqrt{7}7​. Give a reason why the student should not use x=12\displaystyle x = \frac{1}{2}x=21​.

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c.

Substitute x=19\displaystyle x = \frac{1}{9}x=91​ into 1+5x1−x≈1+3x−32x2\displaystyle \sqrt{\dfrac{1 + 5x}{1 - x}} \approx 1 + 3x - \frac{3}{2}x^21−x1+5x​​≈1+3x−23​x2 to obtain an approximation for 7\sqrt{7}7​. Give your answer as a fraction in its simplest form.

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Markscheme

1.7.1 Binomial expansion Questions

  1. A Level
  2. /Maths
  3. /1.7.1 Binomial expansion

144 exam-style questions on AQA A Level Maths 1.7.1 Binomial expansion. Each one has a worked solution and a mark scheme showing where the marks go.

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