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3.3 Sequences and series (A-level only)

3.3 Sequences and series (A-level only)

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Question 148

The strength of a magnetic field BBB, measured in microteslas, at a distance rrr cm from a specific electronic component is modeled by the function:

B(r)=(10r+3)(1−14r)12,0≤r<4 B(r) = (10r + 3)\left(1 - \frac{1}{4}r\right)^{12}, \quad 0 \le r < 4 B(r)=(10r+3)(1−41​r)12,0≤r<4
a.

Find the first four terms, in ascending powers of rrr, of the binomial expansion of

(1−14r)12 \left(1 - \frac{1}{4}r\right)^{12} (1−41​r)12

giving each term in simplest form.

[4]
b.

Hence determine the coefficient of r3r^3r3 in the expansion of B(r)B(r)B(r), giving the answer in simplest form.

[3]
Markscheme

3.3 Sequences and series (A-level only) Questions

  1. A Level
  2. /Maths
  3. /3.3 Sequences and series (A-level only)

200 exam-style questions on CCEA A Level Maths 3.3 Sequences and series (A-level only), covering 3.3.1 Sequences and series (A-level only), 3.3.2 Sequences and series (A-level only), 3.3.3 Sequences and series (A-level only), 3.3.4 Sequences and series (A-level only), 3.3.5 Sequences and series (A-level only), 3.3.6 Sequences and series (A-level only), 3.3.7 Sequences and series (A-level only), and 3.3.8 Sequences and series (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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