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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 128

A precise micro-sensor measures the relative volume V V\,V of a specialized crystal alloy as it undergoes temperature changes TTT. The relationship is modelled by the formula V(T)=1+pT3V(T) = \sqrt[3]{1 + pT}V(T)=31+pT​, where p p\,p is a constant. The binomial expansion of V(T)V(T)V(T) in ascending powers of TTT, up to the term in T3T^3T3, is 1+16T+CT2+DT3\displaystyle 1 + \frac{1}{6}T + CT^2 + DT^31+61​T+CT2+DT3 for ∣pT∣<1|pT| < 1∣pT∣<1.

a.

(i) Find the value of ppp.

(ii) Find the values of the constants C C\,C and DDD.

[5]
b.

Use the expansion to find an approximate value for 1.13\sqrt[3]{1.1}31.1​, showing your working and giving your answer to 6 decimal places.

[4]
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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