In a precision chemical synthesis, the concentration CCC, in moles per litre, of a specific reagent is modelled by the function C(x)=(12−4x)10C(x) = \left( \frac{1}{2} - 4x \right)^{10}C(x)=(21−4x)10 for 0≤x<0.1250 \le x < 0.1250≤x<0.125, where xxx represents the mass in grams of a stabilizer added.
Determine the first four terms, in ascending powers of xxx, of the binomial expansion of C(x)C(x)C(x). Give each coefficient as a simplified fraction or an integer.
308 exam-style questions on OCR A Level Maths 1.4 Sequences and Series, covering 1.4.1 Binomial expansion for positive integer n, 1.4.2 Link to binomial probabilities, 1.4.3 Binomial expansion for rational n (A-level only), 1.4.4 Validity of the expansion (A-level only), 1.4.5 Sequences (A-level only), 1.4.6 Increasing, decreasing and periodic sequences (A-level only), 1.4.7 Sigma notation (A-level only), 1.4.8 Arithmetic sequences and series (A-level only), 1.4.9 Geometric sequences and series (A-level only), 1.4.10 Sum to infinity of a geometric series (A-level only), and 1.4.11 Modelling with sequences and series (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.