The signal noise $N\,$ in a high-precision sensor is modeled by the function $N(c)=(3+c4)9\displaystyle N(c) = \left(3 + \frac{c}{4}\right)^9$ , where $c\,$ represents the concentration of a dopant in parts per million (ppm).

Find, in ascending powers of $c$ , up to and including the term in $c^3$ , the binomial expansion of $N (c)$ , fully simplifying each coefficient.

Use your expansion from part (a) to find an approximation for $3.025^9$ . Give your answer to 2 decimal places.

Without calculating the exact value of $3.025^9$ , state, with a reason, whether the answer to part (b) is an underestimate or an overestimate.

Find, in ascending powers of $c$ , up to and including the term in $c^3$ , the binomial expansion of $N (c)$ , fully simplifying each coefficient.

Use your expansion from part (a) to find an approximation for $3.025^9$ . Give your answer to 2 decimal places.

Without calculating the exact value of $3.025^9$ , state, with a reason, whether the answer to part (b) is an underestimate or an overestimate.

1.7.1 Binomial expansion

Question 44

Markscheme

1.7.1 Binomial expansion

Question 44

Markscheme

1.7.1 Binomial expansion

Question 44

1.7.1 Binomial expansion Questions

1.7.1 Binomial expansion

Question 44

1.7.1 Binomial expansion Questions