1.6.1 Binomial expansion for positive integer n

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Question 61

The power output $P$ , in kilowatts, of a prototype wind turbine is modeled by the function

\left(2 + \frac{v}{10}\right)^{12}

where $\ge 0$ is the wind speed in m/s. Find, in ascending powers of $v$ , up to and including the term in $v^3$ , the binomial expansion of $P (v)$ , fully simplifying each coefficient.

[4]

Use the answer to part (a) to find an approximation for the power output when the wind speed is $0.5$ m/s, which corresponds to evaluating $2.05^{12}$ . Give your answer to 2 decimal places.

[2]

Without calculating the exact value of $2.05^{12}$ , state, with a reason, whether the answer to part (b) is an overestimate or an underestimate.

[1]

The power output $P$ , in kilowatts, of a prototype wind turbine is modeled by the function

\left(2 + \frac{v}{10}\right)^{12}

where $\ge 0$ is the wind speed in m/s. Find, in ascending powers of $v$ , up to and including the term in $v^3$ , the binomial expansion of $P (v)$ , fully simplifying each coefficient.

Use the answer to part (a) to find an approximation for the power output when the wind speed is $0.5$ m/s, which corresponds to evaluating $2.05^{12}$ . Give your answer to 2 decimal places.

[2]

Without calculating the exact value of $2.05^{12}$ , state, with a reason, whether the answer to part (b) is an overestimate or an underestimate.

[1]

1.6.1 Binomial expansion for positive integer n

Question 61

Markscheme

1.6.1 Binomial expansion for positive integer n

Question 61

Markscheme

1.6.1 Binomial expansion for positive integer n

Question 61

1.6.1 Binomial expansion for positive integer n Questions

1.6.1 Binomial expansion for positive integer n

Question 61

1.6.1 Binomial expansion for positive integer n Questions