OCR PURE — Question 6 3 marks

Exam BoardOCR
ModulePURE
Marks3
PaperDownload PDF ↗
TopicExponential Functions
TypeExponential growth/decay model setup
DifficultyEasy -1.2 This is a straightforward proportionality question requiring students to set up P = kv³, find k using given values, then solve a simple cubic equation. It involves only basic algebraic manipulation and is easier than average A-level questions which typically require multiple techniques or deeper reasoning.
Spec1.02r Proportional relationships: and their graphs
6 The power output, \(P\) watts, of a certain wind turbine is proportional to the cube of the wind speed \(v \mathrm {~ms} ^ { - 1 }\). When \(v = 3.6 , P = 50\).
Determine the wind speed that will give a power output of 225 watts.
Question 6:
AnswerMarks Guidance
\(k = \frac{50}{3.6^3}\) or \(\frac{3125}{2916}\) or \(1.07(167)\)M1 Attempt find \(k\). Must involve division, and cube or cube root. Can be implied by 1.07 seen, or correct \(v\)
\(\text{'1.07'}v^3 = 225\) or \(v^3 = \frac{225}{\text{'1.07'}}\) oe or \(v = \sqrt[3]{\frac{225}{\text{'1.07167'}}}\)M1 or \(v = \sqrt[3]{\frac{225}{\text{their } k}}\) oe. SC \(k = \frac{50}{3.6^2}\) oe Max M1M0A0
Alternative: \(\frac{v^3}{3.6^3} = \frac{225}{50}\), \(\frac{v}{3.6} = \sqrt[3]{\frac{225}{50}}\) or \(v = 3.6\times\sqrt[3]{\frac{225}{50}}\)M1, M1 Attempt use proportion. Must involve cube or cube root. Correct expression for \(v\)
\(v = 5.94\) (3 sf)A1 Allow without units
(Wind speed \(= 5.94\) m/s)[3] 
# Question 6:
| $k = \frac{50}{3.6^3}$ or $\frac{3125}{2916}$ or $1.07(167)$ | M1 | Attempt find $k$. Must involve division, and cube or cube root. Can be implied by 1.07 seen, or correct $v$ |
|---|---|---|
| $\text{'1.07'}v^3 = 225$ or $v^3 = \frac{225}{\text{'1.07'}}$ oe or $v = \sqrt[3]{\frac{225}{\text{'1.07167'}}}$ | M1 | or $v = \sqrt[3]{\frac{225}{\text{their } k}}$ oe. SC $k = \frac{50}{3.6^2}$ oe Max M1M0A0 |
| **Alternative:** $\frac{v^3}{3.6^3} = \frac{225}{50}$, $\frac{v}{3.6} = \sqrt[3]{\frac{225}{50}}$ or $v = 3.6\times\sqrt[3]{\frac{225}{50}}$ | M1, M1 | Attempt use proportion. Must involve cube or cube root. Correct expression for $v$ |
| $v = 5.94$ (3 sf) | A1 | Allow without units |
| (Wind speed $= 5.94$ m/s) | [3] | |

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6 The power output, $P$ watts, of a certain wind turbine is proportional to the cube of the wind speed $v \mathrm {~ms} ^ { - 1 }$.

When $v = 3.6 , P = 50$.\\
Determine the wind speed that will give a power output of 225 watts.

\hfill \mbox{\textit{OCR PURE  Q6 [3]}}
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