Moderate -0.8 This is a straightforward algebraic manipulation requiring only basic rearrangement (multiply both sides by 3, divide by π(a+b), then take the positive square root). It's simpler than typical A-level questions as it involves no problem-solving or conceptual understanding beyond routine algebraic techniques, though the presence of multiple variables and a square root makes it slightly less trivial than the simplest index law recall questions.
\(r = \sqrt{\dfrac{3V}{\pi(a+b)}}\) (oe, www as final answer)
3 marks total
- Dealing correctly with 3
M1
M0 if triple-decker fraction at the stage where it happens, then ft
- Dealing correctly with \(\pi(a+b)\)
M1 (ft)
Condone missing bracket at rh end
- Correctly finding square root, ft; square root symbol must extend below the fraction line
M1
M0 if \(\pm\)... or \(r >\) ...; for M3, final answer must be correct
## Question 3:
$r = \sqrt{\dfrac{3V}{\pi(a+b)}}$ (oe, www as final answer) | 3 marks total |
- Dealing correctly with 3 | M1 | M0 if triple-decker fraction at the stage where it happens, then ft
- Dealing correctly with $\pi(a+b)$ | M1 (ft) | Condone missing bracket at rh end
- Correctly finding square root, ft; square root symbol must extend below the fraction line | M1 | M0 if $\pm$... or $r >$ ...; for M3, final answer must be correct
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3 Rearrange the following formula to make $r$ the subject, where $r > 0$.
$$V = \frac { 1 } { 3 } \pi r ^ { 2 } ( a + b )$$
\hfill \mbox{\textit{OCR MEI C1 Q3 [3]}}