Higher November 2021 Paper 2 Q15
15 \(L\) is directly proportional to \(D^2\)
\(L = 85 \quad\) when \(\quad D = 10\)
(a) Work out an equation connecting \(L\) and \(D\). [3 marks]
(b) Work out the value of \(L\) when \(\quad D = 5\) [2 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| \(L = kD^2\) | M1 | oe equation |
| \(85 = 10^2k\) or \(85 = 100k\) or \((k =)\ 0.85\) | M1dep | oe implies M2 |
| \(L = 0.85D^2\) | A1 | oe equation |
| Alternative method 2 | ||
| \(cL = D^2\) | M1 | oe equation |
| \(85c = 10^2\) or \(85c = 100\) or \((c =)\) \(\dfrac{100}{85}\) | M1dep | oe allow \((c =)\ [1.176, 1.18]\) implies M2 |
| \(\dfrac{100}{85}L = D^2\) | A1 | oe equation allow \([1.176, 1.18]L = D^2\) |
Additional guidance
| Condone use of \(\propto\) for up to M1M1A0 eg Alt 1 \(L \propto kD^2\) \(85 \propto 100k\) \(L \propto 0.85D^2\) | M1 M1 A0 |
| \(L = 0.85D^2\) oe | M1M1A1 |
| \(L \propto D^2\) is M0 with no further correct working |
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 If using alt 1 in (a) | ||
| their \(k \times 5^2\) | M1 | oe their \(k\) from (a) |
| 21.25 | A1ft | oe correct or ft their \(k \times 5^2\) |
| Alternative method 2 If using alt 2 in (a) | ||
| \(5^2 \div\) their \(c\) | M1 | oe their \(c\) from (a) |
| 21.25 | A1ft | oe correct or ft \(5^2 \div\) their \(c\) do not follow through an approximated value for \(\dfrac{100}{85}\) |
Additional guidance
| \(L \propto 21.25\) on answer line | M1A0 |
| Alt 2 (a) \(1.18L = D^2\) (scores 3 marks in (a)) (b) \(25 \div 1.18 = 21.19\) | M1A0 |