Higher June 2019 Paper 3 Q20
20 \(d\) is directly proportional to the square of \(v\).
\(d = 6\) when \(v = 20\)
(a) Work out an equation connecting \(d\) and \(v\). [3 marks]
(b) Work out the value of \(d\) when \(v = 30\) [2 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(d \propto v^2\) or \(d = \text{k} \times v^2\) or \(6 = \text{k} \times 20^2\) or \(\text{c} \times d = v^2\) or \(\text{c} \times 6 = 20^2\) | M1 | oe eg \(v = \text{k}d^{\frac{1}{2}}\) |
| \((\text{k} =)\ 6 \div 20^2\) or 0.015 or \((\text{c} =)\ 20^2 \div 6\) or 66.66… or 66.67 | M1dep | oe eg \(\dfrac{6}{400}\) or \(\dfrac{3}{200}\) \(\dfrac{400}{6}\) or \(\dfrac{200}{3}\) |
| \(d = 0.015 \times v^2\) or \(\dfrac{200}{3} \times d = v^2\) | A1 | oe equation |
Additional guidance
| Working for second M mark must follow from their initial equation | |
| \(d \propto 0.015 \times v^2\) | M1M1A0 |
| \((\text{k} =)\ 0.015\) or \((\text{c} =)\ \dfrac{200}{3}\) with no incorrect working | M1M1A0 |
| \(0.015v^2\) or \(\dfrac{200}{3}d\) | M1M1A0 |
| Answer | Mark | Comments |
|---|---|---|
| their \(0.015 \times 30^2\) or their \(0.015 \times 900\) or \(6 \times \left(\dfrac{30}{20}\right)^2\) or \(30^2 \div\) their \(\dfrac{200}{3}\) or \(900 \div \dfrac{200}{3}\) or \(6 \div \left(\dfrac{20}{30}\right)^2\) | M1 | oe |
| 13.5 | A1ft | oe ft their 0.015 provided using \(d =\) their \(0.015 \times v^2\) |
Additional guidance
| Must use \(\times 30^2\) or \(\times 900\) or \(\times \left(\dfrac{30}{20}\right)^2\) for M1 | |
| \(d \propto 13.5\) | M1A0 |
| If in part (a) \(d = \text{k} \times v \quad 6 = \text{k} \times 20 \quad d = \dfrac{6}{20}v\) and in part (b) \(d = \dfrac{6}{20} \times 30, \quad d = 9\) | M0 part (a) M0 part (b) |
| If in part (a) \(d = \text{k} \times v \quad 6 = \text{k} \times 20 \quad d = \dfrac{6}{20}v\) and in part (b) \(d = \dfrac{6}{20} \times 30^2, \quad d = 270\) | M0 part (a) M1A1ft part (b) |