Higher June 2024 Paper 2 Q24
24 A room is kept at a constant temperature of \(21^\circ\)C for 6 hours.
The heating is then turned off and the room begins to cool.
Here is a sketch graph showing the temperature, \(y^\circ\)C, of the room at time \(x\) hours.
(a) Assume the equation of the curved part is \(\quad y = \dfrac{k}{x} \quad\) where \(k\) is a constant.
Work out the value of \(y\) when \(\quad x = 12\) [2 marks]
(b) In fact,
the equation of the curved part is \(\quad y = A \times \left(\dfrac{1}{3}\right)^{\frac{1}{6}x} \quad\) where \(A\) is a different constant.
How does this affect the value of \(y\) when \(x = 12\) ?
Tick one box.
You must show working to support your answer. [2 marks]
- The value of \(y\) is greater than the answer to part (a).
- The value of \(y\) is less than the answer to part (a).
- The value of \(y\) is the same as the answer to part (a).
| Answer | Mark | Comments |
|---|---|---|
| \((k =)\ 21 \times 6\) or \((k =)\ 126\) | M1 | oe may be implied eg \(y = \dfrac{126}{x}\) |
| 10.5 or \(\dfrac{21}{2}\) | A1 | oe value eg \(\dfrac{126}{12}\) ignore units |
Additional guidance
| Ignore simplification or conversion attempt after correct answer seen | |
| 10.5 only seen embedded eg \(10.5 \times 12 = 126\) | M1A0 |
| Answer | Mark | Comments |
|---|---|---|
| \(21 = A \times \dfrac{1}{3}\) or \((A =)\ 21 \times 3\) or \((A =)\ 63\) | M1 | oe eg \(21 = A \times \left(\dfrac{1}{3}\right)^{\frac{1}{6} \times 6}\) implied by \((y =)\ 7\) |
| \((y =)\ 7\) and middle box ticked | A1ft | ft decision using their 10.5 in (a) must have \((y =)\ 7\) |
Additional guidance
A correct value is sufficient for showing working
Decision may be indicated by selecting a box or a statement in the working lines
Decision cannot be implied only by an inequality