Foundation November 2017 Paper 1 Q13
13. This formula can be used to find the time it takes to cook a joint of meat.
\[t = 25p + 20\]where \(t\) is the time in minutes,
\(p\) is the mass of the meat in pounds.
When \(p = 0\), \(t = 20\).
Explain whether the formula is valid when \(p = 0\). [1]
Complete the table below, then draw the graph of \(t = 25p + 20\) for \(1 \leqslant p \leqslant 4\) on the graph paper below. [3]
| \(p\) | 1 | 2 | 3 | 4 |
| \(t\) |
Tasniah wants to cook a joint of meat that has a mass of 2 pounds.
She also wants to bake some potatoes.
She knows the potatoes will take \(\dfrac{3}{4}\) of an hour to bake.
When the meat has finished cooking, it must be taken out of the oven and left for 15 minutes before it is ready to be served.
She wants to serve the potatoes at the same time as the meat.
How long after Tasniah puts the meat in the oven should she put the potatoes in the oven to bake? [2]
| Scheme | Marks | Comments |
|---|---|---|
| No and valid explanation e.g. ‘According to the formula, it takes 20 minutes to cook no meat.’ or ‘\(t\) should be 0 when \(p\) is 0.’ | E1 | Allow e.g. ‘No because if p = 0 then the meat wouldn’t exist and would not need cooking.’ Do not allow e.g. ‘It is not valid as there would be no pounds.’ |
| Scheme | Marks | Comments | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
(i) Completes table correctly.
| B1 | May be implied by correct line drawn, even if it extends outside the given domain. | ||||||||||
| Plots all four points correctly | P1 | May be implied FT their points if possible for P1 and L1 | ||||||||||
| Draws a single, straight line through their points | L1 | May not be ruled; tolerance 1 small square in all directions. | ||||||||||
| (ii) 2.8 (pounds) | B1 | FT their graph or accept answers in the range 2.75 to 2.85 (pounds). |
| Scheme | Marks | Comments |
|---|---|---|
| (When \(p = 2\), \(t = 70\), so required time is 70 + 15 – 45 =) 40 (minutes) | B2 | FT their value of \(t\) when \(p = 2\) from their graph or their table; for B2 their value of \(t\) must be greater than 45 B1 for the calculation ‘their 70’ + 15 – 45 or equivalent, seen or implied or SC1 for a final answer of 25 (minutes) or equivalent (ignoring the 15 minutes extra for the meat) |
| (7) |