Higher June 2024 Paper 5 Q3
3
(a) Ryan makes a journey of 200 miles from his home to the coast.
\(\frac{1}{10}\) of the journey is on roads with a speed limit of 40 miles per hour.
40% of the journey is on roads with a speed limit of 50 miles per hour.
The remainder of the journey takes a time of 1 hour 30 minutes.
\(\frac{1}{10}\) of the journey is on roads with a speed limit of 40 miles per hour.
40% of the journey is on roads with a speed limit of 50 miles per hour.
The remainder of the journey takes a time of 1 hour 30 minutes.
Ryan leaves home at 08 50 and does not exceed the speed limits on the journey.
Find the earliest time that Ryan could arrive at the coast.
You must show your working. [6]
(b) Write down an assumption you have made when working out the answer to part (a). [1]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 12 26 with correct working | 6 | B5 for 3 hours 36 mins with correct working or 12 26 am with correct working OR | Correct working requires evidence of at least M2M2 Accept 12 26 pm for 6 marks |
| Method to find time in 1st stage M2 for \(\frac{1}{10} \times 200 \div 40\) [× 60] oe or M1 for \(\frac{1}{10} \times 200\) oe AND | M2 implied by 0.5[h], \(\frac{1}{2}\) [h] or 30 [mins] nfww M1 implied by 20 [miles] nfww | ||
| Method to find time in 2nd stage M2 for \(0.4 \times 200 \div 50\) oe or M1 for 0.4 × 200 oe AND | M2 implied by \(\frac{8}{5}\) [h], \(1\frac{3}{5}\) [h], 1.6 [h] isw, 96[mins] or 1[h] 36[min] nfww M1 implied by 80 [miles] nfww | ||
| M1dep on M2M2 for their 30[mins] + their 96[mins] + 1hr30[mins] If 0 or 1 or 2 scored, instead award SC3 for answer 12 26 or 12 26 pm If 0 or 1 scored, instead award SC2 for 3 h 36 [mins] or 12 26 am | M1 implied by addition onto 0850 | ||
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| Correct response e.g. Ryan drives at the speed limit and does not drive slower or is delayed | 1 | Accept any valid reason why Ryan may not be able to travel at Maximum Speed at all times e.g. Ryan does not get stuck in traffic There are no roadworks etc He does not stop on the journey Car does not breakdown Do not accept incorrect statements e.g he travels at a constant speed Mark best response as long as not contradictory or incorrect See Appendix 1 | |
Appendix 1: Question 3(b)
| Response | Mark | |
|---|---|---|
| 1 | That Ryan does not stop along the way | 1 |
| 2 | He stayed the exact speed limit and was not below the limit | 1 |
| 3 | That he didn’t speed and met the speed limit (travels at speed limit) | 1 |
| 4 | He travels at the speed limit | 1 |
| 5 | Does not have to stop [for fuel, lunch etc] | 1 |
| 6 | Ryan stays at 40 mph and 50mph when on these roads (BOD referencing the roads with the speed limits) | 1BOD |
| 7 | There was no traffic so Ryan kept on moving (BOD implies that he isn’t stopped/slowed down by traffic) | 1BOD |
| 8 | That Ryan stayed at a constant speed in each section of the journey | 0 |
| 9 | That he didn’t stop for a break and drove the same speed (drove same speed is incorrect) | 0 |
| 10 | He makes stops on his journey (He must be travelling at max speed at all times) | 0 |
| 11 | Could not be true due to traffic | 0 |
| 12 | There will not be much traffic | 0 |
| 13 | They are at 50mph and 40mph the whole time (for the third part he doesn’t travel at 50mph or 40mph so this is incorrect) | 0 |
| 14 | He travelled at a constant speed (this is not true) | 0 |
| 15 | The speed limit does not change (this is not true) | 0 |
| 16 | He drove at constant speed and did not stop for lunch (part of statement is incorrect-constant speed) | 0 |
| 17 | There is no traffic (not quite enough – need to say e.g. traffic is not holding them up) | 0 |