Higher June 2025 Paper 4 Q6
6 The distance of a car race is 420 km.
A car completes the first 210 km at an average speed of 150 km/h.
The same car completes the final 210 km at an average speed of 100 km/h.
Show that the average speed of the car for the whole race is less than 125 km/h. [5]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| \(\frac{210}{150}\) oe or 1.4 | M1 | implied by 1 [h] 24 [m] or 84 [m] | |
| \(\frac{210}{100}\) oe or 2.1 | M1 | implied by 2 [h] 6 [m] or 126 [m] | |
| their 1.4 + their 2.1 or 3.5 | M1 | their 3.5 could be 3½, 3 [h] 30[m] or 210 [m] | |
| \(\dfrac{210 + 210}{\textit{their } 3.5}\) oe or \(125 \times\) their 3.5 oe or \(420 \div 125\) | M1 | use of \(\dfrac{\text{total distance}}{\text{total time}}\) and allow total time=3.30 or in mins | |
| 120 or \(420 \lt 437.5\) oe or \(3.36 \lt 3.5\) oe | A1 | A1 dep. on M4 | see appendix e.g. 420 is less distance than 437.5 e.g. 3.36 is faster than 3.5 |
Appendix: exemplar responses for Q6
| Response | Mark |
|---|---|
| 120 and no comment | A1 |
| It takes 3 and a half hours and to be below 125 it has to be above 3 hours 21 minutes | A1 |
| If the ave. speed is 125, it must be 3.36 h but it is 3.5 h so the ave. speed is less than 125 | A1 |
| \(120 \gt 125\) | A0 |
| (3.5 and 3.36 shown) it is slower than if it travelled at 125 | A0 |